VIRTUAL REALITY: CONSCIOUSNESS REALLY EXPLAINED!

(Why, How, Where and What: A Radical Proposal)

SECOND EDITION

Jerome Iglowitzjiglowitz@rcsis.com

Copyright January 1, 2007All Rights Reserved

Dedication

For Chris and my Girls.

TABLE OF CONTENTS

--redo THIS!!!

PUT IN OLD ONE AS REFERENCE INFO ONLY!!!

Preface:

“Abandon hope, all ye who enter here.”

I think that in many ways the mind-body dilemma is like Dante’s problem in his mythical journey to “Paradiso”1 long ago. If you think ours is an ordinary problem, (albeit a very difficult one), we really don’t have anything further to discuss –our perspectives are too different. I think it is closer to Dante’s journey -I think it is “Copernican” in the extreme. Let me paraphrase Dante’s book which I read over 50 years ago, (if I get it a little wrong, put it down to the imprecise memory of an old man).

The protagonist, Dante, enters Hell with his guide Virgil through the gateway which bears the label stated above: “Abandon Hope, All Ye Who Enter Here!” He is required to descend through the multiple rings of hell, each of which represents some profound defect in human nature, (cognition?). Finally, he comes to the bottom and passes beside the devil’s frozen but live and active carcass in middle earth.

But then he is again obliged to climb up the mount of purgatory –again many tiered- until he is finally allowed to enter into the glory of Heaven. Ernst Cassirer, (a very reputable modern philosopher of science), used a very similar metaphor in referring to the mind-brain problem and to the revolutionary epistemology which necessarily lies at its base:

“For man it follows that he must traverse his appointed orbit, in order at the end of his road to find his way back again to its beginning. That is the fate imposed by our ‘circular world’.2 ‘Paradise is bolted fast, and the cherub far behind us; we must travel around the world and see whether perchance an entrance can be found somewhere from the rear.’” “Spirit and Life”, P.858 in “The Philosophy of Ernst Cassirer”, Tudor, 1958 (Cassirer’s quotation is from Kleist’s “The Marionette Theatre”.)

Let me paraphrase his metaphor: Man has been expelled from the eastern gate of Eden, (from simplistic connection to his naive world), by his acquisition of knowledge and the skepticism innate in it. The gate is now guarded by an angel with a flaming sword, (the consequence of reason), preventing his return. Forced to face the harsh and bitter world outside, he has embarked to walk clear round the world, (in his acquisition of knowledge), and hopes to find a gate unguarded on the other side so that he may re-enter paradise! Man was shut off from simple contact with reality when he first questioned that contact. Cassirer asserts that the whole of the human project of knowledge was to return to the ingenuousness from whence we came!

I feel we are now very close to that other gate. Rationality and perception, mind and reality need no longer be antithetical. But it will take hard work to get there. This is not a journey for the timid.

1 Dante’s “Divine Comedy” –I will attempt to be Virgil!2 Please remember this and note the similarity to Merleau-Ponty’s perspective when we

come to Chapter 1.

I think this is the hardest problem there is, and I will make one last try to communicate what I believe is its first viable scientific answer. My methodology has always centered around a bitter struggle between me and myself, questioning the very foundations of my belief each and every day and forcing me to re-validate them against the strength of the standard paradigm. My style is therefore contentious –I gave myself no mercy –ever. But the debate has always been with myself, not with you. I allowed myself this liberty with me –it is my method of work. I did not mean it to apply to you!

I demand of my reader just one thing –an unflinching courage to risk the impossible. We must pass through that gate and enter Hell. Hopefully we will together come to reach that western gate, (mixing the metaphor). To get there we must question the basis of each and every belief and tool we possess to include the very logic by which we reason, -the very tool we are using right now!

I think Cassirer brackets the initial problem precisely -the most important problem for the mind-brain dilemma lies in the limitations of contemporary logic itself:

“Every attempt to transform logic must concentrate above all upon this one point: all criticism of formal logic is comprised in criticism of the general doctrine of the construction of concepts.” (Ernst Cassirer) 3

He believed that our contemporary logical concept –the “concept” that lies at the very bottom of our reasoning right here - is seriously flawed. He goes on with a concise statement of his answer. I consider it mirabile dictum 4–i.e. it is said so well that it is useless to expand on it.

“When we form the concept of metal by connecting gold, silver, copper and lead, we cannot indeed ascribe to the abstract object that comes into being the particular color of gold, or the particular luster of silver, or the weight of copper, or the density of lead; however it would be no less inadmissible if we simply attempted to deny all these particular determinations of it. …

It would not suffice to characterize “metal”, for instance, “that it is neither red nor yellow, neither of this or that specific weight, neither of this or that hardness or resisting power”; but it is necessary to add that it ‘is colored in some way in every case, that it is of some degree of hardness, density and luster.’ Similarly, we would not retain the general concept of ‘animal’, ‘if we abandoned in it all thought of the aspects of procreation, of movement and of respiration, because there is no form of procreation, of breathing, etc., which can be pointed out as common to all animals.’

Can one really object to this argument and still maintain the sense of his thoughts? What is “stove” without a color? What is “house” without some kind of roof? “Stove”, “House”, “Metal”, “animal”, … are not sufficiently characterized in the hierarchical manner –nor, I think, is much else other than very specialized and delimitated mathematical and logical entities.5 This, I think, lies at the root of our dilemma. 3 “Substance and Function”, (more precise translation: “Substance Concepts and Function Concepts”)4 As was said of Kant’s exposition5 It is worth noting, for instance, that in the fundamental, standard Zermelo-Frankel

construction of arithmetic the only thing that is allowed to truly exist is the empty set – and sets of…sets of …the empty set!

Cassirer proposed a different Concept instead, which he called “the functional Concept of mathematics”:

“Lambert pointed out that it was the exclusive merit of mathematical ‘general concepts’ not to cancel the determinations of the special cases, but in all strictness fully to retain them. When a mathematician makes his formula more general, this means not only that he is to retain all the more special cases, but also be able to deduce them from the universal formula.”6

Cassirer concluded that we must question the very foundations of our logic and, finally, even of our perceptions. But isn’t that immediately obvious in our modern conception of the mind-brain problem? How (in our modern mechanistic view of the world) could mechanistic biological organisms, (ourselves), “know” anything at all -much less about the world outside of themselves? What could “knowing” even mean to a machine? There must be some other rationale for cognition!

------------------------------------------------------------------------------------------------

I began my quest with one blinding insight, i.e. of the pregnant implications of David Hilbert’s revolutionary mathematical idea of “implicit definition” for the problem of the mind plus an unswerving fanaticism to just two criteria which I considered as absolutely fundamental realist prerequisites. Without resolving them I felt that we could only attain pseudo solutions, (I still think so). These two prerequisites were:

(1) the existence of a reality external to myself, and,

(2), the existence of consciousness

- both taken in their naïve senses! These constitute the absolute minimum and necessary presuppositions for the problem to which I have dedicated my life. They are contained as part of Hillary Putnam’s tenets of basic realism. George Lakoff and Gerald Edelman restate them as follows:

1. External Reality: “(1) a real world (including humans but not depending on them).”2. Concepts,(Mind), and the World: “(2) a linkage between concepts and that world”3. Some relationship: (3) “a stable knowledge that is gained through that link.”

The combination of my three themes will confirm Putnam-Lakoff-Edelman’s first and second postulates, but the “knowledge” in (3) will be argued as mathematically and scientifically relativistic in its significance and pragmatic, (i.e. algorithmic), in its justification.

I propose to give the first scientifically viable answer to the mind-brain problem.

6 A circle, for example, is a special case of an ellipse, or the square is a special case of the rectangle.

The Argument from Dogmatic Materialism:

Most of the force of the materialist argument lies, I think, in the “bragging mode”, (i.e. “Put up or shut up!”), rather than in logical argument! By this, I mean that materialists can point to the fact that at every moment, new confirmations of their fundamental thesis arise -from new PET scan procedures to new antibiotics, to the discovery of new atomic particles - even to the development of new and different ways of playing the game of marbles -and an integration of just about everything in between. It goes on and on and is eminently successful. They can and do retort to any argument by demonstration, not primarily by a resort to logic. Their perspective is so “perfect” that logic is largely irrelevant! I tried to make this point in my book. (There are holes in their position –mainly in what they will not look at—see Gleich, Van Fraasen, etc.)

I have been trying to formulate a better answer to their position than “they will never explain the mind-brain relationship”. That is clearly not good enough, and can never suffice from their own perspective until and unless an alternative can provide new devices, new results –new “toys”. This is what the acceptance of Einstein’s relativity by materialists was all about even though it embodied a perspective radically different from their own. Or of the acceptance of Bohr’s Quantum Theory for that matter! Materialism, moreover, is an inbuilt perspective - framed and dictated, I believe, by biology itself. (This is the whole sense of Chapter 1.) The best response I had come up with at the point of the first edition of my book was:

“Is it not more believable, (under the very Naturalist assumption), that we have merely expressed our own particular mode of existence, -that human civilization, like a swarm of bees, has simply built a (closed) hive? What is this logic we are so sure of? Ultimately, biologically, it is an expression of the “structural coupling7” of the race with its environment. But the invariants of that coupling are derived from the structure of the uniquely human brain. Other brains, other modes of coupling almost certainly would embody another protologic.8 Ordinary logic, (i.e. “associationist” logic -in Dreyfus’ terminology), denies its biological roots. It believes it has touched eternity and verity. How? Why? What teleological mystery does it hide? When we thought that man was created by God in his image and that God gave us this open channel to truth, then there was a meaningful rationale for such a view. But when man became purely and simply a material animal, derived mechanistically and randomly by material combination, then this mechanistic process lost all justification as correlating with anything other than its own mechanical necessities. But it works! How and why? Perhaps that is itself the answer. It is an operative process that works (superbly) in the world in which it lives! This provides no guarantee of its ontological posits at all however -it is an operative process, (an algorithm), that works -and that’s all!” (But there are transformations other than Isomorphism which allow “working” as I will discuss in Chapter 1.) It is, I admit, a superb working nonetheless! How could it be otherwise?

7 after Maturana8 Have you ever considered that the “aliens” we look for in outer space and who are hoped

to rescue us from ourselves –are already here? I suggest that they are our “creatures”-the animals and organisms we parasitize. This argument should make sense to a biologist.

But is that answer good enough? Frankly, the answer is no. But it is early times for the conception I have birthed. Copernicus stood in like stead –it took two hundred years for Newton to finally achieve a synthesis. I hope to give a better, more specific answer than the above this time around. Welcome to Hell!

Introduction

“Popper [said that] ... hypotheses are interesting only if they are bold -that is, if they are improbable and thus likely to be falsified. For then, to withstand falsification by rigorous testing is a triumph, and such a hypothesis is significant. Safe (that is, probable) hypotheses are a dime a dozen, and the safest are logical truths. If what science is seeking is primarily a body of certain truths, it should stick to spinning out logical theorems. The trouble with such safety, however, is that it doesn’t get us anywhere.” (P.S. Churchland, 1988, P.260)

Is anyone really interested in an answer to the mind-body problem? And why should they be? If science is able one day to deal with all of the ravages of mental illness, and to explain the whole of human behavior as biological phenomena -as it surely will- then the problem would seem fit for the debates of philosophers with philosophers alone, and of interest to no one else.

But, as in science generally, there is also a problem of organization - how do we organize these biological phenomena? And more importantly -how do we predict and integrate them? It is one thing to catalogue prior experiment, and it is quite another to integrate it into a comprehensive and predictive framework useful to empiric practice. Ptolemean vs. Copernican cosmology is the prototypical illustration of the distinction. Ptolemean theory was quite capable of cataloging any celestial movement, but it could not lead to Kepler’s –nor to Newton’s laws. It was sterile for the progress of future deep science. Heisenberg and Schroedinger9 supply a more modern instance. Heisenberg’s matrix conception of quantum mechanics was comprehensive, but not predictive. Schroedinger’s alternative was.

There is a fundamental prejudice in the history of human thought: it is that the large-scale organization of reality is simple in principle. The whole history of science seems to confirm this premise. From Euclid to Copernicus, from Galileo to Newton to Maxwell and Hertz to Einstein to Heisenberg and Schroedinger and Bohr, from Aristotle to Darwin and Pauling...ad infinitum, this is our central premise.

The problem of the organization of the brain, our central and necessarily self-referential problem, is then either the exception to this rule, (paradoxically it is also the center of our understanding, i.e. man’s organization, of all the other organizations), or it will itself be organized on such a principle. But is the Copernican center of that organization to be found in the fundamental principles -and organization- of biology and chemistry, or does it lay in principles unique to the brain itself? In short, is a “Newtonian physics” of the brain possible? If it is, then the problems of “mind” and “mind-brain” become crucial as they supply critical clues to that organization.

But there is another aspect to the general problem presented here. It is not only that no solution has yet been presented for the mind-brain problem, but rather that the consensus of contemporary scientific opinion seems to be that there is no solution possible consistent

9 Cf, for instance, Cassidy, David. "Uncertainty: the Life and Science of WernerHeisenberg", 1992 for a lucid discussion of the problem.

with our ordinary, (i.e. “folk”), understanding of mind and perception. The consensus, (in the community of “hard scientists”), is that only actions and mechanical processes are possible, that “understanding” and “perception” must necessarily be reduced to the mechanical vocalizations, (and the precursors of such vocalizations), of linguistic automatons. I do not claim that this is not a formally consistent solution, but its center of organization clearly lies in the central principles of biology and of physics and not in the principles of the brain per se.

If another solution is submitted, it must be appraised in terms of the new possibilities it opens. To be worthy of serious consideration, it must promise -and specifically suggest- pathways to new and powerful empirical results: philosophy is not enough. Though it may offend basic dogma, though it may profoundly offend our sensibilities, if it also proffers deep and profound scientific advance, then it must be considered seriously. The solution I will present here, though highly esoteric, (in a mathematical sense of the word10), has definite and specific implications for the directions of empirical research. Though scientifically and philosophically radical, I believe it resolves the whole of the mind-brain problem for the very first time. It is, moreover, eminently compatible with the very same sort of radicalism which grounds modern physical science.

Let me state a caveat at the outset:The first two chapters of this book constitute a constructive reductio ad absurdum of the ordinary scientific view of the mind-brain relationship. Like the usual reductio arguments, they assume that which I will ultimately refute. Do not let them deter you if you are coming from a different perspective. …And yet they present what I believe are superior answers to the problems they address –i.e. the scientific perspective of the brain and the scientific perspective of the mind. The work will not be for nothing, however, as those conclusions are embodied in the perspective we will finally reach, albeit relativistically. For that, (relativism), is what this science of the mind-brain will ultimately be forced to -as should have been visible since the time of Kant. It is time for Philosophy to grow up. Physics has already reached a comparable answer, and the two answers are compatible.

Let me be very clear. My purpose is passionately empiric and my conclusion pointedly scientific, not merely philosophical. I postulate a deep reorientation of the very foundations of neuroscience with an unswerving focus on productivity. But as Cassirer, for instance, has amply illustrated, it is the case for all the crucial turning points in the history of science that deep progress necessitates serious re-examination of what were considered before as philosophic certainties. Those prior “certainties” have always precluded the profound leaps necessary to the discovery of our greatest scientific theories. Philosophy has been the crucial business of the greatest of our scientists –at the very points where their most significant work was done.11

10 i.e. “abstractly beautiful”11 "A glance at the history of physics shows that precisely its most weighty and

fundamental achievements stand in closest connection with considerations of a general epistemological nature. Galileo's 'Dialogues on the Two Systems of the World' are filled with such considerations and his Aristotelian opponents could urge against Gallilei that he had devoted more years to the study of philosophy than months to the study of physics. Kepler lays the foundation for his work on the motion of Mars and for his chief work on the harmony of the world in his 'Apology for Tycho', in which he gives a

Stylistic and Semantic Notes:Because of the complexity of my conception and because it is so far removed from the accepted paradigms, I have had to solve severe artistic and semantic problems to give what I hope will be a lucid exposition. 12 My thesis is a synergistic combination of three very radical ideas. Each of these by itself is capable of a linear, (though not simple), exposition and argument. Each, however, raises profound new difficulties which must be answered. It is only in their combination that a plausible and, I think, a convincing rationale can be made. I therefore face a difficulty of much the same sort that Kant faced in the exposition of his ideas which faced a similar difficulty and which he illustrated with the problem of explaining the parts of the body. To understand the hand, (he argued), the arm and the heart and the brain must be understood, -and conversely. The parts are only truly intelligible in their integration into the whole. I had originally tried, (reasonably I thought), to present an overview and synopsis of my individual themes and their interconnection in an introductory chapter, giving at least a general answer to the problems they raised.

When I circulated early versions of my ideas for comment, I received numerous initial reactions of high interest from persons whom I considered bright and able, (not because they were interested!) But most of these contacts just “died away”, with no further response. A few brave souls, (or those with more background in the field), managed to get past the initial statement and into the “meat” of my theory, and they have helped me enormously with their criticisms and suggestions. I do not think the others dropped out because of a lack of ability or willingness -or because of disbelief. It is my experience that most people are not shy about expressing disagreement, but that never happened. Those I contacted told me they simply “bogged down” in the Introduction and Synopsis, (the original Chapter 1), and got lost.

I think this was a fault of my presentation. I concluded that the sheer density, the innate complexity, and the necessary abstractness of such a synopsis, undertaken without prior familiarity, were enough to “boggle” almost any mind. If these were not my own ideas, I would probably stand likewise. They are simply too far from the standard paradigm to be presented in such a form.

complete methodological account of hypotheses and their various fundamental forms; an account by which he really created the modern concept of physical theory and gave it a definite concrete content. Newton also, in the midst of his considerations on the structure of the world, comes back to the most general norms of physical knowledge, to the regulae philosophandi. In more recent times, Helmholtz introduces his work, 'Uber der Erhaltung der Kraft'... with a consideration of the causal principle... and Heinrich Hertz expressly asserts in the preface of his 'Prinzipien der Mechanik' that what is new in the work and what alone he values is 'the order and arrangement of the whole, thus the logical, or, if one will, the philosophical side of the subject.' But all these great historical examples of the real inner connection between epistemological problems and physical problems are almost outdone by the way in which this connection has been verified in the foundations of the theory of relativity.... Einstein...appeals primarily to an epistemological motive, to which he grants...a decisive significance." (Cassirer: "Einstein's Theory of Relativity",P.353-354)

12 As an aside, let me remark that “hypertext” would have made some sense as a format for my book. It is frankly beyond me at this point, and I doubt, as well, that it is a proper medium for a serious treatise. To a very real extent, however, I have used footnotes and the multiple appendices to the same end. This was done in an attempt to give at least preliminary answers to the “obvious” objections that must occur almost everywhere.

The alternative presentation raised difficulties of its own, but I concluded that it was the only way to make my ideas comprehensible in a lucid form. That alternative was to just “dive in”, to give just a very general statement -which I give here- to the effect that I will present three radical themes, (1. a biological rationale for the brain, 2. a logical rationale for the mind, and 3. an epistemological rationale which reconciles the first two inside of a consistent and explanatory worldview). Each is unsettling however, and it is only in combination that they become convincing. Or, rather, each is individually plausible, but the new difficulties each raises are resolved and plausible only in their synergistic combination. Each offers a specific and constructive counterproposal to accepted wisdom.

My biological thesis, as an example, proposes that “cognition” and human reality, (viewed from a contemporary Naturalist perspective), is virtual. It proposes that it is a schematic and internally organizational, (rather than a representational), artifact of ordinary evolutionary metacellular process. My larger, overall argument is considerably more complicated than that, however, postulating original logical and epistemological dimensions to the problem and ultimately suggesting a plausible home for “mind” itself.

I will therefore present each of the theses in order, each as a separate chapter,13 and ask for a suspension of judgment until all three are completed. This is asking for a lot, I know, but it will allow a linear comprehension, and should be within the scope of a diligent reader.

The very (logical) form of my argument, especially at certain key turning points, is quite complex and might be confusing however. I do not believe this complexity is of my doing but that it is a necessary reflection of the complexity of the problem itself. I have therefore provided a logical outline and synopsis of the argument as an Appendix. You may refer to it as needed, but I discourage it, (at least until after completing the first two chapters), for the reasons cited above.

The one reader who might properly be excepted from this injunction is the Professional Philosopher who might want to turn to the outline before starting the body of the book. There are a number of apparent self-contradictions in my argument which might induce such a reader to dismiss my thesis out of hand. They are, however, only apparent as I will make clear in the outline.

A Few Practical Matters:Let me conclude this introduction with a couple of practical matters. I have been asked “Who is my intended audience and what are the prerequisites?”

I speak to an imaginary audience which includes the best of the Naturalist philosophers and scientists,14 but the ghosts of the “old ones” –Descartes, Hume, Kant, Newton, Darwin, Hilbert, Einstein, Bohr, Quine ... are there as well. At the deepest level, it is written for the most serious workers in the field. But even from them I do not expect an easy reception. The problem I anticipate derives from my multipli-radical as well as multidisciplinary approach –i.e. it proposes radical (but commensurate) solutions within all the disciplines it encompasses. It is my hope that these workers will see the plausibility of my ideas as regards their own specialties and that this will make them open to question conventionality

13 the third thesis as three chapters14 I especially court mathematicians; I especially court biologists.

in disciplines outside their own.15 Sadly, too often this is not the case –respectability in one field is bought at the price of orthodoxy everywhere else. My thesis is not “multidisciplinary” just because it cites several disciplines; it is multidisciplinary because it is grounded across several disciplines. The subject requires it.

I assume that all serious workers in the field, no matter which aspect is their special interest, will have mastered at least all of the major popular works about it16 as well as those of the classical thinkers. The sheer size and variegation of the issues – i.e. the ground we must cover, (our subject is the human mind and human cognition itself after all), -makes it necessary to assume a familiarity with that material.

A Thesis for the Young:There is another level on which this book may be read, however. It may be read “naively”. By this I mean that it may be read as a simple exposition of a thesis, rather than as the answer to the profound objections which have been raised against all previous attempts at explicating the mind-body problem.17 On such a first reading you may skip the footnotes, the references and even the appendices, though you must go back to them ultimately. For this kind of reading, the actual prerequisites are small. I require only, (as many a mathematical text begins), a “mathematical maturity”. By this I mean that my ideas are to be taken literally and precisely. This is an argument from fundamentals, very much in the Kantian spirit, but informed by modern mathematics and biology. Even on such a reading it remains a difficult theory because it is conceptually complex and novel however, not because it is full of details to be mastered. It does not require prior knowledge so much as an openness of understanding.

It is, therefore, a thesis for the young -or the young at heart. If I am fortunate enough to capture their genuine attention, however, then they must broaden their reading to appreciate its full and far reaching implications. This is not an elementary text. The Bibliography is just a suggestion of where to start. As a minimal beginning I would recommend Maturana and Varela’s “Tree of Knowledge”, at least the first chapter of Cassirer’s “Substance and Function”, Cassirer’s “Einstein’s Theory of Relativity”, Kant’s “Prolegomena to any Future Metaphysics”, and Penrose’s “The Emperor’s New Mind”, (the latter mostly for its summation of modern physics and its criteria of theories). P.S. Churchland’s “Neurophilosophy” would be a next logical step, Dennett’s “Consciousness Explained” the following, probably Lakoff’s “Women, Fire…” and Edelman’s “Bright Air…” next,18 and

15 To get way ahead of myself, if I could dissect the biology out of Walter J. Freeman’s brain, the epistemology out of Gerald Edelman’s, and the logic out of Ernst Cassirer’s and David Hilbert’s and integrate them into a new brain, I think a reasonable similarity to my own ideas would arise.16 E.g. Dennett, Churchland, Maturana, Edelman, etc. I believe the cases they make are

profound and compelling, and they should be familiar to any serious student of the subject. My task is to answer those cases and propose a viable alternative, not to restate them.

17 Which is the way experts must read it.18 Regretfully I had not read either Lakoff or Edelman till after the completion of the

essential draft of my book. Because of time and life constraints, I have been unable to give both of these profound conceptions the service they are due. I have gone back and tried to tie their ideas with my own –particularly in the prefaces- and have added a last

from there the choice is yours. (Though I totally disagree with Dennett on the answer, for instance, it is a beautifully reasoned book and lays out the problem in uncompromising terms.)

This is an important field to enter at this time. I believe it holds the actual “Rosetta Stone” for the future of humankind and, as such, is the desperate and urgent need of our insane age.19 It holds critical and hopeful clues across all the disciplines -not the least of which is ethics.20 How will this species survive? I think the answer does lie in knowledge itself –but better and deeper knowledge and soon! Pompous though it might sound, the answer is that we must fix Man before he destroys himself! This book is meant as my modest contribution to that task.

This is a very large idea, the distillation of almost 50 years of independent, (“cloistered”), thought.21 It is too large and too different to be digested at a single sitting. I would suggest that you master the first thesis by itself, then approach the second. Then I would suggest that you consider them together as a unit, (i.e. evaluate their specific synergism –i.e. “the concordance”). Finally I suggest you approach the third and conceptually most difficult thesis from that secure ground.

“Mind-body” and “cognition” are really a complexity of problems wrapped in a loose ribbon of words. They are really the problem of everything! But then you already knew that, didn’t you? Though my solution is (necessarily) complex in presentation, once understood, it is very simple and natural in concept. I think the conception is actually quite elegant -in the mathematical sense of the word.

appendix, (“Afterword”), dealing specifically with their conceptions. To a large extent I agree with their conclusions, (though not necessarily with their mechanics) –though on different grounds. They do not achieve the necessary sophistication to resolve the mind-body problem however. Nor are they internally consistent –they fail in their treatment of a “God’s eye” view of the world. cf Afterword.

19 I will confine my publications to this particular subject as I think it is the keystone. The problem must not be diluted!

20 I think it provides the beginnings of a scientific ethics, and a scientific aesthetics. But the latter is a huge component in the advancement of science as well as history shows. Stephen Hawkins internet question, (“Can the human race survive?”), posed for the general public is profoundly pertinent, I believe.

21 My particular problem in this book is to translate it into the conceptual language of the current dialogue. Yours is to comprehend a paradigm very different from anything you have seen before.

Preface to Chapter 1: on Realism and Mind as a Non-Representative Model(Signpost #1: These chapter prefaces are meant to be signposts along a long and difficult road.)

Sometimes in the attempt to solve an exceedingly difficult or a seemingly impossible problem we tentatively adopt what is, on the face of it, an ostensibly absurd or even an outrageous22 hypothesis and see where it leads. Sometimes we discover that its consequences are not so outrageous after all.

I agree with David Chalmers23 that the problem of consciousness is “the hard problem”. But I think it is considerably harder than even he seems to think it is. I think its final scientific solution requires new heuristic principles as deep and as wrenching to our innate preconceptions as, (though different from), the “uncertainty”, “complementarity” and (physical) “relativity” that were crucial to the successful advance of physics early in the 20th century.24 Its resolution involves a profound extension, (though not a refutation), of classical logic as well. A full consideration of these deep new cognitive principles: “cognitive closure”, (Kant, Maturana, Edelman), “scientific epistemological relativity”,25 (Cassirer and Quine), and of the necessary extension of logic, (Cassirer, Hilbert, Rosch, Lakoff, Edelman, Iglowitz), must await later chapters however. In a very real sense, moreover, it is a “chicken and egg” problem. I must ask for some latitude therefore. This is too big a problem to be focused in a single chapter.

In this chapter I will propose, instead, just the first and conceptually -though not mechanically- simplest part of a three pronged and multidisciplinary hypothesis for a solution of the problem of consciousness. This first biological hypothesis proposes, (“outrageously”), that the evolutionary rationale for the brains of biological organisms was not representation26 -nor reactive parallelism -nor transcendent logic!27 -as is generally asserted. It proposes instead that it was specifically an optimizing, non-representational, internal and purely operational organization by metacellulars solely of their own primitive reactive biologic process instead. I will argue that our very perceptual and conceptual objects are themselves nothing but metaphors of that internal organization.

I will propose a quite specific model of brain function and go on to argue that its particular method of organization was vital for the adroit functioning of profoundly complex metacellular organisms in an alien and hostile environment. I will argue, moreover, that this organization was antithetical to a representative role! Representation, I will maintain, is in actual conflict with the optimization of biological response!

22 I really wish that Crick hadn’t trivialized this word in the context of the mind-brain problem. His is really a very orthodox conception in the context of the current literature.

23 Chalmers. 199524 For a vivid recreation of that time and the comparable intellectual dilemmas presented by the empirical findings of quantum physics see “Uncertainty: the Life and Science of Werner Heisenberg". Cassidy, 1992, for instance. 25 This is not an ad hoc relativism, but a scientifically structured one –I will elaborate this point shortly and develop it at length as the subject of Chapter 4.26 This is not so peculiar an idea as it may seem but is being advocated more and more frequently by eminent biologists of our day- e.g. Maturana and Varela, Freeman and Edelman.27 I.e. an ultimate, objective logic dealing with the ultimate, objective, (ontic), world -the absolute world in which we exist. This is Kant's distinction between "transcendent" and "transcendental".

This is a truly “outrageous” hypothesis in that it proposes a premise which presumes our ordinary physical and evolutionary world, (i.e. ordinary biology), in its very statement, while the consequences of that selfsame premise are that our ordinary worldview, (to include the aforementioned “ordinary physical and evolutionary world” in which it was framed), is neither probably, nor even likely, to be (metaphysically28) correct!29 We humans, after all, are metacellulars too. We are ourselves “ordinary biological organisms”, and the consequences of my arguments apply to us, (and me), as well!

How is this possible? How can it not be a logical absurdity? The answer lies in the conception of fundamental epistemological relativism first propounded by Ernst Cassirer almost a century ago! Cassirer’s relativism, (his “Theory of Symbolic Forms”), will allow a cogent realist resolution of this seeming “reductio” in Chapters 3 and 4 drawing from Kant, Cassirer, Quine and Bohr. I will argue with Cassirer that our science is a relativistic30 organization of organic phenomena, (“experience”), and not metaphysically, (i.e. absolutely), referential.31 This proposal, like Bohr’s, will resolve the apparent self-contradiction of this first premise by placing it as a scientifically significant and useful relative32, (i.e. organizational), but not metaphysically referential assertion.

28 "Metaphysics", as a word, refers not just to historically obsolete scientific ideas such as "final causes", "purpose", et al, but also to ultimate being -i.e. "ontology". This aspect of metaphysics, (i.e. what is the world really?), still remains at the core of most conceptions of science and philosophy despite Kant's Herculean efforts. Though unfashionable to give it a name, that which it names is ubiquitous. I will address the issue at length in Chapters 3, 4, and 5 as its clarification is crucial to the mind-body problem just as it was crucial to the successful advance of modern physics.29 The same dilemma is shared, clearly, by Maturana and Varela, Freeman, Lakoff, Edelman, … Maturana calls it “the razor’s edge”.30 I had probably best clarify mine, (and Cassirer's), meaning of the word "relativism" right here. It does not have the sense of "cultural relativism", "ethical relativism", or that "anything is as good, (or true!), as anything else". It does not signify an abandonment of truth or legitimacy. Rather, we understand the word in the mathematical and scientific sense -in the sense of Einstein's Special Relativity for instance. It denotes an exact and invariant rule of connection. One set of measurements in a particular frame of reference is not arbitrary as regards another set of measurements in another frame under Special Relativity for instance. Instead it is related to it in a rigid and invariant relation -i.e. via the specific equations of the theory of special relativity. This is the sense of "relativism" and "invariance" that Cassirer and I utilize, and it is diametrically opposed to "capriciousness".31 I will argue that the business of science is the prediction of correlations of events, not about what those correlations ultimately correspond to in some ultimate ontic "nether world". I will argue, with Maturana and Varela, and with Gerald Edelman that brains, (and the product of those brains), are adaptive, (e.g. “ex post facto selective of preexisting internal variation" using Edelman’s terminology -cf Edelman, 1992, p.82), and not information processing. But "adaptation" does not imply isomorphism or objective mapping, it implies competence, which is quite different from implying a "God's eye" knowledge of the world, (information). I will pursue this discussion in Chapter 3. Edelman draws a similar conclusion, but then goes on, inexplicably, to propose exactly such a "God's eye" view himself! I attempt to resolve that difficulty in Chapter 4 in a modification of Cassirer's "Symbolic Forms".32 see footnote above

It is proposed, (itself!), as a legitimate and scientifically productive automorphism33 within our ordinary world, not as a metaphysical (objective) mapping to an external, absolute domain.

My overall thesis is neither solipsistic nor idealistic however, but scientific and realist. Ultimately I will propose that our ordinary world, (our “folk world”34), is a blind working algorithm, (in just Bohr’s sense for quantum mechanics), on the Kantian ultimate reality.35 But it incorporates, like physics, a principle of fundamental epistemological uncertainty. It is, therefore, a realist36 hypothesis in the essential meaning of that phrase. It is “Kantian” without the categories.

I will show in later chapters how this first hypothesis, (in concert with ancillary logical and epistemological hypotheses37), opens the first real possibility for an actual and adequate solution of the problem of “consciousness” that is commensurate with the legitimacy of science. It leads to an actual solution of the fundamental paradoxes of sentiency. I assert that my solution actually explicates those paradoxes rather than merely denying or reducing, (i.e. eviscerating them), as has been the case heretofore. Explanatory ability, as opposed to evisceration and dismissal, is a crucial measure of a new theory. My thesis, moreover, foreshadows the beginnings of a truly scientific psychiatry, (i.e. a mathematical one), for the first time.

The Alternative Positions:The nonrealist philosophies: dualism, idealism and solipsism appear to have a certain advantage in the problem of consciousness. Admittedly, they circumvent certain of the primal difficulties, but they do so at a price too costly for most scientists and other practical minds. Because they detach38

physical presentation, (i.e. sensory perception39), from our consciousness, (or discount it entirely), the problems of “the homunculus” and of how we know clearly disappear -at least in regard to external perceptions. We know because we know. We begin by knowing. There is, they claim therefore, no problem of knowing!

But it is only an illusory advantage for these philosophies do not solve an even deeper problem of “presentation” and another “homunculus” implicit in our very logic itself. How can this part of even a “mental stuff” know that part?40 How, in Leibniz’s formulation of the problem, could “the many” be known to “the one”? Whence comes the integration of the parts? Whence, furthermore, comes the “abstraction” and “attention”41 at the theoretical foundations of the classical logical “concept”/”category” –i.e. at the very basis of classical logic itself?42 What do we abstract from -33 In mathematics, an automorphism is an isomorphism from a mathematical object to [all

of]itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. (Wikipedia)

34 and ultimately, (as an extension of that world), our science as well35 “nuomena”36 Contrary to his own (grudging) acceptance of the label of "critical idealist", Kant was very much a realist. His arguments in "Prolegomena" very clearly and pointedly distinguish him from classical idealism. A more modern classification, I propose, would be "ontic indeterminist". The "categories", I believe, are a different issue, and open to question. See Introduction to Chapter 2 for an elaboration of essential realism.37 As set forth in chapter 2, and in chapters 3 through 538 or reinterpret39 to whatever extent it may exist for them40 other than that mind is "nonextensional" and "non-divisible" -i.e. "it just does"!41 cf Chapter 2 -Cassirer42 This is the subject of chapter 2

and where, and what do we pay attention to -in our formal theory of concepts -and how? How can there be even a logical homunculus? How can there be meaning?43

This is the problem of logical presentation. I call it the logical problem of consciousness and it is the hardest problem. It is a problem that no philosophy has yet answered. It is the purpose of this chapter to present the first of three synergistic44 hypotheses intended, (at their end), to answer it fully, and the core of the mind-body problem as well in a manner consistent with science and realism.

Ordinary realism, (ordinary materialism), on the other hand, throws away the baby with the bath. It leads inexorably to the conclusion, as Dennett45 has so forcefully argued, that we can have no consciousness -we are all automatons -“zombies”! Simply put, there is no way that one part of a spatially and temporally distributed process46 can know another part.47 There is no “place” that knowing can be; -there can be no “Cartesian Theater”! We are “multiple drafts” published on a mechanical “demon press”. Emergence, supervenance and epiphenomenalism,48 on the other hand, are profoundly challenged by Occam’s razor49 since by definition they are capable of adding nothing causative to physical explanations.50

43 A large part of the problem of "mind" and of "consciousness" lies in our inability even to properly and adequately frame it. This ambiguity is pretty much admitted by all parties. I believe it is a consequence of the lack of an adequate underlying conceptual framework, and not because of a lack of substance to the problems themselves. It is only when an adequate substrate theory has been formulated, (or while it is being formulated), that the problems will take on clear and logical form, and solutions will be cogent. There are clear precedents in the history of science to illustrate the case. How, for instance, could the perspectives, (the questions and the answers), of Galilean or Newtonian physics be formulated in the causative framework of Aristotle or the cosmological framework of Ptolemy? The answer is that they could not. It was only in the evolution of a different context and a different science that they could be explicitly formulated at all. The problems and the answers of "mind" and of "consciousness" are considerably clearer within my thesis -i.e. they can achieve a concise formulation, but not in a prelude to it.44 and, thereby, individually somewhat perplexing45 Dennett, 1991. I will not reiterate these kinds of arguments within this book -we have much larger and original ground to cover. They have been powerfully and beautifully made innumerable times before. (Cf, for instance, Dennett, P.S. Churchland, Paul Churchland, -even Edelman!) Furthermore I accept their conclusions within the context within which they were made and expect my intended reader to have been strongly challenged by them. It is that context itself we must examine but we must do so without presupposing our conclusions, “heterophenomenologically”, as Dennett would say46 the process of the brain, for instance47 (though it can react to it!)48 and property dualism ...49 The principle that entities are not to be multiplied beyond necessity, i.e. beyond explanatory sufficiency.50 Have you ever actually performed the reduction of one system of mathematical axioms to a different set of axioms? It illustrates the counter-case to Churchland’s argument perfectly. Only after reducing the secondary axioms to the primary ones are we then allowed to disregard the latter and incorporate the possible operative efficiency of the former. In fact nothing substantive “emerges” except efficiency. But this is the paradigm case of theoretical reduction in general.

The real problem for those of us who believe we “have a life” therefore is how to account for both consciousness and a reality external to that consciousness in a philosophy of realism and science. I will argue ultimately that it requires a reduction of the excessive and blatantly metaphysical51 demands made on realism while retaining the essential core we vitally require. This (essentially Kantian) realism52 will enable a viable solution to the logical problem in my second thesis, (and to the problem of meaning as well), and answers our innate demands for both science and consciousness. My third hypothesis53, (in conjunction with the first two), undertakes to supply the actual “substance” -the “matter of mind”- within the context of that same realism. Consciousness without realism and science is inconsequential. Science and realism without consciousness is pointless.

Sometimes it is necessary to walk around a mountain in order to climb the hill beyond. It is the particular mountain of “representation”, and the cliff, (notion), of “presentation” itself, (to include logical presentation), embedded on its very face, I will argue, which blocks the way towards a solution of the problem of consciousness. This first chapter points out the path around the mountain so that we may approach the more manageable grades beyond. “Presentation”, I hold, is not implicit in consciousness nor is it innate in realism.

Let me now present just the first of three synergistic hypotheses whose combination I will ultimately propose as a scientifically plausible solution for the problem of consciousness. This first hypothesis is not intended to stand on its own. Though it opens new and fruitful perspectives on the problem, it raises very large problems itself. The latter are the subject of the second, (Chapter 2), and third hypotheses, (chapters 3, 4, and 5). Their adequate resolution involves a paradigm shift of monumental proportions and is dependent on the whole of the three hypotheses. It is the latter fact, I believe, which has made the problem so long intractable.

The Churchlands confabulate a prayer with a viable argument.)51 i.e. ontological –see footnote above defining “ontology”52 see prior footnote concerning Kant’s realism53 Chapters 3, 4, and 5

Chapter one: Mind: The Argument from Evolutionary Biology

1. Representation: the perspective from biology

Maturana and Varela’s “Tree of Knowledge”,54 is a compelling argument based in the mechanics of physical science and biology against even the very possibility of a biological organism’s possession of a representative model of its environment. They and other respected biologists, (Walter J. Freeman, Gerald Edelman), argue even against “information” itself. They maintain that information never passes between the environment and organisms; there is only the mutual “triggering” of structurally determinate organic forms.55 I believe theirs is the inescapable conclusion of modern science. I will now present a specific and constructive counterproposal for another kind of model however which I call “the Schematic Operative Model”. Contrary to the case of the representative model, it does remain viable within the critical context of modern science. I believe that we, as human organisms, do in fact embody a model. I believe it is the stuff of mind!

2. The “schematic model”: definition and examples. (Defining what it means to be “an object”)

Normally, when we think of “models”, we mean reductive or at least parallel models. In the first we think of a structure that contains just the essential properties of what is to be mirrored. When we normally use the term “schematic model”, we talk about the preservation of the “schema”, or “sense” of what is mirrored. Again it is reductive, however- it is logically reductive. It is, as has been claimed, “just a level of abstraction”. There are other uses for models, however, -those that involve superior organizations! This is the new sense of “schematic model” that I propose to identify.

2.1 The primitive case: a definition by example56

Even our most simplistic models, the models of our mundane training seminars, suggest the possibility of another usage for models very different than as representative schemas. They demonstrate the possibility of a wholly different paradigm whose primary function is organization instead.

Look first at the very simplest of models. Consider the models of simplistic training seminars -seminars in a sales organization for instance, (“Amway” ©, let us say). “’Motivation’ plus ‘technique’ yields ‘sales’.”, we might hear at a sales meeting.

Or, (escalating just a bit), “’Self-awareness of the masses’ informed by ‘Marxist-dialectic’ produces ‘revolution’!”, we might hear from our local revolutionary at a Saturday night cell

54 ? Maturana and Varela, 198755 I will treat Maturana’s thesis extensively as the subject of Chapter 3.56 Though this discussion is conceptually difficult, it will ultimately lead to the resolution of the

problem of consciousness itself. Take your time and try to get “inside” of it.

meeting. Visual aids, (models), and diagrams are ubiquitous in these presentations. A lecturer stands at his chalkboard and asks us to accept drawings of triangles, squares, cookies, horseshoes... as meaningful objects -with a “calculus” of relations, (viz: an “arithmetic” of signs taken in its most primitive mathematical sense),57 between them, (arrows, squiggles, et al). The icons, (objects), of those graphics are to be stand-ins for concepts or processes as diverse, (escalating just a bit more), as “motivation”, “the nuclear threat”, “sexuality”, “productivity”, and “evolution”. Those icons need not stand in place of actual entities in objective reality, however. Just what is “a productivity” or “a sexuality”, for instance? What things are these?

Consider this: two different lecturers might invoke different symbols, and a different “calculus” to explicate the same topic. In analyzing the French Revolution in a history classroom, let us say, (a classroom is a kind of training seminar after all!), a fascist, a royalist, a democrat might alternatively invoke “the Nietzschean superman”, “the divine right of kings”, “freedom”, ... as actual “objects” on his blackboard, (with appropriate symbols).58 He will redistribute certain of the explanatory aspects, (and properties), of a Marxist’s entities, (figures) -or reject them as entities altogether.59 That which is unmistakably explanatory, (“wealth”, let us say), in the Marxist’s entities, (and so which must be accounted for by all of them), might be embodied instead solely within the fascist’s “calculus” or in an interaction between his “objects” and his “calculus”.

Thus and conversely the Marxist would, (and ordinarily does), reinterpret the royalist’s “God”-figure, (and his –the Marxist’s- admitted function of that “God” in social interaction60 ), as “a self-serving invention of the ruling class”. ”God” becomes solely an expression of his “calculus” and is not embodied as a distinct symbol, (i.e. object), on his blackboard. The “objects” of these lecturers - as objects per se - need not be compatible! As Edelman pertinently noted: “certain symbols do not match categories in the world. ... Individuals understand events and categories in more than one way and sometimes the ways are inconsistent.”61

57 ? Webster’s defines “calculus”: “(math) a method of calculation, any process of reasoning by use of symbols”. I am using it here in contradistinction to “the calculus”, i.e. differential and integral calculus.

58 This was one of the beautiful things at the University of Chicago –we were actually given a choice between alternatives like this! Madeline and Trotsky were read jointly for instance. This is what a liberal education used to be about.

59 ? Is this not the usual case between conflicting theories and perspectives?60 ? Dennett’s term “heterophenomenological” -i.e. with neutral ontological import -is apt here.

61 ? Edelman, 1992, pps. 236-237, his emphasis

Figure 1

Figure 2

What is important is that a viable calculus-plus-objects, (any given model), must explain or predict the history of events -that is, it must be compatible with the phenomena, (in this particular example the phenomena of history). But the argument applies to a much broader scope. I will argue in a later chapter,62 (following the strong case of Hertz and Cassirer), that the same accounting may be

62 ? See Chapter 4

given of competing scientific theories, philosophies, and, indeed, of any alternatively viable explanations. (This is the relativism at the core of Cassirer’s “Theory of Symbolic Forms”.)

Consider Heinrich Hertz:

“The [scientific] images of which we are speaking are our ideas of things; they have with things the one essential agreement which lies in the fulfillment of the stated requirement, [of successful consequences], but further agreement with things is not necessary to their purpose. Actually we do not know and have no means of finding out whether our ideas of things accord with them in any other respect than in this one fundamental relation.” (Hertz, “Die Prinzipien der Mechanik”, my emphasis)

The mere existence of a multiplicity of alternately viable calculuses, (sic), and the allowable incommensurability of their objects63 suggests an interpretation of the objects of those models contrary to representation or denotation however. It suggests the converse possibility that the function and the motivation of the objects of those models, specifically as entities, (in what I will call these “schematic models”), is instead to illustrate, to enable, -to crystallize and simplify the very calculus of relation proposed between them!64 Their “objects”, I propose, are manifestations of the structure;65 the structure is not a resolution of the objects. It is the structure which is predictive; its objects merely enable it!

2.1.1 Reversing our perspective:

I propose that the boundaries -the demarcations and delimitations of these schematic objects, (their “contiguity” if you will) -are formed specifically to meet the needs of the operations themselves. I propose that they exist to serve the structure, (the rules of the “calculus”) - not the converse.66 I propose that their objects –specifically as objects per se - serve to organize process, (i.e. analysis or response). They are not representations of actual objects or actual entities in reality.67 This, I propose, is why they are taken as “things” in the first place. They functionally bridge reality in a way that physical objects do not and I suggest that they are, in fact, materialized metaphors of analysis or response. The rationale for using them, (as any good “seminarian” would tell you), is clarity, organization and efficiency.

Though set in a plebian context, the primitive case –the “training seminar”, (as presented), illustrates and defines the most general and abstract case of schematic non-representative models in that it presumes no particular agenda. It is easily generalized: it might as well be a classroom in nuclear physics or mathematics, the boardroom of a multinational corporation, -or a student organizing his love life on a scratchpad.

63 ? together: the possible conceptual contexts64 ? see the arguments of Chapters Two and Four for a detailed rationale

65 Hilbert’s “implicit definition” treated in chapter 2 will make this clearer.66 See “Afterward: Lakoff/Edelman” for a discussion of mathematical “ideals” which bears on this discussion.

67 this relates to the issues of “hierarchy” which I will discuss in Chapter 2.

Figure_ 3 Figure 4

2.2 A case for schematism more specific to our special problem: (Narrowing the focus: the engineering argument)

Engineers’ instrumentation and control systems provide an example of the organizational, non-representational use of models and “entities” in another setting. These entities, and the context in which they exist, provide another kind of “chalkboard”.68  Their objects need not mirror objective reality either. A gauge, a readout display, a control device, (the “objects” designed for such systems), need not mimic a single parameter -or an actual physical entity. Indeed, in the monitoring of a complex or dangerous process, they should not. Rather, the readout for instance should represent an efficacious synthesis of just those aspects of the process which are relevant to effective response, -and be crystallized around those relevant responses!

A warning light or a status indicator, for instance, need not refer to just one parameter. It may refer to electrical overload and/or excessive pressure and/or... Or it may refer to an optimal relationship, (perhaps a complexly functional relationship), between many parameters -to a relationship between temperature, volume, mass, etc. in a chemical process, for instance, or critical mass aspects of a nuclear power reactor configuration.69

The exactly parallel case holds for its control devices. A single control may orchestrate a multiplicity of (possibly disjoint) objective responses. The accelerator pedal in a modern automobile, as a simple example, may integrate fuel injection volumes, spark timing, transmission gearing...

Ideally, (given urgent constraints), instrumentation and control might unify in the selfsame “object”. We could then manipulate the very object of the display and it in itself could be the control device as well. Consider the advantages of manipulating a graphic or tactile object which is simultaneously both a readout and a control mechanism under urgent or dangerous circumstances. Now think about this same possibility in relation to our ordinary objects of perception -in relation to the sensory-motor coordination of the brain and the objects of naive realism in the real world! The brain is a control system, after all. It is an organ of control and its mechanics must be considered in that perspective. Its function is exceedingly complex and the continuation of life itself is at stake -it is a complex and dangerous world. Might not our naïve world itself be such a combined schematic control system?

68 ? Their designers are the “lecturers”, and the instruments they design are the “objects” of their schematic models69 Think of an oscilloscope, for instance.

2.3 The “GUI”: the most pertinent and sophisticated example of a schematic model: (the special case)

The “object” in the graphic user interface, (GUI), of a computer is perhaps the best example of a purely schematic usage currently available. In my simplistic manipulation of the schematic objects of my computer’s GUI, I am, in fact, effecting and coordinating quite diverse, disparate and unbelievably complex operations at the physical level of the computer. These are operations impossible, (in a practical sense), to accomplish directly. What a computer object, (icon), represents and what its manipulation does, at the physical level, is exceedingly complex and disjoint. Nor is there a necessarily non-random assignment of function!70 The disparate voltages and physical locations, (or operations), represented by a single “object”, and the (possibly different) ones effected by manipulating it, correlate to a metaphysical object only in this “schematic” sense. Its efficacy lies precisely in the simplicity71 of the “calculus” it enables!  (It is the interface that must be simple!)

Contemporary usage is admittedly primitive. Software designers have limiting preconceptions of the “entities” to be manipulated, of a necessary preservation of hierarchy, and of the operations to be accomplished in the physical computer by their icons and interface.72 But I assert that GUI’s and their “objects”, (icons), have a deeper potentiality of “free formation”. They have the potential to link to any selection across a substrate, i.e. they could “cross party lines”. They could cross categories of “things in the world”, (Lakoff’s “objectivist categories”),73 and acquire thereby the possibility of organizing on the different and the most pressing issue: i.e. urgency / risk. They need preserve neither parallelism nor hierarchy.74

Biology supplies fortuitous examples of the sort of thing I am suggesting for GUI’s –e.g. in the brain’s “global mapping” noted by Edelman.75 (I will present Walter J. Freeman’s more explicit case in detail shortly). The non-topological connectivity Edelman notes from the brain’s “topobiological” maps, (i.e. the multiple, topological maps in the cortex), and specifically the connectivity, (the “global mapping”), from the objects of those maps to the non-mapped areas of the brain he describes supply a concrete illustration of the kind of potential I wish to urge for a GUI. Ultimately I will urge it as the rationale for the brain itself. This global mapping allows “... selectional events”, [and, I suggest, their “objects” as well], “occurring in its local maps ... to be 70 Think of just buying a new cell phone or a new digital watch, (mini computers in themselves), and learning its proprioceptor -i.e. muscle memory- interface –which is what reading the manual is all about. There is no obvious assignment of function!71 Or not72 Working with Microsoft Windows®, for instance, at any but a superficial level might disaffect you as to its hierarchical structure. IT people will understand my meaning, I think. Actually, it is possible that the difficulties of the modern computer OS might develop into a strong argument for my thesis. Because they are necessarily the composite of many different minds, and different perspectives, it is more than possible that they illustrate Edelman’s statement quoted above. “certain symbols do not match categories in the world. ... Individuals understand events and categories in more than one way and sometimes the ways are inconsistent.”73 Cf Lakoff, 1987. Also see “Afterward: Lakoff, Edelman…”74 There is the issue of a necessary domain that must be addressed here. I will do so in the

“implicit definition” appendix. It is not inherent that all domains must be consistent or capable of concatenation. This probably especially true of biology -think of multiple predators! What works for one may be entirely counterproductive for another.

75 Edelman, 1992

connected to the animal’s motor behavior, to new sensory samplings of the world, and to further successive reentry events.” But this is explicitly a non-topological mapping. This particular mapping, (the global mapping), does not preserve contiguity. Nor need it preserve hierarchy.

Here is a biological model demonstrating the more abstract possibility of a connection of localized “objects”76, (in a GUI), to non-topological (distributed) process -to “non-objectivist categories “, using Lakoff’s terminology. As such, it illustrates “schematism” in its broadest sense. Edelman’s fundamental rationale is “Neural Darwinism”, the ex post facto adaptation of process, not “information”, and is thus consistent with such an interpretation. It does not require “information”. Nor does it require “representation”. Edelman, (unfortunately), correlates his topobiological maps, (as sensory maps), directly and representatively, (i.e. hierarchically), with “the world”. This is a clear inconsistency in his epistemology. It is in conflict with his early and continual repudiation of “the God’s eye view” on which he grounds the whole of his biologic epistemology.

76 ? in the brain’s spatial maps

Figure 5: A Graphic Rendering of Edelman’s Epistemology(Note: hierarchy and contiguity are implicit!)

But what if we turn Edelman’s perspective around however? What if we blink the “God’s eye” he has himself so strongly objected to, and step back from the prejudice of our human (animal) cognition. What if the maps and their objects both were taken as existing to serve blind primitive process instead of information? (Figure 6) What if they were organizational rather than representative?

Figure 6: A More Consistent Rendering of Edelman’s Epistemology Suggesting a New Paradigm for GUI’s(Note: Neither hierarchy nor contiguity are implicit in this model.)

This is the case I wish to suggest as an illustration of the broadest implementation of the GUI, (which I will argue shortly) –i.e. a specifically non-topological correlation! It opens a further fascinating possibility moreover. It suggests that evolution’s “good trick”, (after P.S. Churchland’s usage), was not representation, but was instead its original organization of primitive process into a topological context. It suggests that the “good trick” was evolution’s creation of the cortex itself! –and in itself!

2.4 Towards a better biological model Figure7

2.4.1 Biology, the real thing: Freeman’s model

What is needed now is a more explicit model, and specific empirical findings which will actualize my proposal. Citing Edelman’s “global mapping” is all very well and good, but it doesn’t really do what it has to. It is “too philosophical”, too general, and as Popper would have predictably urged, not falsifiable.

A more detailed and quite specific model comes from the work of the noted neurophysiologist, Walter J. Freeman. Based on research first with the olfactory cortex, (arguably evolution’s first cortex), and then with the visual and other cortices, Freeman argues that the brain does not process information at all –it does other things! He has approached the problem directly and addressed the crux of the issue: what is the correlation between sensory input and resultant brain states? Is there one? This is explicitly empirical research clearly pertinent to the problems of parallelism and hierarchy and, if its conclusions are viable, it is totally relevant as a concrete instantiation of my prior arguments for the generalized “schematic model”. It is falsifiable! But, conversely, it is capable of falsifying the very premise of the standard paradigm -i.e. that of “representation” itself.

First, however, please look at Freeman’s model, and note the striking similarity to my own Figure 6 just above and conceived before I ever saw Freeman’s papers.77 Strikingly similar, that is, if we interpret his “topographic projections” as following behind Edelman’s “topobiological maps”. (Feature detectors?)

77 ? This was a shocking and happy surprise!

Fig. 8, (from Freeman’s Fig 2): ”The input path from receptors to the bulb has some topographic” [topological] ”specificity. The output path to the prepyriform has broad axonal divergence, which provides a basis for spatial integration of bulbar output and extraction of the ‘carrier’ wave.” (From Freeman 1983, reproduced by permission.)“It is based on a striking difference between two types of central path, one that provides topographic mapping from an array of transmitting neurons to an array of receiving neurons, the other having divergence of axons that provides for spatial 78integration of the transmitted activity.” (Freeman, 1994, my

emphasis –please see footnote below on Freeman’s usage of the word “spatial”).

Now compare Freeman’s Figure 2 with my Figure 6 shortly before it. They are identical in all major aspects! This is an explicit case, truly drawn from biology illustrating the actual non-topological mapping potential of virtual systems. Freeman’s map is not topological, does not preserve hierarchy, and does not preserve information. It is an actual case demonstrating the ultimate potential of schematic GUI’s for distributing, (or conversely, for centralizing), function into objects. Freeman’s model exposes a new paradigm for models. It demonstrates an organizational potential of models beyond representation.

78 I think it would be wise to consider and keep in mind Freeman’s two usages of the word “spatially” at this point. One is concerned with the physical geometry of the brain itself, and the other is concerned with the topology of mappings within it. [There is] “a striking difference between two types of central path, one that provides topographic mapping from an array of transmitting neurons to an array of receiving neurons, the other having divergence of axons that provides for spatial integration” [within the physical space of the brain] “of the transmitted activity.” The latter usage: “The output path to the prepyriform has broad axonal divergence” [as] ”a basis for spatial integration of bulbar output” refers to the brain in a meta-model sense – in terms of functionality and brain physiology, not spatial content in the sense of dimensionality or topology within a model. In another passage, he states “The code of sensory, motor and autonomic parts of the peripheral nervous system is the spatial”, [topological], “pattern of temporal pulse rates. The same code appears to hold...for the ascending and descending pathways and relays in the brainstem and spinal cord.” This is an intra-model usage, not a meta-model, (physical), usage.

Freeman begins:

“This book had its origin ... in an experimental finding....I was tracing the path taken by neural activity that accompanied and followed a sensory stimulus in brains of rabbits. I traced it from the sensory receptors into the cerebral cortex and there found that the activity vanished, just like the rabbit down the rabbit hole in ‘Alice in Wonderland’. What appeared in place of the stimulus-evoked activity was a new pattern of cortical activity that was created by the rabbit brain... My students and I first noticed this anomaly in the olfactory system... and in looking elsewhere we found it in the visual, auditory, and somatic cortices too... In all the systems the traces of stimuli seemed to be replaced by constructions of neural activity, which lacked invariance with respect to the stimuli that triggered them. The conclusion seemed compelling. The only knowledge that the rabbit could have of the world outside itself was what it had made in its own brain.” (Freeman, 1995)

What does this mean? What does it mean that the new pattern “lacked invariance” in regard to the stimuli? The “invariance” demanded correlates precisely to the “passage of information” -and it could not be found!

“The visual, auditory, somatic and olfactory cortices generate... waves [that] reveal macroscopic activity ... from millions of neurons. ... These spatial AM patterns are unique to each subject, are not invariant with respect to stimuli, and cannot be derived from the stimuli by logical operations!” (Freeman, 1994)

In this paper79 Freeman actually makes two cases –one structural and one functional. The structural case is purely physiological and absolutely pertinent to my case. It deals with the actual connectivity of nerve tissue and argues against the possibility of maintaining topological integrity within the cortex. (His other case is for “Chaos theory” as an explanation of function to which I will refer later.) It is the former case that I want to pursue here as I think it supplies an explicit and actual illustration of my argument for the non-topological possibilities of schematic models. This is what I believe evolution did and how it did it. It does present profound problems to logic and to epistemology however. (I will address these in chapters 2 through 4.)

He divides nerve physiology into two categories:

(1) Those which preserve topological integrity: this is the case for the sensory nerves for instance.

“Sensory neurons exist in large arrays in the skin, inner ear, retina...so that a stimulus is expressed as a spatial pattern...carried in parallel along sensory nerves. Typically only a small fraction of the axons in a nerve is activated...with the others remaining silent” [for isolation] “...so that the ‘signal’ of the stimulus is said to be ‘encoded’ in the frequencies of firing of that subset of axons subserving ...the activated...receptors.”

“The code of sensory, motor and autonomic parts of the peripheral nervous system is the spatial”, [topological80], “pattern of temporal pulse rates. The same code appears to

79 ? “Chaotic Oscillations...”, 199580 See prior footnote on his usage of “spatially”

hold...for the ascending and descending pathways and relays in the brainstem and spinal cord. ...Serious efforts have been made to extend this model to the cerebral cortex with considerable success in characterizing the receptive fields and ‘feature detector’ properties of cortical neurons in primary sensory areas.” (Freeman, 1994) (He argues that ‘feature detection” occurs only early in cortical process however. Thereafter topographic projection disappears!)

(2) Within the cortex, however, it is a different story. Cortical neurons typically have short dendritic trees on the order of ½ millimeter. They are not, however, typically connected to the neurons physically adjacent to them.

“The main neurons in cortex ...intertwine at unimaginable density, so that each neuron makes contact with 5,000 to 10,000 other neurons within its dendritic and axonal arbors, but those neighbors so contacted are less than one percent of the neurons lying within the radius of contact. The chance of any one pair of cortical neurons being in mutual contact is less than one in a million.” (Freeman, 1995)

“Peripheral neurons”, [on the other hand], “seldom interact with other neurons, but offer each a private path from the receptor to the central nervous system. In contrast, each cortical neuron is embedded in a milieu of millions of neurons, and it continually transmits to a subset of several thousand other neurons sparsely distributed among those millions and receives from several thousand others in a different subset.” (Freeman, 1994)

This is reminiscent of Maturana’s comment:

“It is enough to contemplate this structure of the nervous system... to be convinced that the effect of projecting an image on the retina is not like an incoming telephone line. Rather, it is like a voice (perturbation) added to many voices during a hectic family discussion (relations of activity among all incoming convergent connections) in which the consensus of actions reached will not depend on what any particular member of the family says.” Maturana, (1987), 163-4.

And Edelman’s:

“… To make matters even more complicated, neurons generally send branches of their axons out in diverging arbors that overlap with those of other neurons, and the same is true of processes called dendrites on recipient neurons …. To put it figuratively, if we ‘asked’ a neuron which input came from which other neuron contributing to the overlapping set of its dendritic connections, it could not ‘know’.” (Edelman, 1992, p.27)

Peripheral neurons are relatively isolated, (“private”), within nerve bundles and support a topological case to the point of ‘feature detection’ at cortex. Within the cortices, however, we are dealing with a different sort of connective process. We are no longer dealing with parallel or hierarchical, (i.e. information preserving), mappings. Because each cortical neuron is embedded in a milieu of millions of neurons, it “continually transmits [to] and receives from several thousand others” with a “continual background activity owing to its synaptic interactions with its neighbors”.

This is a characteristic property of cortical neural populations not shared by peripheral neuron arrays.

Cortical process disburses function spatially81 , (physiologically), through the brain, (“with strong axonal divergence”), through intertwined nerve process. It connects point-to-point fitfully within the volumetric space of the brain set-theoretically, not topologically. These cell assemblages act as units which “provide for spatial integration [projection] of the transmitted activity.” The cortices generate dendritic potentials…arising from synaptic interactions of millions of neurons. They share “a spatially82 coherent oscillation… by which spatial patterns of amplitude modulation are transmitted in distinctive configurations… The neurons sharing the macroscopic, aperiodic oscillations comprise a local neighborhood that can be viewed as an equivalence class.”83

These “equivalence classes” thereby provide a non-contiguous, non-topological spatial distribution onto the physical space of the brain. These spatially extensive and intertwined complexes of cells throughout the cortex achieve a connectivity that mere parallelism, (or hierarchy), cannot.  Freeman shows us how a topological mathematical space can be mapped onto the specifically physical space of the brain non-topologically!  But that particular physical space is determined by its specific connectivity -by evolution and ontogeny, not representation.  Determined by genetics and learning, (ontogeny), it has the ability to connect specific process “ad hoc”.  It has the ability to self-organize on principles other than topological ones.

“The local neighborhoods corresponding to cortical columns and hypercolumns seldom have anatomical boundaries of their internal synaptic connections, so that an area of cortex composed of hundreds and even thousands of neighborhoods can act as a coherent element of function in generating a spatially coherent carrier wave. These distributed neural populations are dynamically unstable and are capable of very rapid global state transitions” [which can] “easily fulfill the most stringent timing requirements encountered in object recognition.” (ibid).

Freeman concludes: “The transform effected by the output path defines the self-organized macroscopic activity as the cortical ‘signal’.” “In brief, ... the central code cannot be the same as the peripheral code!”(Freeman, 1994, my emphasis)

Ultimately he concludes that the brain is a self-organizing entity, specifically obeying the laws of Chaos theory. (“Chaos can make as well as destroy information!”). I am frankly unqualified to judge this latter aspect of his argument.84

81 See prior footnote on his use of the word “spatially”82 See prior footnote83 Freeman, 1994, my emphasis

84 It is, however, the crucial area for a practical development of my ideas as it is necessary for an actual calculus of the brain. It was at this exact stage that Heisenberg’s matrix theory sealed the progress of quantum theory and validated it, later leading to Schroedinger’s results. “Hilbert suggested to Heisenberg that he find the differential equation that would correspond to his matrix equations. Had he taken Hilbert's advice, Heisenberg may have discovered the Schrödinger equation before Schrödinger.” (Thall's History of Quantum Mechanics) I had found a similar quote much earlier –to much the same substance –I thought it Cassidy, but was unable to locate it. This is precisely the point at which brain science, under my conception, will either succeed or not –

His physiological case: i.e. the connectivity of the CNS, however, is entirely sufficient in itself to demonstrate the kind of mapping, the broadest logical potential of “schematic GUI’s” and their explicit relevance to cognition as I have claimed. This model actually does “cross party lines”. I think this is how the brain and specifically, the cortex, actually works.

That the brain is, in fact, “self-organized” is exactly the case I am making. In fact, I will ask the question: How, in our modern worldview, could it be otherwise for a biological organism absent an act of God? I argue that it is self-organized specifically for optimal efficiency of primitive process, (re: urgency / risk), however, not for reference.85 Freeman’s case, I believe, constitutes an actual instance demonstrating the deepest possibilities of “schematic models” and “free formation”. It demonstrates the possibility of a truly useful model organized on non-topological principles, and, as such, demonstrates the deepest capabilities of a schematic GUI. This is not just “a level of abstraction.”

But where, accepting Freeman’s description of the actual brain, do these cell assemblages, (these “equivalence classes”), come from, and what is their function? How do these particular entangled arrays of cells, interconnecting and overarching “the less than one percent of the neurons lying within the radius of contact”, arise? I propose that they arise evolutionarily –as internal, blind organizations of function. This is exactly what we would expect the organizing principle of a “self-organizing” metacellular entity to be.86

Representation is neither required, nor, accepting Freeman, is it possible in cortex. This is what we would expect if neural organization were modeled on efficiency over “truth” -and how. Our “percepts”, moreover, are what we would expect if we joined the loop of output to input!

“In particular, Maurice Merleau-Ponty in “The Phenomenology of Perception” [2] conceived of perception as the outcome of the “intentional arc”, by which experience derives from the intentional actions of individuals that control sensory input and perception. Action into the world with reaction that changes the self is indivisible in reality, and must be analyzed in terms of “circular causality” as distinct from the linear causality of events as commonly perceived and analyzed in the physical world.”  W.J. Freeman, 199787

2.4.2 An explicit model of the mind:

i.e. the development of a viable calculus. A viable calculus must be found, though not necessarily in Chaos theory. It does not seem as if chaos theory and complexity theory are finished sciences as yet however. And yet the prime criterion for complexity theory is “self-organization” which echoes a crucial aspect of my own ideas. Self-organization is exactly what I claim is the organizational rationale of the whole of the process of the brain. It is the self-organization of primitive evolutionary process.

85 ? There are purely logical and mathematical difficulties which arise here and which I will address in Chapter 2.

86 ? See Maturana, 1987 and Edelman, 199287 My function, however, is to introduce a mechanics –which I have done.  Merleau-Ponty is not “my philosopher”, but the concept is profoundly pregnant.

“Some people turn to chemicals as a way to deepen the privacy within solipsistic chasms, and in order to retreat from social stress into inner space. A few have induced these states so as to peer through the solipsistic bars and dirty windows in order to see what is ‘really there’, although, as minds disintegrate, what comes are swirls and tinglings, and ultimately the points of receptor inputs like stars, flies or grains of sand.” (W.J.Freeman, 1995, my emphasis)

Freeman and I have the same problem -in our innate resistance to the consequences of our own nonrepresentationalism. I too have wrestled with the “points” of sensory input -“like stars, flies or grains of sand”. The conclusion I have reached however is that our “points” are, in fact, primitive, atomic, (unspecified) process, not information. From the simpler perspective of ordinary biology, this is more obvious. These processes, (i.e. pragmatic and adequate, but not informational processes), are the necessary basic building blocks of biological cognition. These are our “points’. The difficulty lies in the automorphism88 we presume in cognition itself, and this is not an easy problem.

Let us suppose that our science maps back, (automorphically), onto the very model we visualize.  The path of the automorphism we seek, I propose, lies through the very “gears and levers” of the original evolutionarily derived topobiological cognitive model itself, (re-using its “objects”) -through another iteration –in another re-entrant mapping which supplies the mechanics and the transformation (back into Freeman’s non-topological dispersive mapping) that we seek. I propose that reafferance within the loop of brain function combines with input from outside the loop, (passing through the environment), to yield a consistent, compound map which either does, or does not confirm our theoretical constructs.  Thus microscopy, anatomy, biology, physics … is fed through the same interface to yield an image—of the body of another being or of our own, for instance, the nature of our environment, or the results of an experiment.  Nowhere does this conception demand the absolute (ontic) reality of those constructs, however.  It is a reuse of our evolutionary pragmatic cortical objects89 saying nothing whatsoever90 about the real (external) world in which we live.91 

I propose that these “images / objects”, (no quotes really necessary any more), are symbols, (biological artifacts), in the topobiological maps of the cortex.  I propose they are the immensely sophisticated evolutionary artifacts of cortex which exist to tie re-entrant output back into the non-linear transform Freeman describes into the rest of the brain.  Merleau-ponty talks about sensations as the result of an organism acting into the world with feedback.  I suggest that these topobiological objects are the optimizers, (like the objects of the GUI’s of computers), that allow hugely multiple mappings of input back into the rest of the brain.  But they are grounded in the evolutionary history of internal optimization, (of adequate function), not in information.  They are purely practical entities. The “objects” are functions of the interface itself, not of an external ontology.  This, I believe, is the mechanics of the automorphism we seek –i.e. the one processed by the brain, using its own transformation and mapping back onto its own map reusing the

88 “Informally, an isomorphism is a map that preserves sets and relations among [corresponding] elements. " is isomorphic to " is written … An isomorphism from a set of elements onto itself [its complete self] is called an automorphism.” Wolfram Mathworld

89 ? Like Rosch's prototypes??90 ? other than pragmatically91 ? Chapter 4 will answer the blatant epistemological questions which clearly arise here.

evolutionary “objects” of that map. It is Edelman plus Freeman plus Merleau-Ponty and back to Edelman.92

If we turn our perspective around and think of our (input) topographic maps as the looping, re-entrant extension of our output, then we can clearly see them, (and their “objects”), in their specific role as organizing artifacts of cortical function itself.  I propose that our “percepts” are just the combined-in-one icons previously described in the “engineering” argument!  They are the “A-D”, (“analog/digital”), converters, so to speak, of the reentrant loop of process.93  This is what we would expect taking “percepts” as expressly schematic objects of process. They are what we would expect to see!94  (See Figure 9)  I propose that our cognitive interface lays precisely in the topobiological models themselves, mediating between an unknowable externality and the optimized functionality of the cortex.  I claim that this constitutes an explicit and non-representational model for the mind. I have demonstrated the possibility of the schematic model in its largest sense. I have demonstrated, via Freeman moreover, that it actually exists in the human brain.

92 ? The automorphism can be skewed by the intent of the model however –i.e. it can be processed to a different purpose.

93 ? This is, at best, a crude metaphor –but it crystallizes the idea nicely.  A more apt characterization would be “topological / non-topological” converters.94 Chapter 2 will make this clearer!

Figure 9

God’s Eye??(Edelman -to Freeman -to Edelman!)

(The whole of this discussion is nonsense, of course, in the absolute form within which it is stated.  Does our feedback really preserve parallelism in the absolute form I have proposed?  It is valid within a context, but in an absolute ontological sense these are things we can never truly know.  A more proper, purely ontological orientation for an organism would consist not in figure 9 as stated, (which is an intra-model perspective), but rather with each of the Freeman mappings reversed! We do not know, (and cannot know), where or how our input reaches us, nor where or how it goes when it leaves us. What we have is a blanked out upper portion of the diagram, coming to

consciousness only at the stage of the objects” themselves, and continuing to the point of the Freeman transform below which it disappears again! (But looping back again to the top as reentrant input.) A proper formulation must await the introduction of a completely new philosophical perspective95which I have detailed in Chapter 4.  This perspective supplies the rigorous, (and biologically necessary), scientific epistemological relativism required by the parameters of the problem and which matches the relativism of modern physics.

What’s the point?

Why are these conclusions an important advance in our perspective on the mind-brain problem?  It is because they will allow the use of my second hypothesis of “implicit definition” in an entirely scientific context.   (Chapter 2).  That second thesis will enable, for the very first time, legitimate scientific conceptions of the most fundamental aspects we demand for “mind” itself:  i.e. a “Cartesian Theatre”, the “homunculus”, and of the problem of “knowing” per se.  This is not a trivial consequence and results in a profound simplification of the problem of consciousness.

Freeman’s researches expose a new paradigm for models. They also expose the possibility of a new correspondence with reality. We want to believe that our knowledge of reality is direct –or at least parallels ultimate reality. How could it be otherwise? How could a model be other than “an abstraction” and still be useful?96 Moreover, what is the evolutionary rationale for all of this? Modern science says that what truly is, absolute reality, (or “ontology” to use the old but precise word), consists of some ultimate particles: atoms or subatomic particles, quarks ... We are allowed to retain our normal view of reality within this view however because we envision our ordinary objects, (baseballs, you, me, the sun, …), as spatial containers, (and logical, theoretical hierarchies), in the new absolute reality we are forced to believe in. We may still preserve the sense of our ordinary objects as physical and logical clusters, (hierarchies), of those deeper existences. I can think of myself as a cluster of atomic particles and fields shaped like me, doing all the things I do, and positioned in ontic reality next to other things and persons just as I ordinarily see myself. There is a necessary belief in a continuity, and a contiguity, (“next-to-ness”), in this belief system. This is the “hierarchy” or “logical containment” implicit in the Newtonian World and it is mirrored in the hierarchies of contemporary mathematics and of logic. Truly modern science, (of the 1900’s!), says otherwise, however. Quantum theory and Relativity say that the world, (reality), is an even stranger place. Freeman’s conclusions, moreover do not allow it at all. If we live anywhere, we live in cortex.

95 ? Following the lead of Cassirer96 Enormous epistemological difficulties obviously arise at this point. I will spend part of each of thenext three chapters paving the road to a plausible answer to be completed by the end of Chapter 4. For instance: what could ontology be and how could it be? How can it not be a single uniform, structured(i.e. set-theoretic) “universe”?

On Churchland:

“At some point in evolutionary history, nature performed a “good trick”. It allowed for an internal representation of environment…. and this allowed competence in the larger world.” (P.S. Churchland, paraphrase)

But how could a (biological) mechanism use97 such an internal model? (I think Churchland’s problem is as big as mine -but without the benefits.) I think “the good trick” was evolution’s creation of the cortex and its potential to centralize function in a topological context. This is our world, not God’s! We do not and cannot have a God’s eye view.

97 Her difficulty lies in what I call “the logical problem of consciousness” which I address in Chapter 2.

3. The formal and abstract problem:

3.1 The formal argumentConsider, finally, the formal and abstract problem. Consider the actual problem that evolution was faced with. Consider the problem of designing instrumentation for the efficient control of both especially complex and especially dangerous processes. In the general case, (imagining yourself the “evolutionary engineer”), what kind of information would you want to pass along and how would you best represent it? Indeed, need the inputs even come from compatible sources? (Consider two predators with their prey caught between them! What are the prey’s options?) How would you design your display and control system?

It would be impossible, obviously, to represent all information about the objective physical reality of a, (any), process or its physical components, (objects). Where would you stop? Is the color of the building in which it is housed, the specific materials of which it is fabricated, that it is effected with gears rather than levers, -or its location in the galaxy- necessarily relevant information? (Contrarily, even its designer’s middle name might be relevant if it involved a computer program and you were considering the possibility of a hacker’s “back door”!) It would be counterproductive even if you could as relevant data would be overwhelmed and the consequent “calculus”, (having to process all that information),98 would become too complex and inefficient for rapid and effective response. Even the use of realistic abstractions could produce enormous difficulties in that you might be interested in many differing, (and, typically, conflicting), significant abstractions and/or their interrelations.99 This would produce severe difficulties in generating an intuitive and efficient “calculus” geared towards optimal response.

For such a complex and dangerous process, the “entities” you create must, (1) necessarily, of course, be viable in relation to both data and control -i.e. they must be adequate in their function.100  But they would also, (2) need to be constructed with a primary intent towards efficiency of response, (rather than realism), as well -the process is, by stipulation, dangerous! The entities you create would need to be specifically fashioned to optimize the “calculus”, (efficient control) while still fulfilling their (perhaps consequently distributed) operative role!

Your “entities” would need to be fabricated primarily in such a way as to intrinsically define a simplistic operative calculus of relationality between them -analogous to the situation in our training seminar. Maximal efficiency, (and safety), therefore, would demand crystallization into schematic virtual “entities” -a “GUI”- which could resolve both demands at a single stroke. Your

98 See Dennett, Dreyfus on the “large database problem”99 ? This is typically the case. A project manager, for instance, must deal with all, (and often conflicting), aspects of his task -from actual operation to acquisition, to personnel problems, to assuring that there are meals and functional bathrooms! Any one of these factors, (or some combination of them), -even the most trivial- could cause failure of his project. A more poignant example might involve a U.N. military commander in Bosnia. He would necessarily need to correlate many conflicting imperatives -from the geopolitical to the humanitarian to the military to the purely mundane! Or, in a metaphor on the earlier discussion, he might need to take a “Marxist” perspective for one aspect of his task, and a “royalist” perspective for another!

100 Simple adequacy is quite distinct from information or parallelism however.

objects could then distribute function, (in a “global / cortical mapping”), so as to concentrate and simplify control, (operation), via an elementary, intuitive calculus. These virtual entities need not necessarily be in a simple (or hierarchical -i.e. via abstraction) correlation with the objects of physical reality however.101   But they would most definitely need to allow rapid and effective control of a process which, considered objectively, might not be simple at all. It is clearly the optimization of the process of response itself –i.e. a simplistic “calculus”- that is crucial here, not literal representation. We, in fact, do not care that the operator knows what function(s) he is actually fulfilling, only that he does it (them) well!

3.2 The specific case of biology

Biological survival is exactly such a problem! It is both especially complex and especially dangerous. It is the penultimate case of complexity and embodies a moment-by-moment confrontation with disaster. It is a schematic model in just this sense that I argue evolution constructed therefore, and I propose it is the basis for both the “percept” and the “mind”.

But it is just the converse of the argument made above that I propose for evolution however. It is not the distribution of function, but rather the centralization of disparate atomic biological function into efficacious schematic -and virtual- objects that evolution effected while compositing the complex metacellular organism. (These are clearly just the complementary perspectives on the same issue.)102

But let’s talk about the “atomic” in the “atomic biological function” of the previous statement. There is another step in the argument to be taken at the level of biology. The “engineering” argument, (made above), deals specifically with the schematic manipulation of “data”. At the level of primitive evolution, however, it is modular (reactive) process that is significant to an organism, not data functions. A given genetic accident corresponds to the addition or modification of a given (behavioral/reactive) process which, for a primitive organism, is clearly and simply merely beneficial or not. The process itself is informationally indeterminate to the organism however -i.e. it is a modular whole. No one can presume that a particular, genetically determined response is informationally, (rather than reactively), significant to a Paramecium or an Escherichia coli, for example, (though we may think of it that way).

It is significant, rather, solely as a modular unit which either increases survivability or not. Let me therefore amend the prior argument to deal with the schematic organization of atomic, (modular), process, rather than of primitive, (i.e. absolute), data. It is my contention that the cognitive model, and cognition itself, is solely constituted as an organization of that atomic modular process, designed for computational and operational efficiency. The atomic processes themselves remain, and will forever remain, informationally indeterminate to the organism.

101 ? See Lakoff/Edelman appendix for a discussion of abstraction and hierarchy

102 ? See Birkhoff & Mac Lane, 1955, p.350, discussion of the “duality principle” which vindicates this move. More simply put, and using Edelman’s vision, it is a question of which end of the “global mapping” we look from!

The evolutionary purpose of the model was computational simplicity! The calculational facility potentiated by a schematic and virtual object constitutes a clear and powerful evolutionary rationale for dealing with a multifarious environment. Such a model, (the “objects” and their “calculus”), allows rapid and efficient response to what cannot be assumed, a priori, to be a simplistic environment. From the viewpoint of the sixty trillion or so individual cells that constitute the human cooperative enterprise, that assumption, (environmental simplicity), is implausible in the extreme!

But theirs, (i.e. that perspective), is the most natural perspective from which to consider the problem. For five-sixths of evolutionary history, (three billion years), it was the one- celled organism which ruled alone. As Stephen Gould puts it, metacellular organisms represent only occasional and unstable spikes from the stable “left wall”, (the unicellulars), of evolutionary history.

“Progress does not rule, (and is not even a primary thrust of) the evolutionary process. For reasons of chemistry and physics, life arises next to the ‘left wall’ of its simplest conceivable and preservable complexity. This style of life (bacterial) has remained most common and most successful. A few creatures occasionally move to the right...”“Therefore, to understand the events and generalities of life’s pathway, we must go beyond principles of evolutionary theory to a paleontological examination of the contingent pattern of life’s history on our planet. ...Such a view of life’s history is highly contrary both to conventional deterministic models of Western science and to the deepest social traditions and psychological hopes of Western culture for a history culminating in humans as life’s highest expression and intended planetary steward.”(Gould, 1994)

3.3 Retrodictive confirmation

Do you not find it strange that the fundamental laws of the sciences, (or of logic), are so few? Or that our (purportedly) accidentally and evolutionarily acquired logic works so well to manipulate the objects of our environment? From the standpoint of contemporary science, this is a subject of wonder -or at least it should be. (cf contra: Minsky, 1985) It is, in fact, a miracle!103 From the standpoint of the schematic model, however, it is a trivial, (obvious), and necessary consequence. It is precisely the purpose of the model itself! This is a profound teleological simplification!

3.4 Conclusion, (section 3)

Evolution, in constructing a profoundly complex metacellular organism such as ours, was confronted with the problem of coordinating the physical structure of its thousands of billions of individual cells. It also faced the problem of coordinating the response of this colossus, this “Aunt Hillary”, (Hofstadter’s “sentient” ant colony).104 It had to coordinate their functional interaction with their environment, raising an organizational problem of profound proportions.

103 The “anthropic principle” is clearly self-serving and tautological.104 ? See Hofstadter, 1979. His is a very nice metaphor for picturing metacellular existence.

Evolution was forced to deal with exactly the problem detailed above. The brain, moreover, is universally accepted as an evolutionary organ of response, (taken broadly105). I propose that a schematic entity, (and its corresponding schematic model), is by far the most credible possibility here. It can efficiently orchestrate the coordination of the ten million sensory neurons with the one million motor neurons,106 -and with the profound milieu beyond. A realistic, (i.e. representational /informational), “entity”, on the other hand, would demand a concomitant “calculus” embodying the very complexity of the objective reality in which the organism exists, and this, I argue, is overwhelmingly implausible.107

Figure 10

105 ? Freeman has objected to my characterization of the human brain as an “organ of response”.  I understand his objection, as it seems to imply acceptance of “stimulus-response” causality” –which is clearly not my intention.  At this level of discussion, I think the characterization is warranted however.  See Chapter 4 for a full and better treatment of this issue.

106 ? Maturana and Varela, 1987107 ? See Dreyfus on the “large database problem”. Also see Appendix A for a “combinatory” counterargument.

Preface to Chapter 2: The Logical Problem -and Realism Again(Signpost #2)

In a problem as complex as this one is and as complex as I propose its solution to be, it will be important to have signposts to look at periodically so that we can orient ourselves. These chapter prefaces are intended to serve as those signposts. So then, where have we gotten to at the end of Chapter 1?

In the first chapter I presented a concrete alternative to the representative model of cognition. It certainly is not sufficient to stand alone as an argument however, nor do I really expect anyone to be convinced at this point. (Those arguments are in the present chapter and in chapters 3, 4, and 5 and in the Appendices.) Indeed, it goes against almost everything we know or believe and, at first blush, it is absurd. Chapter 1 was intended only to explain one aspect of the theme.

But discursive arguments would not serve in any case to change the minds of realists and practical scientists on the issues of our most fundamental paradigm –of our realistic worldview itself. Yet I speak to none other than those –realists and practical scientists! Realists question their most fundamental paradigm only when innovative perspectives illuminate vast new areas or simplify whole aspects of important problems leading to pragmatic results –and then only to the extent implicit in the gain. (The theories of Relativity and Quantum Mechanics are profound recent examples of just such radical modifications of the realist paradigm.) What realists will never question however, -nor will I as I stand with them- is realism itself.

But what is “realism”? To be a realist, does it mean that we must assume all the baggage that comes with the name at this particular moment in history? Was it not identical, then, with the realism of the Ptolemean/Aristotelians who stood against the counter-intuitive theories of Copernicus? Had Dr. Johnson lived then, might he not have kicked the nearest rock, rejoining Copernicus: “Now it is moving!”108 But is it identical, now, with the realism of Pierce’s chalk, which he threatened to drop and break and thereby prove its reality? Does realism mean today that, besides an inviolate faith in the existence of an absolute ultimate reality, we must assume the possibility of absolute knowledge of that (ontic) reality as well –even at some coarse scale?

Physicists, (the penultimate realists), have been forced to embrace algorithmicity and epistemological uncertainty at the very small, the very large and the very fast scales. If our middle scale objects were taken as the objects of a biological algorithm –prototypes109 of biological logic110 as well, (as I have argued), then continuity would be reestablished to epistemology across the board.111 But was not even fundamental epistemological uncertainty, (i.e. the general case), as well as physical uncertainty always a possibility within the basic confines of realism?

As I expounded earlier, Gerald Edelman, (following Putnam and Lakoff), lists the three essential tenets of what he calls “scientific realism”, (Lakoff calls it “basic realism”, Putnam “internal 108 Johnson, of course, is famous for his demonstrative argument against idealism. He is said to have kicked a rock saying: “I refute it thus!”109 Cf Rosch, Lakoff, Edelman110 (process)111 This is another profound simplification to epistemology!

realism”): “(1) a real world (including humans but not depending on them); (2) a linkage between concepts and that world; and (3) a stable knowledge that is gained through that link.”112 The combination of my three themes will confirm Edelman’s first and second postulates,113 but the “knowledge” in his (3) will be argued as mathematically and scientifically relativistic114 in its significance and pragmatic, (i.e. algorithmic), in its justification.

In Chapters 3 and 4 I will argue on biological and Kantian grounds for just two fundamental “axioms” of realism however: (1) the “axiom of externality”, (developed in its most primitive form in Chapter 3), and (2) the “axiom of experience”, (Chapter 4), which roughly correspond to Edelman’s first two requirements. Together they define the absolute minimum and necessity of the realist position.

In Chapter 4, I will argue for a rigorous scientific relativism of knowledge in general. But it will be a special kind of relativism however, based (in seeming contradiction) on an absolute! It is based on an invariant -the invariant of experience. “Invariants”, the mathematical conception of that which does not change under varying (relativistic) perspectives, (varying coordinate systems for instance), are the basis of Einstein’s Special Relativity, of course. The rigid, i.e. unvarying and concrete equations of Einstein’s theory supply an explicit illustration of the kind of relativism and stability115 that I wish to argue, (following but modifying Cassirer), for knowledge in general. It is diametrically opposed to “capricious relativism”, “specious relativism”, “Whorfian relativism”, “cultural relativism”, or the relativism of Solipsism, for instance. Nor is it “idealism”! Anything does not go! Knowledge must be commensurate with experience, (to include the experience of the results of scientific experiment), but its organization, its “co-ordinate system”, (of which I argue its “objects” are a part), is not innately fixed thereby. It is experience itself, i.e. that which must be accounted for,116 and not any particular organization of that experience which is a necessary (second) metaphysical, (i.e. ontological), posit of realism.Edelman, basing his arguments in Lakoff’s, (and, ultimately, Putnam’s), argues –as I will argue- against the further extension of the realist position into “metaphysical realism” –against its incorporation of “objectivism”. (I have used the name “Naturalism”):

“objectivism assumes, in addition to scientific realism, that the [actual] world has a definite structure made of entities, properties and their interrelationships….[that] the world is arranged in such a fashion that it can be completely modeled by what mathematicians and logicians would call set-theoretical models. … Symbols in these models are made meaningful (or given semantic significance) in a unique fashion by assuming that they correspond to entities and categories” [which themselves exist] “in the world. Ibid, p.231-2, my emphasis

112 Edelman 1992, p.230113 I argue that the “linkage” in Edelman’s second postulate is real but blind however.

Cf Chapters 1, 3, 4, 5 and Appendices A & B.114 see below115 in agreement with Edelman’s third postulate of realism.116 In the sense of chapter 1 and which I will argue explicitly as the subject of

chapter 4. See especially the “King of Petrolia” fable.

Edelman, like Lakoff and Putnam, argues against this “objectivism”. He argues against a privileged “God’s eye view of the world”. His arguments constitute a critique of logic –based in Lakoff’s synthesis of extensive empirical studies of actual humans, actual cultures, and actual languages which challenge the classical theory of the category and based in Edelman’s own work in immunology and brain structure. (Freeman’s work is the definitive end to this argument.) Thereby they question classical logic, (of which it is the foundation), itself. Edelman’s motivation, however, derives from his theory of neuronal group selection, (TNGS), -“Neural Darwinism”- wherein he argues that the brain is not informational but “ex post facto selective”.117 Brains, Edelman argues, are not commensurate between individuals at the finest scale –even between genetically identical individuals. They are therefore not the sort of things that information or programs run on. He argues the human genome is too small to create such an “information machine”.118 Edelman’s arguments are made in support of his theory of “Neural Darwinism”. While it is a very plausible theory, (and the sort of thing my thesis would suggest), it has yet to be confirmed.119 In chapter 3, I will base my arguments to the same end in Maturana and Varela’s. Their arguments are made from the fundamental principles of biology itself, (and physical science in general), however and so carry a greater generality and force.

In this second chapter I will show that my first thesis, in concert with my extension of Cassirer’s logical hypothesis, does accomplish the kind of expansion and illumination –the explanatory power- that realists require to seriously re-examine their premises. For one, the conjunction allows a viable and natural theory of meaning for the first time.120 More significantly it also supplies a realistically tenable theory of what, (were the word not pre-empted), I would be tempted to simply label “cognition”. By this I would mean not “performance” or “problem solving”, (in the sense used in Cognitive Science), but knowing!

There is, of course, a definitional problem here. “Knowing”, “awareness”, “cognition" are all often understood as referential, operational, et al. But the other sense: i.e. conscious knowing, conscious awareness, conscious cognition, is precisely the problem we are here to solve. It does not consist in showing how an automaton, a “zombie”, a Turing machine –or even a biological organism- can be constructed to be indistinguishable from a human respondent. Dennett, and almost every other realist writer on the subject, (even Edelman sidesteps the problem), thinks that our ordinary sense of these words is impossible. The “homunculus”, the “color phi”, etc. are arguments against a “Cartesian theatre”. It is the subject of this chapter to show how just such a “theatre” can be constructed, consistent with scientific logic.

How is it possible to know? How is it possible for one part of a physically and temporally separated process, (the process –or material- of the constituent parts of the brain in space for

117 i.e. brains select from pre-existing internal variation on pragmatic rather than informational grounds as the immune system does118 Edelman, 1992, P. 224. His argument is very similar in form and purpose to my argument of Appendix. A.

119 ? Walter Freeman told me that Edelman wouldn’t even talk to him. How sad –such a mistake!120 Putnam and Lakoff argue against even the logical consistency of the standard solution –a truth-functional mapping from a formal system to a model.

instance), to know, (rather than merely interact with121), another part? How would it be possible for one part of even a mental space to know another part? This is the problem that Leibniz characterized as the problem of “the many and the one”. How can the many be known to the one? How can there be knowing without a homunculus? How can there be knowing without a mystery? How can there be a “Cartesian Theatre”?122 This is the target of Chapter 2.

Meaning

The adoption of my first thesis enables the utilization of perhaps the most profound proposal ever suggested for the problem of meaning: i.e. Hilbert’s mathematical conception of “implicit definition”. (It is very important that this not be confused with mathematical “formalism” –a theory of proof- of which he was also the author.)123 Hilbert proposed that the “things” of mathematics –for mathematics- are solely a function of the laws, (axioms), in which they are framed and that their “meaning” is exactly their role (function) in those laws. Its “objects” are “implicitly defined” by its axioms. 124 They are logical objects!

My first hypothesis enables Hilbert’s “implicit definition” to function as a general theory of meaning as opposed to its present limited usage as a theory of specifically mathematical meaning. If our (human) model is internal and algorithmic rather than referential, (the first hypothesis), if our “objects” are metaphors of process, if even our very logic is taken as a biological rule of function vis-à-vis environment, (as a “constitutive logic” in Kant’s terminology), rather than as transcendent125 revelation, (as I will argue in this chapter), then the meaning of its now “bio-logical” objects may reasonably be understood as their implicitly defined role in that process. (This is the “metaphor” I referred to previously.) This is very close to our ordinary, naïve sense of “meaning”126 and quite different from its proposed formalistic and counterintuitive definition as “reference” or truth functional mapping.

Knowing:

The first hypothesis, in combination with an extension of Cassirer’s logical hypothesis and Hilbert’s mathematical conception, also enables “knowing”. It allows a solution of the problem of

121 “Interaction” is process/doing; it is not “knowing”. 122 After Dennett's usage123 This is not a superfluous caution considering, for instance, Lakoff’s treatment of formal systems and meaning, (nor Edelman’s cavalier dismissal of axiom systems). It is in the assignment of a truth function from a formal system to a model wherein he challenges the logical validity of the objectivist theory of meaning based on Putnam’s argument. “Implicit definition” must be strongly distinguished from “formalism” which was conceived by Hilbert as a theory of proof. Implicit definition”, however, was conceived specifically as a theory of meaning. It derives instead, I think, from his background as the “king of invariants”. The “things” are the solely logical invariants of the axioms.

124 I.e. They are specified from primitive operations rather than from primitive properties.125 In Kant’s sense of the word126 “Meaning”, normally understood, has to do with connectivity to other meanings.

the “many in the one” / the “Cartesian Theatre” without magic by extending the very logic within which we conceive it. This is a logical problem for which I will propose a concrete logical solution as the subject of this chapter.

Anthropological and Linguistic, and Logical Commensurability

I have mentioned the commensurability of my first hypothesis with existing empirical findings reported by Rosch, Lakoff, et al., and will go into the subject further in the “Afterward: Lakoff, Edelman and Hierarchy”, so I will not belabor the point. I submit that it is a pretty good fit with the whole of these extensive studies.

Realism Again:But are the retrodictive solutions of these admittedly profound problems sufficient to cause a realist to accept such a distasteful diminution of his supposed powers? My answer, (as I would expect yours to be), is “no”! These kinds of answers –however good they may be127- are at best only hints to the progress of science.

Conversely, however, these are the kinds of things that we would like any viable theory to explicate. They are strong and viable clues to any acceptable theory and no proposed realist theory before this has done other than to deny them.

This is why I argue my answer only as a tentative one. It is the future of science which will answer this question. It is only in broad new consequences –pragmatic consequences- that a compelling case could be made. But to conceive consequences, we must first entertain the premise.128

As a realist then –talking to other realists-, I ask only that you truly practice your own realism at its strongest. But realism is ruthless by nature! It is concerned, ultimately, only with what works –no matter how painful that may be to our cherished prejudices. I ask that your realism be a ruthless –and honest- one therefore, both for and against my hypothesis! I think it will surprise you.

This next chapter will be difficult and technical. For this, I apologize. It will be necessary to examine the technical foundations of logic itself because the implications of classical logic and its modern embodiment, (taken as a necessary and sufficient tool rather than as a special case), force us to abandon an important part of our realism, i.e., ourselves, normally taken! Formal logic provides an important and specific clue to the nature of mind itself.

The foundations of logic are especially relevant to the mind-brain problem because ultimately, (I will argue), logic is itself a biological and evolutionary phenomenon, and not, (following Kant’s usage), “transcendent”. Logic is not God-given! I will propose a reformulation of classical logic

127 And I think they are very good!128 I will discuss this issue further in the “Lakoff/Edelman appendix. My thesis has direct

implications for neuroscience, but it also has implications for the foundations of mathematics and logic and thereby for the whole of hard science itself. It challenges the adequacy, (but not the validity), of even that lynchpin of modern thought –the mathematical set! In the “Dennett” appendix, I have also sketched what I believe could be the beginnings of a first scientific psychiatry.

based in the proposals of Ernst Cassirer who questioned its adequacy and proposed an extension almost a century ago. I will extend Cassirer’s thesis, and then marry it to my first, biological hypothesis to arrive at what I will propose as an actual solution of the problems of the “homunculus” and the “Cartesian Theatre”, (the problem of “knowing”), a solution absolutely consistent with the dictates of modern biology.

My logical answer superficially resembles the conclusions of Edelman and Lakoff, but is of a greater generality and depth. That greater generality will be necessary for the resolution of the obvious epistemological contradictions129 in which those authors embroil themselves. It is necessary for the resolution of the specifically logical paradoxes of sentiency.

Cassirer’s logical thesis was in many respects driven by the same forces as Lakoff’s, but it was a more rigorous, realistically plausible and cogent solution I believe. The difficulty with Lakoff’s proposed solution130 is that concepts/categories131 can be anything at all! They are arbitrary and dependent on history. How, then, can a logic, (or a worldview), based on categories be formed? Lakoff’s conception is considerably better than this,132 I admit, in that it is grounded in empirical considerations –in anthropological and linguistic findings. But at the base –wherein are we to ground and evaluate these findings? There is no possibility of a formalism! If anything is provable, then it is a triviality that nothing is provable. We stand on quicksand.

Cassirer’s extension of the classical concept/category however was grounded firmly in the history of the successful advance of mathematics and physical science but it was not arbitrary. He, like Wittgenstein, Lakoff and Edelman, challenged the set-theoretic foundation of logic. He argued that our concepts, (categories), in the most general case –and especially in the case of mathematics and science- are not grounded in a commonality, (an intersection), of properties of the members. Cassirer’s is a natural and plausible extension of classical logic. It retains classical logic as its truly natural limit case133 in just the sense that the limit cases of mathematics are truly natural. It is neither ad hoc nor arbitrary. Cassirer’s general concept/category, (“the functional concept of mathematics” [i.e. derived from mathematics]), is a function of functions, a rule. I will postulate a further but still natural extension of Cassirer’s logical hypothesis in this chapter: “the Concept, (category), of Implicit Definition”. It too is rule-based, but it is based in the unified rule of an axiom system, (i.e. the conjunction of the axioms). It too is a lawful conception.

129 They both emphatically disclaim the possibility of a “God’s eye view” of the world, and then both proceed to supply exactly that –a (sophisticated) “naïve realistic” , (i.e. “objectivist”), answer in a “naïve realistic” , (“objectivist”), world! Both embed their answers precisely inside the particular “container” schema! Maturana and Varela encounter the same difficulty.

130 ? Cf Afterword: Lakoff / Edelman131 ? I will use these interchangeably

132 More accurately, it is based in ICM’s, (“idealized cognitive models”), derived from bodily function. But all of these ICM's are defined precisely within the particular “container schema”, (the set-theoretic ICM), of the body in space! It supplies therefore the very “God’s eye view whose possibility he disclaims. Lakoff’s relativism does not satisfy the paradox he creates. cf “Lakoff/Edelman Appendix”

133 Classical logic represents the special case of a rule of series wherein the rule is identity.

I will conclude this chapter with an assertion of “concordance” which I argue is the strongest present argument for my hypotheses.134 The form of the solution attained by my biological argument for the brain, (chapter 1 and expounded further in chapter 3 and the appendices), and the form of the solution for mind, (attained independently on purely logical grounds in this chapter 2), are perfectly commensurate! Mind, I will argue ultimately, is the unified rule of behavior135 –but that rule, (as I will argue for my logical hypothesis in this chapter), knows its “objects” –they are implicitly defined! Leibniz’s problem is solved.

At this point, (at the conclusion of Chapter 2), I will have satisfied the logical and organizational requirements of mind-brain problem. I will not at that point have provided an answer to the “substance” of mind however. That requirement will be addressed in my third and final hypothesis, the subject of chapters 3, 4 and 5.

What do we require as realists?

As realists, we require an assumption of externality roughly equivalent to Edelman’s first tenet of scientific realism, but as just the same sort of realists we require an assumption of self and knowing as well. If we kick a stone, (with Johnson), or drop a piece of chalk and expect it to shatter, (with Pierce), we expect to know these things. (We also fear the possibility of a broken toe or the inability to continue our lecture!) The specifically metaphysical, (ontic), existence of our experience is part of that selfsame realist demand. How else do we, (as realists), judge the viability of theories of that very externality -except by their compliance with experience?

As a realist, and if a choice were forced between the two, I suppose my tendencies would tend, (barely), toward “externality”. But this is precisely the kind of choice, forced by logic, which would make me, (also as a realist), question logic itself. It is probably the only situation, moreover, -wherein a crucial aspect of our realism is challenged –where such a suggestion would be entertained seriously at all. Discursive arguments, logical antinomies, mathematical anomalies, “cats on mats”136, anthropological and linguistic research … –all these, (to the extent they are plausible or even compelling), would be, (and have been), walled off and isolated from our basic realism and the logic in which we conceive it. Who cares who shaves the hypothetical barber, after all?

The predominant Naturalist school of neuroscience feels that it has been forced to make the very choice I have described –and with very compelling (logical) arguments.137 It feels it must choose between “externality” and self. Best and most frankly framed by Dennett, it concludes that we are physical automatons, “zombies”.138 But the context –the comprehensive worldview- in which we, (you and I), are right here enmeshed in considering this problem does not exist according to Dennett! This “Cartesian theatre” is not a part of these zombies –you or I or Dennett himself. The

134 There are other strong grounds as well. In line with the “productivity requirement” I referred to above, it yields new insights into the foundations of mathematics and logic. These are not trivial concerns in light of the acknowledged discordances in set theory and logic. Rosch’s and Lakoff’s empirical findings are a strong fit as well.

135 In a more general sense, (using the terminology of Maturana), of “ontogenic coupling”136 see Lakoff re: Putnam137 Cf P.S. Churchland, or Dennett for instance

138 My apologies to Dennett, but, as I reflect in a later footnote, his “unfair to quote this out of context” prohibition does not refute the fact that after several hundred pages, he says just that.

only place it might exist –and Dennett makes explicit mention of the fact- is in logic itself, (in the robot Shakey’s program139). Dennett’s worldview which contains his solution to the mind-brain problem does not, (for Dennett), exist in Dennett! It exists, (as a particular draft), in the logic of his book! This is linguistic idealism.

Naturalists cannot admit even the possibility of a “mind”140, (Dennett calls it a “figment”), because they cannot solve the problems of the homunculus and the Cartesian Theatre. Specifically they cannot solve the logical problems inherent therein. For there to be a whole, (“a one”), there must be a “little man” inside who sees it as such. But for him to see it, there must be another little man inside… This infinite regression, and the framing of the problem which generates its necessity –as well as the logical difficulties of the “Cartesian Theatre” are the result of the limitations of the classical, set-theoretic (“container” 141) logic in which they are conceived. And yet, as I think Dennett conclusively shows, they are the necessary result of applying that logic to the mind-brain problem. If, as realists, we accept the adequacy of classical logic, and of the Aristotelian concept/category which is its foundation, then the “self”, and the “experience”, (normally and not behaviorally and mechanistically taken), which are profound parts of our selfsame realism must die!

I consider Dennett’s, Churchland’s … arguments convincing. In fact, I consider them as conclusive when taken in conjunction with the classical logic within which they are framed. But this conclusion was always implicit within classical materialism –which I also take very seriously. Simply put, and to repeat myself, there is, (under the presuppositions), no way that part of a spatially and temporally separated process –or material- can “know” another part. If ordinary classical logic is definitive, then my form of realism, (ours?), is dead. I choose, however, to question the premise. I, as a realist, choose to question logic.

139 Cf Dennett 1991, P.130140 normally taken141 In Lakoff’s terminology, it is a hierarchical “container schema”.

Chapter 2. How? The Logical Problem of Consciousness(Cassirer- Hilbert- Maturana: an Archimedean Fulcrum) or:Consciousness, a Simpler Approach to the Mind-Brain Problem -Implicit Definition, Virtual Reality and the Mind

“... Every attempt to transform logic must concentrate above all upon this one point: all criticism of formal logic is comprised in criticism of the general doctrine of the construction of concepts.” (Ernst Cassirer)142

=====================================================================

We began our journey with this citation from Cassirer in the Preface. Now we must pursue the conclusions of Chapter One in the light of his ideas, to finally arrive at a viable conception of “mind” as we normally conceive it. The problem, we will come to see, originated in our notion of the formal logical “concept” itself.

The problem of “consciousness” and the profoundest paradoxes of the mind-body problem: the “Cartesian theater”, the “mind’s eye”, and the “homunculus” are specifically logical problems. They are problems of logical possibility itself. How could cognition, how could mind, ordinarily taken, even exist? It is not so much a problem of what it is that they actually are, but rather a problem of how is it even possible that they could be! How, as Leibniz framed it, could “the many be expressed in the one”? How could we know? In the context of conventional realism, ordinary logic allows not even a possibility -other than an eliminative reduction, (a denial), of the problem -and of sentiency itself.

142 ? Cassirer 1923 pps.3-4 He continues: "The Aristotelian logic, in its general principles, is a true expression and mirror of the Aristotelian metaphysics. Only in connection with the belief upon which the latter rests, can it be understood in its peculiar motives. The conception of the nature and divisions of being predetermines the conception of the fundamental forms of thought. In the further development of logic, however, its connections with the Aristotelian ontology in its special form begin to loosen; still its connection with the basic doctrine of the latter persists, and clearly reappears at definite turning points of historical evolution. Indeed, the basic significance, which is ascribed to the theory of the concept in the structure of logic, points to this connection. ..."

[But] "... The work of centuries in the formulation of fundamental doctrines seems more and more to crumble away; while on the other hand, great new groups of problems, resulting from the general mathematical theory of the manifold, now press to the foreground. This theory appears increasingly as the common goal toward which the various logical problems, that were formerly investigated separately, tend and through which they receive their ideal unity."

It is just this "general mathematical theory of the manifold" to which he refers at the end which I will argue forces an even further extension of Cassirer's own arguments.

The “schematic model” of my first hypothesis cuts to the core of these problems. Coupled with Ernst Cassirer’s extension of traditional logic, (his “Functional Concept of Mathematics”), itself extended again in light of the expansion of logical possibility innate in David Hilbert’s mathematically conceived “implicit definition”143 for the axiom systems of pure mathematics, it illuminates them and demonstrates a specific “how” for the first time. The answer turns on an extension of the formal logical Concept144 and with it, of logic itself. Surprisingly that answer will allow us to retain our normal, (“folk”), conception of mind as well.

Cassirer and Classical Logic:2. Cassirer argued that “the object” of modern mathematics, and “the object of mathematical physics” as well, (their “ideal” objects), are conceptual objects only. He maintained that the Concept they actually embody in modern science is not the classical (Aristotelian) “generic Concept” however, but is rather a new “Functional Concept of Mathematics”, (Cassirer’s Concept). He argued that modern mathematics and modern physics have already reconceived the formal logical “Concept” itself, albeit tacitly.145

The Classical Concept:146

Cassirer summarized the genesis -and the still-continuing usage- of the classical generic Concept as the simple abstraction and the idealization, through “attention”, of a commonality of “marks”, (properties), in a series of presentations.

“But what was beyond all doubt, as if by tacit agreement of the conflicting parties, was just this: that the concept was to be conceived as a universal genus, as the common element in a series of similar or resembling particular things.”147

A series of presentations with characteristics: (d,a,c,b), (a,c,d), (c,e,a), for instance, is held to bring forth the classical concept: {a,c}. From mere abstraction, (via attention), the whole of the doctrine of the classical Concept follows from these simplistic origins.

“Every series of comparable objects has a supreme generic concept, which comprehends within itself all the determinations in which these objects agree, while on the other hand, within this supreme genus, the sub-species at various levels are defined by properties belonging only to a part of the elements.”148

But the successive broadening of a concept necessarily correlates to a progressive lessening of its content; “so that finally, the most general concepts we can reach no longer possess any definite

143 as strongly distinguished from his "Formalism" which is quite a different issue144 I will be employing a convention of capitalizing the word “concept” when it denotes the formal, technical notion of the concept to avoid such verbiage as “the concept of the concept”, etc.145 ibid. Also see his "Einstein's Theory of Relativity"146 See also “Afterword: Lakoff, Edelman…” for another discussion of the classical concept.

147 "Substance and Function", p.9148 ibid p.5 This passage, (delineating, incidentally, the mathematical "power set"), suggests also the absolute hierarchy of concepts, (and theories), implicit in the classical conception. Cassirer's alternative, (which I will discuss shortly), reveals a new possibility, developing into his theory of "symbolic forms" which I will elaborate in Chapter 4.

content.”149, [at all!]. The ultimate genus -“something”- is totally (and logically) devoid of specific content!

Contra the Aristotelian Concept:The Concept in this form, however, is clearly not adequate or consistent with scientific, nor even with ordinary usage. I will requote this brief section to reestablish context:

“When we form the concept of metal by connecting gold, silver, copper and lead, we cannot indeed ascribe to the abstract object that comes into being the particular color of gold, or the particular luster of silver, or the weight of copper, or the density of lead; however, it would be no less inadmissible if we simply attempted to deny all these particular determinations of it.”150

It would not suffice to characterize “metal”, for instance, “that it is neither red nor yellow, neither of this or that specific weight, neither of this or that hardness or resisting power”; but it is necessary to add that it “is colored in some way in every case, that it is of some degree of hardness, density and luster.” Similarly, we would not retain the general concept of “animal”, “if we abandoned in it all thought of the aspects of procreation, of movement and of respiration, because there is no form of procreation, of breathing, etc., which can be pointed out as common to all animals.”151

Cassirer’s Alternative: “The Functional Concept of Mathematics”:Cassirer proposed an alternative and considerably more plausible basis for a different technical logical Concept -borrowed from mathematics - “the Functional Concept of Mathematics”:

“Lambert pointed out that it was the exclusive merit of mathematical ‘general concepts’ not to cancel the determinations of the special cases, but in all strictness fully to retain them. When a mathematician makes his formula more general, this means not only that he is to retain all the more special cases, but also be able to deduce them from the universal formula.”152

But this possibility of deduction does not exist in the case of the scholastic, (Aristotelian), concepts, “since these, according to the traditional formula, are formed by neglecting the particular, and hence the reproduction of the particular moments of the concept seems excluded.”153

“The ideal of a scientific concept here appears in opposition to the schematic general presentation which is expressed by a mere word. The genuine concept does not disregard the peculiarities and particularities, which it holds under it, but seeks to show the necessity of the occurrence and connection of just these particularities. What it gives is a universal rule for the connection of the particulars themselves.... Fixed properties are replaced by universal rules that permit us to survey a total series of possible determinations at a single glance.”154

We do not go therefore from a series: a-alpha1-beta1, a-alpha2-beta2, a-alpha3-beta3... directly to their common element a, (Cassirer argues), but replace the alphas by a variable x, and the betas by a variable y. Therein we unify the totality in the expression “a-x-y”, (actually w-x-y, where “w” is

149 op. cit p.6150 ibid P.22151 ibid P.22152 ibid P.20-23153 ibid P.20-23, my emphasis154 ibid P.20-23

the constant function w(p) = a, (for all p) -which is equivalent to the “generic concept”). This expression can be changed into the “concrete totality” of the members of the series by a continuous transformation, and therefore “perfectly represents the structure and logical divisions of the concept”!155

Cassirer’s “series” may be ordered by radically variant principles however: “according to equality”, (which is the special case of the “generic concept”), “or inequality, number and magnitude, spatial and temporal relations, or causal dependence”156 -so long as the principle is definite and consistent.

Thus he fundamentally reconceives the formal Concept, this our ultimate logical building block, as “the “Functional Concept of Mathematics”. It is the functional rule, F(x,y,z,...), which organizes and embodies the totality of its extension.157

Concept vs. Presentation:Importantly, Cassirer’s new formal Concept is no longer logically derivable from its extension however:

“The meaning of the law that connects the individual members is not to be exhausted by the enumeration of any number of instances of the law; for such enumeration lacks the generating principle that enables us to connect the individual members into a functional whole.”158

If we know the relation according to which a b c . . . are ordered, we can deduce them by reflection and isolate them as objects of thought. “It is impossible, on the other hand, to discover the special character of the connecting relation from the mere juxtaposition of a,b,c in presentation.”159 160

“That which binds the elements of the series a,b,c,... together is not itself a new element, that was factually blended with them, but it is the rule of progression, which remains the same, no matter in which member it is represented. The function F(a,b), F(b,c),..., which determines the

155 ibid, P.23 As one of Kant's commentators urged about one of the latter's arguments, I find this argument as "mirabile dictu". It is in fact the clear and true expression of what we mean by a "Concept". It is the functional assemblage of a set of rules. Rosch and Lakoff have argued in more recent times, (based in hard empirical data), that the categories of actual human beings, actual human cultures, actual human languages are not, in fact, grounded in the classical Aristotelian "Concept" but are based, instead, in prototype, metaphor, metonymy, association, radial categories, etc. But what are these, (in their anthropological totality), but the free posit of rules of category formation? Cassirer has provided a more classical and rigorous conceptualization. It incorporates the possibility of all (consistent) rules in a classical formulation.

Clearly this does better correspond with ordinary and scientific usage than does the classical concept. It is the functionality of our definitions which specifies the concept. The mathematical "subset" is the limiting, rather than the typical case.156 ibid P.16157 It is interesting to conceive the Cassirerian Concept as a hypersurface! Where could this line of

reasoning go?158 ibid P.26159 ibid P.26, my emphasis160 cf. Stewart, 1995, "Fibonacci Forgeries". Stewart's article illustrates the case. The "insufficiency of small numbers" leads to an indeterminability of the rule of any finite series.

sort of dependence between the successive members, is obviously not to be pointed out as itself a member of the series, which exists and develops according to it.”161

This is the definitive argument against “abstraction” as the general case and “presentation” as an ultimate foundation for logic. The association of the members of a series by the possession of a common “property” is only a special case of logically possible connections in general. But the connection of the members “is in every case produced by some general law of arrangement through which a thorough-going rule of succession is established.”162

Contra the Theory of Attention: The “theory of attention”163 therefore “loses all application in a deeper phenomenology of the pure thought processes”, (i.e. cognition). The similarity of certain elements, (under the classical view), can only be (conceptually) meaningful when a certain point of view has already been established164

from which the elements can be distinguished as like or unlike. This identity of reference under which the comparison takes place is, however, “something distinctive and new as regards the compared contents themselves!”165

The distinction between the concept and its extension, therefore, is categorical166 and “belongs to the ‘forms of consciousness’”.167 It is “a new expression of the characteristic contrast between the member of the series and the form of the series”!168

Cassirer argued that it is his “Functional Concept of Mathematics”, rather than the generic concept, that is the actual “Concept” which has been employed throughout the history of modern science.169

He offered a convincing co-thesis, furthermore, that the objects of mathematics and science are “implicitly defined”, (in Hilbert’s sense), specifically.170 The “functional concepts”, (their primitive laws), implicitly define their conceptual “objects” -and these are the actual working objects of science.

161 ibid P.17162 ibid P.17, my emphasis163 It is "presentation" vs. "attention" which is at the basis of the oppositional orientation of classical logic, and which is ultimately, I will argue, the origin of the problem of the homunculus.164 Compare Lakoff: “Category cue validity defined for such psychological (or interactional) attributes might correlate“, (his emphasis), “with basic-level categorization, but it would not pick out basic-level categories; they would already have to have been picked out in order to apply the definition of category cue validity so that there was such a correlation.” (Lakoff: P.54, my emphasis) See Afterward: Lakoff / Edelman. This is surely directly relevant to the context problem as well, (i.e. "the frame problem), in Artificial Intelligence research. (cf. Dreyfus, 1992)165 ibid p.25166 But see my discussion later.167 op. cit P.25168 ibid p.26169 "...the concept of function constitutes the general schema and model according to which the modern concept of nature has been molded in its progressive historical development." (ibid, P.21) See also especially: Einstein's Theory of Relativity, Cassirer 1923170 Discussing Hilbert, Cassirer says: "The procedure of mathematics here", (implicit definition), "points to the analogous procedure of theoretical natural science, for which it contains the key and justification." ibid p.94

Major Consequences:Cassirer’s “Functional Concept” marks a profound advance to understanding (and our specific problem), in two respects:

(1) it redefines the formal Concept, fundamentally, as exactly a “functional rule”

and,

(2), it isolates the concept as (logically) separate from, -as from a “different world” than the “objects” it “orders”.

The concept is no longer inherent in the elements it orders, (e.g. of “perception”), nor is it (logically) derived from them. It is:

“a new ‘object’ ... whose total content is expressed in the relations established between the individual elements by the act of unification.”171

Re: Presentation:

The Concept is a purely intellectual -and original- entity, a “peculiar form of consciousness, such as cannot be reduced to the consciousness of sensation or perception.”172 It is neither a copy of nor an abstraction from its extension. It is an independent and “mathematically” functional “ordering” –an act of unification! It is a rule not logically derivable173 from presentation. This rule, I will argue, is provided by biology, not by revelation.174

Cassirer has removed logic, (through his critique of the formal logical Concept), from the simple abstraction of perceptual objects, (i.e. presentation). It becomes instead an internal function of the mind, (and hence, I will argue, of biology) –i.e. it becomes a “new form of consciousness”.

I will now proceed to argue a very natural extension (and, I think, a completion) of Cassirer’s thesis: i.e. “the Concept of Implicit Definition”. This Concept, part of that same “new form of consciousness” is also internal and logically independent from perceptual presentation as well. I will argue, in fact, that it actually creates its “objects” – its “extension” -within the same free act of unification.///// Consider, finally, Patricia Churchland's comment about theoretical systems:

"It emerged that the meaning", (my emphasis), "of the most respectable of theoretical terms was defined implicitly by the theory the terms figured in, not by the empirical consequences of the theory. Terms such as 'force field', 'energy', and 'electromagnetic radiation' were prime

171 ibid P.24172 ibid p.25, my emphasis173 i.e. under classical logic174 i.e. it is not transcendent –nor does it provide a “God’s eye view”!

examples where meaning was a function of the embedding theory and where operational definitions were laughable."

"Whole theories have empirical consequences, and it is whole theories that are the basic units of meaning", (my emphasis), " -not terms, not sentences, and not subparts of the network. To be acceptable as an account of nature, a theoretical network must, as a whole, touch an observational base, but not every acceptable sentence or term in the network must do so." (P.S. Churchland, 1986, pps. 265-266)

///INSERT CHURCHLAND QUOTE HERE –SCIENTIFIC OBJECTS DON’T TOUCH REALITY –GET QUOTE//// Our very “perceptual objects”, (as well as our “intellectual objects”), I will argue, are resolved within the same internal (biological) act. This will remove, (in agreement with Maturana, Walter J. Freeman, and Edelman), the need for “presentation”, (metaphysically taken), altogether. It is the (presented) “perceptual object”, I will argue, which has been hypostasized! A new formulation of the Concept and its subsequent logic will allow the resolution of the specifically logical paradoxes of sentiency.

Cassirer’s Concept, (his Functional Concept of Mathematics), is unique in that its arguments show that the fundamental logical Concept is not derived from presentation or perception. It is a free and independent act (of unification). It is a “new form of consciousness” not dependent on presentation or perception. But if his arguments are believed, (and I think they are totally cogent), then there is a very natural extension of that Concept wherein the rule, (which determines the concept), can be likened to the conjunction of the axioms in a mathematical axiom system and its objects, therefore, to the objects of implicit definition. That result opens a new possibility –it potentiates the possibility that perceptual objects as well, (and not just intellectual concepts), can be free creations, acts of unification of that same new consciousness not dependent on presentation or perception either!175

It is clearly in “presentation” itself that the paradoxes of the homunculus and of the Cartesian Theatre arise, after all. If our perceptions were presented to us,176 -if mind, consciousness and perception were presentational and dualistic, (which is implicit in the presentation/attention abstraction of classical logic) -then the paradoxes of sentiency would be innate and irresolvable. But if those perceptions arose within us, and if consciousness arose as a whole, (as the unified rule of “ontogenic coupling”, after Maturana, as I will argue in Chapter 3), then sufficient grounds for a complete resolution of the problem would be established. This is not an answer from solipsism, dualism or idealism however, but from realism sans information and presentation. To see the possibilities this opens, we must now turn to David Hilbert –recognized as perhaps the most significant mathematician of the 20th century.

The Concept of Implicit Definition:(a natural extension of Cassirer’s “Functional Concept of Mathematics”)

175 Recall the perspective of chapter 1!176 as is assumed under the classical view

David Hilbert’s book, “Foundations of Geometry”177, is a recognized milestone in the history of mathematics. In it, he proposed a new axiomatic foundation for Euclidean geometry. But his novelty and the real import of his book lay in his methodology which was subsequently applied across the whole field of mathematics. (I propose that it provides the Rosetta Stone which will decipher the problem of the mind as well.)

His axioms, (as usual), referred to certain objects: “points”, “lines” and “planes” and to relations between them: “to belong to”, “between”, and “congruent to”. Hilbert’s radical innovation, however, lay in the fact that he quite purposefully never specified, (and never had to specify), what “point”, “line” and “plane” were to be or the meanings of the specified relations. He never required a specification of properties. He stipulated that the sole significance and exclusive consequence of his “objects”, (undefined terms), was to be in their operationality as expressed in the axioms. They were to be “implicitly defined” by those axioms. The success and the fertility of the subsequent extension of his approach across the whole of modern mathematics178 illustrated thereby that mathematical axiom systems, insofar as they are indeed mathematical, need define their terms and their elements, (their “objects”), only operationally and internally, not referentially. They do not define those terms in terms of set theoretic operations on primitive properties, (presentation/attention/abstraction of properties).

Consider the “integral domain” of Modern Algebra, (like the integers of ordinary arithmetic), as a typical application of Hilbert’s ideas.179 He begins his axiomatization with the simple assumption, (conditionally only) of a set of “elements”, (objects), -its “domain”- which obey a set of rules, (axioms). These objects of its domain, (and “existence” terms generally), are assumed only, (as Wilder points out) “presumptive(ly)” and “permissive(ly)” however –i.e. the elements of the domain are assumed solely to allow the operations. We are told nothing about them in an objective sense.

The whole of the process of specification -i.e. the whole of the definitional content of the elements, (objects), of the integral domain is achieved solely in terms of blind operations specified in the axioms acting on property-indiscernible, also blind objects and not by set theoretic refinements on primitive, (atomic), properties of these elements. Nowhere in this axiomatic system are the primitive operations identified with real integer operations, (or any other “real” operations), nor are they dependent upon them. The case is the same for the elements/objects of the system. Nowhere are they dependent upon any “real” objects, so no real properties may be legitimately identified with them. And yet he still achieved a working model of the real integers!

Compare Cassirer:

"…we have in pure mathematics a field of knowledge, in which things and their properties are disregarded in principle, and in whose fundamental concepts therefore, no general property of things can be contained." ("Substance & Function", p.18)

177 "Foundations of Geometry", Hilbert, 1910.178 See “Implicit Definition Appendix” for an elaboration and justification.179 I have included an appendix which treats this subject in considerably more detail for those who

wish to pursue it. This is a deep and contentious –but highly plausible – issue in modern mathematics involving multiple aspects. I propose that the problem of the “mind” has something to teach mathematics as well as the converse!

(Does this mean that we must follow Hilbert into his independently conceived "Formalism"180 -i.e. the simple manipulation of "marks"?181 I don't think so, for there is nothing particular about any given choice of marks in an axiom system- e.g. the identity elements might be named by any other marks, so long as the usage is consistent. It is the relationality, the operationality of those marks in a connective system which is significant. What "implicit definition" furnishes, then, is a concept embodying the invariant relationality of the system under all consistent substitutions. What is important about it is that this invariant relationality is non-trivial -e.g. that an “integral domain", (taken abstractly), can correspond with the real (?) integers "up to isomorphism"!182)

This is, as Schlick says, a genuine “Copernican revolution”, (after Kant’s usage of the words), in the history of mathematics. More, it is a new kind of logic, distinct from the logic of Aristotle which is wholly dependent on set theoretic refinement of original properties of its objects.183

Hilbert’s conception results in a novel and very different kind of “object”,184 one which is wholly constituted as an expression of the logical relations of the axioms. It is a purely an internal logical object! Hilbert’s brilliant reformulation of its foundations, almost trivial in appearance, has become the heart and soul of modern mathematics. Mathematics no longer looks to experience for its substance185 -for its validity. It concerns itself, rather,186 solely with the fertility and the

180 “Formalism” was Hilbert’s theory of proofs. It consists in the formal manipulation of systems of marks which are taken stripped of meaning.

181 Some people think that "implicit definition" merely means refining down to or eliminating extraneous possibilities so that only one possibility is left.  It is for them thus a process of categorical refinement, (under the old pre-Cassirerian Concept), to a given definition.  Neither Hilbert nor Schlick meant it that way.   For them, "implicit definition" reflected a generation from and within the rules themselves.  For this perspective see Shapiro’s characterization of Hilbert’s “implicit definition” as “structural definition” and his discussion of the Hilbert / Frege correspondence.  “Implicit Definition" in Hilbert's sense doesn't mean "innately points to some specific thing", it means "generates from within".  It arises within, it is not applied to the process.I make a very large distinction between "implicit definition" and "formalism", both products of Hilbert's sweeping intellect. The latter deals with a formal and mechanical methodology of proof while the former deals with actual and internal logical implication -which is not the same as its formal expression. Most working mathematicians are not particularly committed to "formalism", but they are very definitely committed to "implicit definition". Every time a mathematician goes to definitions, (which is all the time), he goes to the undefined terms of the system he is dealing with -and no further! Cassirer’s extension of the logical Concept is profoundly pertinent to these issues.

Hilbert was a "catholic" mathematician in the small "c" sense -he had enormous scope. It is the "king of invariants" who sired "implicit definition", I believe, and not his twin –i.e. the father of "formalism".

182 (Birkhoff & Mac Lane, 1953, p. 34)

183 Cf. The section immediately following this and the Afterword: Lakoff / Edelman for a further discussion of Aristotelian Logic.184 Consider the "object" of Chapter 1 in this light.

rigorous internal consequences of systems of explicit ideas. Ultimately, I believe, it is the science of the total possibility of order.187

Schlick characterized Hilbert’s innovation this way:188 “The revolution lay in the stipulation that the basic or primitive concepts are to be defined189 just by the fact that they satisfy the axioms.

[They] “acquire meaning only by virtue of the axiom system, and possess only the content that it bestows upon them. They stand for entities whose whole being is to be bearers of the relations laid down by the system.” (my emphasis)

This is the description of a genuine and profound “Copernican Revolution” in logic itself. Here “relation”190 logically defines “entity”, not the converse.191 This entity is an internal function of (logical) process. But “implicit definition” has another deep logical significance. It does not define its “objects” within the dualistic and oppositional context implicit in the foundations of classical Aristotelian logic. Like Cassirer’s “functional Concept of mathematics, it does not define them within the classical schema of presentation192 / attention193 abstraction194 of properties.195 It defines and resolves its objects, rather, by internal and logical resolution of its fundamental operations alone, and therein supplies the first clue to a logical possibility for sentiency -i.e. for the many-in-the-one.196

Cassirer’s analysis, (and actual reformulation), of the formal logical Concept197 is crucial to an appreciation of the full implications however. Hilbert and Cassirer together, in company with the “schematic object” of Chapter 1, supply a new logical ground -the logical ground necessary for a resolution of the problems of sentiency, and, finally, for a resolution of the mind-body problem.

185 ? As Cassirer commented, this does not mean that it does not look to experience as the origin, the suggestion for its ideas, but rather that it does not accept experience as the arbiter of its substance.186 ? as is clearly visible in the evolution and reassessment of modern geometry -in the grounds for the resolution of the "parallel postulate" problem and Non-Euclidean geometries, for instance, and in the whole of Abstract Algebra.

187 This is the lesson of Abstract Algebra. I will make this case later in this chapter as part of the argument for the Concept of Implicit Definition.

188 See also Einstein (1954), P.234, and Wilder (1967), Pps.3-8 189 It is crucial to understand that "defined" is used in a very different sense in mathematics than in the sense of ordinary "dictionary definition". It specifies the actual, the whole and exclusive existence -for mathematics- of the entity defined. Mathematics students are ingrained in this as the very first step towards "mathematical maturity".190 i.e. the constitutive relations specified in the axioms191 This is the paradigm which justifies my initial claim in chapter 1 for the most primitive, “sales

organization” model.192 cognition of objects/sets of atomic properties193 attention to specific properties of the former194 abstraction = set theoretic intersection of those properties195 The problem of the "homunculus", I will argue shortly, is already implicit in this (classical) framing of the concept.

196 –i.e. that our objects are not perceived or referential objects, but created ones!.197 Cassirer, 1923, Pps.3-233, especially Pps. 3-26

3. Cassirer’s “Functional Concept of Mathematics” does not exhaust the possibilities however -not even for mathematics. The “implicit definition” of axiomatic mathematics has specific and converse consequences for the formal Concept. Since, (following Cassirer), an actual concept is now defined by any (definite and consistent) conceptual rule, I propose that a mathematical axiom system is itself a perfectly good Concept in Cassirer’s sense. Axiom systems embody more profound rules than Cassirer considered however, and I propose that they define the ultimate concepts. Here it is a logically complex, (and typically non-serial), rule which defines the concept, (i.e. the conjunction of the axioms), and conversely and significantly, (following Hilbert and modern mathematics), it is a definite, logically precise and consistent rule of generation of its “extension” -i.e., of its implicitly defined elements as well.198 But axiom systems are not logically “dimensional”, (strictly implied in Cassirer’s F(x,y,z...)), nor do they normally define a “series”; they define the raw (broadest) manifold itself.199

There is no a priori presumption of dimensionality in the domain of an abstract axiom system. Nor can the elements of the mathematical manifold be characterized a priori, (dimensionally), as functional values of the individual axioms. Their “objects” are not “objects” of the sort: (a1(x), a2(y), a3(z), ...). Axioms do not interact dimensionally, they interact operationally. The combination of axioms, and their rule of generation, (Cassirer’s “continuous transformation”), is purely, profoundly and complexly logical. A mathematical axiom system need not characterize a “series” or a “series of series” moreover.200 Indeed, this is the exception rather than the rule. What it must and does embody, however, is the raw manifold itself, (its domain).201 It embodies the “logical continuum” generated by its axioms. It embodies an “order” of a higher degree of freedom.198 I am concerned here with the object of implicit definition only insofar as it is a logical object,

only insofar as it is a mathematical object. This is the actual object of implicit definition. I am not concerned with the (different) objects of models with which it may be made to correspond, i.e. with the objects of its possible realizations. This is quite a different case and quite a different object. It is the logical object per se, I will argue, that solves the homunculus. –See discussion in “Implicit Definition Appendix”. I will deal with the issues of Platonism, universals and ontology in that appendix as well.

.199 I.e. the abstract set taken in its broadest, most general, non-structured mathematical sense200 Cassirer, like Kant before him, considered the "series", (or a series of series), as the ultimate possible mode of logical and conceptual organization. He saw it as the ultimate expression, and only possible principle, (rule), for a logical function, (i.e. a logical principle which specifies its extension), other than identity. He based his new formal concept, ("the Functional Concept of Mathematics"), upon that belief.

But that conception is inadequate and inaccurate for the case of modern mathematics. Axiom systems exactly describe, (specify), elements, (their extension), that are not generally, (i.e. not a priori), organizable on a series principle. Axiom systems embody a larger and broader logical principle, (a rule which specifies its instances), and a broader logical concept, (as demonstrated, I suspect, by Gödel). The elements of a mathematical domain are fully prescribed, ("functionally" in Cassirer's sense), by their axioms, (their rule), but this rule is not "series". It is a complex logical rule -not referring to, but internally generating its extension as a virtual expression of its own innate ordering. It is the rule of implicit definition. This rule, following Cassirer, (I will argue), defines a new concept, the "Concept of Implicit Definition".201 which is not, a priori, implicitly dimensional.

The instances of Cassirer’s “Functional Concept”, (the objects of its extension), are the continuous generation of its rule. The instances of the implicit definition of mathematical axiom systems, the implicitly defined “elements” of their manifolds, are logically continuous as well -they are the continuous generation of a more profound rule which, by definition, exhausts, (and defines), its extension.202 The “elements” of the mathematical domain are precisely all and only those “values” implicitly defined by, (logically generated by), a particular system of axioms -in a sense precisely parallel to Cassirer’s. They are the pure embodiment, (crystallization), of the “order” of its rule. Its elements are virtual elements expressing its innate order. The whole of their meaning and the whole of their being, (mathematically), is solely such. The manifold, (domain), represents the functional and conceptual “values” of its system of “generating relations”. Its elements are logical elements.

The “elements”, (mathematically conceived), of axiom systems are not “objects” upon which a system of “generating relations” acts, however, or to which it relates. They are products of it. There is no a priori presumption of their distinct and separate existence. Wilder, pertinently, characterizes the “existence” terms of axiom systems as “presumptive” and “permissive” only. 203 Axiomatic “existence” is an operative term only. The elements -the objects- of axiom systems are logical “invariants” of their generating relations and internal to the rule itself.204 Neither “presentation”, (nor reference), is implicit in them. They are “entities whose whole being is to be bearers of the relations laid down by the system.”

I urge that this -the Concept of Implicit Definition- is the ultimate logical rule, and the ultimate “ordering”. It captures the ultimate functionality, (in Cassirer’s sense), of a logical system and generates its extension, (its abstract “domain”), as a virtual embodiment of its own (logical) “ordering” -its rule. An axiom system, (conceived mathematically), is a rule which wholly specifies its “elements” -by definition.205

(This discussion must be amplified and amended in the light of my conclusions reached in the “Dennett Appendix” on the “static problem. I concluded we must add axioms of intentionality –which is perfectly consistent with W.J. Freeman’s conclusions. It does not affect my basic conclusions, however, but adds a new dimension to them. The discussion is lengthy, however, and is better reserved for that appendix. (Note from April 24, 2007)

I propose, therefore, a new and largest formal “Concept”: the Concept of Implicit Definition. I propose it in strict analogy to the case of the mathematical axiom system and in strict extension of Cassirer’s Concept. It is the natural extension of Cassirer’s Functional Concept of Mathematics, and embodies, I propose, the ultimate rule, (in Cassirer’s sense), of order. But it is a generalization of Cassirer’s formal concept, not an instance of it. Conceptual “dimensionality”, (a “series of series”), implicit in Cassirer’s linear function of functions: F(x,y,z..), is a special case of the “rule” -and of the formal Concept.

202 See “Implicit Definition Appendix for a discussion of Gödel, Platonism, etc.203 Wilder, 1967, P.18204 Contrary to this view, Resnik,(Resnik, 1992), criticized an example of such a "structuralist" conception of mathematics in terms of the theory of reference. Under my hypothesis, however, the theory of reference itself becomes highly problematic. (cf Quine, 1953, pps.139-159, "Reference and Modality") Also see Chapter 4.

205 See prior "Elaboration" discussion

The concept of an axiom system, its “rule” of implicit definition, embodies something absolutely new and unique amongst concepts however. Its extension is precisely its own analycity. The “being”, (and the “meaning”206), of its elements are, by definition, identical with the purely logical “singularities” of the (complex) rule -and the concept- itself. They “are ... defined just by the fact that they satisfy the axioms.”207

Implicit Definition vis a vis Presentation:Like Cassirer’s Concept, (its conceptual progenitor), the Concept of Implicit Definition is not oppositional: i.e. it does not (logically) presuppose “abstraction” or “attention” either. It too is a “peculiar form of consciousness”, an “act of unification ... not reducible to the consciousness of sensation or perception”. But this particular “act”, (unlike Cassirer’s), does not presuppose “presentation” either. It does not just logically specify its extension; it logically encompasses it! The rule of “implicit definition” itself then, following Cassirer, is logical exhaustion and its “objects” are purely logical objects. They are “crystallizations” - i.e. logical “invariants”208 of and internal to the rule itself.209 This Concept, I suggest, does not entail “extension” at all -it is a (complex) unity.

Cassirer’s Concept, (the Functional Concept of Mathematics), is unique in that its arguments show that the fundamental logical Concept is not derived from presentation or perception but is a free and independent act of unification. It is a “new form of consciousness” not dependent on them. The Concept of Implicit Definition, (an extension of Cassirer’s thesis), opens a further possibility, however. It potentiates the possibility that objects as well can be free creations, acts of unification of that same new consciousness, (and biological organism I argue210), and not derived from presentation or perception either. This is a radical idea admittedly. Though somewhat repugnant and somewhat astounding to our preconceptions, it is certainly consistent with the biological conclusions of Maturana, Edelman, and Freeman wherein perception and consciousness, (whatever those may or may not be for these authors –more generally, the internal biological function), of an organism do not derive information from the world. But that is just what perceptual presentation would imply. The positive and the immediate consequence of this new rendering of the Concept, (C.I.D.211), is that we now have the tools to understand –completely resolve in fact- the problems of the “homunculus” and the Cartesian theatre. The virtual objects of implicit definition are known to

206 see above --Schlick207 Wilder quotes Nagel: "Indeed, if geometry is to be deductive ... only the relations specified in the propositions and definitions employed may legitimately be taken into account." (Wilder, 1967, p.7)208 cf Cassirer, 1923 pps.36-41209 Implicit definition is important when something significant is actually defined. The "objects" of abstract mathematics, (integers, for instance), are, (in opposition to Mill),"concrete", viable and fruitful. Its element specifies a particular kind of object, and that object is specifically a "crystallization" of a peculiar kind of "ordering"! It embodies the logical and relational essence of that ordering -and that's all! Its "objects" are "crystallizations" of its rule -just like the objects of the training seminar. The rules here, (and there), I argue, define the object, not the converse. But here the actual mechanism of that "crystallization" is transparent. The "calculus" defines the object, and the definitional mechanism is implicit definition.210 Recall the context of chapter 1 again!211 my “Concept of Implicit Definition”

the system as a whole. For it is only as implicitly defined internal resolutions of the system as a whole that they exist at all! This is a major advance on the problem and enables the only realist solution of the problem yet proposed other than a denial of the problem itself. It was in “presentation” itself that the irresolvable paradoxes arose after all. To repeat myself however, the denial of (metaphysical) “presentation” does not result in solipsism, but in realism sans information and presentation.

Why is this relevant to mind?4. Why is this significant to the problem at hand? It is because this Concept seems “tailor-made” to the logical problem of mind: It is capable of solving the homunculus problem and that of the Cartesian theatre. It can resolve objects without presentation, (without “the homunculus”), and supplies the “theatre” as well! It also supplies an autonomous theory of meaning.

Cassirer has established the equivalence of “concept” and “rule”. If, (1) following the arguments of chapter 1,212 we are no longer concerned with representation, (nor, with it, of “presentation”), and (2) if, tentatively, mind were taken as the unified rule, (the “act of unification”), of brain response,213 -if it were taken as the unified rule of the “structural coupling”214 of the brain -then (3), (following Cassirer), “mind” might reasonably be identified with the “concept”, (in the larger constitutive sense), of the brain. If that particular concept were analogous to the “Concept of Implicit Definition” in mathematical axiom systems furthermore,215 then it would not just “take account” of the elements of its “extension”, it would know them!216 Their “meaning” and their “being” would be logically manifest internal to that concept, (and rule), itself. They would be resolved as virtual expressions of that very rule. They would “acquire meaning ... and possess only the content that it bestow[ed] upon them.” They would be logical entities “whose whole being [was] to be bearers of the relations laid down by the system.” (I argue that the “logic” just mentioned is a constitutive logic217. I will argue presently that it is the schematic calculus of Chapter 1!)

But these particular entities -as cognitive and perceptual entities- no longer (metaphysically) presuppose attention or abstraction -nor do they presuppose presentation. Therefore, they do not presuppose that which it would be presented to -i.e. a “seer”! The logical problems of “the object” -the problem of the homunculus, the problem of “the mind’s eye”, the “Cartesian theatre”, (which are the principal enigmas of consciousness) -are thereby solved in principle. The fundamental duality, implicit in classical logic, between “seer” and “seen”, “thinker” and “object of thought”, “perceiver” and “perceived”, or, more fundamentally, between cognition and presentation, is bridged. The unity, and the very possibility of cognition of “the object” -the global perspective of the many in the one- is explained in the unity of its existence as a virtual object of implicit definition. For it is only globally that such a virtual object even exists as an object. In our rational

212 and of Chapter 3, and of Maturana and Varela, Edelman and Freeman213 i.e. As an organizational rather than a representative model as I argued in chapter 1214 See Chapter 3: Maturana and Varela215 This is consistent, certainly, with the "schematic object" presented earlier. How could evolution crystallize its (schematic) objects? The implicit definition of process -of "rule"- provides an explicit mechanism and rationale! 216 If there is a tendency to characterize my thesis as a variation of functionalism, then it should be noted that it involves a totally different notion of "function", (and "relation").217 after Kant's usage

universe, then, the Concept of Implicit Definition seems the most appropriate,218 as a model, to the logical problem of “consciousness”. There is no categorical disjunction between the “form of the series” -i.e. the “rule” of implicit definition- and its “elements”. They are unified in the concept itself.

Contra Cassirer:Cassirer “bent” the focus, however:

“There is no danger of hypostasizing the pure concept, of giving it an independent reality along with the particular things. ... Its ‘being’ consists exclusively in the logical determination by which it is clearly differentiated from other possible serial forms ... and this determination can only be expressed by a synthetic act of definition, and not by a simple sensuous intuition.”219

There are two crucial flaws in his argument, however:

(1): In the axiom systems of pure mathematics, the elements are also expressed by an “act of definition”, (albeit an analytical one) -i.e. that of “implicit definition”. They are themselves manifestations of that “peculiar form of consciousness, such as cannot be reduced to the consciousness of sensation or perception.”

(2): While he states that the application of the Functional Concept is embodied in the concept itself,220 he argues that concepts are different in kind from their extension. These are “objects” of a different world from that of the “particular things” -the objects of “simple sensuous intuition”. I argue, (in concert with the conclusions of chapter one), that the “objects” of “simple sensuous intuition” are themselves ultimately objects of “implicit definition” and part of that same “peculiar form of consciousness”. It follows, then, (given my hypothesis), that there is no simple sensuous intuition at all -it does not exist! It is the perceptual object which has been hypostasized! His dichotomy of the “being” of the pure concept and the “being” of the “particular things” need not stand on either leg.

Cassirer did not generalize the “Functional Concept of Mathematics” into “the Concept of Implicit Definition”. The “new consciousness”, furthermore, stopped short of “sensuous impressions” themselves. For him, the latter were absolute and unknowable. They were, in effect, the focal point upon which the various forms of knowledge, his “Symbolic Forms”,221 were oriented, but could never reach. They were the rock upon which he erected, in Swabey’s characterization, his “epistemological theory of relativity”.222 His “object of knowledge” was a purely conceptual object, implicitly defined by the fundamental laws of the sciences, -their “generating relations”. The “objects of perception”, the “particular things”, were of a different and untouchable world, the rock splitting the intellect in two.

218 the only appropriate yet suggested!219 Cassirer, 1923, P.26220 "if I know the relation according to which a b c ... are ordered, I can deduce them by reflection and isolate them as objects of thought" ibid p.26221 cf Cassirer 1953 and Chapter 4222 op. cit P.v. I will have much more to say about "Symbolic Forms" in Chapter 4.

The Crux of the Issue: Presentation Cassirer did Promethean work, however. He demonstrated the fundamental inadequacies of the classical Concept, both in its scope and specifically as regards “perception”. He illuminated the profound and expressly logical chasm between the Concept and the perceptual realm, (the “material” with which it purportedly deals!), and hence the pervasive duality which “perception”, i.e. “sensuous impressions”, necessitates for mind and logic. Even Cassirer’s “Functional Concept of Mathematics” was insufficient to the fundamental problem, however, and he remained inside the “magic circle” of perception. The opposition of “Concept” and “percept”, (e.g. “attention/abstraction” and “presentation” or still even the opposition of Cassirer’s “Functional Concept” and presentation -“sensuous intuition”), and the dualism which is implicit in it, is the essence of the issue. It is a genuine antinomy and the actual genesis of the problem. Already contained in “abstraction”, already implicit in “attention”, already embodied in “presentation” is the dualistic homunculus: i.e. that to which “presentation” is offered. There was no way heretofore that we could even conceive of an answer to this problem because it was the formal Concept itself which generated it. This was the retort in which the “homunculus” was conjured!

“Implicit definition”, however, belongs totally to the “new form of consciousness” -as do the “objects” which it “orders”. But here, (beyond Cassirer), there is no longer the assumption of a presentation of “elements”, (psychological impressions or otherwise), from one world to an intellectualizing, (cognitive), faculty in another. There remains, therefore, no innate need for the dualistic homunculus in cognition. This explains why the two worlds are compatible. There are not two worlds, but one. This “peculiar form of consciousness”, this “new consciousness” I maintain, is the only consciousness.

Mind-Brain: The Hypothesis:“... every transformation of the genuinely ‘formal’ concept produces a new interpretation of the whole field that is characterized and ordered by it” (op. cit. p.26)

6. Let us suppose that “mind” is the “implicit definition” of the process, (rule), of brain response. Let us suppose that the relationality of brain process is like the system of “generating relations” of an axiom system,223 and that even the “objects of perception”, the “sensuous impressions” themselves, are implicitly defined within that system,224 (alternatively that our “objects” embody the “calculus” of evolutionary design as per Chapter 1). The “objects of perception”, then, are not imposed upon the brain, (or presented to it), but are logical invariants of brain process itself.225 The “objects” are products of the “categorical act” -the implicit definition of the brain.

“Implicit definition”, as a thesis for mind, does not presuppose “presentation” to generate its “objects” nor is it antinomical. Its “objects” derive from the logical connection of process. “Sensuous impressions”, therefore, are not presentations to a process, they arise internal to the process itself.

223 I will suggest a physical paradigm shortly.224 i.e., that "perturbation", "triggering" modifies process! cf Maturana and Varela (1987), pps. 166-171, on brain plasticity.225 If "mind" is the "concept of brain process", then its rule -implicit definition- is primal logic itself. Conversely, if "logic", at its root, is the embodiment of that rule, then the relevancy of logic, as the expression of the ontogenic coupling of the brain, requires no teleological presumptions!

If we take “the object of perception” as being a specific “object of conception”, (taken in the new, larger sense of “Concept”)226 -if it is not, in fact, a copy, a “mirror” of externality, but an internal functional construct -a schematic artifact of the process of brain response as I have argued in my first thesis, then we have arrived at a viable solution to the whole of the general problem of cognition. The unity of the object is the unity of its implicit definition as a virtual element in a system of fundamental constitutive relationality227. But the “relationality” purported here is not the relationality of Functionalism. It is not the classical conception, nor even a Cassirerian “functional” conception of the relationality of fine-grained brain structure, but rather the (logical) “generating relationality” of implicit definition -of the brain as process.

A Possible Physical Paradigm: //////ALREADY DID FREEMAN!! –PERHAPS EXPAND A LITTLE////

7. What is desperately needed at this point, obviously, is a physical paradigm. How might this “axiom system” model -which seems to fit the fundamental logical problem of “mind” so well- be implemented as a biological model? An operational approach seems quite promising. Considering brain dynamically, -in terms of what it does, (its function), rather than in its fine-grained physical structure, certainly fits the necessary context of “structural coupling”, (response).228 The perplexing simplicity of the division of the brain into definite gross anatomical substructures, for instance, is suggestive. (If it were “wired” randomly and incrementally on a “breadboard”, as we would expect if it were developed in response to incrementally acquired evolutionary information, we would expect an amorphous clutter. Instead, we see very definite gross structure.)

Might not the distinctive, purely and abstractly geometrical function of the cerebellum,229 -considered as a functional unit of response -provide a pointer in the right direction?230 Might not these, or some other structural sub-units, considered as modular units of process -of “ontogenic coupling” -be “axioms”?231 232 But let us go back to chapter one –to Edelman and more specifically to Walter Freeman. Might not Freeman’s “equivalence classes” provide exactly the “axioms” that we need?////CHECK AND EXPAND/////

226 I.e. within the context of a constitutive logic227 i.e., in Maturana’s terminology, of “ontogenic coupling”

228 see Chapter 3229 i.e. doing tensor transformations. See Churchland, 1986, pps. 412-458230 The training seminar may still have things to teach us.

231 Or, as another possibility, think about the multiplicity of specific types of neurotransmitters in the brain. If the brain is monolithically structural –with the axons and dendrites as “wires” of a sort and the synaptic neurotransmitters as a sort of variable “solder”, then why did evolution go to the trouble of making so many kinds?

The fact of their multiplicity of type suggests another interpretation: that of multiple, superimposed structures, (modules?), sharing neurons and distinguished by their response to specific neurotransmitters. This raw speculation would be another possible conception of “axioms”, i.e. functional blocks in the brain.

232 This suggests a very definite line of research, i.e., the detailed investigation of gross substructures in primitive nervous systems. It suggests a line of interpretation in terms of modules of response, i.e. "axioms", whose interaction would define the "objects" of their perceptual worlds! What is it like to be a planarian worm? This may not be a ludicrous idea after all!

If the “objects of perception”, the “sensuous impressions” themselves, are “objects of the intellect”,- i.e. implicitly defined purely conceptual entities, (“conception” in the larger sense), then a Copernican revolution into a new logical world-view, centered in the “Concept of Implicit Definition”, resolves the whole of the problem of cognition. The processes of judgement, intellect, even “perception” -are not profoundly distinct or separate from the “objects” judged, from the “objects” with which they deal. Perception, conception,233 logic, and “object” are all aspects of the same process -the implicit definition of the “generating relations” of brain.

But what of “meaning”? In short, let me repeat Schlick’s comment with a different emphasis: “’point’, ‘straight line’, ‘plane’, ‘between’, ‘outside of’, and the like) ... to begin with, have no meaning or content. These terms acquire meaning only by virtue of the axiom system, and possess only the content that it bestows upon them.” Meaning itself can be explicated as a function of “implicit definition”. It is an expression of logical “positionality”, (order), in the context of relationality in which it is realized.234 (This is actually very close to the naive sense of “meaning”.)

Consider, finally, Patricia Churchland’s comment about theoretical systems:

“It emerged that the meaning”, (my emphasis), “of the most respectable of theoretical terms was defined implicitly by the theory the terms figured in, not by the empirical consequences of the theory. Terms such as ‘force field’, ‘energy’, and ‘electromagnetic radiation’ were prime examples where meaning was a function of the embedding theory and where operational definitions were laughable.”

“Whole theories have empirical consequences, and it is whole theories that are the basic units of meaning”, (my emphasis), “-not terms, not sentences, and not subparts of the network. To be acceptable as an account of nature, a theoretical network must, as a whole, touch an observational base, but not every acceptable sentence or term in the network must do so.” (P.S. Churchland, 1986, pps. 265-266)

I am proposing that the human mind itself is a theoretical (and operative) network, and it is only as a whole that it touches its base -i.e. its environment. As a whole it determines the meaning of its terms and implicitly defines its “objects”. I propose that not only our theories and the meanings of their terms, but that our cognitive objects themselves are implicitly defined as well. It is only in the context of the system of response that they “touch” our environment, (“have empirical consequences”). The “object” of cognition refers to its, (the system’s), own operationality and not to an external object. I propose that it is not the objects of the system that touch objective reality, externality; its “axioms” do!

If the brain/mind relationship is like the relationship of the axiom system to its implicit definition, then “we” do not deal with “presentations” to us, either for abstraction, conception or perception.

233 The "elements" of the manifold are "implicitly defined" by their generating relations, but so is "between", "line", ... Could not the "purely intellectual" object, (concept), -as distinguished from the perceptual object- be conceived as the product of co-definition from embedded axiom systems. It would then be an implicitly defined "object" of a different precision, a different "resolution". The element of a group, for instance, is less "resolved", in this sense, than the element of an integral domain or a field. 234 ? See Dreyfus 1992 for the context/"frame" problem

Rather, “we” are the system of implicit definition in which the so-called “presentations” are created. This completes, I feel, a reasonable and appropriate preliminary definition235 of “mind”.236

Convergence.8. My (second) thesis furnishes the basis for a coherent biological explication for “mind” and “consciousness”. If even the “percept” is just a special (and natural) aspect of the (extended) “concept”, then mind is clearly a logical237 continuum, (what else is there?) But that logical continuum would clearly be complementary to the operational continuum proposed under the first thesis. This concordance suggests an identity: that our “objects” are logical as well as operational objects238 and vivifies my logical hypothesis of mind.

The evolutionarily argued object of the first thesis is a virtual and schematic object of process. It is a continuous manifestation of the field of process which underlies it. The independently argued object of the second thesis, (derived from considerations of formal logic), is a virtual and schematic object of logic. It, too, is a continuous manifestation of the (here logical) process which underlies it. This strongly suggests an isomorphic correspondence between the results of two very different and plausible approaches to the problem. It is the discovery of just such correspondences that are crucial to the advancement of science.

But biology itself argues the correspondence. Taking a biological, (and reductive materialist), perspective,239 logic itself must be taken as a human, (and evolutionary), artifact. The alternative would be to assign transcendent240 properties to logic, a position clearly contrary to the very spirit and rationale of materialism itself. From the standpoint of biology, both “logic” and “concept” must themselves be considered reductively and evolutionarily.

The final biological rationale for human logic itself, (i.e. that aspect of human behavior which we call logic), is clearly evolutionary, -i.e. it is determined by natural selection. Logic is then necessarily a pragmatic rule of correspondence, (a procedural rule), between the brain and its environment. The (primitive) rule of “logic” itself is therefore operational, (rather than transcendent), and “concept”, as part of that logic, must be considered likewise. This suggests a striking conclusion: the first two theses are equivalent! The “mind” is the “logical”, (-i.e. “bio-

235 cf Chapter 5236 Incidentally," implicit definition" suggests another, more mature perspective than those presented in the earlier discussion on "models". Under this perspective even the schematic models and their artifacts are not (evolutionarily) "constructed" for (efficient) "use". The "objects" arise incidentally -they are implicitly defined as a result of the evolutionary optimization of brain organization around process and response. They are the "undefined terms" of a categorical "axiom system". Under this perspective we do not use our model, we live in it.237 in the sense of Kant's constitutive logic

238 This correspondence has the potential of supplying a vital and fundamental biological heuristic principle to psychology itself which, if realized, could be as important to psychology as evolution has been to biology. It could supply a fundamental operative rationale and tool for the investigation of mind and consciousness based in biology.

239 whose use I will justify in Chapter 4240 rather than "transcendental" -after Kant's usage.

logically” operational), “concept”241 of the brain.242 It is the “unified rule” of brain process. (Within this context, I assert that Hilbert’s thesis serves as the clear foundation for a deep and autonomous theory of meaning.)

This, I propose, supplies the actual basis, grounded in a new formal Concept, for the “constitutive logic” which Kant postulated to lie beneath our perceptions. I propose that my first thesis provides its specific and precise biological rationale and my second thesis explicates its “objects”. Our perceptual objects are not objects in reality; they are the implicitly defined logical objects, (alternatively, clearly now, operative objects), of this constitutive logic. They are objects of process.

A crucial turning point in my argument:9. This, I maintain, constitutes the final physical answer to the mind-body problem. Naturalists can accept this answer as complete, (and the problem as solved), if they like and dismiss any further questions. But inherent in my thesis as well is the assertion that our objects are not representative and informational. To believe that they could still remain so becomes, (under my thesis), equivalent to a hypothesis of “divine harmony”, (possible but implausible). This, (right here then), is a crucial turning point in my argument. I hereby reorient the whole of my argument up to this point and declare it243 as a constructive reductio ad absurdum of ordinary Naturalism244. By this, I most definitely do not reject the relationality245 of Naturalism or of Naturalist science. But I do maintain that I have demonstrated the implausibility of absolute reference and absolute information.246 The next chapters will elaborate this point explicitly and invoke a variation of Cassirer’s scientific epistemological relativism247, which preserves Naturalist science in a deeper realism. The argument up to this point has been in the demonstration of a counterexample, -a significantly better counterexample I think- which fits the presumptions of Naturalism and the facts of the problem as seen from the Naturalist perspective.

The unity of consciousness, the unity of mind is a logical, a conceptual and operational, rather than a spatial unity.248 The paradoxes of the Cartesian Theater do not derive from an innate flaw -or fantasy- in “mind”; they derive from a deficiency of ordinary logic.

241 "concept" and "logic" both conceived reductively as biologic processes.242 This, as I noted before, removes another "miracle", i.e. the startling simplicity and scarcity of the rules of logic and science. From the standpoint of my theses, the appropriateness of our "objects" and the simplicity of their mutual relationality are precisely the point of their existence!243 I have not been "cute" nor, I think, deceptive. It was necessary to establish the language of discussion and a context. The audience I seek is that of working scientists, and I have addressed myself to them. I seek to extend the field in much the same direction -and to the same purpose - as modern physics extended itself. I will resolve the obvious difficulties in the next three chapters.

244 As distinguished from "relativized Naturalism" -see Chapter 4245 i.e. the web of implication and predictivity

246 cf Chapters 1, 3 and Appendix A247 This is the second of this profound thinker’s brilliant insights I will address.248 Just "Where" and How this unity exists, (i.e. What), will be addressed in the third thesis, (Chapter 5). Incidentally Dennett also concluded that "mind" is a logical entity! See Appendix F: "Dennett".

Hubert Dreyfus249 concluded that the brain cannot be simulated in a digitally based computer,250 but he explicitly allowed the possibility of an analog implementation. Cassirer produced, in fact, an analog, (i.e. a functional), concept -“the functional concept of mathematics”. He suggested the requisite (analog) expansion of logic as well:

“..it must become evident that we stand here before a mere beginning that points beyond itself. The categorical acts which we characterize by the concepts of the whole and its parts, and of the thing and its attributes, are not isolated but belong to a system of logical categories, which moreover they by no means exhaust. After we have conceived the plan of this system in a general logical theory of relations”, (my emphasis), “we can, from this standpoint, determine its details. On the other hand, it is not possible to gain a view of all possible forms of connection from the limited standpoint of certain relations emphasized in the naive view of the world. The category of the thing shows itself unsuited for this purpose in the very fact that we have in pure mathematics a field of knowledge, in which things and their properties are disregarded in principle, and in whose fundamental concepts therefore, no general property of things can be contained.”251

The “general logical theory of relations” he predicts, though it involves an extension of his own “Concept” is, I propose, the “generating relationality” of implicit definition. The concept of the axiom system -the Concept of Implicit Definition- resolves the problem Dreyfus so correctly defined, but it resolves it, (contrary to Dreyfus’ expectations), within the platonic tradition.252

My thesis resolves the fundamental problems of “mind” and “consciousness”, i.e. “perception” and the primal logical problems of the “homunculus”, the “Cartesian theatre”, and meaning -and it is the only theory yet proposed that does. But these are the greatest enigmas of mind. (The other is that of providing a possible substance for mind which I have addressed in chapters 3, 4 and 5.)

How can a part of a whole be comprehensible to a whole? How can a mind “see” its contents without an infinite regress? How can a spatially and temporally distributed process cognate a part of itself? Other than an eliminative reduction of mind itself -i.e. an actual negation of mind in our normal sense altogether, (which is the answer of most –realist- modern theorists), there seems no other possibility. Supervenience, unless taken magically, doesn’t really make a lot of sense.253 //////”Grandmother cells” or “pontifical cells”, (William James), do not work. Eliminative reduction, on the other hand, throws away the baby with the bath. Its answer is that there is no “mind” in our normal meaning of the term. We are linguistic automatons -i.e. “zombies”.254

Plain talk:10. Let’s talk loosely for a bit. We do not start with absolutes anywhere in our logical and scientific endeavors. Somewhere we start with beliefs. I, for one, believe that I have a mind and a consciousness in the naive senses of those words. I think most of you believe that you do too. By this we do not just mean that our bodies mechanically and robotically produce words and actions

249 See Appendix C: "Dreyfus"250 His arguments are strong but I do not necessarily agree with his conclusion.251 Cassirer op cit P.18

252 cf Dreyfus Appendix253 see prior footnote -///get ref254 cf Appendix F: Dennett

which “cover the territory” -which merely simulate, (substitute for), sentiency in our naive sense of it, but that there is some universal and unified existence which is aware. But how?

Contemporary Naturalists, (Dennett, the Churchlands, Hofstadter, ...), universally and necessarily deny naive sentiency -the “mind’s eye”, the “matter”, the “figment” of mind. They preserve only linguistic and neural process. They forthrightly, (their forthrightness is to their credit), reduce mind to strict mechanism -to spatially and temporally distributed process. Mind, in a non-reductive, (i.e. a non-reinterpreted), sense, cannot exist for them. In this, I feel, they have completely lost credibility. They ask me to deny me in order to retain my beliefs about ordinary things.

Even idealism and dualism do not resolve the underlying logical problem however -the how of Leibniz’s “expression of the many in the one”, for even then how could this part of even a mental “substance” know that part? These are logical problems -the problem of the “homunculus” and the problem of the “Cartesian theatre”. Where does there exist even the possibility of a solution?

Implicit definition, virtual existence -and logic as biology- this is the only example within our intellectual horizons that seems to hold even any promise for sentiency in this our ordinary sense of it. It suggests the only scientifically plausible solution to “the mind’s eye” and the “Cartesian theatre” and the only non-eliminativist, (for “mind”), answer to the homunculus problem. These are answers which must exist if mind in our ordinary sense is, in fact, to be real. Implicit definition permits knowing, (as a whole), what are, in some real sense, our distinct and separate parts -precisely because those parts, (objects), are in fact non-localized and virtual (logical) expressions of the whole. It opens the first genuine possibility, therefore, for a resolution of this essential requirement of “naive” consciousness.

But that pathway, (implicit definition), does not make sense from the standpoint of representation! For implicit definition solves the problem logically -from the standpoint of constitutive logic -and speaks to nothing other than its own internal structure. “Objects”, (under implicit definition), are known to a system, (i.e. universally/globally), only because they are specifically expressions of the system. It becomes a viable and natural solution to the problem of awareness, therefore, only when the objects of consciousness themselves are conceived operationally and schematically, (and specifically, logically255), rather than representatively.256 When our objects are taken as specifically schematic representations of process however, (as per my first thesis), the solution becomes both natural and plausible -the logical problem of sentiency is resolved. 257 I assert that no other actual solution, (other than a denial of the problem itself), has ever been suggested. This is the argument from the second to the first hypothesis -and different from the argument from the first to the second presented earlier.

But this conclusion is greatly strengthened by the arguments of the first chapter and of Appendix A –and by the conclusions of several eminent contemporary biologists. My biological thesis, considered biologically, (i.e. aside from its admittedly profound, but purely epistemological difficulties -which I will make good in chapter 4), is exceedingly strong. How could evolution organize -as it had to organize- the reactive function of this colossus of sixty trillion cells? Even

255 and “bio-logically”256 That the objects of this constitutive logic would further represent, however, would be a genuine assumption of the miraculous -possible but difficult.257 though not the substance problem. That is a separate metaphysical issue addressed by my third thesis.

this formulation of the question disregards the yet more profound complexity of the reactivity of the individual cells -also organisms- themselves! It was the overwhelmingly crucial issue in the evolution of complex metacellulars. My thesis of schematism is both viable and plausible in this context. But what does this evolutionary development and organization of the reactive process of complex metacellulars have to do with “information”?258 //////////////

That the progressive evolutionary reactivity of this megacollosus occurred under the bounds of real necessity is, of course, a given. It is the basic axiom of Darwinian “survival”. But that it could match that possibility -i.e. that it could achieve a (reactive) parallelism to that bound -i.e. “information!” -is a hypothesis of quite another order and teleologically distinct. [See Illustration]///GET ILLUSTRATON//////

It is, I assert moreover, mathematically immature. Objective reality is a bound to the evolutionary possibility of organisms, but under that bound infinitely diverse possibilities remain.259 I may, as a crude illustration for instance, posit an infinity of functions under the arbitrary bound Y = 64,000,000. I may cite semi-circles, many of the trigonometric functions, planar figures, curves, lines ... ad infinitum. Only one of these matches the bound, and only a specific subset, (the horizontal lines Y = a, a 64,000,000), parallels it. It is a question of the distinction between a bound and a limit. The reactive evolutionary actuality of an organism certainly exists within, (and embodies), a lower bound of biologically possibility. But that some such, (any such), organism, (to include the human organism!), embodies a greatest lower bound -i.e. that it, (or its reactivity), matches and meets, (or parallels, i.e. knows!), the real world does not follow. That premise is incommensurate with the fundamental premise of “natural selection” and stands as the “parallel postulate” of evolutionary theory. Organisms do not know, organisms do! Organisms survive!

How much more plausible is it not that the primary and crucial thrust of evolution was coordination, and specifically a coordination of allowable or appropriate, (rather than “informed”), reactive response? I submit that, even solely biologically, the schematic object is far more plausible than the representative one. It involves no “magic”, and is totally consistent with our ordinary conceptions of biology.

In the realm of beliefs, however, my alternative, like the Naturalists’, is also bad. It also goes against gut beliefs when it says that we have no direct, (even a mediated/sophisticated), referential knowledge of metaphysical reality. But this is exactly the finding of contemporary physical science. It was the crucial enabling insight of quantum mechanics, for instance. Though my thesis goes against instinct, the whole course of modern physics stands by its side.

I submit that no other viable, (i.e. non-eliminative or non-dualistic), explanation, i.e., an actual explanation rather than a prevarication, has ever even been offered for mind and consciousness as

258 ///// “Information” is a subject that must be discussed, obviously. Both the materialists and myself see the function of the brain in the light of optimized efficiency. From their standpoint, this is accomplished by the incorporation of a realistic model of externality within it. FROM MY STANDPOINT THIS IS AN IMPOSSIBILITY –IT GOES AGAINST THE WHOLE GRAIN OF THE EVOLUTIONARY STANDPOINT. EVOLUTION WORKS BY THE SELECTION OF PROCESSES. BUT THE IDEA OF “INFORMATION PROCESSES” INVOKES A MIRACLE. HOW DID, AND HOW COULD IT START? /////EXPAND///////259 As an illustration, (as I quoted Edelman in the "Afterword"), there are numerous different ways that an antibody, for instance, can cope with an antigen -see Afterword.

understood in our ordinary sense. The argument, then, is one of demonstration. If no truly viable alternative can be offered, then this one must be considered seriously.

I argue that the operational process of brain, (and its evolutionarily determined structural optimization), implicitly defines its “objects”, its “entities” in the same sense and in the same manner that the “process” of an axiom system implicitly defines its “objects”. The “objects of perception”, I argue, are “mental objects”. They are constitutive conceptual objects. But they are schematic objects, (alternatively, “operational objects”), only, in no necessarily simple correspondence with objective reality. They are metaphors of response!260

Conclusion: (chapter)11. Considered physically, I propose that mind is a rule. But it is a rule that internally and logically resolves objects. Following Cassirer it is, (because it is a rule), therefore a concept as well. But it is a new and larger form of Concept. This is the reason we were unable heretofore even to conceive of a solution to the problems of the homunculus, of the “mind’s eye”, and the “Cartesian Theatre”. It was because our formal Concept itself, (and the rule in which we encompassed it), was too small!

In the next sections I will correlate my evolutionary and logical hypotheses with the standard paradigms of biology and physical science -and argue that they are a better “fit” than that of naive realism or contemporary Naturalism. Maturana and Varela’s evolutionary perspective is absolutely pertinent here, -and their arguments are impeccably drawn. The brain, as brain, is a reactive system -functioning “with operational closure” -and not a (realistically) representational one.

/////INSERT “A WORKING MODEL OF MIND”?????////////////////////////OLD CHAP 2 ABOVE/////////////

//////////////////////////////////////////////////FROM WEBPAGE BELOW/////////////////

section above is the working one!!!!////////////////////////HARVEST THE BELOW -MUCH GOOD STUFF IN IT TO INCLUDE ILLUSTRATIONS

Chapter 2. How? The Logical Problem of Consciousness(Cassirer- Hilbert- Maturana: an Archimedean Fulcrum)

Consciousness, a Simpler Approach to the Mind-Brain Problem -Implicit Definition, Virtual Reality and the Mind

1. The need for an explicit model:

There are several ways to present any given idea. For a proposed solution to the mind-brain problem, this becomes important. The approach from biology which was begun in Chapter one is the only logically self-contained one I think. It must begin from a solid biological perspective to credibly propose any viable or original solution to the problem of consciousness. That was not easy reading however. There is another route that could be taken. It is not logically autonomous, but it

260 Cf Chapter 1

provides an easier access to the ideas I would like to present here. It begins with an attack on the difficulties of “consciousness” per se.Nowhere in all the profound and litigious debate on the mind-brain problem can I find any concrete model of consciousness even suggested. Consciousness is identified, variously, with meaning, linguistic function, computation, brain process... Demands like “unity” and “understanding” are either vaguely conceptualized, disputed in principle, or reduced to distributed mechanical or logical process and eliminated. Nowhere are the tenets of the “mental side” of dualism, (e.g. wholeness, unity, knowing, meaning, non-extension, non-spatiality…), more than simply posited (or denied), -and quite vaguely at that. “Emergence”, to this date, has made no concrete suggestion -other than, (paraphrasing): “whatever neuroscience eventually concludes about brain function is what it is!  Consciousness emerges from that!”261 What is needed is some explicit model of consciousness within which the dialogue might be visualized.I would like to propose such a model here, and then examine how well it meets our desires for a description of consciousness. If it is plausible, then I think we will have made a positive advance. The initial model I will propose is an old one and abstract. It is, moreover, flawed in reputation and insufficient as it stands. Nonetheless, I think it provides an indication as to where we would like to go and the beginnings of a viable language in which to envision our goal. The model, drawn from mathematics, is that of “implicit definition”./////////////////cuts here//////////////////1.4 A VIRTUAL MODEL:Does this have promise as the beginnings of a model of consciousness then? Could it be considered in any sense as the beginnings of an explicit model? Yes, I think it could if we considered such a system as a virtual model -as a virtual reality! Its “entities” would then become genuine, (i.e. “tactile”), objects existing within a virtual world. They would become tangible !But existing examples of virtual realities, (games and instruments), specifically input into our sensory organs you will understandably object. The “realities” they embody still imply a “me”, a “seer” to make them tangible and known. This particular virtual model makes sense for our purposes when we reconceive it, (and its objects), in a special way -not as something to be seen , but rather, as the seer itself -i.e. as the mind itself.  It makes sense when we consider it not as some tool we use in mental conception, but rather as the “we” itself, the constitutive model implicitly defined by the operative process of the brain. If this were consciousness, then our objects would in fact be known to the whole. The problem of “the one and the many” would be solved. The antinomies of the homunculus and the Cartesian Theater would disappear. It does not require yet another seer; it is itself the Cartesian Theater. Perceptual objects, (and conceptual objects), would no longer be presented to another seer, they would be implicitly defined as part of  the seer and known . They would not be known in reference!Imagine yourself and the objects of your mind as a product of implicit definition. Imagine them as the implicitly defined, operational artifacts of the axioms of your brain. (The self-reference dilemma is addressed specifically in the Appendix of “Mind: the Argument from Evolutionary Biology”.)  Those axioms, I propose, are the modular, macroscopic physical components of brain physiology. I propose that those “axioms” are the modular units of response. They implicitly and virtually define a world and a mind.This is the case I suggest as a prototype model for the consideration of mind and I think it fits many of our intuitive ideas of what a mind actually is. It supplies the beginnings of an answer to the issues of wholeness, unity, knowing, meaning, non-extension, non-spatiality. It is also biologically

261 This is pretty much what Churchland asserts.

cogent, as it supplies the beginnings of a non-eliminative answer to the problem of how a biological organism, considered as a system of physical process, {9} could internally embody knowing or meaning at all. The rules of this system, (its “axioms”), {10} are, I argue, the adaptive and pragmatic rules of evolutionary survival. These are the operative rules of the brain. (They needn’t be simple however.)

The gross anatomy of the brain seems to argue for such a modular, (axiomatic), approach. {11} The perplexing simplicity of the division of the brain into definite gross anatomical substructures is corroborative. If the brain were “wired” randomly and incrementally on a “breadboard”, {12} (as we would expect if it were developed in response to incrementally acquired evolutionary information), we would expect an amorphous clutter. Instead, we see very definite gross structure.Previously there was no conceptual model matching the requirements for a mind at all. A virtual model logically paralleling axiomatic mathematics supplies the first prototype conceptual model fitting the fundamental requirements. I admit that this model is nowhere near specific enough as it stands and presents many further problems. I do think it is a long advance on the present situation however -i.e. of no cogent conceptual model at all. For the first time it gives us a way to conceive an answer to the problem of how a brain, (a system of pure biological process), could “know” anything . It supplies clues to “meaning” and to “objects”. It resolves the “homunculus” and the “Cartesian Theater” and, (perhaps most importantly), the model is logically and biologically autonomous .

The problems raised by this hypothesis are, of course, enormous and varied. The Churchlands, for example, have raised reasonable questions about the actual scale of the purported “unity” of consciousness. These are undoubtedly legitimate objections, (and not particularly new), {13} but I do not think they answer the need for some minimal core of unity. There are many other questions as well, but they are not within the scope of this particular writing. {14} The real problems I should be discussing here are those dealing with the actual viability and possible extensions of the proposed model itself. One of the key issues is that which I will dub the “static problem”. It is a technical issue and important.

///////1.5 THE “STATIC PROBLEM”The axiom systems of mathematics tend to create uniform, “static” fields of objects: the integers, for instance, or the real numbers. True, there are special, unique objects within them, pi, or e, or 1 for instance, but these are not promising for the kind of usage we will need to see for viable mental objects. To this point, the model I have proposed stands more in the sense of a Platonic “form”, and lacks the viability of Aristotle’s conjunction of “form and matter” for the existence of actual, special objects. Let me try to suggest the beginnings of a solution for the existence of such objects within such a system. Let me try to suggest a rationale for actual perceptual objects!

Daniel Dennett, (though he is a confirmed anti-mentalist), has provided an inspiration. It derives from his treatment of the “color phi” phenomenon, -though his conclusion must be stood on its head. I suggest that the answer to the “static problem” and the ground of viable perceptual objects lies in recognizing intentionality as a primary component of brain process. {15} It is a necessary component of the set of “axioms”. {16}

2. THE COLOR PHI: TOWARDS THE NECESSARY EXTENSION OF THE MODEL

2.1 DENNETT ON THE COLOR PHI

“The color phi” names an actual experiment wherein two spots of light are projected in succession, (at different locations), on a darkened screen for 150 msec intervals with a 50 msec interval between them, (citing Dennett). The first spot is of a different color, (red, say), than the second, (green). Just as in the case of motion pictures, (the “phi phenomenon”), subjects report seeing the continuous motion of a single spot, but interestingly, they report that it changes color, (from red to green), midway between the two termini! { 1 7} Dennett bases a very interesting, (and, I feel a very important), argument against the very possibility of a “Cartesian Theater” -against a unity, (and “figment” = substance), of consciousness on this well documented and reproducible experiment. Dennett’s argument, in brief, is this:

Mental states or a “Cartesian Theater”, if they exist, are subject to the laws of causality, of time precedence. For one event to affect another, it must occur before it. Let me, for discussion’s sake, label the events described. Let E1 be the (“heterophenomenological” {18} ), perception, (hereinafter to be called by me “h-perception”), of the first, (red), spot. Let E2 be the h-perception of the red-changing-to-green midpoint, and let E3 be the h-perception of the final green spot.Dennett argues, based on the principle of causality that E2 cannot occur until after E3. Since there were only two actual, (physical), events, (the first and second projected spots), he argues that the h-perceived midpoint, (the “mental event”, i.e. red-changing-to-green), cannot occur until after the reception of the second actual event, (green projection), as it was that which provided the very sensory data necessary to the h-perception of change. Other than a (mystical) hypothesis of “projection backward in time”, there remain for Dennett just two possibilities for an internal, “Cartesian Theater” consistent with the experiment: the “Stalinesque” and the “Orwellian” hypotheses.

The first involves the creation of a “show trial” staged by a subterranean “central committee”, (after the fact of both real events, of course, and involving a “delay loop”), wherein the complete, (and partially fabricated), sequence, (red ->red-changing-to-green -> green), is “projected”, (i.e. achieves sentiency). Under this hypothesis, the whole of our sentiency, (our consciousness), occurs “after the fact”. The second possibility, the “Orwellian” hypothesis, is that the actual events are received by our sentient faculty as is , but that our memory then rewrites history, (just as the thought police of Orwell’s “1984” did), so that we remember not two disjoint and separate events, but the connected, and pragmatically more probable sequence red -> red-changing-to-green -> green.

Dennett argues that ultimately neither theory is decidable -that either is consistent with whatever level and kind of experimental detail science may ultimately supply, and that, therefore, the only pragmatic distinction between them is purely linguistic, and therefore trivial. He argues that there is no “great divide”, no actual moment, (nor existence), of sentiency, but only the underlying brain process itself, (which all theories must countenance). Based on this “spatial and temporal smearing of the observer’s point of view”, he expounds his thesis of “multiple drafts” wherein there is no “theater”, only brain process -and its various “speakings”, (drafts).

And yet the observer himself has absolutely no problem with these events! His perspective is very clear: E1 > E2 > E3. It is our interpretation (and rationale), for this sequence that causes the problem.

I think Dennett has a very strong argument, but I want to refocus it. Nondecidability is all very well and good, but it is a much weaker line than the one he started out with- on the possibility of synchronization! In a very real sense, I feel it is very similar in intent and consequence to Einstein’s famous “train argument” against simultaneity.

2.2 DENNETT AND EINSTEIN: ON SYNCHRONY

Consider, (with Einstein), an imaginary train moving (very fast {19} ) down a track, with an observer, (train observer =TO), standing midway on top of the moving train and observing two (hypothetically instantaneous) flashbulbs going off at either end of the train. The train goes by another observer, (this observer to be stationary =SO), standing (hypothetically infinitely close) by the track and the moving observer as the bulbs go off. Suppose that the moving observer, (TO), reports both flashes as simultaneous. He argues that since both photon pulses reach him simultaneously, (simultaneity is granted for all frames on the local, infinitesimal scale, and thus agreed on (?) by both observers who are assumed infinitely close -i.e. side by side), that therefore the pulse from the rear of the train, having to “catch” him, must have left its source sooner than the pulse from the front which added his velocity to its own and so must have left later. Relative to SO, (the stationary observer), however, the two sources travel the same distance to a stationary target, (himself). Since TO and SO are momentarily adjacent to each other, (i.e. within a local frame), they should be able to agree that the two pulses arrive there simultaneously. What they cannot agree on, however, (in that instance), is whether the events, (the flashes), occurred simultaneously - nor that the other could have thought, (i.e. could have observed), them so! Time, in Dennett’s words, is “smeared”! {20} (We could, of course and significantly, {21} vary the parameters to make either event “earlier” and the other “later”.)

Just as Einstein’s two observers, near the limits of physical possibility, cannot agree whether the two lights were simultaneously flashed at the ends of the train or not, (i.e. cannot establish a common temporal frame of reference), nor, (given that situation), that the other could observe them locally as such, neither, given Dennett’s pointed argument, can we establish a common temporal frame of reference for “the world” and “the mind” at the limits of cognition. For macroscopic science, these limits are at the scale of the speed of light. For atomic physics, they are at the scale of Planck’s constant. For the brain, I suggest, they are at the scale of minimal biological response times, i.e. in the 100 msec. range.

I agree with Dennett that “the color phi” identifies a legitimate and critical aspect of the mind-body problem. The spatial and temporal “smearing” of the percept and the non-explicit reference of qualia that he demonstrates forces a profound extension to our traditional conception of the “theater”. But his dimensional “smearing” actually fits very well {22} with the model I am proposing. I submit that it is more plausible in terms of the “focus” and “function” of an operational object than in terms of his “multiple drafts”, “demons” and “memes” in the “real world”. His objections to the ordinary “Cartesian Theater” are admittedly valid, -but so were those of Helmholtz and Cassirer long before him:

2.3 HELMHOLTZ AND CASSIRER ON DENNETT’S DILEMMA

“If we conceive the different perceptual images, which we receive from one and the same ‘object’ according to our distance from it and according to changing illumination, as comprehended in a series of perceptual images, then from the standpoint of immediate psychological experience, no property can be indicated at first by which any of these varying images should have preeminence over any other.” {23}

It is only the totality of these data of perception that constitutes what we call empirical knowledge of the object; “and in this totality no single element is absolutely superfluous.” No one of the successive perspective aspects can claim to be the only valid, absolute expression of the ‘object’ itself; “rather all the cognitive value of any particular perception belongs to it only in connection with other contents, with which it combines into an empirical whole.”

“...In this sense, the presentation of the stereometric form plays ‘the role of a concept ‘”, (my emphasis –please remember this point), “’compounded from a great series of sense perceptions, through the living presentation of the law, according to which the perspective images follow each other. This ordering by a concept means, however, that the various elements do not lie alongside of each other like the parts of an aggregate, but that we estimate each of them according to its systematic significance....”

Consider the strong consequences of these observations however. Our actual (physical) percept is not only constructed from a temporal series of sense impressions, but from lateral ones as well. It is specifically named as a “stereometric “image -from two eyes! So must it be constructed from the rest of our perceptual input as well -from audible, olfactory, and tactile impressions. Surely the multiple cortical maps are pertinent as well.

2.4 WHAT CASSIRER MEANT BY SAYING THAT THE PERCEPT PLAYS THE ROLE OF “A CONCEPT” HOWEVER

“The cognitive value of any percept belongs to it only in connection with the other contents, with which it combines into an empirical whole.” “In this sense the presentation of the stereometric form”, [the percept], “ plays the role of a concept”. [my emphasis]

The meaning of this statement, (from Cassirer!), is important. Cassirer spent much of his life in a debate on the actual constitution of the technical logical “Concept” {23’} whose traditional Aristotelian interpretation he strongly disputed. His original reformulation of the formal logical Concept must be considered for an understanding of his argument here. Consider the force of his examples:

When we form the concept of metal …we cannot indeed ascribe to the abstract object that comes into being the particular color of gold, or the particular luster of silver, or the weight of copper, or the density of lead; however, it would be no less inadmissible if we simply attempted to deny all these particular determinations of it.” (The latter would be the classical interpretation -my emphasis.)

It would not suffice to characterize the concept “metal”, he argues “that it is neither red nor yellow, neither of this or that specific weight, neither of this or that hardness or resisting power”. But it is

necessary to add “that it is colored in some way in every case, that it is of some degree of hardness, density and luster.” Nor could we entertain the general concept of “animal”, “if we abandoned in it all thought of the aspects of procreation, of movement and of respiration, because there is no [one] form of procreation, of breathing, etc., which can be pointed out as common”, (my emphasis), “to all animals.” {24}

2.5 CASSIRER’S ALTERNATIVE: “THE FUNCTIONAL CONCEPT OF MATHEMATICS”He proposed instead a reformulation of the logical Concept itself as the “Functional Concept of Mathematics” extending the concept-making process of mathematics to logic generally. Here the special cases are not lost to abstraction , but rather are retained in functional form in the generalization to a genus. A simple mathematical example is the general equation of the straight line: y = mx + b. As m and b range through real values, it fully embodies all the straight lines in the plane. The equation fully embodies and can reconstruct the whole of its domain. This is not an abstractive definition.  It is the same for the generalized equation of the ellipse: p(x-a) 2 + q(y-b) 2 = r .  Again the whole, ( all ellipses including the circle), are totally embodied, (and recoverable), in a functional concept. But this, after all, is now the usual method of generalization, (genus-making), in mathematics. These are not abstractive, (i.e. via logical abstraction), concepts. Cassirer argues convincingly moreover that this  embodies the actual method and working “Concept” of modern science generally since, at least, Isaac Newton.Cassirer reformulates the logical “Concept” instead as a function. “Metal”, for instance, is necessarily colored in some way”, [x], in every case, it is of some degree [y], “of hardness, density”, [z], “luster”, [w]. He reformulates the formal Concept as a functional rule , f(x,y,z,...), (alternatively a multi-dimensional surface), which organizes and fully embodies the totality of its extension. The concept is “the form of a series”. That “series” may be ordered by radically variant principles however: “according to equality”, (which is the special case of the “generic Aristotelian concept”), “or inequality, number and magnitude, spatial and temporal relations, or causal dependence” {25} -so long as the principle is definite and consistent.But, (and this is the crucial point),  if the concept is indeed functional, it follows  that the “Concept” cannot be the mere abstraction of its extension. It is an independent and original contribution instead, logically distinct from what it orders!

“That which binds the elements of [a] series a, b, c, ... together is not itself a new element, that was factually blended with them, but it is the rule of progression, which remains the same, no matter in which member it is represented. The function F(a,b), F(b,c),..., which determines the sort of dependence between the successive members, is obviously not to be pointed out as itself a member of the series, which exists and develops according to it.” {26}

2.6 CASSIRER’S CRUCIAL RESULT FOR COGNITION This is a profound result for cognitive science.  Helmholtz and Cassirer have driven a wedge between “information” and the percept itself! If the percept indeed “plays the role of a concept”, then that percept is now constructed, not deduced. It is neither wholly an abstraction nor a representation of “information”.  It is intentional. The distinction between the percept, (“playing the role of a concept”), and that which it “orders” is “a new expression of the characteristic contrast between the member of the series and the form of the series”.

This is the “systematic significance”, (the “playing the role of a concept”), he purports with Helmholtz as necessary for “the presentation of the stereometric form” and “ empirical knowledge

of the object” -i.e. it is a rule of construction . But that rule is not (deductively) derived, ( as “F(a,b)” ), from the contents themselves. It is a new and original content - “a new form of consciousness” at work. (The source of this contribution, I strongly suggest, is evolution {27} , not logic!) I urge, extending Cassirer’s insight, that the stereometric form itself, the percept itself, {28} is wholly a function. Following Hertz and Cassirer, we do not perceive even our simple perceptual objects in any direct sense. We construct them. (See also Freeman, 1994, {28’})  I will argue shortly that this “new form of consciousness” is the only form of consciousness!

If we take the mind as specifically a “predictive” and “intentional” {29} model, (surely biologically cogent and which extension I will suggest shortly), rather than a static and “representative” one {30} , then the temporal and spatial “smearing” of the percept do not have the implications against the “theater” per se that Dennett attributes to them. I argue that even simple percepts themselves, (e.g. even the very E1 and E3 themselves), are conceptual, (albeit specialized, invariant and constitutive), and therefore functional, (following Cassirer). They are entities of order and process -and they are “smeared”. But it is the ordinary nature of functions to be smeared! What Dennett explains by “multiple drafts”, (and the “demonic” process he envisions beneath them), I explain by “focus”. We focus the percept, (via implicit definition) according to operational need.

2.7 THE FACTS OF PHI

The fact is that the midpoint E2 is actually experienced in repeated experimental confirmations! It does have actual conscious existence, (assuming you believe there is such a consciousness in the first place)! The conscious existence of E2 is clearly and specifically intentional however -whatever else could it be? Thereby it provides a crucial clue to viable mental objects in general -to include the very E1 and E3 themselves! I suggest that all of our mental objects - all our actual mental objects are intentionally constituted! I suggest that the solution to the “static problem” lies in adding axioms of intentionality to the axioms of ordinary process.

The original “phi phenomenon”, (the illusion of motion in a motion picture), is even more significant to the problem of consciousness than the “color phi” phenomenon however. The frank credibility and intentional depth, (i.e. the realism), of a series of oversized, rapidly sequenced still pictures, (a movie), is quite suggestive. Its potential for an uncanny parallelism with our ordinary experience suggests that the latter, (i.e. ordinary experience itself), is itself a predictive and integrative phenomenon grounded in an intentional model in precisely the same manner as I propose the “color phi” to be.

The cognitive effect of motion pictures is clearly intentional, as are the objects within them. To the extent that they are not merely patterns on a screen, their objects come alive. We believe them. We agree or disagree with them. We like them or hate them. They give us “experience” which we did not have previously and provide interpretations of future events! Their objects are clearly intentional objects however, in just the same sense as the color phi objects. They are just the interposition of a series of oversized, rapidly sequenced still pictures!

3. AN EXTENSION OF THE MODEL: A BRIEF SKETCH

Let me try to flesh out this model briefly. Let me try to sketch the design of real minds! Follow me in a thought experiment! Keeping your eyes fixed to the front, you perceive this paper in front of you, (in your conscious perceptual model), the wall behind it, and, perhaps, the pictures of your family. There may be pens and pencils, books. You may hear music from the stereo next to you, (and perhaps still in peripheral vision). There may be a window, and the lights of the neighbor’s house beyond it. But there is no wall behind you!

There is no car in the driveway outside of your house -indeed, there is no “house” at all. There is no city, no taxes, no friends. The sun does not exist in this model. There is no government, no “universe”, -no tomorrow! The (purely?) perceptual model is incomplete as a model of “reality” and it is, (Naturally!), inadequate even to keep you alive. There is something else necessary for completeness of any model of your sentiency, i.e. a new perspective on it. It is an intentional aspect. It is necessary to supply the object behind your back and the reality “over the hill”! It supplies the connection to “tomorrow” and “yesterday”. It supplies “causality”. It is necessary for the completeness of a model of “the world”. {31}

It is necessary, (specifically following Dennett’s line of argument!), even for the individual “objects” of perception itself, (E1 and E3 for instance {32} ). This model, I suggest, is where E2, (the object of Dennett’s perplexity), lives. It cohabits there very comfortably with E1 and E3 which, I argue, are also predictive and intentional objects. There is a seamless integration, (above the scale of 100 ms, let us say), of what we normally think of as our pure percepts and the intentional fabric within which they are woven. {33} This model, I propose, is the actual “home” of mind, and the legitimate purview of a truly scientific psychiatry.

I propose that the whole of our consciousness is a virtual intentional model. I propose that the field of virtual reality could be the archetypal science of the mind. It could be the primitive beginning of scientific psychiatry as well. {34} ///////////////SALVAGE THE IMAGE BELOW///////////   

4. FURTHER CONSIDERATIONS

But what could axioms of intentionality be? They would be theorizing axioms. Not axioms of a theory, mind you, but axioms of theory construction. Brains theorize to cope with an ever-changing reality. Penrose made a start towards analyzing the criteria of good theories. {35} All the great theorists acknowledge aesthetic criteria in theory construction. Even the current debate acknowledges at least some -“Occam’s Razor” is a case in point. There are others.

But why posit theory construction as the basic function of brains? It is because it is difficult to posit knowledge to biological systems. Their functioning entails only survival. The methods of

survival, however, are not fixed. Edelman, for instance, speaks of the multiple possibilities for response to a given antigen. Successful response does not depend on prior knowledge of the antigen. {36} It depends, rather, on the prior, evolutionarily determined existence of empirically adequate, (but cognitively blind), responses, (antibodies). So too must be our other cognitive response. It consists in the integration and theoretical organization of our other empirically adequate , (but equally blind), behavioral response. It is an intentional program!

5. CONCLUSION

As a conceptual model, implicit definition makes positive inroads on the problem of consciousness. It is, I think, the only cogent model on the table. (But see below). It provides explanatory ideas and makes sense within the current dialogue while at the same time providing answers to the ancient questions. It must be admitted that it opens more questions than it answers, but that is the nature of science. It is, moreover, just what we might hope for in a new discipline.

6. POSTSCRIPT: ARE THERE OTHER EXPLICIT MODELS?

In the paragraph above, I made the claim that this is the only explicit model on the table. What I meant by this was that it was the only explicit model of consciousness specifically. But any theory of mind must marry with biology! Without that tie, it is mere dialectic. Let me therefore briefly critique the few explicit models actually proposed. They are all biological: Crick’s, Penrose’s, Maturana’s, Edelman’s, and Freeman’s…. All of them have strengths, some more than others. None of them actually provide a rationale for consciousness however - they are theories of brain function. Some are logically compromised, (Maturana, Edelman, Freeman) -they lose the legitimacy of their own language by the epistemology implicit in them. (This is a long discussion, outside the confines of this paper.) {37}

6.1 STANDARD NEUROSCIENCE

Standard neuroscience is eliminative for “mind”. It attempts to reduce brain function to discreet steps. As research, it is impeccable, but it retains “mind” only as a hope. The Churchlands express that hope best as “emergence”. Somehow mind, as we normally conceive it, will emerge from the complication of process just as water emerges from the properties of its constituent hydrogen and oxygen. I think they are wrong -they obfuscate the reduction of theories with their fundamental premise of a necessary ontological reduction to “material”. The necessary discreteness of brain process in space and time implicit in the latter does not admit the possibility of a unified mind and consciousness. Crick’s hypothesis, as part of this category, provides a synchronization of process; it does not unify or explain consciousness. It explains the synchrony of brain function, but gives no clue to autonomous meaning or internal cognition.

6.2 EDELMAN’S HYPOTHESIS

Edelman’s hypothesis is somewhat more complex, but is deficient on the same grounds as Crick’s. His epistemology is more complex, (and nearer to the truth, I think), but with it he compromises the language within which he expresses it. He supplies the very “God’s Eye View” whose non-existence was his own essential premise.

6.3 FREEMAN’S HYPOTHESIS

Walter Freeman’s is the most interesting of the proposed models to me. He begins by trying to understand just one small part of the incredibly complex brain completely, (the olfactory system). The olfactory system is the most primitive sensory system and sensory input is surely the heart of the representation problem. He has started from what seems to be the soundest approach to the mind-brain problem -take the most primitive, the simplest part and follow an evolutionary rationale. He concluded that his empirical results were incompatible with “information” and “representation” and proposed a solution grounded in nonlinear dynamics instead. He proposes an extension of his conclusions to the brain as a whole. Though I am woefully ignorant of nonlinear dynamics, his general approach is certainly the right one. What particularly interests me is his incorporation of intentionality, (via the limbic system), and his disavowal of “information” and “representation” in his conception. I do not think he has solved the problem of consciousness however.  This is a deep and specifically logical problem!

His “sequences of amplitude modulated spatial patterns observed in the brains of animals and humans in the gamma range of the EEG” do not show that “consciousness is organized and based in discrete global patterns in much the way that a black-and-white cinema is composed of frames with a high repetition rate.” His problem in this, like the others, is that spatial frames integrate -become conscious -only to an observer. (It is the “homunculus” revisited.) Alternatively, even taking the whole global pattern as the mind itself, how does one part of even that mental space know another part? His mental space is specifically a physical space. Thisis the unequivocally logical problem which I have addressed with “implicit definition”. {38} I think that his work may have an even more profound import for this problem, however. Integrating sensory and intentional perspectives, it suggests itself that he may actually be laying the broader, biological foundation for an expansion of technical logic itself -a deep logic which would include intentionality.

Freeman has beautifully crystallized and profoundly reoriented the problem of the mind. He correctly argues that it is not a problem of the perception of “sensations”, (Kant, Cassirer), but a problem of response and the generation of a different, (though related), perceptual world internal to the organism. For Freeman, (and for Edelman, and Maturana as well), “information” never passes! The chaotic boundary he describes between the two corresponds to Maturana’s “structural coupling” and to my “interface”! {38’} But it is internal to this interface that the problem of consciousness must be solved -not in the plain physical description of it. This is the coupling between biology and logic that I have argued elsewhere as the “concordance” {39} between biology and logic. This is the ground within which the problem must be solved.

Logic, however, is itself biology!  It is a biological and evolutionary program organizing response. From that point on however, I argue that meaning, knowing and “wholeness”, (all the aspects of sentiency), must be generated internally to the new logic so constructed. . {40}   If my supposition is true, then Freeman’s hypothesis could supply the link between the purely logical “implicit definition” I have proposed and its concrete biological foundation. It would supply the biological basis for consciousness and a truly “embodied logic”. {41}

Like Edelman, (because of their common covenant with biology), Freeman disavows “representationalism”, and he names himself an “epistemological solipsist”. This is unfortunate. There are other epistemological positions better suited to his conclusions and the demands of modern science. Cassirer’s “Symbolic Forms” is more fitting. {42} It is the very embodiment of the epistemological relativity required by Freeman’s, (and my), formulation of the problem. It exonerates our doing science and our behaving as we do, (as brains ourselves), in a world our brains cannot ultimately know.

“Epistemological but not ontological solipsism” is an explicit contradiction in terms!  How can we name something that is real, (i.e. ontologically), solipsistically?  Edelman makes this claim, and Freeman does as well.  Maturana comes close.  I am sympathetic to their meaning, but strongly reject their language precisely because these authors use ontological language to make their cases. This is just plain wrong.  What is it they describe?  It is the same case I made against Maturana, (described at length in Chapter 3 of my book), that I make against all such cases.  What is needed, what is truly consistent and productive, (though harder conceptually), is an ontological indeterminism and an epistemological relativism.  This was exactly the case made by Ernst Cassirer in his “Symbolic Forms” as expounded in Chapter 4.|| HOME ||

/////////////////////////////////////////////FROM WEBPAGE ABOVE –CHAP2////////////////

///////////////////////////OLD CHAPS 3-END BELOW –EDIT AND CORRECT AND EXPAND/////////////////////////

Introduction to Chapters 3, 4 and 5, (towards a Resolution of the Paradox)

In Chapter 2, I proposed a concise Naturalistic explanation of mind, i.e. that the mind is the (materially reduced) "concept", (alternatively, “the rule”), of the brain! I said that Naturalists could accept that explanation as the final and conclusive answer to the problem if they chose, but, if they did, they accepted a profound antinomy therein, as it still does not produce a "live" mind. Awareness was still not possible except as "awareness" was itself physically reduced. We would remain, therefore, linguistic automatons.

My third thesis, (chapter 5), will address this problem directly and, in the process of its development, (chapters 3 and 4), will resolve the severe epistemological difficulties raised by the first two theses. It will resolve them, moreover, in a manner consistent with the outlook of modern physical science. I will argue a final "Copernican revolution" away from the purely Naturalistic perspective,262 retaining the results of Naturalistic science however, (and our ordinary world), under a thesis of scientific epistemological relativism, (a variation of Cassirer's "Symbolic Forms"). Building on Kant's fundamental insights, I will argue that the problem of the “substance” of the mind263 is really a problem of metaphysics, and that Naturalism's own metaphysics, (and it definitely has one), is faulty. Besides its seemingly irreducible incorporation of reference, it is its overstrong metaphysical assumptions which make impossible the existence of a "matter" of mind. In the words of Van Fraassen: "Scientism, [Naturalist metaphysics] is also essentially negative; it denies reality to what it does not countenance. [my emphasis] Its world is as chock-full as an egg; it has room for nothing else."264

My thesis has questioned the very basis of cognition. But what are the truly necessary presumptions of science? I will examine those necessary assumptions from the standpoint of modern biology, (Maturana and Varela), and from the foundations laid by Kant to arrive at the "axiom of externality", and from the work of Quine and Cassirer to arrive at the "axiom of experience". These, I maintain, are the two actual primitives of realist reason.

I will employ an extension of Cassirer’s relativism, (a rigorous scientific and mathematical epistemological relativism), to deal with the problem of reference. On the issue of substance, I will argue, (in Chapter 5), that the only "really real", (i.e. ontic or metaphysical), supposition that anyone, (to include behaviorists, material reductionists...-even dualists!), is rationally allowed to make -yet which all must make- is that of the existence, (however taken), of our interface to externality itself. But the truly necessary, (i.e. apodictic), part of that interface must be conceived minimally and mathematically, i.e. as a limit! It is the synthesis of the most abstract understandings of our necessary realist primitives: "experience" and "externality". As such, it is implicit in every realist stance in some form -"memes", "linguistic coupling", "reductionist

262 ? or, using the terminology of Putnam, Lakoff and Edelman, away from the “objectivist perspective”. It is actually my third Copernican revolution as each of the theses could be characterized as such. Each reorients the prior terms and arguments as is the usual nature of Copernican revolutions.263 ? Dennett's "figment"264 ? "Quantum Mechanics" P. 17

process", "behaviorism", .... This is Maturana's "structural coupling"265 reconceived in its most abstract form, i.e. relieved from its specifically Naturalistic setting.

This interface is therefore necessary and, I will argue, it is also sufficient to the problem as well. It is this minimal interface, itself taken as metaphysically real, (as it must be266), that I will propose, (going beyond Kant), as a new metaphysical substance. It is, I will argue, the "substance" of the mind. If that interface is therefore actual, (i.e. ontic), and if it is, furthermore, structured as I have proposed in my first two theses, (which is my third and final hypothesis), then mind exists. It is an actual mind. We are actually aware. We are actually conscious.267

265 ? cf Chapter 3266 ? If it does not exist, then there is no link between externality and experience, and the whole, (any), realist intellectual enterprise collapses. It is therefore itself ontic and apodictic.267 ? [An aside: If I were to substantially revise this book, I would have been tempted to base

Chapter 3 in Edelman’s “Bright Air, …” , 1992 as it might have provided a simpler basis for the exposition of those ideas. He argues to the same end as do Maturana and Varela that the brain is not informational but “ex post facto selective”. His arguments are based in his theory of neuronal group selection, (TNGS), grounded in embryology and immunology. While I think it is a very plausible theory, it is specific and unproven. Maturana and Varela make the more general case however, based in first principles. It is a more abstract and conceptually difficult approach, but I think it is worth the work. We must endure the arid complexities of the law to finalize the divorce of realism, (and “externality”), from representation.]

Chapter 3. Biology_Part II: Towards the Where and the What?Biology & Epistemology

(Maturana and Varela and Kant)

"If in a new science which is wholly isolated and unique in its kind, we started with the prejudice that we can judge of things by means of alleged knowledge previously acquired -though this is precisely what has first to be called in question -we should only fancy we saw everywhere what we had already known, because the expressions have a similar sound. But everything would appear utterly metamorphosed, senseless, and unintelligible, because we should have as a foundation our own thoughts, made by long habit a second nature, instead of the author's." (Kant, Prolegomena, p.10)

From our ordinary way of looking at things, my third and final thesis, (which will be formally stated in Chapter 5), will appear convoluted, esoteric and disturbing. When the inverting glasses of habit are removed and a proper perspective is attained, however, it will become elegantly simple268, plausible and profoundly more compatible with modern science than any proposed alternative. To reach that perspective and before I can even begin to properly state this thesis however, I must deal with several seemingly divergent, (but actually closely related), issues. This chapter will discuss the first of them. I must address the epistemological dilemma created by the conclusion of the first two theses.

Nobody writing meaningfully about the mind-body problem today appears to take Immanuel Kant as seriously and as literally as I do, and yet he seems to be the thinker most pertinent to it.269 The problem of mind-body is, in one profound respect, the problem of knowing, (epistemology), itself. The questions of what we, as organisms, do know, or even can know -and how- reflect back on the very knowledge by which we judge the problem itself.

In an ancillary and important respect, moreover, the problem Kant faced in attempting to communicate his ideas is very similar to the one I face. (I referred to this in the introduction.) Both theses totally contravene the common wisdom, and (therefore) make sense only as a whole and not in their parts. Like his problem "of pure reason", (which is clearly a part of my own problem), my problem:

"is a sphere so separate and self-contained that we cannot touch a part without affecting all the rest. We can do nothing without first determining the position of each part and its relation to the rest; for, as our judgement within this sphere cannot be corrected by anything without, the validity and use of every part depends upon the relation in which it stands to all the rest within the domain [of reason]. As in the structure of an organized body, the end of each member can only be deduced from the full conception of the whole. It may, then, be said of such [a

268 ? in a mathematical sense of the term

269 ? "This is an advantage no other science", [than epistemology/metaphysics], "has or can have, because there is none so fully isolated and independent of others and so exclusively concerned with the faculty of cognition pure and simple". Kant, "Prolegomena", Lewis Beck translation, Bobs-Merill, 1950, p.131, my emphasis

critique] that it is never trustworthy except it be perfectly complete, down to the minute elements [of pure reason]. In the sphere of this faculty you can determine and define either everything or nothing." ("Prolegomena", P. 11)

The combination of my first two theses provides radical and powerful simplifications to the mind-body problem. It raises a new and seemingly overwhelming difficulty however; if it is true, then what do we know, and what can we know of the reality in which we exist? Since my very arguments depend, moreover, on accepted knowledge270 of that world, have I not reduced my own case to absurdity? The path to my third thesis will answer these questions and supply, (at its conclusion), the single remaining part of my promised complete solution to the mind-body problem. The latter is the answer to the problem of the "substance" of the mind. What is "mind" and where is it? How could it be? Before I can formally state my third thesis which will answer these questions, (in Chapter 5), however, we must look at the problem of knowing, (epistemology), and at the broader problem of cognition generally, to include perception. It demarcates the problem of "substance". It sets the bounds and defines the very context within which we must consider it. The pivotal issue will be "closure"!271

Closure:

A mathematical domain D is called "closed" under operations "*" and "#", (let us say –or think of the Real numbers under addition, subtraction, multiplication and division), if for every x and y in D, "x*y" and "x#y" are necessarily in D as well. The result of all such operations on the domain is, no matter how far concatenated, always again within the domain. It never "escapes" itself! I will argue that our human cognitive domain is itself likewise closed, (though bounded),272 under its operations. This was Kant's, (and Maturana's), conclusion as well. Surprisingly it will simplify the problem of "substance" and resolve the intolerable dilemma I (so innocently) raised as well. It is not that the problem of substance is itself so difficult; it is the demands that we make on the answer.

Kant was the most scientific, (I might equally say "mathematical"), thinker on this problem, and he is confirmed more recently, from the logical side by Quine,273 and, from the side of biology, by Maturana and Varela. Though Kant's arguments belong to another era, his overall conclusions and

270 ? e.g. Darwinian evolution

271 ? This is, as an emotional issue, the most difficult of my theses and I must expect to lose my credibility with many of you here. It is a strange and esoteric idea, but, I believe, true. It must, on my part, be presented with the utmost delicacy. On your part, I must ask for a very careful reading as it may not be as it seems at first.

272 ? A simple mathematical example of a closed and bounded domain would be the domain of the open interval -1 < x,y < 1 under the operation of multiplication. Another would be the open domain bounded by unit circle: for all (x,y): -1 < x,y < 1 with the operation #: (x,y)#(u,v) = (x*u,y*v). The integers are, of course, closed under addition and multiplication, the rationals under addition, multiplication, and division, ...

his rigorous identification of the basic and necessary assumptions remains intact. Sanity and plausibility depend on just two, (by definition "metaphysical"), postulates of absolute existence: "externality" and "experience", ("intuition"). Without them, there is no reason for reason! But those postulates operate solely within the closed domain of reason: "our judgement within this sphere cannot be corrected by anything without."274

While fully affirming the existence of our external world as a necessary prerequisite to reason, Kant concluded that we are inherently incapable of knowing any of its independent properties, (to include time, space, extension, tactility -impenetrability), independent of their revelation in, and in combination with, human cognitive forms. Kant argued, (in quite a modern vein –think of Heisenberg!), that it is impossible to separate our "instrument", (the peculiarities of biological human cognition), from what it "measures", i.e. the world it cognates. His genuinely relativistic conclusion gains modern physical credence from the theories of relativity and quantum mechanics, and logical credence, (though it contravenes certain of his own, dated, arguments), from the axiomatic foundation of mathematics. He arrived at a position which I will call "ontic indeterminism"275, (i.e. an indeterminism as to properties, but not as to the existence of external reality). More recently, Quine276 has argued that our "system of knowledge and beliefs" is logically closed, and Maturana and Varela277 have argued that biological organisms are operationally and cognitively closed -by definition!

I will argue that our knowledge and, even more broadly, cognition generally278, (to include perception!), is a closed, (i.e. self-referential), domain whose "boundary conditions"279 are:

(1) the most general, (i.e. the weakest and most abstract), possible assumption of "externality" itself, and

(2) "experience" as an uninterpreted primitive, i.e. not the interpretation or organization of

274 ? ibid

275 ? Kant himself was never satisfied with "critical idealism" but was forced to retain it for historical reasons. "This being the state of the case, I could wish, in order to avoid all misunderstanding, to have named this conception of mine otherwise, but to alter it altogether is probably impossible. It may be permitted me however, in future, as has been above intimated, to term it 'formal' or, better still, 'critical' idealism, to distinguish it from the dogmatic idealism of Berkeley and from the skeptical idealism of Descartes." -"Prolegomena", Pps.124-125

276 ? W.V.O. Quine, 1960. I will elaborate Quine's position in Chapter 4.

277 ? Maturana and Varela, 1987

278 ? Cognition has two aspects. Repeating the definition cited earlier, (Websters. "cognition: the act or process of knowing, including both awareness and judgement". Also, "Perception: (4a) direct or intuitive cognition.")

279 ? See Chapter 4, re: Quine

that "experience" -not, for example, its interpretation as "sense impressions"280. The connection between these two assumptions is not necessarily simplistic. This chapter elaborates the first of them.

In this chapter, I will examine Maturana and Varela's arguments as set forth in "The Tree of Knowledge". (Maturana and Varela, 1987) They consummate the viewpoint of modern biology on the issue of closure. This penetrating work, very much the biological complement of Kant's "Prolegomena" I feel, defines the secure biological context in which they develop a single heuristic principle, ("structural coupling"), crucial to the mind-body problem. I will differ strongly with the conclusions they draw from it, however, as they were unwilling to accept the devastating consequences of their own arguments. I do.

Maturana and Varela characterize their book as an argument against a representative model of environment in the brain, against the existence of a current "map" which we use to compute behavior appropriate for survival in our contemporaneous world. Their argument propounds, instead, a closed, (and evolutionarily determined), reactive parallelism to environment -i.e. "congruent structural coupling". They argue that organisms do not behave as they do because of the nature of their current surroundings; they behave alongside of it!281 Organisms, as reactive physical systems, are "operationally closed". Their closed ontogenic state is only "triggered" by their environment. Environment is a "boundary condition" of survival, not a motivation for action. They conclude there is no current model because there is no flow of current "information". They develop their fundamental thesis, "structural coupling", at the ground level of primitive evolution. It is a principle of purely mechanistic coexistence between "organism" and "environment" which preserves "autopoiesis", (reproduction). It is, I will argue however, weaker than the strict parallelism, ("congruence"), they demand of it. Their argument, examined more deeply, is against "information" between an organism and its environment at any stage -to include that of natural selection! "Congruence"282, however, would clearly be evolutionary information!283 "Structural coupling" and the "conservation of autopoiesis", (and Darwin's "natural selection" itself), are quintessentially principles of raw appropriateness however.284 They are not informational. They say: "This works!"; they do not say: "This is what is!" (They do not exhaust 280 ? But if our perceptual objects are cognitions, then how can they be a boundary condition of cognition as well? How can our perceptual objects and the things they do be "experience" themselves? I will argue that they are not! "Experience" is their invariant relationality across all orientations including even those which might distribute the "objects" themselves! Does perceptual cognition equate with "experience"? No, it is a particular (evolutionarily derived and "pictorial") orientation of that relationality! See Chap.4 and the "King of Petrolia".

281 ? Their argument is considerably subtler than this as I will detail below.

282 ? as in "congruent structural coupling"

283 ? cf Edelman, 1992. He argues that the human genome is simply too small for the purposes of information

284 ? i.e. they are boundary conditions, not limits!

or mirror the whole of possibility). Neither parallelism, ("congruence"), nor embodiment are legitimate consequences of these principles, I will argue, even at the evolutionary level. There are correlations between domains other than "isomorphism" or "congruence" which preserve pertinency. The mappings and transformations of abstract algebra are obvious counterexamples disproving the inference. It is only necessary that (some) feature(s) compatible with the milieu of the domain be preserved. I will argue that the presumed necessity of "evolutionary congruence" is a human precept and part of the closed and specifically human cognitive model.

INSERT BOUNDS GRAPH HERE!!////

I will now attempt to summarize Maturana and Varela's thesis. Please forgive the length of my citations, but I feel their arguments are profound, subtle, and more concise than any paraphrase. I believe they are, up to a certain point, conclusive.

Maturana and Varela:Maturana and Varela,285 make a profound and phenomenologically pure286 argument proceeding from first principles. It leads to severe epistemological consequences. They begin by outlining minimal and necessary biological specifications for "living organisms". Those then become a sufficient rationale for the whole of metacellular organisms and their (nervous) behavior.287 The argument is wholly operational and constructive.288

"Our intention, therefore, is to proceed scientifically: if we cannot provide a list that characterizes a living being, why not propose a system that generates all the phenomena proper to a living being? The evidence that an autopoietic unity has exactly all these features becomes evident in the light of what we know about the interdependence between metabolism and cellular structure."289

Plausibly, they characterize a "living organism" as an "autopoietic unity", i.e. a replicating (cellular) physical entity. In so doing, they clarify the inherent nature of biological phenomenology itself, (i.e. its innate categories and operative principles).

"the potential diversification and plasticity in the family of organic molecules has made possible the formation of networks of molecular reactions that produce the same types of molecules that they embody, while at the same time they set the boundaries of the space in which they are formed. These molecular networks and interactions that produce themselves and specify their own limits are ... living beings."290

"Autopoietic unities specify biological phenomenology as the phenomenology proper of those unities", (my emphasis), "with features distinct from physical phenomenology... because the phenomena they generate in functioning as autopoietic unities depend on their organization and the way this organization comes about, and not on the physical nature of their components."291

The legitimate and minimal principles appropriate to biological process are operational closure and independence.

285 ? afterwards "Maturana"286 ? i.e. they do not mix their contexts or the origins of their presumptions287 ? "And how can we tell when we have reached a satisfactory explanation of the phenomenon of knowing? ...when we have set forth a conceptual system that can generate the cognitive phenomenon as a result of the action of a living being, and when we have shown that this process can produce living beings like ourselves, able to generate descriptions and reflect on them as a result of their fulfillment as living beings operating effectively in their fields of existence." (op.cit P.30)288 ? Please come back and review Maturana's preamble when you have gotten through Chapter

4, particularly Hertz's reflections on the nature of science. I think the connection is important.289 ? ibid P.48, my emphasis290 ? ibid Pps. 39-40291 ? ibid P.51

"Ontogeny is the history of structural changes in a particular living being. In this history each living being begins with an initial structure. This structure conditions the course of its interactions and restricts the structural changes that the interactions may trigger in it", (my emphasis). "At the same time, it is born in a particular place, in a medium that constitutes the ambience in which it emerges and in which it interacts. This ambience appears to have a structural dynamics of its own, operationally distinct from the living being. This is a crucial point. As observers, we have distinguished the living system as a unity from its background and have characterized it as a definite organization. We have thus distinguished two structures that are going to be considered operationally independent of each other, (my emphasis), "living being and environment."292

Physical science's primal principle of "mechanism", however, leads to a distinct point of view on the interactions of the "autopoietic unity" with its environment: "triggering", "perturbation", and "structural coupling". Organism and environment are coincident, not operationally dependent!

"Every ontogeny occurs within an environment; we, as observers, can describe both as having a particular structure such as diffusion, secretion, temperature. In describing autopoietic unity as having a particular structure, it will become clear to us that the interactions (as long as they are recurrent) between unity and environment will consist of reciprocal perturbations. In these interactions, the structure of the environment only triggers structural changes in the autopoietic unities (it does not specify or direct them)", (my emphasis), "and vice versa for the environment. The result will be a history of mutual congruent structural changes as long as the autopoietic unity and its containing environment do not disintegrate: there will be a structural coupling."293

(I argue that their phenomenology applies to genetic modification as well as ontogenic modification. A genetic change -randomly and not causally obtained- is retained simply if it is a benefit to the functioning of the organism -i.e. solely on the basis of appropriateness. It, and the summation of such genetic changes, therefore, do not actually imply "congruence", but some pertinent, (beneficial or at least non-destructive), correlation between domains. "Structural coupling" and "conservation of autopoiesis" are not determinate. They are not "specified or directed" by the environment either; they are bounded by it. Structural coupling is therefore a weaker and more abstract condition than they presume.)294

Between the living being and the environment there is a "necessary structural congruence", [but see my comment above], "(or the unity disappears)." But organisms must, (in the innate

292 ? ibid P.63

293 ? ibid Pps. 74-75

294 ? Cognition as a coordination of atomic primitives, (as argued in chapter 1), makes a great deal of sense in this context. The organization is not itself correlative to externality, but is an operative device working on ultimately indeterminate primitives.

phenomenology of biology), be considered as independently reactive to, rather than determinately, (i.e. informationally), guided by their environment. The conclusion is grounded in the structure of science itself:

"In the interactions between the living being and the environment within this structural congruence, the perturbations of the environment do not determine what happens to the living being; rather, it is the structure of the living being that determines what change occurs in it. This interaction is not instructive",295 (my emphasis), "for it does not determine what its effects are going to be. Therefore, we have used the expression 'to trigger' an effect. In this way we refer to the fact that the changes that result from the environment are brought about by the disturbing agent but determined by the structure of the disturbed system. The same holds true for the environment: the living being is a source of perturbations and not of instructions."296

"The key to understanding all this is indeed simple: as scientists, we can deal only with unities that are structurally determined. That is, we can deal only with systems in which all their changes are determined by their structure, whatever it may be, and in which those structural changes are a result of their own dynamics or triggered by their interactions."297

Organisms react! They react, moreover, in the operational closure of their current (physical) structure. The latter is determined by their "ontogeny", (i.e. on their summed history of structural change as individuals), which has modified the original phenotypic structure:

"This ongoing structural change occurs in the unity from moment to moment, either as a change triggered by interactions coming from the environment in which it exists or as a result of its internal dynamics. As regards its continuous interactions with the environment, the cell unity classifies them and sees them in accordance with its structure at every instant. That structure, in turn continuously changes because of its internal dynamics. The overall result is that the ontogenic transformation of a unity ceases only with its disintegration."298

Maturana goes on to define "second order" and "third order structural coupling" as the structural coupling of the multicellular organism with its environment, and the coupling of intraspecies' behavioral interaction, (e.g. linguistic behavior), with environment respectively. But these are always dependent upon the necessary conservation of the autopoiesis of the germ cell. The scope of the subsequent development, (the operational range), of the metacellular organism299 is determinate from its unicellular stage, and subject to its phenomenology. "The life of a 295 ? i.e. informational

296 ? ibid Pps. 63-64

297 ? ibid P.96

298 ? ibid P.74

multicellular individual as a unity goes on through the operation of its components, but it is not determined by their properties. Each one of these pluricellular individuals...results from the division and segregation of a lineage of cells that originate ... (from) a single cell or zygote. ...It is as simple as this: the logic of the constitution of each metacellular organism demands that it be part of a cycle in which there is a necessary unicellular stage"300. The conservation of the autopoiesis of that unicellular stage is the necessary boundary condition of the (independent and coincident) function of any organism, unicellular or multicellular.

"Living beings are not unique in their determination nor in their structural coupling. What is proper to them, however, is that structural determination and coupling in them take place within the framework of ongoing conservation of the autopoiesis that defines them, whether of the first or second order, and that everything in them is subordinate to that conservation. Thus, even the autopoiesis of the cells that make up a metacellular system is subordinate to its autopoiesis as a second-order autopoietic system. Therefore, every structural change occurs in a living being necessarily limited by the conservation of its autopoiesis; and those interactions that trigger in it structural changes compatible with that conservation are perturbations, whereas those that do not are destructive interactions. Ongoing structural change of living beings with conservation of their autopoiesis is occurring at every moment, continuously, in many ways at the same time. It is the throbbing of all life."301

Behavior, from the biochemical behavior of the amoeba to the nervous behavior of man, is simply an aspect of primary structural coupling. It is the correlation of sensory surfaces with motor surfaces: "...the sequence of movements of the amoeba is therefore produced through the maintenance of an internal correlation between the degree of change of its membrane and those protoplasmic changes we see as pseudopods. That is, a recurrent or invariable correlation is established between a perturbed or sensory surface of the organism and an area capable of producing movement (motor surface), which maintains unchanged a set of internal relations in the amoeba."302

"This basic architecture of the nervous system is universal and valid not only for the hydra, but also for higher vertebrates, including human beings. ... the basic organization of this immensely complicated human nervous system follows essentially the same logic as in the humble hydra ...the nervous tissue understood as a network of neurons has been separated like a compartment inside the animal, with nerves along which pass connections that come and go from the sensory surfaces and motor surfaces. The sole difference lies not in the fundamental organization of the network that generates sensorimotor correlations, but in the form in which this network is embodied through neurons and connections that vary from one animal

300 ? ibid Pps. 80-81

301 ? ibid Pps. 95-102, (my emphasis)

302 ? ibid Pps.147-148

species to the other. ... But we emphasize: ... this is the key mechanism whereby the nervous system expands the realm of interactions of an organism: it couples the sensory and motor surfaces through a network of neurons whose pattern can be quite varied. Once established, however, it permits many different realms of behavior in the phylogeny of metazoa. In fact, the nervous systems of varied species essentially differ only in the specific patterns of their interneuronal networks."303

Brain cells do not connect only to motor and receptor cells, however, most of them connect to other brain cells: "in humans, some 1011 (one hundred billion) interneurons interconnect some 106

(one million) motoneurons that activate a few thousand muscles, with some 107 (ten million) sensory cells304 distributed as receptor surfaces throughout the body. Between motor and sensory neurons lies the brain, like a gigantic mass of interneurons that interconnects them (at a ratio 10:100,000:1) in an ever-changing dynamic."305

The sensory surface includes, however, not only those cells that we see externally as receptors capable of being perturbed by the environment, "but also those cells capable of being perturbed by the organism itself, including the neuronal network."

"Thus the nervous system participates in the operation of a metacellular as a mechanism that maintains within certain limits the structural changes of the organism. This occurs through multiple circuits of neuronal activity structurally coupled to the medium. In this sense, the nervous system can be characterized as having operational closure", (my emphasis). "In other words, the nervous system's organization is a network of active components in which every change of relations of activity leads to further changes of relations of activity. Some of these relationships remain invariant through continuous perturbation both due to the nervous system's own dynamics and due to the interactions of the organism it integrates. In other words, the nervous system functions as a closed network of changes in relations of activity between its components."306

External perturbations only modulate the constant interplay of internal balances of sensorimotor correlations. "It is enough to contemplate this structure of the nervous system... to be convinced that the effect of projecting an image on the retina is not like an incoming telephone line. Rather, it is like a voice (perturbation) added to many voices during a hectic family discussion (relations of activity among all incoming convergent connections) in which the consensus of actions reached will not depend on what any particular member of the family says."307

303 ? ibid Pps.157-159

304 ? cf Appendix A

305 ? ibid p.159

306 ? ibid Pps.163,164

"a nervous system...as part of an organism, will have to function in it by contributing to its structural determination from moment to moment. This contribution will be due both to its very structure and to the fact that the result of its operation (e.g., language) forms part of the environment which, from instant to instant, will operate as a selector in the structural drift of the organism with conservation of adaptation. Living beings (with or without a nervous system), therefore, function always in their structural present. The past as a reference to interactions gone by and the future as a reference to interactions yet to come are valuable dimensions for us to communicate...however, they do not operate in the structural determinism of the organism at every moment. With or without a nervous system, all organisms (ourselves included) function as they function and are where they are at each instant, because of their structural coupling."308

Maturana presents a sufficient and scientifically necessary rationale for the whole of "living organisms" -to include their "behavior". It is convincing because of the purity and the correctness of his phenomenology as biology. At each step of evolution, on each fundamental aspect of the functioning of an "organism", on the reconciliation of the metacellular, (in all its functions), with the germ cell, these are the biologically definitive categories and principles proper to a "living being". Its "purity" lies in the fact that he never, (and never has to), step outside this phenomenology -this context- to complete his thesis. It is necessary and sufficient, -and legitimate, (in the legal sense),- to the whole of "living beings". It is, therefore, completely plausible.Nowhere does his mechanics involve "representation", however! Indeed, "representation" is inconsistent with the mechanics itself. He concludes as a necessary consequence of scientific principle that neither organisms, nor their brains, operate with representations of their surroundings. "Representation" is inconsistent with the necessary phenomenology of organisms -and extrinsic, (and inessential), to the "mechanism" of science. The principle of parsimony, (i.e. least cause), dictates his conclusion. Organisms are structurally closed systems, only "perturbed" by their environment, never "in knowledge" of it.

"The most popular and current view of the nervous system considers it an instrument whereby the organism gets information from the environment which it then uses to build a representation of the world that it uses to compute behavior adequate for its survival in the world. This view requires that the environment imprint in the nervous system the characteristics proper to it and that the nervous system use them to generate behavior, much the same as we use a map to plot a route. We know, however, that the nervous system as part of an organism operates with structural determination. Therefore, the structure of the environment cannot

307 ? ibid Pps. 161-163. Also consider Edelman’s comment on this same issue: “… To make matters even more complicated, neurons generally send branches of their axons out in diverging arbors that overlap with those of other neurons, and the same is true of processes called dendrites on recipient neurons …. To put it figuratively, if we ‘asked’ a neuron which input came from which other neuron contributing to the overlapping set of its dendritic connections, it could not ‘know’.” Edelman, 1992, p.27

308 ? ibid P.124, my emphasis

specify its changes, but can only trigger them. ...Our first tendency to describe what happens .." (is in) "... some form of the metaphor of 'getting information' from the environment represented 'within'. Our course of reasoning, however, has made it clear that to use this type of metaphor contradicts everything we know about living beings."309

His argument is not specifically against models in general, however, but, rather, against representative models, and in this I think it is conclusive.310 It leaves very little room for objection. It is consistent, convincing and in the mainstream of science. It leads, perplexingly, to a disastrous paradox: "We are faced with a formidable snag because it seems that the only alternative to a view of the nervous system as operating with representations is to deny the surrounding reality"! (This is the clearest statement of biology’s dilemma that I have seen, though I will argue against his particular resolution of it.)

"Indeed, if the nervous system does not operate -and cannot operate -with a representation of the surrounding world, what brings about the extraordinary functional effectiveness of man and animal and their enormous capacity to learn and manipulate the world? If we deny the objectivity of a knowable world, are we not in the chaos of total arbitrariness because everything is possible? This is like walking on the razor's edge. On one side there is a trap: the impossibility of understanding cognitive phenomena if we assume a world of objects that informs us because there is no mechanism that makes that 'information' possible", (my emphasis). On the other side, there is another trap: the chaos and arbitrariness of nonobjectivity, where everything seems possible."311

"In fact, on the one hand there is the trap of assuming that the nervous system operates with representations of the world. And it is a trap, because it blinds us to the possibility of realizing how the nervous system functions from moment to moment as a definite system with operational closure. ... On the other hand, there is the other trap: denying the surrounding environment on the assumption that the nervous system functions completely in a vacuum, where everything is valid and everything is possible. This is the other extreme: absolute cognitive solitude or solipsism. ... And it is a trap because it does not allow us to explain how there is a due proportion or commensurability between the operation of the organism and its world."312

309 ? ibid Pps.129-133, my emphasis310 I have proposed a very different, and plausible, alternative model in chapter 1. I

proposed that organisms do use models, but that those models are schematic; their "objects" schematic objects only, aspects of operationally closed process. The "objects" of that model are not "entities" in reality; they are optimizing loci of process itself.

I propose that models do, in fact, exist in the human brain, but they are schematic models. Their virtual "objects", (in no necessarily simple correlation with externality), are evolutionarily derived schematic artifacts of process like the "objects" of the training seminar of chapter 1. They effectively coordinate the sensory and motor faculties of the brain!

311 ? op.cit p.133312 ? ibid Pps. 133-134

Maturana and Varela have honed their "razor's edge" with the same care and meticulous skill with which, as biologists, they would undoubtedly hone a microtome. I suggest they are proposing that we stand, therefore, not on a razor's edge, but on a microtome's! That, as any biologist should surely know, is an invitation to suicide.313 They have created a full-blown antinomy. The usual method of dealing with antinomies is to examine the presuppositions.

Wait though, you must surely be thinking! Couldn't we just deny "mind" in its ordinary sense, then? Isn't this the simplest solution to the difficulty? Why not just abandon (organic) "cognition" entirely, and "experience" and "externality", (in our normal meanings of them), right along with it- and go back solely to parallel and congruent behavior itself -i.e. to parallel reactivity, predetermined by evolution? Why not just deal with the reactivity and the (reductionist) process of the brain as part of the world,314 accepting the arguments for the inadequacy and the inconsistency of organic cognition as a final reductio ad absurdum of "mental states" and deal only with organisms' (behavioral) function?

Maturana and Varela have, you might correctly continue, specified a phenomenology specific to organisms, but they have specified it within the context of an actual physical world. Couldn't we, therefore, just deny the "figment"315 of the mind, (the "consciousness", the "awareness" of the brain -or organism), as "folk psychology" and myth?316 Couldn't we consider "mind" as just a linguistic and behavioral phenomenon? Sure we could, and it is a necessary consequence of ordinary Naturalism. But then we are right back, (necessarily), in Maturana's317 dilemma, but invoked at a deeper level! For how then does even the behavioral, and especially the linguistic318 function, (our descriptive language), of (human) organisms, as behavior, come to be specifically, (i.e. informationally), relevant to the world? Is this not linguistic idealism?319 Maturana's whole argument -and Darwin's as well - is one of simple appropriateness. It is "survival" and "structural coupling", not "information". This Naturalist argument presumes that organisms' reactivity -third order coupling, (language), and behavior- determined from the beginning by evolution for the phenotype and operationally closed thereafter, is categorical320! 321 This, however, is the only plausible course left to ordinary322 Naturalism after Maturana, but it is a difficult one. It assumes that whatever evolution determines, (whatever "parallelism" or "congruency" or "adaptability" that evolution gets for an organism), is embodied in the genotype and subsequently in the phenotype. From that point on, the argument is necessarily entrapped in the operational closure of the

313 ? It is likely to result, depending on the angle of fall, in decapitation or, as seems to have happened here, in a severing of the corpus callosum. :-)314 ? as most current Naturalists, in fact, actually do315 ? cf Dennett, 1991316 ? cf P.S. Churchland, 1986, Dennett, 1991317 ? and Quine's and Kant's which are themselves the children of an ancient line of legitimate skepticism.318 ? for behavioral "knowledge"319 ? As I suggested earlier was also the case with Dennett’s thesis320 ? any two models are isomorphic321 ? This is an astounding conclusion and more than the principles, (and Occam's razor), will bear! At best it is petitio principii, (assuming what you have to prove), at worst it is magic!322 ? cf Chapter 4 for my distinction of "ordinary Naturalism" from "relativized Naturalism".

organism. That closed system must determine its reactivity, (its supposed "parallel reactivity"), forever after throughout its subsequent ontogenic history.

But if even the weather is not determinate from a fixed set of principles and starting point, then how are we to believe that evolution has embodied the complexity of day to day, week to week, or year to year physical reality in such a fixed beginning? What model does evolution, (as embodied in the genotype), itself have that it is trying to parallel? If a butterfly in Australia can cause a hurricane in Florida then how are we to believe that evolution has a model at all, much less that it can embody such in closed (behavioral or linguistic) principles and laws of reactivity for the phenotype.

The argument assumes that evolution launched a closed operational system, (the phenotype), out into the world. But evolution could not know what that phenotype must be functional with -i.e. evolution has no model itself! Evolution cannot predict the world -especially in its human-scale features. It cannot predict the weather, the pattern of rocks, foliage, water and heat -i.e. "the facts"- in an ecosystem, and, if not them, then it surely cannot predict the more complex reactivity of the organism's fellow biological creatures -pinching claws, a stalking tiger, or an infection by vibrio comma, (cholera). "Chaos theory", (for instance), argues that while cyclical processes, (e.g. the large-scale motions of the planets and stars), produce regular and predictable results, non-linear processes do not.

But physical process, (the ongoing world), especially at the human scale, is dynamic and non-linear. Moreover it is, by and large, not cyclical. It is, therefore, not predictable in a determinate model. To assume that such a correspondence to the physical world can be implemented throughout the lifespan of an organism in a fixed and determinate, and specifically a parallel operative model, (an informational model), is a difficult premise. (See specifically the arguments of Appendix A or Lakoff's arguments in the Lakoff/Edelman appendix). For the specifically biological world, the biological ecosystem, it is more than difficult. More plausible is that evolution works by the creation of dynamic and operative local -and not informational -functions, that are intimately and locally connected to changing process.

The creation of a multitude of these atomic functions that track, (i.e. trigger from), incremental change in the physical world is a more plausible evolutionary scenario than the representationist one. But this is exactly my first hypothesis: that evolution created local functions like this at the cellular level. The organization of these atomic processes then becomes the real problem for the "evolutionary engineer", and it is this organization which, I propose, was accomplished incrementally by the schematic model. Our (biological) "objects" are organizers, I argue, organizing loci of these atomic processes and not informational representations. The schematic object is an organization of atomic processes, which latter track we-know-not-what.

For how could even evolution know what that "what" might be? Evolution produces the operationally closed structural coupling of the phenotype, but that structural coupling must be specifically dynamic rather than informational. What evolution can deal with are such processes, not information. It can deal with processes that work on the local, tactical level.

The representationalist schema, (of ordinary Naturalism), is not plausible. No, that is not quite true, it is plausible inside of our own human cognitive model. It is plausible because it happens that way! My argument is that it happens that way because it is inside of our model!

To quote Dennett, (a surprising passage for me):

"it is not the point of our sensory systems that they should detect 'basic' or 'natural' properties of the environment, but just that they should serve our 'narcissistic' purposes in staying alive; nature doesn't build epistemic engines." Dennett, 1991, P.382, my emphasis.323

This is an antinomy. No, more accurately, it is a specific and pointed reductio ad absurdum of the (ordinary) Naturalist premise!324 What Bertrand Russell says of naive realism applies to ordinary Naturalism, its (natural) child:

"We all start from 'naive realism'. We think that grass is green, that stones are hard, and that snow is cold. But physics assures us that the greenness of grass, the hardness of stones, and the coldness of snow are not the greenness, hardness, and coldness that we know in our own experience, but something very different. The observer, when he seems to himself to be observing a stone, is really, if physics is to be believed, observing the effects of the stone upon himself. Thus science seems to be at war with itself: when it most means to be objective, it finds itself plunged into subjectivity against its will. Naive realism leads to physics, and physics, if true, shows that naive realism is false. Therefore naive realism, if true, is false; therefore it is false." "An Inquiry into Meaning and Truth", Bertrand Russell, Pp. 14-15

To paraphrase Russell, if we know, then we can't know. Therefore we do not know.

Maturana and Varela characterized the dilemma incorrectly, however. They specified a necessary choice between solipsism on the one hand, and representationalism/realism on the other, and this is not the case.

We needn't deny reality based on their arguments, just our specific knowledge of it! Nor need we deny "mind" either. It is the acceptance of an "Axiom of Externality", in its most abstract form, taken axiomatically, that is demanded here,325 and that is not denied by their arguments. It is the improper extension of that demand, and its confusion with the particulars of our specifically human organic process, (to include cognition), that generates the difficulty.

As realists we must grant the presumption of "externality" -the simple posit of an ontic existence solely. “Externality” is fundamental to sanity and to plausibility. The posit of our world, men and baseballs and trees and planets as necessary ontic entities, however, is not! Even our perceptual

323 ? I find this a very curious statement –coming from Dennett.324 ? but not of relativized Naturalism! cf Chapter 4

325 both here and in the foundations of physics

world is a part of our closed cognitive process. I have argued, (in chapter 1), that it is an operative, (and dynamic), artifact.

But, (you surely object once again), we cannot deny the "objects of our very experience" and their apparent relationality! I agree, it is these objects which provide the stability of our life experience and ground the very essence of sanity, (my thesis is not solipsism). In the next chapter, I will show why we need not.We all want our naive world to be real: trucks, men, planets and baseballs, and all our normal relations between them -i.e. all the things they do. It is a necessary component of "sanity", and distinguishes it from dreams, fantasies, and, baldly, insanity. If a rock hits me on the head, it will hurt!

But, contrarily, our best science says that our naive world is not real! What is real for science are atoms, forces, photons, quarks,... all embedded in some mathematically esoteric spatial context. For it, myself and the man in front of me are, in fact, biological pluralities, or, deeper still, atomic amalgams... down to the deepest levels of physical conception. Naturalism, (the scientifically extended326 form of our naive conception and the verity Maturana is loathe to lose), allows this heresy only because it says that our natural world is hierarchically,327 (and isomorphically), embedded in that primitive existence which science posits, and that those hierarchical entities, (our normal "objects"), act as units. It maintains that this reduction is specifically a hierarchical328 one which maintains all the spatial and material relationships down through each and all of the depths

326 ? to whatever level of sophistication!327 ? See Afterword: Lakoff and Edelman for a detailed discussion of hierarchy328 ? The reduction of scientific theories, (and theoretic reduction in general), is subject to a fundamental logical limitation under the classical, (pre-Cassirerian), concept. In the last chapter, (chapter 2), I exhibited Cassirer's arguments that the whole root of the classical formal concept is set-theoretical. Concepts, or concepts of "things", (to include, for instance, our ordinary objects), were reducible only in a set-theoretic sense, i.e. by abstraction, (intersection), of common properties. They are, therefore, subject to Russell's "theory of types". At the bottom level, and there must be a bottom level according to the theory of types, there are atomic primitives. Each of the levels above that must be hierarchically oriented, each containing the one above it, (i.e. the "things" of the next higher level are abstractions -intersections- of the ones below). This theory of types was the logically necessary result of the antinomies discovered in the roots of set theory. The most famous is, of course, Russell's paradox.

Cassirer's fundamental advance on the classical formal concept, "the mathematical concept of function" however, provides an escape. There is no "Cassirer's paradox" in the universal formation of concepts. There is no "concept of all concepts", because concepts are now constituted as an assemblage of (consistent) generative rules, not as a (set-theoretic) abstraction (intersection) of properties -which currently stands for the process of scientific reduction. There is clearly no "rule of all rules" as some rules obviously contravene others. At the level of my "concept of implicit definition", concepts are assemblages of "axioms", (i.e. fundamental and consistent generative rules), and the same situation obtains. But, just as is the well demonstrated case for mathematical axiom systems, it is possible to exchange an appropriate subset of theorems for the pre-existing axioms, (while still absolutely preserving the integrity -the interior relationality- of the mathematical subject), so is it possible to "cross-reduce" theories. We do not have one single preferred perspective.

of scale -hence their reality! Modern science has not confirmed, but rather has seriously questioned, that assertion. What are we to embed them in? At the bottom level of physics, "matter", "space", even "existence", in the sense in which naive realism uses them, are anomalous terms. Even "cardinality" as such -the "how many of it"- is dubious!329

Even ordinary Naturalism330 does not, therefore, maintain the integrity of our naive objects! But is its insistence on the maintenance of the hierarchical integrity of those objects a necessary, or even a plausible presupposition at this juncture in our intellectual history?

My hypothesis of the schematic object, contrarily, says that our naive world -to include its relationality, (its laws and happenings),-is more probably unhierarchically, (but rather transformationally), correspondent with absolute externality, whatever and however the latter may be. Ultimately it says that our naive world is in correspondence to "points" of atomic process,331

and not to "points" of ontology. It is a metaphor of response. It says that the further correspondence between those atomic processes themselves and ontology is completely indeterminate to us as biological and cognitive entities!

The Axiom of Externality

The acceptance of the raw existence332 of such a correlation, however, constitutes a necessary requirement for any sane or plausible argument -to include my own.*333 This is the assertion, the "Axiom of Externality" in its most abstract form, and constitutes the first of the two necessary, (apodictic), premises for realist reason.334 (The other is the "Axiom of Experience" which I will treat in the following chapter.)

The "realism" Maturana impeaches is, in fact, (ordinary) "Naturalism". Nor has he really made a case that solipsism is the only other alternative.335 While his case against representationalism does

This is the relativism of Cassirer's "symbolic forms". What remains is the "web" of relationality, the "invariants" of experience that must be preserved under all comprehensive perspectives. But that web, those invariants must be viewed, in Van Fraassen's term, in a "coordinate-free" sense, i.e. they must be viewed in their abstract relationality, not from any particular orientation. cf. Chapter 4 and Afterword: Lakoff / Edelman.

329 ? Cf Penrose on the twin-slit experiment, for instance330 i.e. scientific naturalism = "scientific realism"331 It is an optimizing organization of primitive, organic process -i.e. of primitive operational process.332 ? which assumes, therefore, both the axiom of existence and the reality of experience333 ? See Appendix B334 ? Is the "axiom of externality" the same as the "realistic imperative" of Hume? Is it an emotional imperative? It orients world-views.335 ? Theirs is a structured isolation. It does not support the implication that "everything is valid and everything is possible"!

destroy the claims of ordinary Naturalism,336 a realistic case is still possible -but it must be a theoretically mature one. Einstein's realism337 is more plausible. That brand of realism involves simply that "theory be organized around a [some] conceptual model of an observer-independent realm".338 My thesis takes this "some" in its most abstract form, as the (pure) limit of reason. This "realism" is certainly more credible in light of today's physics. Realism is more robust than Maturana assumes, and is capable of greater sophistication than a mere linear extension of the naive world-view. In Fine's words, it is an "attitude". In disagreement with Fine however, I believe it is a robust attitude.

Maturana came very close to the answer I propose. His "object" of cognition339 is an object of process: "cognition does not concern" [external] "objects, for cognition is effective action." He relapses, however, into the "objects" of the Naturalistic context in which he framed the problem:

"Thus, human cognition as effective action pertains to the biological domain, but it is always lived in a cultural tradition. The explanation of cognitive phenomena that we have presented in this book is based on the tradition of science and is valid insofar as it satisfies scientific criteria. It is singular within that tradition, however, in that it brings forth a basic conceptual change: cognition does not concern objects, for cognition is effective action...""At the same time, as a phenomenon of languaging in the network of social and linguistic coupling, the mind is not something that is within my brain. Consciousness and mind belong to the realm of social coupling. That is the locus of their dynamics....Language was never invented by anyone only to take in an outside world. Therefore, it cannot be used as a tool to reveal that world. Rather, it is by languaging that the act of knowing, in the behavioral coordination which is language, brings forth a world. ...We find ourselves in this co-ontogenic coupling, not as a preexisting reference nor in reference to an origin, but as an ongoing transformation in the becoming of the linguistic world that we build with other human beings", (metacellular organisms).340

But "language ... cannot be used as a tool to reveal [the] world." Hence, (accepting his own conclusion and applying it to himself all his “entites” at the final telling are "entities" solely of linguistic (and ontogenic) coupling, and, as such, his “entities” have themselves no absolute referent! He maintains that we are wrong in characterizing the actual world "in reference to an origin". Yet he does exactly that himself. He frames his primitives: structural coupling,

336 ? Since it assumes the premise of naturalism and ends in a contradiction, it is, in fact, a reductio ad absurdum.337 ? "It is existence and reality that one wishes to comprehend. ... When we strip the (this) statement of its mystical elements we mean that we are seeking for the simplest possible system of thought which will bind together the observed facts." (Einstein 1934, Pps. 112-113)338 ? cf Fine, 1986. p.97339 ? In fact, they do not actually allow an "object" of cognition, as the following citation shows. I am referring here to that aspect of brain process -the effective action- which corresponds to their object of linguistic coupling -which latter is the only "object" they will explicitly allow.340 ? op.cit Pps.234-244, my emphasis

metacellular coupling, intraspecies' coupling, ("third order coupling"), and linguistic coupling as interactions of "autopoietic [biological] unities"!

What "autopoietic unities"? And where? Where do these linguistic domains exist -and between what and whom? Where does his book exist? Does it, and, if so, how is it relevant to anything at all? What "history of evolution"? These linguistic terms supposedly do not "reveal the world"!

He is, in fact, committed to a Naturalist ground, and it contains real organisms, i.e. " autopoietic objects". His "object" is ambiguous however. On the one hand it is solely a product of linguistic coupling, (the object of language), but, on the other hand, (in his presupposition of objects/biological unities which are coupled), it is also the basis of his ontology. This is an explicit and fatal self-contradiction. Either the object, i.e. the organism, exists -providing the ground of this linguistic coupling, -or does not -in which case "linguistic coupling" is vacuous!

Putting the shoe on the other foot, does my thesis make our objects not real, then?341 Does it mean that there is no connection between them and the "externality" we must assume? The answer is an emphatic "No!" The connection is in the interface itself, ("structural coupling") and "experience". But the latter must be understood in terms of the former. We are not justified in assigning a particular ontic interpretation to "experience".342

In my next chapter I will "slice" this problem from another side, (citing Quine and Cassirer), and argue that "experience", as an ontic posit -and a cognitive primitive -while absolutely justified as such, can be legitimately described only as the most abstract conception of that which remains invariant under all possible (viable) interpretations, (and I will argue there is always more than one). But "invariants" are in themselves a very concrete logical and mathematical form: they stand, for instance, as the foundation of the Theory of Relativity. Our human cognitive world, and specifically our perceptual world: people and baseballs and the things they do, are real, but they are real in the most general interpretation of their relationality, (them and the things they do). This is not so strange a conception -it is implicit in the reductions of science already. But the latter's requirements of hierarchy and isomorphism are not inherent; they constitute the crux of the problem. It is those requirements which lead to the disastrous end of Maturana's noble and profound enterprise. Beneficial connection, pertinent connection between domains, (i.e. "structural coupling"), does not require "parallelism", it does not imply "congruence", it does not require "hierarchy".343 Virtual embodiment demonstrates another, non-hierarchical yet exhaustive possibility of compatibility, and it is this that I have argued in my first thesis.

///INSERT GRAPHIC???/////

341 ? I will make this case in greater detail in the next chapter.342 ? Naturalism's mistake is in trying to assign an ontic reference to our whole cognitive domain. As I have argued, we are justified in making only two primitive ontic, (metaphysical), assertions: "externality" and "experience". These are the minimal and the maximal legitimate ontic posits. See Chapter 4.343 ? Could there be a congruent correspondence, (though admittedly not apodictic), however? Sure, but would be "magic" of a high order- "and then a miracle occurs"! Dennett, 1991

Maturana's thesis of "structural coupling" is of profound importance. It is an epistemological principle of the highest significance.344 It is a necessary consequence of his Naturalist beginnings -and impeaches them! It precedes and supersedes even its biological origin in its relation to the fundamental problem of knowledge. Biology, therefore, must integrate into a new and larger frame, a new orientation of the whole context of our world and our reality. But the Copernican center of that frame must be structural coupling itself. It is "structural coupling" which must ground biology; not biology which must ground "structural coupling"!345

I propose to accept absolutely the consequences of "structural coupling": that the "object" of biological cognition is a function of brain process itself, and not an embodiment of its environment.346 But this must necessarily translate into a Copernican revolution in our own very world-view: if we are biological organisms, then the objects of our human world-view are objects of process, of response as well. They are "objects" of "effective action"!

Maturana and Varela's profound heuristic principle reduces their premise to absurdity -i.e. the metaphysical certitude of the ordinary Naturalist world-view from which they started. The naive-realistic world, (the represented "naturalist" world), can have no internal relevance to the organism, as organism. But this does not impeach the science, (evolution and biology), which is their ground -no more than did Einstein's Relativity impeach the physics which was his ground! The viable relationality, (the viable system of predictivity), of biology and evolution, (and of science generally), can be, (must be!), preserved, (as was the observed relationality of Ptolemean astronomy -times and angles and relative positions- in the Copernican system which replaced it), but it must be "reduced"!347

Are we to throw away the whole of our human enterprise then -to include its science? Of course not -that would be unthinkable! But the most profound and most radical advances in human thought, its "Copernican revolutions" and "SUPERB348 theories", have always, (by necessity), subsumed the viable parts of pre-existing knowledge. In the present case, the subsumption of the preponderance of naive realism and the preponderance of naturalist science stand as necessities. They work, after all, with a power and effectiveness which is awesome. My proposal does not suggest or imply that they be considered any less important. It subsumes the whole of those vistas, but it subsumes them in their viable relationality,349 and not in their specific ontic (metaphysical) reference! Their connection to externality is operational, and not referential. In their whole, they

344 ? It is, in fact, a biological and epistemological principle of relativity. This does not imply that it is a frivolous relativity, (i.e. solipsism), however, no more than did Einstein's Relativity imply a lawlessness in physics!345 ? It is not an unusual, (nor inconsistent), practice in mathematics to begin by constructing a new mathematical discipline from one set of premises, and then to start all over with what were originally derivative consequences as the new, (and more appropriate), primitives.346 ? Though this might still seem self-contradictory, please bear with me for a few more paragraphs. I will explain myself fully in the next chapter.347 ? Though my reasons for using this word are obvious, it is clearly inappropriate to my conception. "Property-preserving or distributive re-interpretation with conservation of relationality" would be more appropriate.348 ? cf Penrose349 ? i.e. their predictivity! I will clarify this point in my next chapter.

constitute a profoundly effective and complex algorithm of unparalleled significance whose link to externality is "structural coupling". The latter, however, is referentially indeterminate, (i.e. metaphysically so).

Science turns recursively back on itself in biology and finds that there is a limitation to knowledge itself. Structural coupling is the antinomy which forces the absolute relativization of all knowing -to include "biology" and "evolution" -and even "perception" - themselves. These are "creatures" of human knowledge, of cognition. They are organizers, not primitives.350 Our true primitive is "experience", (under the necessary premise of "externality"), not any particular interpretation -or organization- of it. My hypothesis implies, then, a relativization of epistemology precisely equivalent to Einstein's relativization of physics. This is what Cassirer concluded as well.351

An Answer to the New Dilemma:

At last I can give a preliminary answer, (which I will complete in the next chapter), to the disturbing question raised at the beginning of the chapter. How can I presume the naturalistic world -with its "evolution"- to prove a hypothesis which severely questions them?352 How can I use a (Darwinian) biological argument, (which presumes a simple correspondence between our cognitions and the real physical world), against that very simplicity -and embodiment- itself? If my thesis is true, then our ultimate external reality, (ontology), is not necessarily, (nor even probably), like the reality of our cognitive model!

The answer is that "evolution" is as much an organizing principle as is "causation". It, (and the objects it treats), is part of the (closed) model itself. It is not a necessary, (or proper!), metaphysical presumption, but is, in Kant's words, a “synthetic a priori” proposition. It is not a necessary part of reality; it is a necessary (plausible), part of our cognition of reality. As such, I can use it with perfect legitimacy within that closed domain. But I use it, (modifying but keeping the sense of Dennett's word), "heterophenomenologically", i.e. with a neutral ontic reference!

My epistemological and metaphysical position, therefore, corresponds very much to Kant's, and ultimately, to Cassirer's. It is neither idealism nor solipsism, but a genuine, (and realistic), ontic indeterminism.353 The term "indeterminism" refers to the impossibility of knowing the nature of

350 ? It is explicit in Maturana's argument, (as we have seen), that "structural coupling" and "the conservation of autopoesis", (and "congruence" itself), are specifically part of the closed, human (biological) cognitive process.351 ? cf chapter 4352 ? This is also, obviously, a reiteration of Maturana's "razor's edge".

that ontic reality independent of our cognition. It does not, however, assert a doubt as to, but rather affirms, its existence.

"Matter is substantia phaenomenon. Whatever is intrinsic to it I seek in all parts of the space that it occupies and in all effects that it exerts, which, after all, can never be anything but phenomena of the outer sense. Thus I have nothing absolute but merely something comparatively internal which, in its turn consists only of external relationships. But what appears to the mere understanding as the absolute essence of matter is again simply a fancy, for matter is never an object of pure understanding; but the transcendental object that may be the ground of this appearance called matter is a bare Something, whose nature we should never be able to understand even though someone could tell us about it. ... The observation and analysis of phenomena press toward a knowledge of the secrets of nature and there is no knowing how far they may penetrate in time. But for all that we shall never succeed in answering those transcendental questions that reach out beyond nature, though all nature were to be revealed to our gaze."354

I will, (in chapter 5), however, make the limiting step that Kant did not. I will posit our cognitive interface, (whatever that may ontically be!), as itself a metaphysical entity. It is a part of the minimal (realistic) ontic posit. It is the synthesis of "externality" and "experience".355

Knowledge is cognitively closed. It is an organizational system that works. It is Quine's "body of statements and beliefs", (see the opening citation of Chapter 4), constrained only by its "boundary conditions", ("experience"). But it exists always within the human (biological) cognitive frame. It can never achieve a "God's eye view"!

"It is by languaging that the act of knowing, in the behavioral coordination which is language, brings forth a world. ...We find ourselves in this co-ontogenic coupling, not as a preexisting reference nor in reference to an origin, but as an ongoing transformation in the becoming of the linguistic world that we build with other human beings."356

In the next chapter I will explore the other axiom of reason, the Axiom of Experience, and conclude my answer to the epistemological problem I have raised. Quine and Cassirer show the way. This will then allow a brief and succinct statement of my third and final thesis in Chapter 5 which resolves the mind-brain dilemma we chose as our target.

354 ? Kant, "Critique of Pure Reason", 2nd edition, 333, translated by Woglom and Hendel, and cited in Cassirer: "The Problem of Knowledge", 1950, Pps. 101-102 I prefer this to Smith's rendering.355 ? cf Chapter 5356 ? op*.cit Pps.234-244, my emphasis

Preface to Chapter 4

Because we have reached a crucial point, and before going further, I would like to recap our current status -i.e. to go back and "touch home". I have presented a plausible and, I believe, a compelling resolution of the mind-body problem, but I have presented it within a context of ordinary Naturalism. But Naturalism, I have argued, is thereby itself, (by virtue of my answer), problematic.

How, to say it once again, can I maintain the legitimacy of my thesis when it seemingly questions its very premises? Cassirer, in his "Philosophy of Symbolic Forms", supplies the grounds for a solution: his thesis of scientific epistemological relativism. He argued that we retain our knowledge, our science, not as reference to an ultimate metaphysical reality, but as relativistic organizations of phenomena. Under this interpretation, the (Naturalistic) primitives of my thesis do not then require what would otherwise be a further, (and self-contradictory), metaphysical presumption of reference -i.e. they are taken as organizational but not as metaphysical primitives.

Cassirer argues, moreover, that there are alternative and equipotent organizations possible even within "nature", (i.e. science), itself.357 Just as in the field of mathematics there are generally differing subsets of axioms which can generate the relationality of a given subject, similarly Cassirer maintains that there is a plurality of alternative and equipotent "Symbolic Forms" which can generate the relationality of experience. Naturalism,358 (to include my scientific thesis of mind-brain which is framed within it), is just one such relative, (but legitimate), form. What is truly absolute, however, are the "invariants" of experience! Underlying the whole problem is the issue of "experience" itself. Let me therefore begin with the latter.

357 Think of the “training seminar” of Chapter 1.358 as embodied in mathematical physics

Chapter 4: Cognition and Experience: Quine and Cassirer(The Epistemological Problem: What do we know?)

Let us begin with a brief but brilliant quote from Quine:

"The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience. A conflict with experience at the periphery occasions readjustments in the interior of the field. Truth values have to be redistributed over some of our statements. Reevaluation of some statements entails reevaluation of others, because of their logical interconnections- the logical laws being in turn simply certain further statements of the system, certain further elements of the field.

Having reevaluated one statement we must reevaluate some others, which may be statements logically connected with the first or may be the statements of logical connections themselves. But the total field is so underdetermined by its boundary conditions, experience, that there is much latitude of choice as to what statements to reevaluate in the light of any single contrary experience. No particular experiences are linked with any particular statements in the interior of the field, except indirectly through considerations of equilibrium affecting the field as a whole....... Furthermore it becomes folly to see a boundary between synthetic statements.. and analytic statements...Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system... Conversely.. no statement is immune to revision.. even the logical law of the excluded middle... and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or Darwin Aristotle?"359

"Experience"! I have argued it as an axiom of sanity, and a minimal realist assumption. But what is it and what does it mean? Is it the same as "sensuous impressions"? Does the posit of absolute experience demand an immediate further commitment to reference? In this chapter I will examine these questions in the light of Quine's and Cassirer's ideas and conclude that the answer to each is "no". I will propose an answer of rigorous and scientific epistemological relativism, (an extension of Cassirer's), which preserves both the phenomena and the validity of the whole dialogue of Naturalism, (including, therefore, that of my first two theses), as organization. It will preserve them without a commitment to metaphysical reference however. "Experience", I will argue, is exactly that which remains (relativistically) invariant under all consistent and comprehensive worldviews. Experience is the phenomena we must preserve and account for, but it is not the specific organization by which we do so. The primitives of a given organization are not legitimized, therefore, on the basis of reference, but on a (relativistic) basis of empirical adequacy.

359 ? Quine, 1953, pps.42-43

In the previous chapter, I began a discussion of cognitive closure and asserted an "Axiom of Externality". In this chapter I will continue with the issue of closure and confirm the other necessary, (apodictic), prerequisite of cognition, i.e. the "Axiom of Experience". Quine's epigram illuminates both. It validates an absolute and ineradicable multiplicity of interpretations for experiment and experience.

To start, let me propose a fantasy, which I think, clarifies the relationship between knowledge, cognition generally, and "experience". It will suggest a viable working definition of the latter.

Please join me in a fantasy:

The remote and newly discovered atoll of Petrolia, deep in the south pacific islands, (and never before touched by modern civilization), was visited by a geological survey party. It was found to lie above enormous undersea oil reserves. Its king and high priest, a primitive but highly intelligent man, asked to see our "magic".360 Seeking to humor him, (and, I am ashamed to tell, selfishly induce him to assign drilling rights to an American company at a ridiculously low price), he was given a "red carpet" tour of the Supercollider Accelerator, our greatest scientific marvel.361

The king was mightily impressed. He saw "magical worms", (traces on oscilloscopes), "dancing arrows", (pointers on analog gauges), and tiny "animal tracks", (particle tracks under a microscope), in this "cavern of the gods". He was convinced that the whim of our gods provided the "magic", (the "physical laws"), of his experience there, as it, (they), seemed quite different from his own! He subsequently engaged in a long and heated debate with one of the technicians over the significance of it all, ending, sad to say, with his casting a set of boar's knuckles and a shrunken head, (hidden in a bag under his robe), onto the cable-strewn floor with disastrous consequences!

Though whimsical, this fable helps to clarify the purest, (weakest), and the minimum, (necessary), assumption of "experience". There are clearly aspects of the situation that the king may have considered significant, (i.e. explanatory), that the scientist did not, (and conversely). The color or shape of an instrument, or the way the technician cleaned his glasses before initiating the experiment, for instance, are things that the king might have considered as ritual, (or physical), necessities, essential to the result. Even the number of floors of the facility, the time of day, or the route by which he entered might be relevant. The technician, of course, considered the king's multicolored ritual headdress, and his pouch of magic bones totally irrelevant, (the king was doing his best to be of help).

What I will call the "abstract frame" of the experiment he witnessed, however, was the same for the king as for the scientist conducting it. The abstract frame, (the total data and the "boundary condition"), for both the scientist and for the King of Petrolia was identical with the abstract, (from

360 ? He was awed when watching reruns of "Gilligan's Island" on the exploratory party's television.

361 ? cf heading above!

interpretation),362 of the whole of the actual experiment itself, (i.e. the whole of the experimental situation).363

The "abstract frame" must include the "background situation" however, i.e. it must include all the details -to include the observers! We do not know, a priori, which of these or what of these is relevant. This is one reason why experiments must the reproducible, (other than the issues of personal integrity or error). It is to eliminate unique factors deriving from the particular experimental context364 and to isolate the essentials through a multiplicitous duplication, hopefully random regarding what is (unknowably) extraneous. We are never on certain ground in that process however. We are never sure that our historically dictated -and contextually limited- design of an experiment does not implicitly incorporate such factors, or that there are not broader, (or different), frames, isolating, (or incorporating), other factors as incidental and irrelevant, (or pertinent and important), in which it could be implemented.365 Following Quine, we are in a process of dynamic reorientation only bounded by the abstract frame! Any theoretical description really compatible with the overall experimental situation366, however, is clearly a legitimate, (i.e. logical), interpretation in Quine's sense!

Consider: was the King of Petrolia's interpretation of the data of the experiment into his theoretical scheme, (worldview), patently false? Not necessarily, according to Quine. Was the scientist's translation into "laws of physics", "particles of matter” -or as an expression of the "primitive building blocks of reality" inherently, (i.e. logically), better? Also not necessarily! Each could use the data to integrate, reinforce or modify his theoretical basis -his world-view.367

362 ? alternatively, the experiential invariant363 ? "Experiment" is clearly an extension, albeit a refined and defined one, of "experience" itself.364 ? e.g. a magnetic field from the coffee-maker, a power surge from the factory down the block, the crumb from an assistant's lunch contaminating a culture365 ? The lack of free ferrous iron in ordinary differential bacteriology plates when looking for Legionnaire's Disease was an example of a too limited context and was the reason for its long mystery.366 ? including one which might dissolve -i.e. redistribute- but exhaustively account for- the apparent relationality of our primitives. Virtual systems clearly suggest a new logical possibility.367 ? Even the cumulative body of scientific experiment can be accounted for by the King. Given an unending stream of counterexamples, he can, via Quine, incrementally account for each. The presumption that this cumulative body rules out any other consistent world-view, that eventually he will be backed into a contradiction is not justified. This is not to say that any consistent theory is just as good as any other consistent theory. The king's theory, spirits and witchcraft, let us say, while it may very well be consistent and capable of accounting for any given fact, clearly falls far short in many aspects, perhaps the most important of which is predictability. The scientist will make strong and definite projections into the future which, by and large, will be clearly and precisely confirmed. He will be able to predict wide ranges of phenomena correctly and efficiently. There are other criteria of good theories as well. Roger Penrose, in his "Emperor's New Mind" has outlined a reasonable standard very concisely. (See Appendix D) The issue, which I will postpone for a little, is whether there cannot be, under the thesis of epistemological relativism which I will assert, multiple, equipotent and comprehensive

The fable, (in concert with Quine I maintain), helps us to see that "experience" as such is not, (a priori or a posteriori), identifiable with any of its organizations or orientations. Rather, it must be identified with the invariant relationality -i.e. with that which remains fixed- under all global, comprehensive and consistent orientations. "Experience", (TENATIVE WORKING DEFINITION), is that for which both the king and the technician must account in some manner!368

It is not itself an orientation, however. It is, rather, that ("thing") which must remain fixed, and I argue that it is a primitive of reason. Scientific experiment extends, (generates), experience and thereby bounds (and shapes) the scope of such consistent theories. It adds new invariant relationality to the abstract frame, (and the history of abstract frames). Following Quine however, it never determines them.

The Epistemological Problem:At the conclusion of Chapter 2, I asserted the definition: The mind is the "bio-logical", (i.e.

materially reduced), "concept" of the brain. (Alternatively, mind is the rule of the brain.) This scientific conclusion, (and the schematic model), of my first two chapters, however, raises profound philosophical and epistemological difficulties, seemingly contradicting itself. It raises questions, moreover, which offend the very foundations of our rational sensibilities. This, however, is not so unusual a circumstance but has always been the case, historically, at the major turning points of science.2 Deep progress has always necessitated radical, (and often distasteful), reorientations, (rather than mere polishings), of our fundamental worldview -often with the loss of cherished convictions. Most recently, this is seen very clearly at the invocations of Relativity and Quantum Mechanics in modern physics which, incidentally, raise much the same sorts of questions as does my thesis, i.e. "realism vs. empiricism/algorithmic" questions. I urge that the problems raised by my thesis are not inherently more difficult -or of a radically new and different type- than have been raised, (and answered), before in the cause of science.1 The real issue is productivity -to whose ultimate judgement I hereby submit my thesis. It is to legitimize and justify my conclusion,

"SUPERB", (using Penrose's classification), theories of reality. The proven equivalence, for example, between Heisenberg's and Schroedinger's (widely divergent) theories of quantum mechanics seems to imply that this may be the case. 368 ? This identifies, I propose, a viable and legitimate -and theory independent- working

definition of experience.1 1 Though admittedly painful, how are the epistemological implications of my thesis so much more difficult than those of modern physics, for instance? At the scale of the very small and at the scale of the very large, physics says that our physical world is profoundly strange and, at the small scale at least, that the picture of science is essentially algorithmic. My thesis proposes that our human scale world is very much the same -but that it is itself a biological and organic algorithm. It is a "tactile" algorithm wherein the "data" we receive and the instrument we manipulate to control it are one and the same. (See Chapter 1). Its elements, however, are purely and abstractly logical, (alternatively "operational"), elements! This is a very different and radical way to look at our "objects", (to include perceptual objects), to be sure. It is, I believe, however, far more compatible with the outlook of modern physics than is ordinary Naturalism. I maintain that our "tactile", "spatial", "extensive" et al. objects are logical, (alternatively "operational"), rather than representative. (cf. conclusion to Chapter 2) But the "logical" here is a (Kantian) "constitutive logic" rather than an "ordinary logic". I will argue a necessary detachment of knowledge from reference -a necessary relinquishment of our ordinary assumption of the independence of our (cognitive) "instrument" from what it measures. This does not require a denial of reality, however, but of our absolute knowledge of reality. But physical science has already reached this conclusion, hasn't it?

however, that I am forced to philosophy and a study of the metaphysical and epistemological presumptions of science -and there are such.

There are really two problems involved with the mind-brain problem. There is a scientific and empirical one, and there is a philosophical and metaphysical one. The combination of my first two theses solves the scientific problem, and my third thesis will explicate the metaphysical problem. This chapter will resolve the apparent paradox created by the first two hypotheses, i.e. the epistemological problem.

I shall now propose a specific answer to the problems which I have raised. This is not the only answer possible. I might as easily have adopted the empiricist, "anti-realist" stance common amongst physicists, for instance. My philosophic answer has something in common with that stance, but I think it is a positive advance on it, as it leads, (in Chapter 5), to a plausible and pointed answer to the question of the substance of mind. Let me emphasize, however, that my real and central claim remains the scientific one, i.e. the result of the combination of my first two theses; my philosophic answer is solely its rationale.

If my scientific conclusion is true, (and I believe the concordance of my first two theses, amongst numerous other reasons, strongly suggests it is), then there seems to be an inherent paradox in knowledge itself, -and my (Naturalist) premises! If both our perceptual and intellectual objects are solely artifacts of biological coordination, then on what ground can knowledge, (and my own argument), stand? If the very language, (to include the very "biological coordination" and "evolution" of my argument), in which I describe the problem, (being part of that self-same human reality), is only internally organizational and not referential, then what is it that am I describing. How can I even discuss the problem itself? Doesn't my theory actually eat itself? How, then, could there be science at all? Notwithstanding the apparent paradox, (which is not unique to my thesis1 and to which I will here propose a solution), I maintain that mine is a very strong and a very pure Naturalist argument and that its conclusion, as such, is valid.

Chapters 1 & 2 might be considered as a constructive reductio ad absurdum of the Naturalist premise. (Chapter 3 is a direct argument to the same effect, building on Kant and Maturana.) Less kindly, they might be considered as constituting a "straw man". Combined, however, they are much more powerful than that as they actually do resolve the whole of the Naturalist dilemma, (other than the epistemological one I just raised), and explicate the actual mind-brain problem in absolutely legitimate, (and empirically promising), Naturalist terms. Clearly, there might be something wrong with the Naturalist program, but need it be fatal?

My argument turns now then, not to argue against the whole sense of Naturalism, but against the part of it I believe is flawed. I base those arguments in an extension of Kant's,2 and,

1 1 This problem is inherent in pretty much the same terms in the whole of Kantian and Neo-Kantian philosophy of science, and in the philosophical dilemmas of modern physics as well. I urge that my solution, in a form very close to that offered by Cassirer, fits with the whole of modern science in a way that none other does.

2 2 Kant's work was concerned primarily with the problem of cognition and therefore has a special relevance here. "This is an advantage no other science", [than epistemology], "has or can have, because there is none so fully isolated and independent of others and so exclusively concerned with the faculty of cognition pure and simple." Prolegomena, P.131

ultimately, of Cassirer's Neo-Kantian position, i.e. his "Theory of Symbolic Forms". The thrust is to split Naturalism from its over-strong metaphysical presumptions.Cassirer Revisited:

My prior arguments do not, however, reduce the system of Naturalist organization, (i.e. its predictive schema), to absurdity, (nor, therefore, the corresponding organizational, i.e. Naturalist, validity of my own first two theses which are framed within it), but only its claim of absolute, (i.e. metaphysical), reference.1 Nor do they question the profound effectiveness of Naturalist science.2

Cassirer suggests a way to preserve that overwhelmingly successful relationality, (i.e. the predictive efficacy), of Naturalism in a relativized sense, not as reference, but as organization, i.e. his thesis of rigorous and scientific epistemological relativism.3 He proposes Naturalism, (and materialism),4 as just one (among several) of the possible -and equipotent- "Symbolic Forms" comprehensively organizing experience. It is only experience itself,369 (the phenomena), that is preserved as a known metaphysical absolute and to which (relativized) reference can be made. "Experience", (Naturalist connotations notwithstanding), must not be confused and identified with its characterization under any particular one of the possible symbolic forms however.

It is the confusion of a particular "frame of reference", i.e. form, (and the assumption that there is only one comprehensive frame possible2), with the invariant relationality of experience in the abstract, (i.e. under all consistent frames), that is the heart of the issue. It results in a confusion of a specific organization (of experience) with the experience itself,3 which is organized. It results in an (improper) assignment of (unique) metaphysical reference rather than a (legitimate) judgement of empirical, (i.e. experiential), adequacy for the primitives of the theory. Cassirer's reformulation of the formal logical concept allows a new logical possibility and an escape from the dilemma.

Just as Einstein relativized measurement and disembodied the ether, so did Cassirer argue for a relativization of knowledge, and a disembodiment of direct reference. But Cassirer's is not a

1 1 again, at whatever level of sophistication the latter is postulated

2 2 The Naturalist organization can be taken within contemporary anti-realism, (i.e. anti "scientific-realism" -the position that scientific theories do not directly describe ultimate, metaphysical reality). I am making a distinction between naturalist organization and naturalist metaphysics. Cassirer I believe, like Van Fraassen, is essentially an antirealist. This is not so surprising, given the fact that they both have Kantian roots, (cf., for instance, Van fraassen's "Laws and Symmetry".) I will most definitely not argue in favor of Naturalism, (i.e. metaphysical naturalism ==scientific realism), but will argue for the (relative and equipotent) naturalist organization. I will argue, therefore, for the structure, but not the reference of that organization.

3 3 Cassirer's is clearly a mathematical perspective, with its roots in modern algebra.

4 4 as embodied in mathematical physics

369 ? Experience is not necessarily, therefore, the same as its Naturalist interpretation, (organization), as "sense impressions". Nor, under my thesis, does experience refer to externality. It is an expression of process.

2 2 i.e. Naturalism

3 3 to include scientific experiment as an extension of ordinary experience

frivolous, laissez-faire relativism, (nor is it solipsism); it is an explicit and technical epistemological relativity rigorously grounded in the phenomenology of science.4

What, exactly, is the length of a rod to a physicist? It depends on the measurements, the frames of reference and the (absolute) equations of the theory of relativity relating them. What is the relevance of a theory, (including a scientific one)? It depends on the experience, the "form", (e.g. physics/Naturalist science), and the (absolute/invariant) relations, ("equations" -i.e. the web of implication), which must be preserved in it. What is constant, under all frames, are the invariants, (in a mathematical sense), which must be preserved in them, i.e. "experience". I have argued a working (and non-referential) definition of "experience" as that which must be maintained under all comprehensive worldviews.1

But what exactly could a relativized substance be then? What could Naturalism's material be under such a conception? It would be an implicitly defined term, (alternatively "symbol"), under a particular interpretation -i.e. it would itself be an "object" implicitly defined by the "generating relations" of the science which specifies it. Even materialism need not, therefore, necessarily carry a metaphysical commitment. It is an organization of experience using the (implicitly defined) terms of "substance".Cassirer's Theory of Symbolic Forms:

Cassirer suggests a new way to look at the relation between theory and experience. He proposes a rigorous epistemological relativism innate in the phenomenology of modern science.

"Mathematicians and physicists were first to gain a clear awareness of this [the] symbolic character of their basic implements. The new ideal of knowledge, to which this whole development points, was brilliantly formulated by Heinrich Hertz in the introduction to his 'Principles of Mechanics'. He declares that the most pressing and important function of our natural science is [simply] to enable us to foresee future experience"1

It is the method by which it derives the future from the past which is significant, however. We make "inner fictions or symbols" of outward objects, and these symbols are "so constituted that the necessary logical consequences, [my emphasis], of the images are always images of the necessary natural consequences of the imaged objects".2 But this analysis -and "image"- must be interpreted carefully:

"...[though] still couched in the language of the copy theory of knowledge -... the concept of the 'image' [itself] had undergone an inner change. In place of the vague demand for a similarity of content between image and thing, we now find expressed

4 4 Why is Einstein not saying that any measurements, (at all!), are valid? Why is Einstein's itself not a laissez-faire physical relativism? It is because there is a rigid structure at the core of his assertion -i.e. the specific, (and precise), invariant equations of relativity. It is the rigid and invariant "equations", (alternatively "the topology"), of experience that structure valid theories. These "equations", this "topology", must be retained as invariant(s) under all viable theories. This is why neither mine, nor Cassirer's, is an irenic relativism.

1 1 Though this is clearly somewhat circular, it is perfectly consistent with my assertion that "experience" is, in fact, an epistemic primitive.

1 1 Cassirer, 1953, p. 75

2 2 ibid, p.75

a highly complex logical relation, [my emphasis], a general intellectual condition, which the basic concepts of physical knowledge must satisfy."3

Its value lies "not in the reflection of a given existence, but in what it accomplishes as an instrument of knowledge,"1 [my emphasis], "in a unity of phenomena, which the phenomena must produce out of themselves." Hertz formulated the distinction very succinctly:

"The images of which we are speaking are our ideas of things; they have with things the one essential agreement which lies in the fulfillment of the stated requirement, [of successful consequences], but further agreement with things is not necessary to their purpose. Actually we do not know and have no means of finding out whether our ideas of things accord with them in any other respect than in this one fundamental relation."2

A system of physical concepts must reflect the relations between objective things and their mutual dependency, but, Cassirer argues, this is only possible "in so far as these concepts pertain from the very outset to a definite, homogeneous intellectual orientation",3 [my emphasis]. It is only within a distinct logical framework that these "images" are significant at all.4 The object cannot be regarded as a "naked thing in itself", independent of the essential categories, (and framework), of natural science: "for only within these categories which are required to constitute its form can it be described at all."

This change of perspective, (a genuine "Copernican Revolution" in Kant's sense), necessitates and validates Cassirer's conclusion of the innate symmetry and a relativity of interpretations for phenomena. "With this critical insight ... science renounces its aspiration and its claim to an 'immediate' grasp and communication of reality."1

It realizes that the only objectivization of which it is capable is, and must remain, mediation, [my emphasis]. And in this insight, another highly significant [critical]2

idealistic consequence is implicit. If the object of knowledge can be defined only

3 3 ibid

1 1 ibid

2 2 H. Hertz, "Die Prinzipien der Mechanik", p.1 ff, my emphasis

3 3 Cassirer, op cit p.76

4 4 Please note the similarity of this situation, as formulated by Hertz and Cassirer, with that I laid out in Chapter one for the training seminar. The objects, ("images"), in a very real sense, are a function of the calculus. Insofar as they are justified, it is on the conjoint basis of utility.

1 1 ibid

2 2 Everywhere, where Cassirer uses "idealism", it must be understood as "critical idealism" in the sense that Kant used it. This is very different from ordinary idealism, and, as I discussed in Chapter 3, is a real misnomer. I have suggested "ontic indeterminism" as a more modern alternative, and one I think both Kant and Cassirer would have been happy with. Also compare the "mere X", (below), with my discussion in Chapter 3.

through the medium of a particular logical and conceptual structure, we are forced to conclude that a variety of media, [my emphasis], will correspond to various structures of the object, to various meanings for 'objective' relations.3

This is the assertion of symmetry and the foundation for his thesis of "Symbolic Forms".Even in 'nature',4 [my emphasis], the physical object will not coincide absolutely with the chemical object, nor the chemical with the biological -because physical, chemical, biological knowledge frame their questions each from its own particular standpoint and, in accordance with this standpoint, subject the phenomena to a special interpretation and formation.5 It might also seem that this consequence in the development of [critical] idealistic thought had conclusively frustrated the expectation in which it began. The end of this development seems to negate its beginning -the unity of being, for which it strove, threatens once more to disintegrate into a mere diversity of existing things. The One Being, to which thought holds fast and which it seems unable to relinquish without destroying its own form, eludes cognition.6

It is the phenomena, (experience), not reference, however, that is the fulcrum of, (and reunifies), this relativity of perspectives. The forms do not refer to (metaphysical) reality, (their objects are not images of reality), they organize experience. Metaphysical reality becomes "a mere X"!1 "The more its metaphysical unity as a 'thing in itself' is asserted, the more it evades all possibility of knowledge, until at last it is relegated entirely to the sphere of the unknowable and becomes a2

mere 'X'", [my emphasis].3 It is the realm of phenomena, "the true sphere of the knowable with its enduring multiplicity, finiteness and relativity", on which we stand. It is the (multiplicitous and relativized) organization of phenomena, not reference to a metaphysical origin, which lies at the basis of knowledge.

3 3 Cassirer, 1954, p.76

4 4 i.e., "science" as opposed to the "cultural forms" -see discussion later.

5 5 But even within Cassirer's primary "natural forms" -in physics, for instance, I argue -beyond Cassirer- that the exact parallel obtains. There are arguably alternative Hertzian formulations of the problem. Alternative objects and alternative calculi are possible. Fine suggests that Relativity and Quantum Mechanics may represent such alternatives, and certainly Schroedinger's and Heisenberg's conceptions of quantum theory illustrate the plausibility.

6 6 ibid

1 1 compare this with the discussion of Chapter 3

2 2 (Kantian)

3 3 ibid

"And to this rigid metaphysical absolute is juxtaposed the realm of phenomena, the true sphere of the knowable4 with its enduring multiplicity, finiteness and relativity.5

But this reorientation does not destroy the either the unity or the coherence of knowledge. "But upon closer scrutiny the fundamental postulate of unity is not discredited by this irreducible diversity, [my emphasis], of the methods and objects of knowledge; it merely assumes a new form. True, the unity of knowledge can no longer be made certain and secure by referring knowledge in all its forms to a 'simple' common object which is related to all these forms as the transcendent prototype to the empirical copies." [my emphasis]1

(This latter demand is, of course, the rationale of the Naturalist claim of reference.)

But instead, a new task arises: to gather the various branches of science with their diverse methodologies - with all their recognized specificity and independence - into one system, whose separate parts precisely through their necessary diversity will complement and further one another. This postulate of a purely functional unity replaces the postulate of a unity of substance and origin, which lay at the core of the ancient concept of being."2

Cassirer conceives his "symbolic forms" functionally, (and serially), i.e. in terms of the "mathematical concept of function".

"And this creates a new task for the philosophical critique of knowledge. It must follow the special sciences and survey them as a whole. It must ask whether the intellectual symbols by means of which the specialized disciplines reflect on and describe reality exist merely side by side or whether they are not diverse manifestations of the same basic human function. And if the latter hypothesis should be confirmed, a philosophical critique must formulate the universal conditions of this function and define the principle underlying it.3

Instead of dogmatic metaphysics, "which seeks absolute unity in a substance to which all the particulars of existence are reducible", he seeks after "a rule governing the concrete diversity of the functions of cognition, a rule which, without negating and destroying them, will gather them into a unity of deed, the unity of a self-contained human endeavor."4 [my emphasis]5

4 4 see Chapter 3

5 5 ibid

1 1 ibid

2 2 ibid

3 3 ibid p.77, my emphasis

4 4 ibid

Perhaps the most succinct overall statement of Cassirer's thesis is found in his "Einstein's Theory of Relativity".1 Each of the perspectives of scientific knowledge: physics, chemistry, biology, ... (the "cognitive forms"), - and ultimately myth, religion and art, ... (the "cultural forms"),2 are taken as alternative and equipotent (organizational) perspectives on the phenomena.

"Each of the original directions of knowledge, each interpretation, which it makes of phenomena to combine them into the unity of a theoretical connection or into a definite unity of meaning, involves a special understanding and formulation of the concept of reality."3

Ordinary Naturalism confuses a particular organization, (mathematical physics), with the phenomena which are organized. That is the basis of its assertion of reference -and "scientific realism"4. "The "objects", (the organizational primitives -i.e. "images"), of one particular form are assumed, (incorrectly), to reference ontology -to relate to "an ultimate metaphysical unity".

"Where there exist such diversities in fundamental direction of consideration, the results of consideration cannot be directly compared and measured with each other. The naive realism of the ordinary view of the world, like the realism of dogmatic metaphysics, falls into this error, ever again. It separates out of the totality of possible concepts of reality a single one and sets it up as a norm and pattern for all the others. Thus certain necessary formal points of view, from which we seek to judge and understand the world of phenomena, are made into things, into absolute beings.[my emphasis]"1 2

What these "formal points of view" do, instead, is organize phenomena. What is consistent under all forms, however, are the phenomena themselves. Naturalism confuses a particular "frame of reference", i.e. form, (and assumes that there is only one comprehensive frame possible3), with the invariant relationality of experience in the abstract, (i.e. under all consistent frames)4 It confuses a specific organization, (and a specific characterization), of experience with the experience itself5

which is organized. It results, (and I repeat myself), in an (improper) assignment of (unique) metaphysical reference rather than a (legitimate) judgement of empirical, (i.e. experiential), adequacy for the primitives of its theories.

1 1 Cassirer 1953

2 2 I will question the eventual scope of his vision presently

3 3 ibid, P.446, my emphasis

4 4 another misnomer

1 1 ibid, p.447

2 2 Naturalism, at whatever level of sophistication, clearly falls under this injunction.

3 3 i.e. Naturalism

4 4 compare Van Fraassen's "co-ordinate-free descriptions". "Quantum Mechanics: an Empiricist's View"

5 5 to include scientific experiment as an extension of ordinary experience

"Only when we resist the temptation to compress the totality of forms, which here result, into an ultimate metaphysical unity, into the unity and simplicity of an absolute 'world ground' and to deduce it from the latter, do we grasp its true concrete import and fullness. No individual form can indeed claim to grasp absolute 'reality' as such and to give it complete and adequate expression.[my emphasis]"6

Cassirer's denial of "completeness" and "adequacy", however, is not the same as denying that any individual form can grasp the whole of the phenomena comprehensively! Nor does it speak definitively on the issue of reduction! I will address both of these issues shortly.1

"It is the task of systematic philosophy, which extends far beyond the theory of knowledge, to free the idea of the world from this one-sidedness. It has to grasp the whole system of symbolic forms, the application of which produces for us the concept of an ordered reality, and by virtue of which subject and object, ego and world are separated and opposed to each other in definite form, and it must refer each individual in this totality to its fixed place. If we assume this problem solved, then the rights would be assured, and the limits fixed, of each of the particular forms of the concept and of knowledge as well of the general forms of the theoretical, ethical, aesthetic and religious understanding of the world. Each particular form would be 'relativized' with regard to the others, but since this 'relativization' is throughout reciprocal and since no single form but only the systematic totality can serve as the expression of 'truth' and 'reality', [my emphasis], the limit that results appears as a thoroughly immanent limit, as one that is removed as soon as we again relate the individual to the system of the whole." 2

Cassirer's is not a capricious relativism; it is a relativism as rigorous in concept as is Einstein's. Just as Einstein characterized his theory as having removed "the last remainder of physical objectivity from space and time", Cassirer's conclusion removes the last remainder of metaphysical, (i.e. absolute), reference from knowledge. It is based in the essential methodology of science: in its (Hertzian) theorizing function! It is the nature of science to construct a form, complete and interdependent between symbols, ("images"), and calculus which acts as a whole.4

6 6 ibid, p.446

1 1 If a given form were, in fact, capable of reducing all other theories, and no other could, it would obviously cut against equipotency and "relativization" -i.e. against the whole sense of his thesis! This is the current rationale for dogmatic Naturalism as grounded, (problematically, I believe), in mathematical physics.)

2 2 ibid, p.447

4 4 cf. the "training seminar" of Chapter 1

Under all the forms, (of "nature", at least), Cassirer maintains that what must be maintained are the "invariants" -i.e. that which must be preserved under any consistent form. These are not "things" or "images", but rather, (mathematically), that which remains constant under all legitimate forms. In the sense which I will expand the notion, I argue that it corresponds to my prior (relativized) definition of "experience".

"But above all it is the general form of natural law which we have to recognize as the real invariant and thus as the real logical framework of nature in general......No sort of things are truly invariant, but always only certain fundamental relations and functional dependencies retained in the symbolic language of our mathematics and physics, in certain equations." 1

I will postpone my critique of Cassirer's thesis for a little. Though I think there are problems and questions which need to be resolved, I would like to make the connection to my own thesis before going into those. In its essence, i.e. the essential relativism of knowledge, and his case against reference, I think the argument is very strong and very fundamental. There are very strong questions and delimitations that I will raise when I return to Cassirer's broader thesis later. They will not, however, question this, his core position.

The solution to the dilemma:Nowhere does Cassirer question the profound effectiveness of modern science, however.

His orientation is wholly and profoundly scientific. Rather, he preserves the various sciences as perspectives, as organizations of phenomena. He has, moreover, provided the tools necessary to resolve the epistemological dilemma created by the combination of my first and second theses.

I therefore propose a fundamental, (and final), "Copernican Revolution" -a profound change in perspective- contrary to that, (i.e. the Naturalist perspective), which I conditionally adopted1 at the end of Chapter 2, (and to the stance I now ultimately proclaim), which "reduces" the materialist position itself to organization and not to reference. I argue against ordinary Naturalism, and for a more sophisticated realism, (essentially a Kantian -and Cassirerian- one),2

consistent with the results of the first two theses. By this, (once again), I do not mean to say that the relationality of Naturalism, (or Naturalist science), is faulty, but that its metaphysical reference as reference is faulty. My thesis, though built with Naturalist "bricks", does not therefore entail the (further and unnecessary) Naturalist "foundation" of reference. Though it assumes the validity of the Naturalist organization, (at least on the human scale), it does not assume the metaphysical reality of Naturalism's primitives. In questioning our actual, (referential), cognition of metaphysical reality, it is not, therefore, innately self-contradictory! Though stated in Naturalist terms, my thesis can legitimately question the actual (metaphysical) existence, (or even the possibility of knowledge), of the referents of those terms.

1 1 Cassirer, 1923, pps. 374-379, my emphasis

1 1 but with perfect legitimacy, I now maintain -as a relative stance

2 2 Kant's thesis is profoundly difficult to accept admittedly, both intellectually and intuitively -but so was Einstein's. Where Einstein relativized the physical world, Kant sought to relativize the epistemological one. His lapses can be assigned to his deprivation of the examples of modern mathematics and modern science -which subjects were always his primary focus -and which could have corrected him. That he was two hundred years before his time is surely not an argument against his credibility.

Ordinary Naturalism, though it will not say so, is through and through grounded in a specifically metaphysical dogma, i.e. absolute reference, (however sophisticated), to absolute, (rather than relativized), "material" == "substance". This is the "material" in "materialism",3 and was the specific target of Kant's and Cassirer's profound arguments.

As realists, contrariwise, (and I speak to no one else), we must posit the existence of an absolute, external reality. It is, I have argued, an axiom of realist reason. But, I further argue based on Kant, on Cassirer, on the advances of modern physics, on Maturana's penetrating analysis and on the results, (and natural concordance), of my first two theses, that human cognition does not know, and can not know that absolute reality. I argue we cannot know that metaphysical world in itself, even in "sophisticated" reference! I propose that we stand, even at the human scale,1 in the same relation to ontology that current physics does, (at least as I understand, let's say, Bohr's or Heisenberg's position to be.) I propose that our human scale cognitive world is as much -and as solely- a pure algorithm as is the worldview of quantum physics. It is utilitarian and not referential. But it is an organic, "tactile" algorithm, (a "GUI"), that evolution constructed.2 This sentence, however, is no longer paradoxical. It must itself now be understood in my larger context, as the very "evolution" in it is itself relativized, (i.e. it is a relative assertion within the (particular) Naturalist form).

The results of my first two theses are therefore consistent under this epistemological rationale. The resolution lies in the scientifically and mathematically, (but most certainly not arbitrarily), conceived relativization of knowledge itself. Relational implications, predictive systems, (to include scientific theories), are not, (with Quine), epistemologically determinate. Rather, their essence, (which is their predictivity), can be isolated, (following Cassirer), as relational invariants, (in a mathematical sense), over the field of consistent hypotheses in a sense parallel to that in which Einstein's equations of special relativity were isolated as invariants from the "ether" in which they were originally grounded by Lorentz. Or, rather, relational implications are invariant, but predictive organizations, (i.e. theories), even comprehensive ones, are not! They are the (better or worse), "SUPERB" or "MISGUIDED"1 "forms" which organize those implications.Whence Cassirer's Thesis:

There is, interestingly, a very real similarity of intent at least, (if not in scope or rationale), between Bas Van Fraassen's "co-ordinate free" and "semantic" approach to modern physics and Cassirer's "symbolic forms". "To formulate a view on the aim of science, I gave a partial answer to the question

of what a scientific theory is. ... It does not follow that a theory is something

3 3 as usually conceived -i.e. not in a Cassirerian sense

1 1 more properly "domain" than "scale", as I do not think this is a size issue. I will expand this momentarily.

2 2 This is the implication of my footnote early in Chapter 1. Let me repeat it here: Ideally instrumentation and control would unify in the same "object". We would manipulate "the object" of the display itself and it would be the control device. Think about this in relation to our ordinary "objects of perception" -in relation to the sensory-motor coordination of the brain and the problem of naive realism! We do not use our biological algorithm, we live in it!

1 1 cf Penrose "The Emperor's New Mind" (his CAPS!). cf Appendix D

essentially linguistic. That we cannot convey information, or say what a theory entails, without using language does not imply that -after all, we cannot say what anything is without using language. We are here at another parting of the ways in philosophy of science. Again I shall advocate one particular view, the semantic view of theories. Despite its name, it is the view which de-emphasizes language."2

"Words are like coordinates. If I present a theory in English, there is a transformation which produces an equivalent description in German. There are also transformations which produce distinct but equivalent English descriptions. This would be easiest to see if I were so conscientious as to present the theory in axiomatic form; for then it could be rewritten so that the body of theorems remains the same, but a different subset of those theorems is designated as the axioms, from which all the rest follow. Translation is thus analogous to coordinate transformation -is there a coordinate-free", [invariant?] "format as well?' [my emphasis] The answer is yes (though the banal point that I can describe it only in words obviously remains)."1

Though Van Fraassen ultimately rejects axiomatics, and confines himself to the domain of physical science, his position has a very definite resemblance to that of Cassirer, at least insofar as the latter is confined to "nature". Each is epistemologically relativistic,2 and each is grounded in invariants. Van Fraassen rejects axiomatics, (which I believe is the most cogent formulation of the problem), however, on the basis of a need for meaning and interpretation, i.e. reference. He goes on:

"To show this, we should look back a little for contrast. Around the turn of the century, foundations of mathematics progressed by increased formalization. Hilbert found many gaps in Euclid's axiomatization of geometry because he rewrote the proofs in a way that did not rely at all on the meaning of the terms (point, line, plane,...). This presented philosophers with the ideal: a pure theory is written in a language devoid of meaning (a pure syntax) plus something that imparts meaning and so connects it with our real concerns."3

My thesis of the "schematic object", however is directed precisely to that point. It is precisely my point that "meaning" be taken in its mathematical sense for such a system. A mathematician understands the meaning of a term to be precisely that which is implied by the syntax, i.e. it is a virtual term "ordering" the system in which it is defined. If the mind and

2 2 Van Fraassen, 1991, pps.4-5

1 1 ibid

2 2 "There are a number of reasons why I advocate an alternative to scientific realism ... One concerns the difference between acceptance and belief; reasons for acceptance include many which ceteris paribus, detract from the likelihood of truth. This point was made very graphically by William James; it is part of the legacy of pragmatism. The reason is that, in constructing and evaluating theories, we follow our desires for information as well as our desire for truth. We want theories with great powers of empirical prediction. For belief itself, however, all but the desire for truth must be 'ulterior motives'." (ibid p.3) Please note the connection to the essential Hertzian perspective. "Information" is concerned with predicting future events; "truth" is something else altogether.

3 3 ibid

perception specifically, (the phenomena), is taken in this sense, ordering process- if it is taken as an organization, and its terms as metaphors of process then there is no longer the metaphysical question of meaning or of reference. The terms mean precisely what the syntax implies -i.e. they are virtual terms only! I maintain these are our real concerns! The real problem is the one that Cassirer defined: that of "experience" itself and how theoretical science relates to it,1 -and that involves a total reevaluation of the problem of reference.

Cassirer's epistemology, of course, is firmly grounded in axiomatics. Discussing Hilbert, Cassirer says:

"The procedure of mathematics here", (implicit definition), "points to the analogous procedure of theoretical natural science, for which it contains the key and justification."2

Contra Cassirer: (What are the real parameters?)Though I accept, (and argue), Cassirer's core position of epistemological relativism, (I

believe it is absolutely warranted on the very pure and very strong phenomenological grounds wherein he evolved it), I will now question its scope and its applicability. What are the legitimate forms?

Cassirer's thesis goes beyond "cognition" and science, ("nature") into a symmetry of cultural forms, (to include science as a special case), as well. Van Fraassen does not, nor did Kant, (who remained entirely within "nature"), but this is a question of scope. There is also a question of the identification of the legitimate (primitive) forms -even within "nature" itself.

Before addressing these questions, however, let me first complete my examination of the broadest formulation of Cassirer's thesis. Going beyond the "natural forms", (physics, biology, chemistry, etc), he extends his thesis into ground which I must at least question. He proposes that the forms of "nature", of "cognition", are only part of the innate symmetry of perspectives across the phenomena. They, (the natural forms), represent those forms which relate phenomena directly to a metaphysical, (cognitive), framework. Phenomena can however, (he asserts), be organized on other grounds: art, myth, religion, etc., but they achieve this universal validity by methods entirely different from the logical concept and logical law.

But again our perspectives widen, [i.e. beyond "nature" and into the purely cultural forms], if we consider that cognition, [itself], however universally and comprehensively we may define it, is only one of the many forms in which the mind can apprehend and interpret being. In giving form to multiplicity it is governed by

1 1 Theory, (seen as a Hertzian, free construct -as developed in this chapter), must match, (in some sense), the "topology" of temporal and spatial consequence in experience. As stated thus far, this idea is, of course, Kantian. Russell however, (in his "Foundations of Geometry"), argued to extend the Kantian frame to projective geometry. I feel it must be broadened again past that -past even topology and into the mathematics of abstract transformations. What is required is that the predicted results of the theoretical system (through some transformation!) must match the results of naive (?) experience, -and conversely! I.e. that the results of naive experience -through some (mathematical) transformation - should match the retrodictive predictions of the theory. But this transformation, (since it is past topology), need not preserve objects, and therefore, not reference! What it must preserve is the web of relationality in its most abstract sense.

2 2 ibid p.94

a specific, hence sharply delimited principle. All cognition, much as it may vary in method and orientation, aims ultimately to subject the multiplicity of phenomena to the unity of a 'fundamental proposition.' The particular must not be left to stand alone, but must be made to take its place in a context, where it appears as part of a logical structure, whether of a teleological, logical, or causal character. Essentially cognition is always oriented toward this essential aim, the articulation of the particular into a universal law and order.1

(I disagree with his distinction -so too do the "cultural forms" embody law. The difference, I believe, is in the orientation -i.e. to cognition -to "externality" as world-ground. Any form, even the "cultural forms", will have, (by definition), its own sense of law and logical structure. It is a question of the meaning of "logical structure".)

"But beside this intellectual synthesis, which operates and expresses itself within a system of scientific concepts, the life of the human spirit as a whole knows other forms. They too can be designated as modes of 'objectivization': i.e., as means of raising the particular to the level of the universally valid; but they achieve this universal validity by methods entirely different from the logical concept and logical law. Every authentic function of the human spirit has this decisive characteristic in common with cognition: it does not merely copy but rather embodies an original, formative power. It does not express passively the mere fact that something is present but contains an independent energy of the human spirit through which the simple presence of the phenomenon assumes a definite 'meaning', a particular ideational content."1

But please note carefully that all of Cassirer's "functions of the human spirit" -even his "cultural forms" specifically articulate phenomena -i.e. they are not free, "idealistic" constructs! ("...an independent energy of the human spirit through which the simple presence of the phenomenon assumes a definite 'meaning', a particular ideational content.")

This is as true of art as it is of cognition; it is as true of myth as of religion. All live in particular image-worlds, which do not merely reflect the empirically given, but which rather produce it in accordance with an independent principle. Each of these functions creates its own symbolic forms which, if not similar to the intellectual symbols, enjoy equal rank as products of the human spirit. None of these forms can simply be reduced to, or derived from, the others; each of them designates a particular approach, in which and through which it constitutes its own aspect of 'reality'. They are not different modes in which an independent reality manifests itself to the human spirit, but roads by which the spirit proceeds towards its objectivization, i.e. its self-revelation."2

(That "none of these forms can simply be reduced to, or derived from, the others" seems to provide an essential argument to dogmatic Naturalism. Conversely, I will argue that it suggests and delimits a more correct extension of Cassirer's solution to the overall problem. I will address these very large problems shortly. His meaning must be examined very closely.)

1 1 Cassirer, 1953, p.77

1 1 ibid. pps. 77-78, my emphasis

2 2 ibid, my emphasis

"If we consider art and language, myth and cognition in this light, they present a common problem which opens up new access to a universal philosophy of the cultural sciences.1

"The 'revolution in method' which Kant brought to theoretical philosophy rests on the fundamental idea that the relation between cognition and its object, generally accepted until then, must be radically modified. Instead of starting from the object", [my emphasis]," as the known and given, we must begin with the law of cognition, which alone is truly accessible and certain in a primary sense; instead of defining the universal qualities of being, like ontological metaphysics, we must, by an analysis of reason, ascertain the fundamental form of judgement and define it in all its numerous ramifications; only if this is done, can objectivity become conceivable. According to Kant, only such an analysis can disclose the conditions on which all knowledge of being and the pure concept of being depend. But the object which transcendental analytics thus places before us is the correlate of the synthetic unity of the understanding, an object determined by purely logical attributes.2 Hence it does not characterize all objectivity as such, but only that form of objective necessity which can be apprehended by the basic concepts of science, particularly the concepts and principles of mathematical physics. ..."3

Cassirer asserts an absolute "spiritual" relativism, (but always articulating the phenomena), -i.e. an absolute symmetry across the whole of the "cultural forms", (the "spirit"), of man.

"There result here not only the characteristic differences of meaning in the objects of science, the distinction of the 'mathematical' object from the 'physical' object, the 'physical' from the 'chemical', the 'chemical' from the 'biological', but there occur also, over against the whole of theoretical scientific knowledge, other forms and meanings of independent type and laws, such as the ethical, the aesthetic 'form'. It appears as the task of a truly universal criticism of knowledge not to level this manifold, this wealth and variety of forms of knowledge and understanding of the world and compress them into a purely abstract unity, but to leave them standing as such."1

Though starting from very stable ground, I think that Cassirer ended up in a somewhat ambiguous position. He, like Kant, used words with great precision,2 so he must be read very carefully -even technically. "Nature", and "the forms of nature", for Cassirer, are technical words.

He defines the "forms of nature" for us -e.g. physics, biology, chemistry. These are some of the "values" of his specific function, (his "purely functional unity"), of the human spirit, (here specifically the cognitive forms). A philosophical critique "must formulate the universal conditions of this function and define the principle underlying it."

1 1 ibid

3 3 ibid

1 1 Cassirer, 1923, p.446

2 2 I think it is a necessary concomitant of the very abstract nature of their ideas

We must place this passage in the context of Cassirer's redefinition of the formal concept however. We must see it in the context of "the mathematical concept of function" to understand it.3 The various forms are functional "values" -in a technical mathematical sense -of a definite, and, for Cassirer, serial ordering, (and principle). They are the alternative orderings of the phenomena, (defined by a serial function), -and constitute a series of series. The phenomena, however, remain always the orientation -the focus -of all the forms, (even the "cultural forms"). There is in this no assertion of comprehensiveness, (and even a seeming denial of it), for any given form however. He seems to argue against reduction,4 (and therefore comprehensiveness), as well -but against "reduction" and "comprehensiveness" in what senses?

Compare: (1) "none of these forms can simply be reduced to, or derived from, the others",1

(2) "no individual form can indeed claim to grasp absolute 'reality' as such and to give it complete and adequate expression."2, and (3) "each particular form would be 'relativized' with regard to the others, but since this 'relativization' is throughout reciprocal and since no single form but only the systematic totality can serve as the expression of 'truth' and 'reality', the limit that results appears as a thoroughly immanent limit, as one that is removed as soon as we again relate the individual to the system of the whole."3

What is the sense of Cassirer's "cannot be simply reduced to or derived from"? That no individual form can give "complete and adequate expression to reality" and that no form can be "simply reduced" does not necessarily imply that reduction, (i.e. translation), in a non-simple sense, or that comprehensiveness, (as a complete accounting for phenomena), is impossible. (3), moreover, seems to contradict (1) and (2).

Consider, moreover, his "invariants of nature": though "no sort of things [his emphasis] are truly invariant, but [it is the]..fundamental relations and functional dependencies retained ... in certain equations..[which are truly invariant]" He proposes these, (the functional invariants), as "the real logical framework of nature in general" [my emphasis]. But "nature" is a pluralistic word for Cassirer -the "natural forms" are all the forms of science!

We have, therefore, an assertion of invariance1 across all the forms of science -and cross-reduction across the invariants. Indeed, this is the only sense in which "invariance" makes any sense at all, (it is a "coordinate-free" perspective). "Invariance", therefore, means invariance across different, (all the different), perspectives of nature -and epistemologic relativity. For what other interpretation of the "relativization" of (3) is there except as alternative orientations of the same phenomena?

Consider also his seeming denial of comprehensiveness. "The 'relativization' [of forms] is throughout reciprocal". "No single form but only the systematic totality can serve as the expression of 'truth' and 'reality'." What he is actually asserting, I argue, is that although multiple forms are legitimate, no single one of them can describe the structure as abstracted from an orientation! What Cassirer is portraying here is exactly a "coordinate free" perspective! It is not,

4 4 "None of these forms can simply be reduced to, or derived from, the others"1 1 ibid, my emphasis

2 2 ibid, p.446

3 3 ibid, p.447

1 1 of functional dependency but not of "things"

therefore, a denial of comprehensiveness2 that he is arguing, but a denial of the (metaphysical) adequacy of any particular orientation. It is only in their multiplicity that he believes that they express "'truth' and 'reality'". "The limit that results appears as a thoroughly immanent limit, as one that is removed as soon as we again relate the individual to the system of the whole."1

If these are "the real logical framework of nature", and they are invariant across all the forms of nature, then all the forms of nature are, by implication, cross reductive and comprehensive! That these forms cannot be "simply...reduced to, or derived from the others", does not mean, therefore, that they cannot be reduced or derived at all!

It is cross-reduction and relativistic invariance which tie the forms together and it is only in their totality that they express reality -and experience. The mathematical axiom system will serve to illustrate the case again. That any (adequate) axiom system for a given discipline will be comprehensive is, of course, clear by definition. But to confuse the discipline itself with one particular, (of many possible), adequate axiom systems, is incorrect. Peano's system is not the same as the positive integers. (A more specific and perhaps a more elegant tool for illustrating this conception lies the mathematical notion of “ideals” in abstract algebra. I have discussed this in detail in the Lakoff/Edelman appendix. cf: Afterward: Lakoff – Edelman)

Cassirer is asserting alternative functional orientations across the phenomena in his thesis of "Symbolic Forms". Each draws different functional, (and serial), perspectives, "diverse

2 2 Comprehensiveness is, of course, a highly pertinent issue because of the very definite, (and very powerful), claim by ordinary Naturalism for just such an (ultimate) comprehensiveness for mathematical physics . (I will address this issue presently). This is a very strong claim, and one I think we all actually do accept -at least in principle. However, if one particular form, (e.g. Naturalism), is actually capable of such comprehensiveness, (even in principle), and no other is, then this would constitute a very definite objection to his thesis.

Cassirer believed that the only salvation for the symmetry and relativism he envisaged lay in his extension across the cultural forms:

"As long as philosophical thought limits itself to analysis of pure cognition, [his emphasis], the naive-realistic view of the world cannot be wholly discredited, [I will disagree with this],. The object of cognition is no doubt determined and formed in some way by cognition and through its original law -but it must nevertheless, so it would seem, also be present and given as something independent outside of this relation to the fundamental categories of knowledge.** If, however, we take as our starting point not the general concept of the world, but rather the general concept of culture, the question assumes a different form. For the content of the concept of culture cannot be detached from the fundamental forms and directions of human activity: here 'being can be apprehended only in 'action'."

I believe the actual salvation of his thesis and the guide to its extension lies in the idea of converse -i.e. mutual reduction. If his basic conception is right, and I think it is, (on phenomenological grounds), then multiple cross-reductions and a true relativism will be possible. The possibility is founded in the conception of alternative axiom systems, (and orientations), in formal mathematics and in my extension of Cassirer's reformulation of the formal logical concept.

1 1 ibid, p.447

manifestations of the same basic human function".1 This is an explicit invocation of his "mathematical concept of function". I suggest, instead, an extension of it: that the objects of knowledge are constituted in different, (and alternative), "axiom systems"370 which "crystallize" the phenomena, (under the "concept of implicit definition"). (This is certainly consistent with the Hertzian perspective, more so, I believe, than even Cassirer's interpretation.) I suggest that it is the phenomena themselves which are the actual invariants!2 It is a solution based, not in the mathematics of functions but, as Cassirer suggested often as the true focus of modern thought, -in that of the manifold itself. What results is a true epistemological relativity, (in a mathematical sense), and the possibility of multiple, each-truly-comprehensive and cross-reductive independent perspectives.371

I will leave the problem of the definition of the actual (valid) forms without reaching a definite conclusion. Cassirer's solution is seductive, to be sure -and may very well be correct, but it is outside of the needs for my thesis. What is unquestionable, I think, is his "coordinate-free" orientation to phenomena. Such a perspective on physics alone would stand sufficient to my requirements and my interests here, and Cassirer's Hertzian stance, narrowed to Van Fraassen's smaller physical perspective, will adequately serve my case. I do, nonetheless, think that the case for the "forms of nature" has definite merit as well,372 but, as Cassirer himself explicitly states, beyond that we leave the arena of "cognition" altogether. But cognition is precisely our area of interest here. Our context here is precisely that of cognition and metaphysics! If my area of interest were to change -if I chose to look at "the phenomena" artistically, let's say, then this would no longer be my orientation, and his broader case might be argued. But then, conversely, I would no longer be able to express it in a cognitive context!1

Cassirer's is a profoundly beautiful and elegant conception, to be sure. I am not sure that I can accept the broadest symmetry that Cassirer asserts however, a symmetry, (and a still further Copernican Revolution), that extends beyond cognition and science itself into the cultural forms: language, religion, myth.2 But I believe the symmetry within cognition and science itself is wholly justified.

1 1 Also: "A philosophical critique must formulate the universal conditions of this function and define the principle underlying it."

370 ? Alternatively, “generators of an Ideal” –cf Afterword2 2 Are the phenomena themselves, then, invariant equations? No, they are what the equations embody.

371 ? See the discussion of mathematical “ideals” in the “Afterword: Lakoff, Edelman,…” for a further elaboration of these ideas.

372 ? Note 6-20-1999: In reflection, I have altered my conception of this. I have concluded that an extension to biology is a necessary component of my thesis. See the footnote to the Afterward: Lakoff - Edelman discussing "embodied logic" and biology as a pure "form". (Hyperlink to Lakoff appendix, relevant section)***

1 1 An interesting and important point comes up here, however. If his broader thesis is correct, and my extension of it as well -i.e. mutual cross-reductions and comprehensiveness - then the "invariants", (if there should be such), of those other forms will be (reductively) retained as invariants even in the sciences! Thus, if there be absolutes, (invariants), in art, in music, in religion, then they will be retained as invariants even in the sciences, (in psychology, for instance). I consider this a very significant scientific conclusion, and running contrary to current social relativism. There may be an ultimate scientific decision possible between, let's say, John Cage and Beethoven! -Or between Zoroaster and Jesus!

The Power of NaturalismNaturalism, however, is a profoundly comprehensive theory! Not only mathematical

physics, but its reductive incorporation of the other disciplines, from biology and chemistry through (proposedly) psychology, philosophy, ethics, religion,1 presents a purportedly complete (comprehensive) theory of all the phenomena. Quine demonstrates, however, that there are always other interpretations of the phenomena, no matter the level of detail. Can there be other comprehensive forms then? I think the answer is necessarily yes! Need they be physical forms? The possibility of alternative, and comprehensive, physical forms, certainly seems quite believable. Heisenberg vs. Schroedinger illustrates the plausibility. Whether Cassirer's other "natural forms": biology, chemistry, etc. are capable of such a legitimate extension to comprehensiveness2 is another issue, however.

Cassirer wrote in another era,3 but this does not, in itself, invalidate his conclusions or their possible extension to a broader relativism. On the subject of biology, for instance, he dealt with the issues of vitalism. In modern times, however, there is a very strong case made on much more rigorous grounds which supports the same, independent case for biology. It is that of Maturana and Varela.1 To appreciate it, it is necessary, of course, to effect the same "Copernican Revolution" which Cassirer suggested. Maturana and Varela's case is made on very pure phenomenological grounds. The biology they propound is not grounded upon mathematical physics. Its primitives are not those of the latter, but rather, physics, (and human knowledge) is derived as a function of linguistic coupling, (third order structural coupling) -i.e. it is contained as a (non-centralized) theoretical derivative of biology's own primitives:

"It is by languaging that the act of knowing, in the behavioral coordination which is language, brings forth a world. ...We find ourselves in this co-ontogenic coupling, not as a preexisting reference nor in reference to an origin, [my emphasis], but as an ongoing transformation in the becoming of the linguistic world that we build with other human beings."2

Maturana and Varela's thesis does not find its epistemological roots in substance, but drives past its materialist beginnings to find its new epistemological center in "autopoietic unities" and "structural coupling". It ends up questioning the very physical ground from which it began. In many ways it represents the "Heisenberg" case of biology. It represents an alternative theoretical perspective on experience and on science. It works because of the purity of its phenomenology. Can other "natural forms" be asserted in this same sense?3 Could chemistry, for instance, be stated

1 1 The primitives of some of these forms are distributed and derivative under the reduction, however.

2 2 with equivalent distributions and derivativeness of primitives

3 3 though not that long ago!

2 2 op.cit Pps.234-244, my emphasis

with the phenomenological purity with which Maturana and Varela stated biology? That is the only real issue. This is Hertz' problem, after all, pure and simple. It is also the case I made for the training seminar in Chapter 1.

I will not profess an absolute conclusion on these questions other than in the case of physics, where I conclude, (on Quinean grounds), that there must be, indeed, multiple possible comprehensive forms. The case for biology seems more than plausible and leads to me to accept the broader case for the "natural forms", though I will not insist on it.

But my conclusion in its essence, and beyond Cassirer's, is a fully relativistic one. The truly fundamental forms are (necessarily) comprehensive forms -i.e. they are fully functional "axiom systems"373 capable of exhausting the phenomena. (Alternatively, "the phenomena" is that which remains constant -i.e. invariant- under all such exhaustive perspectives.) They "slice" the phenomena, (all the phenomena), from different perspectives. To be fully relativistic, each form must be complete. Though Cassirer seemed to drive towards this complete relativism, he didn't ever complete it.2

But must not a comprehensive organization be categorical, i.e. must there not be only one? (If we could achieve the Laplacean ideal, would it not be unique?)3 Or, rather, might there not be 373 Cf Afterword: Lakoff and Edelman on mathematical "ideals"2 2 I believe because of the limitation in his formal concept

3 3 The Laplacean ideal is not realist by definition.

"In the introduction to his "Theorie analytique des probabilites" Laplace envisages an all-embracing spirit possessing complete knowledge of the state of the universe at a given moment, for whom the whole universe in every detail of its existence and development would thus be completely determined. Such a spirit, knowing all forces operative in nature and exact positions of all the particles that make up the universe, would only have to subject these data to mathematical analysis in order to arrive at a cosmic formula that would incorporate the movements both of the largest bodies and of the lightest atoms. Nothing would be uncertain for it; future and past would lie before its gaze with the same clarity. ...Du Bois-Reymond elevated scientific knowledge far above all accidental, merely empirical bounds...If it were possible for human understanding to raise itself to the ideal of the Laplacean spirit, the universe in every single detail past and future would be completely transparent. 'For such a spirit the hairs on our head would be numbered and no sparrow would fall to the ground without his knowledge. He would be a prophet facing forward and backward for whom the universe would be a single fact, one great truth'." Cassirer, "Determinism and Indeterminism in Modern Physics", pps.3-4

Under a functional logic, (i.e. one not based in the generic concept), there is the possibility of alternative "axiom systems", (organizational perspectives), exposing alternative utilities, (e.g. biology, psychology, etc. -or alternative physical theories). The Laplacean ideal does not, therefore, presuppose a unique theory, (Newtonian, for instance), and reference.

If we were, in fact, to achieve a science, (theory), such that "the hairs on our head would be numbered and no sparrow would fall to the ground without his [our] knowledge", i.e., comprehensiveness, I maintain that it still not need be unique. The Laplacean ideal is not tied necessarily to Newtonian or any other particular theory, but constitutes the basis of determinism and could apply to raw empiricism as well. (ibid)

alternative yet still comprehensive predictive organizations with different perspectives and different utilities? Under the Aristotelian logic, and assuming comprehensiveness, (i.e. assuming the possibility of a single and complete accounting of all phenomena), there is a linear reduction of all true theories to a single substratum of primitives.374

Hierarchy, (set-theoretic, type ordered inclusion), is an essential component of the existing Naturalist perspective: i.e. that there is a necessary hierarchy of spatial scale. It argues that that hierarchy is mirrored in the process of the reduction of scientific theories: e.g. biology is a subset of chemistry, and chemistry of physics. (Thus psychology and all the phenomena of experience, of knowledge, and of the "spirit" as well, are embedded in that hierarchical ordering -as biological subsets.) It presumes that our naive world, (or at least most of it), is hierarchically mirrored in the primitives of any true theory, (i.e. that the objects of naive realism are objects of that true theory as well). It presumes that they can be represented as legitimate and necessary groupings of those primitives. Thus our ordinary objects and the ordinary things they do are, in fact, real and necessary metaphysical objects and happenings. This argument is crucial to the strength of Naturalism and its metaphysical claim!

But scale is not a priori inherent or the only way to preserve the phenomena, i.e. it need not necessarily "cut reality at the joints". 1 If other organizations, more effective, (i.e. other schematic organizations), are found, then they are legitimate as well. Our naive objects, as objects, are not necessarily metaphysical objects.

Science, until very recently has supported such a spatial, (and theoretical), hierarchy -from the macro to the human scale to the micro to the atomic, (which, of course, theoretical reduction generally supports -i.e. biology -> chemistry -> physics), -or from cosmology right down through the human scale to the atomic.

At the smallest level of scale, of course, (and at the largest scale as well -EPR), the case for hierarchy has broken down in this century. As an example, let me cite Penrose's "most optimistic" view of quantum mechanics, (most optimistic for scientific realism, that is):

"I shall follow the more positive line which attributes objective physical reality to the quantum description: the quantum state. .

"I have been taking the view that the 'objectively real' state of an individual particle is indeed described by its wavefunction psi. It seems that many people find this a difficult position to adhere to in a serious way. One reason for this appears to be that it involves our regarding individual particles being spread out spatially, rather than always being concentrated at single points. For a momentum state, this spread is at its most extreme, since psi is distributed equally all over the whole of space, (my emphasis),...It would seem that we must indeed come to terms with this picture of a particle which can be spread out over large regions of space, and which is likely to remain spread out until the next position measurement is carried out...."

The particle -this smallest part of our "object"- is not included, (spatially, reductively), within the spatiality of the atom or within the molecule -or even within the human scale object of which it is the theoretical (and supposed material) foundation. Naturalism can no longer support, therefore, a consistent hierarchy of scale! At the human level, of course, it is a very useful tool, and that is just what I propose it is -constructed by evolution! Schematism, (and "Symbolic Forms" as well),

374 See Afterword: Lakoff and Edelman for a further discussion of classical logic and science

suggests other, non-scaled and non-hierarchical organizations -i.e. they support any other efficacious organization. It is a simple matter of utility.

Naturalism's primitive substratum, (the primitives of mathematical physics), is deemed unique and "true of" == "refers (isomorphically) to" ontology. It is Naturalism's epistemological basis for a claim of reference.1 But under a functional logic, (i.e. a logic not based in the generic concept), there is the possibility of alternative "axiom systems", (different functional logical concepts/theories, -not as class abstractions from phenomena or as hierarchical spatial perspectives into the phenomena, but as lines drawn across phenomena -as connective functional rules), and a different sort of "reduction", (i.e. translation), exposing alternative utilities, (e.g. biology, psychology, etc. -or alternative purely physical conceptions). So may we consider the new possibility that the relationality of experience, (and experiment), can be entirely preserved under varying (comprehensive) functional perspectives, no one of which stands as the canonical revelation of ontology/experience. The assertion of comprehensiveness for a given reducing theory would not then imply that it would necessarily, therefore, be the sole and unique organizational primitive -i.e. that would be the only one.

This is the sense of my extension of Cassirer's "symbolic forms". I argue, with Cassirer, for a relativism of forms which organize the phenomena, but against reference. I do not argue for his particular specification, (choices), of these forms, nor do I assert my own alternatives to these forms, but I do argue for his general conclusion.

It is in Cassirer's sense of the organizational, rather than the referential relevance of theories that I propose that the relations of ordinary Naturalism -and my own thesis as well- can be, (must be), retained in a deeper realism. "Experience", our true primitive, (and, I have argued, the other axiom of reason), is not the same as any particular organization of it. It is not identical with its (legitimate but particular) characterization as "sense impressions" under the Naturalist form, for instance. I have argued a (broadest -and truly relativistic) definition of "experience" as that which remains invariant under all consistent and comprehensive worldviews.1

What must be preserved is the web of implication of experience in our world, but hierarchy as such need not be maintained. A comprehensive theory, ("form"), e.g. Naturalism, stands as an "axiom system" to generate the field of experience. But if other theories, (forms), and other "axiom systems" are found, (and Quine definitely implies their existence), also comprehensive, then the preference is no longer epistemological but utilitarian. Each, however, must fully preserve "experience" -to include the whole body of past (and future) scientific experiment.1

1 1 cf. Appendix E

1 1 But does "experience" itself absolutely, (i.e. metaphysically), refer to something else? My thesis proposes that it does not. I propose, rather, that it is an organization of atomic, (and indeterminate), process. It is, therefore, real and ontic, but irreducible and non-referencial.

1 1 This is the point on which I question, (but do not necessarily deny), Cassirer's suggestions of the particular comprehensive "symbolic forms" -i.e. in that I believe that they must each embody the whole as past and future scientific experiment. In defense of his choice, however, that relationality of experiment need not necessarily be maintained as "central" to the organization of a particular form. That is, it need not lie close to its "axiomatic" base, but need only be maintained somewhere and somehow within the form as a whole. Thus biology could stand as such a "form" in Maturana's conception, for instance, wherein the experimental results of science would be maintained within third order

I have proposed that our ordinary perceptual world -our innate and functional organic naive realism- is such an organization itself, constructed by evolution, (as stated in relative -but legitimate- Naturalist terms), for efficient viability. At the human scale, Naturalism is an extension of that existing organization -i.e. of that which evolution has given us. But there is clearly no paradox remaining in these statements in light of the prior discussion. My thesis is, therefore, self-consistent and the epistemological dilemma is resolved.

structural coupling, for example. But how would science be retained in a mythical form, for instance? Or language? And yet he has touched something very powerful in both of these. That I am, as yet, unable to see the specific relevance of these suggestions does not convince me that they are, therefore, wrong! In the specific case of religion, for instance, however, I believe that Cassirer has misconstrued the problem. Let me make a countersuggestion: that religion, identified not with its ordinary practice, but with its incarnations in the religious mystics - exhibits an alternative biological form corresponding to the rational form suggested by Quine, i.e., one in which "ordinary objects" are no longer the organizing rationale. (cf. William James "Varieties of Religious Experience").

My thesis is, I believe however, more than consistent. Even from a purely Naturalistic perspective, I maintain that it is the only complete and consistent explanation yet offered of what it is we have set out to understand -i.e. the whole of cognition! The problem of the "Cartesian theatre", (sentiency), for instance, has heretofore either been trivialized and eliminated by ordinary Naturalism, (leading to a sort of linguistic or materialistic "idealism"), or it has been referred, for instance, to epiphenomenalism or emergence. But the latter are little more than an invocation of magic, (they do not vivify the ghosts they summon).

On its own grounds, I believe my scientific thesis stands well vis a vis its competition -it is biologically, psychologically, logically and teleologically cogent. It is, moreover, far more compatible with the epistemology of modern physics than is any other alternative -it speaks the same language. It "covers the territory", (of mind and mind-brain), for the first time and assumes no "magic", (also for the first time).

But our "ordinary objects", (the objects of naive realism), need not be, (and in fact, are not), preserved as metaphysical primitives -i.e. as necessary unities. Quine acknowledged the possibility: "One could even end up, though we ourselves shall not, by finding that the

smoothest and most adequate overall account of the world does not after all accord existence to ordinary physical things.....Such eventual departures from Johnsonian usage1 could partake of the spirit of science and even of the evolutionary spirit of ordinary language itself."2

This is exactly the case I have made. I argue that the "smoothest and most adequate overall account of the world" does not, indeed, accord existence to ordinary physical things. My departure from Johnsonian usage does "partake of the spirit of science and the evolutionary spirit of ordinary language itself".

This concludes the epistemological argument. In the next chapter, I will complete my solution of the mind-body problem with a statement of my third thesis which will supply the "what", the "matter of mind". All the hard work has already been done, however, so the chapter will be brief. The problem is not so hard; it was our presuppositions which made it seem so.

1 1 Johnson demonstrated the reality of a stone by kicking it!

2 W.V.O. Quine 1960, pps. 3-4

Preface to Chapter 5, (the Final Step)

So where have we got to with our realism? Realism must accept or propose two basic postulates as metaphysical, ontological postulates: the actual metaphysical/ontological existence of externality and also the real metaphysical/ontological existence of experience. But for these two postulates to have any meaning, there is a presupposition: the existence in that same sense –i.e. the real metaphysical/ontological existence of some connection between the two. This is the existence that Kant did not mention, but which is implicit in his writings. That interconnection, that relationship between the two, is what I will call “interface”. That that particular existence, (of the interface), must be described in context-free375 terms -that we cannot describe it from a particular perspective -is the lesson of chapter 4. It is that abstract, that invariant concept of interface whose existence we must also metaphysically posit as realists. Assuming, moreover, that it were structured in the way that I have proposed under the concept of implicit definition, (and this is my third hypothesis), then it supplies the actual reality and the metaphysical/ontological existence of mind.

This is an abstract thesis, but it is necessarily abstract. It is the conclusion that I believe realism must come to.

375 cf Van Fraasen

Chapter 5: What? The Substance of Mind

"We can still distinguish science from scientism, a view in which science, which allows us so admirably to find our way around in the world, is elevated (?) to the status of metaphysics. By metaphysics I mean here a position, reaching far beyond the ken of even possible experience, on what there is, or on what the world is really like. Scientism is also essentially negative; it denies reality to what it does not countenance. Its world is as chock-full as an egg; it has room for nothing else. Commitment to the scientific enterprise does not require this. If anyone adopts such a belief, he or she does it as a leap of faith. To make such a leap does not make us ipso facto irrational; but we should be able to live in the light of day, where our decisions are acknowledged and avowed as our own, and not disguised as the compulsion of reason."1

Though I have argued against the "material" and the "substance" of Naturalism as metaphysical existences, there is a deeper -and truly metaphysical- sense of substance that I do wish to maintain. It is embodied in our, (and Kant's), minimal realist assumptions -in the axioms of externality and of experience.

Though Cassirer argues for a broad range of symbolic forms, there is another form implicit in his thesis, (roughly equivalent to the whole of the natural forms), -and innate in Kant's as well. It is the metaphysical form, i.e. the whole of the metaphysical context of the problem itself. (It was as a "Prolegomena to any Future Metaphysics" that Kant himself characterized his work, after all.) This metaphysical form is the proper context for any conception of cognition, (and realism), but, precisely because of Kant, it is necessarily severely restricted and analytic.

Inside of the form of metaphysics, (wherein we are now framing the problem), we are constrained by Kantian parameters -i.e. the fundamental, (rather than the historically limited), parameters discussed in chapter 3. These abstract limits, the axioms of externality, and of experience, and the relativity of perception to the (human) instrument whereby it is effected, dictate a general, relativized and abstract solution to the problem.

Always implicit in Kant, however, was the assumption of some connection between our cognition, and the reality which is perceived, (metaphysical reality), -and that connection was assumed to be reflected in experience, ("intuition"). Always implicit in Kant is the relationship between the absolute external existence which he affirms and the modifying, coupling relationship of cognition itself. Kant's is very much a modern mathematical conception. He argues that we cannot separate the facts of our "instrument", (our cognition), from that which it "measures", (cognates). The relationship between that cognating entity and its object, however, is understood in a very profound and sophisticated sense -very much in the sense of modern algebra. His concept of intuition, (experience), is a relativistic one. The connection is seen as a limit concept -as the most abstract possibility- conceived relativistically to "the X" of metaphysical reality. Alternatively, we might today characterize this connection as the most abstract reinterpretation of Maturana and Varela's "structural coupling", but removed from its strict Naturalistic (metaphysical) formulation. I think the most natural characterization of it is, simply and abstractly,

1 1 Bas Van Fraassen, Quantum Mechanics, p.17

"interface"! This interface, this connectivity, between cognator and that which is cognated, is assumed in any realist conception of reality, (most definitely to include Kant's itself). It is implicit in materialism, in dualism ...; it is implicit in behaviorism, and identicism ..., in "memes" and in neural process. I mean it to be the minimum intersection, (the limit), of all of these realist, (i.e. non-idealist), possibilities. This minimum conception of interface is then, (by definition), necessary and apodictic to any realist position. Realistically, it does, therefore, metaphysically exist! This is the metaphysical reality that Kant does not name, but which is implicit in his, and any other realist position. As a realist, I claim it therefore to truly metaphysically exist, and I call it "substance". This is not, however, the "substance" of materialism, but an analytic conception -i.e. it is the metaphysically minimal necessity of realist cognition.1

That there is something more, some other "substance", some externality other than the interface,2 is also apodictic to realism -it is presumed in the axiom of externality -and I confirm it as well. Kant has stripped the latter of all knowable determinate form, (but not of existence),3 but it is the former with which I wish to concern myself here.The Last Hurdle1 1 There is an understandable demand here for a more precise definition, a more concrete characterization of this "interface". But I think the demand, truly considered, is really for a metaphysical characterization of precisely the kind that Kant and Cassirer obviated. It is the essential and invariant -i.e. the relativistic and "context-free" component of all realist philosophies that I wish to isolate, and that is approached, legitimately and solely, as a limit concept. Mathematicians will best understand my meaning. It is the analytic and limiting essence, (i.e. invariant), of the connectivity of cognition in general that I define as "interface" and that I propose as apodictic to all realist philosophies and as itself metaphysically real.

2 2 Though real, matter, (external substance), itself is, for Kant, "substantia phaenomenon".

3 3 Cassirer's "Symbolic Forms" is an extension of the Kantian position, and relativizes experience. Or rather, it relativizes the interpretation of experience. Experience itself is a primitive. We can describe it in various ways under the differing "forms", (e.g. sensuous impressions" under Naturalism), but ultimately it is a limit concept. (See Kant "limits" vs. "bounds"), -it is what remains invariant under all consistent interpretations, (forms). "Objects" are implicitly defined within the variant forms. Are there ontic objects, then, (i.e. ontic localizations)? We will never know!

Consider Kant:

"Now, if I go farther and, for weighty reason, rank as mere appearances the remaining qualities of bodies also, which are called primary (such as extension, place, and, in general, space, with all that which belongs to it (impenetrability or materiality), shape, etc.) -no one in the least can adduce the reason of its being inadmissible. As little as the man who admits colors not to be properties of the object in itself, but only as modifications of the sense of sight, should on that account be called an idealist, so little can my thesis be named idealistic merely because I find that more, nay, all the properties which constitute the intuition of a body [object] belong merely to its appearance." Kant, Prolegomena, P.37, his emphasis.

He goes on: "The existence of the thing”, (my emphasis), “that appears is thereby not destroyed, as in genuine idealism, but it is only shown that we cannot possibly know it”, (my emphasis), “by the senses as it is in itself."

There remains one last difficulty with my (Naturalist) hypothesis of chapter 2. From the standpoint of my original claim of a complete solution to the mind-body problem, "mind", (at the stage of chapter 2 -and even at the stage of Chapter 4), remains conceivable only in a reductively materialist, (alternatively: an organizational), sense. It remains only process and without "awareness" except as the latter is itself considered reductively.

What is "mind" and where is it? How could it be? The answer is that it is! It must "be". For it is the (apodictic and metaphysical) "substance" of the interface itself that I propose is the substance of mind. The reality, the metaphysical presence of this interface is the immediate and necessary consequence of the synthesis of our two realist fundamentals: externality and experience. It is the relativistic equation between a cognitive entity and externality. This necessary presumption of connective "substance" supplies the last remaining element for the complete solution of the mind-body problem. The Third Hypothesis: a formal statement:

Given that the interface, (as just defined), metaphysically exists1 and given further that it is structured as postulated in my first and second hypotheses, (and this is my third hypothesis), then it internally and necessarily defines our objects and what they do -and they too exist! And, as demonstrated by my arguments in Chapter 2, it knows them! All the problems of structure, all the problems of logic have been dealt with in the previous hypotheses, and a plausible Naturalist rationale is in place. All that remained was existence. It is the metaphysical existence of the interface itself which supplies the reality, (the existence), of sentiency! Mind is the unified concept,376 (the rule), of this interface. Under the combination of my three hypotheses, then, mind becomes quickened, becomes aware, becomes "live". We do know, we are aware, we are real.2

I would modify Kant's last sentence to delete "of the thing". [To: "The existence that appears is thereby not destroyed, as in genuine idealism, but it is only shown that we cannot possibly know it by the senses as it is in itself."] If extension, place, space, impenetrability, materiality, shape are brought into question, (even cardinality in QM), then objects, as objects are also questioned. What remains are my two axioms: the Axiom of Externality and the Axiom of Experience. But these are limit concepts in a strict mathematical, (and Kantian), sense.

1 1 which I have demonstrated that we must, as realists, assume

376 ? i.e. the unified constitutive concept

What we are sentient and aware about however, is not metaphysical externality. Rather, it is the metaphorical organization of primitive process with which we deal.

The problem was that the "egg" of Naturalist metaphysics, (as characterized by Van Fraassen), was just too full and left no room for anything else. Or, rather, we were ignoring the shell!

The difficulty of the substance of mind was the result of an illegitimate metaphysical dogmatism, (presumed, incorrectly, as innate to Naturalism) -by its asserting more than we can ever know. It asserted relative organizations -i.e. its "material objects" as absolute referents to absolute material reality and thereby claimed completeness, (and exhaustion), of reference. Nowhere in that domain, however, could specifically sentient mind exist. It excluded the very possibility of "mind" in our ordinary sense of it.

The problem is resolved, however, by reducing our metaphysical presumptions to the minimal -and legitimate- basis possible. That basis is the minimal and universal assumption of ontic interface, (conceived in its most abstract mathematical sense), which proves to supply the "matter" of mind sufficient in itself.377

Philosophical ImplicationsI think my thesis opens a new perspective on the classical dilemma of idealism versus

materialism, i.e., the question of the primacy of the mind versus the primacy of the physical world. My metaphysical answer comes down, therefore, on the side of the mind, relativizing Naturalism. In that sense my answer is "idealistic". But, (big "but"), "mind", as I redefine and reduce it, (in a very real sense of the word "reduction"), is specifically a metaphysical interface. This interface is real, that is to say, "substantive" (=="physical"). I do not say, (nor do I believe), that it is all that is real but rather that it is innately impossible to know the unmediated nature of that something more. This latter, of course, is just a restatement of Kant's essential conclusion.

That interface, as I propose it, is not the ephemeral and capricious "mind" of classical speculation. It is not "spirit" as opposed to "material". It is specifically and scientifically interface. Mind is purely "physical" in that sense -i.e., it is a metaphysical thing and no more. It is part of the world -it is real, but it is not separate or "purely personal". This is what we know exists. That more exists, we must also accept as realists. But, once again, specifically as realists we must accept the interface as well. The interface is the only assumption needed for mind, and that is all, I propose, that mind is.

Given the reality of a system of axiomatic relationality in the sense of my first two theses, then "mind" becomes "live" in all the senses we normally demand of it. The mind-body problem is solved in all its aspects. I think I have "cracked the code" of mind and brain.1 It is a strange and disturbing one, I admit, but I believe it is, overall, the most plausible alternative on the table.

This concludes the presentation of the core of my overall thesis. The next chapter is a brief statement of conclusions and consequences, and the last chapter serves as an epilogue. Appendix F will deal briefly with Dennett's "color phi" and briefly foreshadow a future extension of my model. Dennett supplies the clue. (The "Afterward: Lakoff / Edelman" is a restatement and further clarification of the logical problem.)

377 ? It is curious to me that materialists always seem to be "bad-mouthing" metaphysics. They are its strongest proponents.

Chapter 6: Conclusions and Opinions

Scientific Conclusions:I consider my most important result, (though you may think this strange), the Naturalist

one: i.e. that "mind" is the (reduced) "concept" of the brain!378 I hold that it is both legitimate and important within the (reinterpreted) Naturalist framework and leads to definite and practical empiric lines of research. That Naturalism is itself thereby relativized detracts neither from its utility nor from its importance -no more than did the introduction of relativity or indeterminacy into modern physics lessen its viability or importance. Rather, it produced profound and immediate practical results. Naive realism is a biological and behavioral algorithm superb for normal life, and Naturalism, its natural extrapolation, is valuable beyond measure -as well it should be under my hypotheses. It is to the ultimate empirical results, (or not), of my thesis, however and finally, that I will equate its ultimate value.Devil's Advocate:

Though I have argued against our knowledge of externality, and for a schematic organization of process, could not our external, metaphysical world still be like the objects of our cognition. Of course it could! The possibility is suggested in my conception of interface. Since it implicitly defines our objects within, conceivably it might, as well, define the "objects" of external reality without! But this is a profession of extreme faith, and not of science.*1

"If anyone adopts such a belief, he or she does it as a leap of faith. To make such a leap does not make us ipso facto irrational; but we should be able to live in the light of day, where our decisions are acknowledged and avowed as our own, and not disguised as the compulsion of reason."2

I, however, do not choose to, (nor do I have to), make such a leap of faith. I propose that what we have is a viable, (and truly real!), working model that simply "does the job", i.e. it is at least compatible, and probably beneficial3 vis a vis absolute externality.

Come, isn't it the height of arrogance to presume, (under the Naturalist presumption), that this race of apes, barely able to scribble for a mere few thousand years, has been able to divine the nature of absolute reality? How much more probable is it not, (changing the metaphor), that we are merely constructing "a hive"?4

378 ? Alternatively, it is the brain's rule of ontogenic coupling1 1 It is a question of bounds and limits again. Or, more simply, of the distinction between an upper bound and a least upper bound. Reality clearly sets definite upper bounds to (evolutionary) developement, but does it convey to the organism a least upper bound, (which would be defining)? The former encompasses (raw) "structural coupling", but the latter would be necessary for "congruent structural coupling". It is an assumption equivalent to the "parallel postulate", you see!

2 2 Bas Van Fraassen, Quantum Mechanics, p.17

3 3 "beneficial" is itself a synthetic a priori perspective

4 4 Why do we think we know even the boundaries of all the possible solutions to all of the problems of reality? Whence comes our arrogance that we feel we have solved the ultimate problems of the universe and of our existence in it?

So Why Bother?But if this is the ultimate answer, if this "ontic indeterminism" is the conclusion we must

reach, what is the point of it all? Near the conclusion of Chapter 2, I admitted the (intuitive) difficulties of my thesis. But modern physics has much the same difficulty -its picture of reality, though intensely beautiful and exotic, offends those same normal sensibilities. The (why bother) answer for physics is that that very picture produces desirable, powerful, and practical results right at the human, (naive), scale, and which we cannot deny. The transistor, nuclear power, working telephones and radios, ... are necessary and practical consequences of that very theory -and they would be impossible without it. I propose that this will be very much the case for my conception. Though admittedly offensive to our (naive) realist sensibilities, if it is correct1 it will lay the theoretical ground necessary for the quantum advances in neuroscience, for instance, which will finally and specifically, (rather than generally and destructively), cure the terrible aberrations of mental illness. But the mind-brain puzzle has far larger implications than that. It deals with the problem of man in all its aspects. It deals with all his social, ethical and artistic parts.1 The final implications must not be underestimated.

This is the "why bother". Even offensive theories can yield useful and powerful results, necessary to man! The final test, the final judgement therefore, must be made on results. But, before results can be obtained, it is necessary, first, to entertain the possibility.

My reconception of fundamentals, though radical, is absolutely consistent with the historical progress of science -of physics, biology, mathematics and logic. It solves the biological and the philosophical problems inherent in the mind-body problem, and exorcises the "homunculus" once and for all. It provides an Archimedean fulcrum to overturn our naive realistic presuppositions, (inherited by "scientific realism"), and let us get on to the serious business of creating a science of mind and brain. It provides a viable context in which I believe workable theories are now, finally, possible.

Is it not more believable, (under the very Naturalist assumption), that we have merely expressed our own particular mode of existence, -that human civilization, like a swarm of bees, has simply built a hive? What is this logic we are so sure of? Ultimately, biologically, it is an expression of the "structural coupling" of the race with its environment. But the invariants of that coupling are derived from the structure of the uniquely human brain. Other brains, other modes of coupling almost certainly would embody another protologic. Ordinary logic, (i.e. "associationist" logic -after Dreyfus' term), denies its biological roots. It believes it has touched eternity and verity. How? Why? What teleological mystery does it hide? When we thought that man was created by God in his image and that God gave us this open channel to truth, then there was a meaningful rationale for such a view. But when man became, purely and simply, a material animal, derived mechanistically and randomly by material combination, then this mechanistic process lost all justification as correlating with anything other than its own mechanical necessities. But it works! How and why? Perhaps that is itself the answer. It is an operative process that works in the world in which it lives! This provides no guarantee of its ontological posits at all however -it is an operative process that works -and that's all!

1 1 and I do not dogmatically assert that it is. The future of science must answer this question.

1 1 I think it would be a real mistake to discount the possibility of real, purely physical implications from my thesis. In the transition beyond "objects", wholly new degrees of freedom may be possible for physics itself.

No substantial progress will ever be made in dealing with "mind", or in the treatment of its terrible, destructive aberrations, (both individual and societal), -until the mind-body problem itself is solved and workable tools are developed. To deal with the mind, we must deal with its "objects" and the relations between them. To deal with the brain, we must deal with its process. To constructively and specifically2 affect the processes of mind3 via the brain, the relationship between the two must be understood!

The simplistic orientations of naive realism, ("though grown up and sporting a beard" -to steal a phrase), just will not stand any longer. Great issues, to include the most profound social, ethical and spiritual aspirations of the race, depend upon the resolution of this problem -and upon its consequent, the establishment of a mature and viable neuroscience. There is too much pain in our world, and too much need, -dependant upon real solutions to these problems, to cling to the playgrounds of our intellectual youth.

How do we live?So, (given my thesis), what is the point? Do we exist, therefore merely contemplating our

navels, lost in the "ontic indeterminism" of metaphysics? No. I, for one, rarely even think about metaphysics, but love and feel pain, pay attention to passing cars, and generally live my life as you, (or any dogmatic Naturalist), would. I practice Descartes' interim life strategy of normalcy, (by necessity), and pretty much live my life as I always have.1 I speak the language of Naturalism because it is good language and because it is, well ..."natural"!

When I choose to consider the connection however, I know that by following my inbuilt model, (and extending it), I am in harmony with that nameless externality. I do not use my model, you see, I live in it!My "Act of Faith":

But what do I, personally and as my act of faith, believe? (I, after all, get to have beliefs as well!) Though I do not believe in the necessity of spatially and temporally separate metaphysical objects, (consistent, certainly, with the views of modern physics), nor in the metaphysical "aether" in which they are still conceived(!), I, (personally), believe in the metaphysical existence of other minds!1 (That there is still more, -an absolute externality, "phaenomena substantia"- I also believe.) But those other minds, specifically as minds, (as per my second thesis), are all precisely products of implicit definition, variations on, (values of), a single universal function. They are, I believe therefore, continuous variations of me. We are all, I believe consequently, more than brothers, but "states" of the same being. "You" are "me" in a different "place", (state) -there is no necessary spatial or temporal separation between us, i.e. there is no necessary metaphysical "aether" between us!

But somebody already said all that, didn't they?"'I tell you the truth, whatever you did for one of the least of these brothers of mine, you did for me. ... whatever you did not do for one of the least of these, you did not do for me.'" (Mat. 25:40-45)

2 2 i.e. at the "fine-grained" level of mind

3 3 or to gain reflective insights on them

1 1 I also believe in a continuity of sentiency, at least with the higher animals -for reasons which should be perfectly obvious by now. Just where the "cutoff point" may be, I would not be presumptuous enough to speculate.

Chapter 7: Epilogue

How do you convince a bird, living in a dying tree, to leave its accustomed perch, its familiar nest, and go to inhabit another. You may praise the new view, and describe fantastic horizons invisible to the old. You may catalogue the prospects of juicy worms, temperate climes, and soaring flights through inestimable thermals. But the bird, clutching stubbornly to its worn branch, may only envision the loss of its well-defined routines. The path to an easy patch of straw for its nest or a worm-rich meadow might become convoluted or even impossible because of distance or predators! It cannot even envision the possibilities of the new place unless it is willing to chance an exploratory flight. Its world is simple and uncomplicated -or at least the complications are well known. This has been my problem here. I believe the mind-body problem is the most difficult in the history of the human intellect. It hinges on the problem of cognition -and that is the problem of everything! Its solution, I feel, involves a brand new "roost" -a new intellectual perspective with horizons different but incomparably broader than before.

Admittedly however, though it proffers "sunsets of unmatched vividness", and "new and fertile meadows", it involves a definite risk as well. It may turn out, after all, that the "nest" I propose lies over fallow fields and iron-hard soil where no "worms" might survive! You are right, therefore, to be conservative and cautious in the selection of your ultimate habitat, but you are wrong if you are timid in your survey -your future may depend on it. I invite you to conquer your fear of vertigo and try your wings in an exploratory flight to this very different tree of knowledge.

"Safe (that is, probable) hypotheses are a dime a dozen, and the safest are logical truths. If what science is seeking is primarily a body of certain truths, it should stick to spinning out logical theorems. The trouble with such safety, however, is that it doesn't get us anywhere."1

There are really just two schools of thought on the mind-body problem. One holds that the relationship between the mind and the brain is inherently unsolvable. It holds that the natures of mind and brain are (1) either absolutely incommensurate, (are of different kinds), or (2) the problem is beyond intrinsic limitations on human understanding. The other school holds that the relationship is perfectly direct and unproblematic, albeit totally one-sided and exceedingly complex. The first offers no practical hope whatsoever for the dysfunctions of the human mind, but the latter destroys the reason for caring in the first place. It's solution is that we are all automatons, "zombies"! Mind, in its ordinary sense, is a fantasy, a "figment" of the imagination! What, then, does it matter whether another automaton makes "pain" noises rather than "happy" noises? Less delicately, what possible objection could there be to the Dachau "fetus series" or to the atrocities in Bosnia? The solutions offered by both schools, moreover, are counterintuitive, limit the scope of empirical investigation and involve significant logical difficulties. I have offered a new alternative capable of resolving the whole of the problem and commensurate with the whole of the human spirit.

My thesis opens the further and distinct possibility of an actual "physics", i.e. a mathematical and scientific mechanics of mind and brain, as it defines, for the first time, an appropriate context in which it could be formulated. Just as the SUPERB1 2 theories of Newton, Maxwell, and Einstein were literally unthinkable in the cosmological context of Ptolemy or in the 1 1 P.S. Churchland, 1988, P.260

1 1 cf Appendix D

physical (and gravitational) context of Aristotle, neither can the SUPERB theories which must eventually encompass the mind and the brain arise without the context -and the continuum -which will make them possible.

I believe the mind-body problem is the most important problem in the history of our (human) species. Subsuming both science and ethics, it will ultimately determine our future as a civilization. Though this sounds overly dramatic and even downright pompous, reflection shows that it is not. Answers to what we are, and why we are will determine what we can do and what we will do.379 Profound belief determines actual practice! The bounds of future civilization will be set by our ultimate understanding of our own being. This problem demands, therefore, the greatest latitude and the greatest tolerance to radical ideas. It is too important to be treated otherwise.

It has been said of scientists, (and it certainly applies to philosophers of mind as well), that they live, alternately, in two disjoint worlds. They do not take their reality home with them. The reality they believe as professionals is not the reality they believe when they dodge cars on the freeway or make love. None will put out a saucer of milk for Schroedinger's cat.

Is Dennett prepared during his self-stimulating monologue, (whilst sitting in his rocker and listening to Vivaldi), to accept himself solely as a "center of narrative gravity", solely as the cumulative product of temporally and spatially separate and discrete processes, (the "Final Edition" published on his "Demonic Press"), lacking "figment" or "qualia"? I, personally, am perhaps willing to accept him as such, but I am certainly not willing to accept me as such.

Like Dennett, I have been wrestling with this problem for over 35 years. I came to it not from philosophical curiosity or "epistemic hunger", but as a result of personal tragedy -the loss of a loved one, (my mother), to the maw of mental illness. Frustration -and anger- at the inability of science to help her and a survey of the dismal "mythological",1 (Freudian and quasi-Freudian), state of then-current thinking on the subject2 caused me to begin a personal and private search, of necessity based in logical and abstract theoretical criteria -but aimed at an empiric goal.3

Emerging from my "cave", (of contemplation), just a few years ago, I was surprised and fascinated by the illuminating and brilliant bonfires which had been lit on the plains of biology and philosophy. Since then, with more than a little trepidation, I have been scouting each of the major encampments so lit. I have concluded that I have something still new and novel to say. I think that my torch, crafted as much by art as by science, carries a unique Promethean flame. I think I have solved the essence of the problem of mind-brain. Now I, like Benjamin Franklin, Rousseau's "backwoods philosopher", stand before the sophisticates of Paris in my bearskin cap.4

Though my thesis admittedly opens new and fundamental problems -more, perhaps, even than it solves, that very fact unlocks whole new worlds of possibility for scientific advance and in

379 ? Consider Nazism, as just one recent example.1 1 echoing Einstein's characterization of Freudianism

2 2 and their damnable and blatant arrogance about it!

3 3 Since then, my perspectives have widened. I have come to believe that the tragedies of mental illness are echoed in the tragedies of the human social condition -the wars, the hatred, the arrogance, the exploitation of man by his fellow man, these are other aspects of the same basic problem. Under the perspective of dogmatic Naturalism, these are normal, and therefore necessary. I do not believe they are.

4 4 Van Doren, 1938

itself constitutes an argument for serious consideration. If, in fact, we have already "arrived", if you are satisfied that we do, in fact, already possess in rough form a valid picture of the whole of our reality, then the very poverty of that reality as regards the human condition must make you very sad -and kindle the hope that something more is possible. I think it is!

Appendix A, (Information and Representation)

(An amplification of the argument in Chapter 1. It is an integral part of that discussion, but I felt it was too long for a footnote, and would otherwise have interrupted the flow.)

"Information", (and "representation" in whatever form), as a rationale for the evolution of the brain, just isn't a viable hypothesis. The brain, I argue, is an organ of (ontogenic) process -of response, not of "information".A Little Combinatorial Argument:

A measure of the complexity of our reality is our context of information about it. The only context in which it has meaning as information for us, however, is of the magnitude: 2 to the power of 107, (=103,010,290), -the possible sensory arrays.1 This is a staggering number. The number of all the subatomic particles in the entire known universe,2 multiplied by the number of seconds in the 4 billion years of evolutionary history is, by comparison, far less than 10102. The latter number, incidentally, may be considered as a gross upper bound to evolutionary possibility!

1. A simple limiting argument:

Maximal assumptions:a. From the beginning of evolutionary history, there were always less organisms than subatomic particles in the known universe1

b. Every organism mutated once every second for this four billion years2

c. Every mutation was beneficiald. Not a single (beneficial) mutation was loste. All mutations were ultimately (somehow) summed into one organism

2 2 T-7 , (1084) is far greater "than there are subatomic particles in the entire known universe"! Asimov, 1977, P.58

1 1 Instead of trying to approximate the possible organisms at any given time, (I started with a Fibonacci series, but abandoned it to a simpler procedure), it suffices to substitute a number greater than the total number of subatomic particles in the universe -surely greater than the required number- for every term. This generates a (gross) upper limit for the series.

2 2 If you won't accept this assumption, multiply it by a few thousands, -or millions, -or even trillions; you are only adding to the final exponent -at most a few tens. You could actually raise it to 1010,188 times per second without affecting even the literal statement of my conclusions. I suspect that long before you got to this huge number, however, that you would be stopped by the ghosts of Planck and Heisenberg! Surely complementarity suggests that there is a lower limit to the relationship between causality, mass, space and time which can have measurable effects -i.e. "information"!

Conclusion: the number of total (beneficial) mutations accrued in the organism named in "e" is less than 10102. 3

Assuming a standard bitwise, (i.e. digital), theory of information, this simple argument demonstrates a discrepancy of more than "just a few" (!) orders-of-magnitude between informational possibility and evolution's ability to incrementally embody any significant portion of it in an internal representative model. Even if every single mutation were model-defining, it is a 3 millions order-of-magnitude discrepancy! ( 10 x 10 x10 …. three million times!) Why so great a gap? How could "representation" be effected?

2. Think about simple digital models. Consider just the three "idiot lights" on the dashboard of my decrepit old Dodge truck as a primitive instance. All eight of its possible states are relevant to response and, considered as an "information model", it must account for each of them. OFF-OFF-OFF is significant -and allows me carefree driving- only in a context of possibility. In fact one of them, (the oil light), is non-functional and not "information" at all. This simple system, in consequence, does not qualify as a representative model. That part of it that does qualify as information, (insofar as it is "information"), requires an accounting for its context of possibility.

3. The hypothesis of an internal representative model as the rationale for the sensory system presumes that evolution progressively correlated a model with each, (or some significant portion), of the possibilities of the sensory array -and with potential response as well.

But evolution had less than 10102 1 chances to achieve this correlation. The most optimistic correlation is 10102 instances,2 and the ratio of model correlation to possible sensory states is

10102 / 103,010,298 < 1 / 103,000,000 !

Even if the model itself were taken as an edifice of (107) actual internal binary bits, (paralleling the sensory array), this would only regress the problem. Evolution still would have the problem of incrementally correlating alternative model states with potential response and the numbers would still stand. The odds of a "designed", or even a significant response would still be less than 1 / 103,000,000 -which is as close to zero as I care to consider!1 Its utilization as "information" would still require an accounting for -and an incremental evolutionary correlation to- its context of possibility. Contrarily, taking my two proposed, (and grossly exaggerated), upper bounds for mutational possibility, 10102 and 1010290 respectively, the same informational possibility

3 3 or, alternately, to 1010,290

1 1 alternatively, 1010,290

2 2 alternatively, 1010,290

1 1 Alternatively, we would have to assume that individual evolutionary mutations could each (accidentally) correlate information to model at a scale of ten to the power of three millions!

could be embodied in just 339 or 34,162 binary receptors respectively!2 Why so many sensory possibilities?

4. But the argument applies equally to the possibility of even an isomorphic parallelism of response, ("congruent structural coupling"), as Maturana and Varela propose moreover, (as distinguished from the case of an internal, representative model). That assumption still requires a correlation to sensory input! (This is the only "trigger" that anyone has postulated.) The (maximum) ratio of "designed" response, (and parallelism), to possible sensory input is less than 1 / 103,000,000!

5. In short, we simply have too many sensors to support the "information scenario"3 -way too many! There are "10" -with three million zeros after it(!) -times too many sensory possibilities for evolution to have done anything with in the entire history of the universe! The entire future of the universe, (assuming a finite model), would be insufficient to dent it either. Shall we talk "parsimony"?380

Paul Churchland has argued that if each synapse is capable of just 10 distinct states, then the brain is capable of 10 to the power of one hundred trillion, (=10100,000,000,000,000), distinct states. This number is impressive and considerably larger than the one I am considering, it is true. It does not refer to the possibility of acquisition of information, (specifically as information), from the environment however nor to the possibility of evolutionary correlation to beneficial action -i.e. utilization. Churchland's number, therefore, only amplifies the discrepancy and the argument I have made!

6. It is evolutionarily plausible, certainly, to consider 10,000,000 sensory inputs as triggers of process. But it is not evolutionarily plausible to think of them as environmentally determinate -

2 2 2339 = 10102 and 234,162 = 1010,290

3 3 That scenario is clearly grounded in the "ontological assumption" that Dreyfus credits to the artificial intelligence community and with which he strongly disagrees. It is the fundamental assumption of the "information" hypothesis for natural intelligence as well.

"The Ontological Assumption: Finally, since all information fed into digital computers must be in bits, the computer model of the mind presupposes that all relevant information about the world, everything essential to the production of intelligent behavior, must in principle be analyzable as a set of situation-free determinate elements. This is the ontological assumption that what there is, is a set of facts each logically independent of all the others. (Dreyfus, 1992)

Dreyfus' arguments, in fact, have nothing to do with copper or silicon -nor even, (except in a very cursory manner), with neurons. They specifically challenge the "information" model of mind and intelligence!

380 Edelman makes an interesting parallel argument to the same end. He argues that the neural systems of both the embryo and the finished phenotype develop according to time, place and event specifics by a principle of “neural Darwinism”. Brains, he argues, are “adaptive”, not informational. They are selective of pre-existing internal variation. He argues that the complexity of time and place specificity, crucial to brain formation, are beyond the information potential of the genome, while event specificity is, of course unpredictable. Brains, he concludes, are not “information systems” or the sort of things that programs run on. Even the brains of identical twins are not commensurable in that sense. Cf Edelman, 1992

i.e. as inputs of information- as this immediately escalates the evolutionary problem exponentially -i.e. to 210,000,000, (minimally)!

7. Maturana and Varela's "congruent structural coupling", Patricia Churchland's "representational structures... organized to enable informed motor performance", Dennett's "good trick" and Hofstadter's "software isomorphism" and, indeed, the whole Naturalist hypothesis requires that evolution has correlated response isomorphically to our actual environment -i.e. its "material" and cause, rather than its effects on us. More precisely, it requires that the objects of our linguistic response embody such an isomorphism. How? I question even its theoretical possibility. Theirs is a hypothesis of the profoundest difficulty and logically distinct from the basic operative principle of evolution!

8. "Information", (and "representation" in whatever form), isn't a viable rationale for the evolution of the brain. I argue that the brain is an organ of (ontogenic) process -of response, and not of "information". The function of that organ is to organize biologic process, not to represent its surroundings. Objective reality is a bound to the evolution of organisms; it is not a limit which can be matched or paralleled.381 [View a simple graphic] [Return to Chapter 1]

381 An objection was made to this argument, (Appendix A), by a mathematician, (an anonymous referee), who invoked a "monte carlo" perspective. An extremely limited random sampling, he argued, is sufficient to sample a huge field of data. The problem I see with his argument is that it presumes a pre-existing context within which to orient and evaluate such a sampling. It is the preexistence of that context which allows such a sampling to be meaningful. But how did evolution acquire such a context -the context of information? It is the definition of the context itself which is exponential and to which my argument is entirely relevant.We, as organisms, do not begin with a given, a priori context within which to plan and take advantage of such a "monte carlo" strategy at the level of my argument. It is the assumption of that context itself which, I argue, is petitio principii.

Appendix B, (Isomorphism and Representation)(An amplification of the discussion of Chapter 3) 1

Early on in their book, Maturana and Varela2 emphasize a seemingly trite but profoundly pertinent point: "everything said is said by someone".3 There is an important and deeper corollary: any discussion will always take place inside of a model, i.e. a context. For the mind-body problem that model may be "physical", "mental", "behavioral", "linguistic" or some new alternative, but there will always be some model. We are locked, i.e. closed, inside a "magic circle", to use Cassirer's term.

When we demand a correlation between objective reality and the brain, what we are really asking for is a correlation between "the brain", as an entity within our human model, and our "objects" and their system of law as further entities of that same model!4 Within this context however, "isomorphism" is a legitimate demand -founded on needs of internal consistency of the model. There must, therefore, be some isomorphism, (i.e. an automorphism), between the brain and the rest of our (human) model of reality. "Isomorphism", however, is a broader concept than Naturalists' use of it.

Technically, two domains are "isomorphic" to each other if a one-to-one correspondence can be specified between them which preserves some (possibly different) operation or operations internal to each of them.1 But the mathematical concept is more general than the isomorphism between integral domains, (e.g. the whole numbers), or between ordered fields, (e.g. the rational numbers), for example. This kind of isomorphism supplies the model for the Naturalist conception, relating "points" to "points", "betweens" to "betweens" or "things" to "things". It provides the rationale of hierarchical reduction as well. The mathematical concept has more profound possibilities, however, residing in its group-theoretic usage. This "isomorphism" can relate entirely different contexts!

Consider the isomorphism between J3, the additive group of integers modulo 3, and the group of rigid rotations2 of an equilateral triangle onto itself as a simple example. This is a correlation between the "objects", ['0', '1', '2'], and a group of transformations, each of the latter

1 1 This discussion really belongs in the body of the discussion from which you were referred. Its necessary length, however, would have disturbed the flow of argument, and a four page footnote would have been unconscionable, so I have placed it here.

2 2 Maturana and Varela, 1987

3 3 This is an assertion of closure.

4 4 I will discuss an ontic correlation presently.

1 1 By definition, if, given a set of "objects" "O", (o1,o2,o3...), with an operation "*" between them, and a set of "objects" "Z", (z1,z2,z3...), with an operation "#" between them, there exists a one-to-one correspondence "&" between the "o's" and the "z's" which preserves their operationality, (i.e. such that &[oi * oj] = &[oi] # &[oj] ), then they are said to be isomorphic under & as regards * and #.

2 2 the rotational symmetries

mapping an infinite domain onto itself. It relates, in strict isomorphism, a domain of "things" to a domain of continuous mathematical functions!3 It illustrates a very different and, I propose, a more appropriate model for the kind of correspondence between "the brain" and "objective reality".

Consider further, and beyond this primitive example, correspondences between "things" of this sort and projective transformations, or topological ones. Finally, consider correspondences between "things" and transformations that go beyond topology and onto abstract sets -i.e. consider transformations in their most abstract sense: "Generally speaking, those one-one transformations of any set of elements which preserve

any given property or properties", [phenomenal invariants?], "of these elements form a group. Felix Klein (Erlanger program, 1872) has eloquently described how the different branches of geometry can be regarded as the study of those properties of suitable spaces which are preserved under appropriate groups of transformations. Thus Euclidean geometry deals with those properties of space preserved under all isometries, and topology with those which are preserved under all homeomorphisms. Similarly, 'projective' and affine' geometry deals with the properties which are preserved under the 'projective' and affine' groups..." (Birkhoff and Mac Lane, "Modern Algebra", p. 125)

But the case of transformations is larger than "spaces":

"The algebra of symmetry can be extended to one-one transformations of any set of elements whatever. Although it is often suggestive to think of the set as a 'space' ... and of its elements as 'points', this picture does not affect the formal algebra." (ibid P.119, my emphasis).

Certainly the brain is a transformation when considered either on the level of behavioral response, (input-output), or on the level of fine-grained neural process. I suggest that the "objects" of the brain, (mind), are transformations coordinating distributed response. I suggest that these are the "objects of effective action"2 named by Maturana and Varela and that they are (group-theoretic) isomorphic to the other, (i.e. "objective") "objects" of our self-same human model! I suggest that it is in this sense of "isomorphism" that they map to the "objective world", (of our model).

The specifically metaphysical question, (as opposed to the question of the internal relationality of the model itself), is another issue. "Structural coupling", (Maturana, 1987) -appropriate relationality- provides the key. It requires that the relationship of an organism to its environment is one of (beneficial) process and not of information. Though that correlation is certainly opportunistic and necessary, it is a long "logical leap" from this to being sufficient, -to capture. It does not, therefore, imply a functional parallelism, (i.e. an isomorphism), but a causal indeterminacy. Though this conclusion enormously complicates our conceptions of "physical" or, more correctly, of ontic- reality, I will argue that it provides the last link in the actual explication of the mind-body problem.

There is a categorical difference between metaphysical reference and the internal, model/model automorphisms of our logically closed human cognitive world. It is the latter which

3 3 This is not strictly true. In this example, the latter have, of course, three points of discontinuity.

2 2 i.e. the only "objects" they will allow for the brain

constitute the problem of science. Here I have suggested a particular kind of automorphism between the brain and its world.

Appendix C, (Mind-Body and Artificial Intelligence: Hubert Dreyfus)

The subject -and the problem- of artificial intelligence, (AI), has an obvious relevance to my discussion. Here pragmatic demands of technology have forced a clarification of fundamental issues -issues common to both the mind-machine and the mind-body problems.

Hubert Dreyfus carried on a running war with the adherents of artificial intelligence for many years. While I differ with many of his conclusions, he has clarified several fundamental problems and has exerted a meaningful influence on its subsequent development. In his book: "What Computers Still Can't Do",1 he maintains that the continuing optimism by AI researchers, (despite what he describes as their forty years pattern “of early successes and consistent long-term failures”2), for the possibility of machine intelligence is based on their deep-seated conviction that the human brain functions like a "general-purpose symbol-manipulating device", (a digital computer). If this is true then, they presume, their ultimate success is assured.3 Dreyfus maintains, however, that their conviction is based on four very questionable assumptions which he asserts they have improperly accepted as axioms. These assumptions are relevant to the mind-body problem as well. They limit the scope of imagination. (1) the biological assumption:

"A biological assumption that on some level of operation -usually supposed to be that of neurons -the brain processes information in discrete operations by way of some biological equivalent of on/off switches"1

(2) the psychological assumption:"A psychological assumption that the mind can be viewed as a device operating on bits of information according to formal rules. Thus, in psychology, the computer serves as a model of the mind as conceived of by empiricists such as Hume (with the bits as atomic impressions) and idealists such as Kant (with the program providing the rules). Both empiricists and idealists have prepared the ground for this model of thinking as data processing -a third-person process in which the involvement of the 'processor' plays no essential role."2

(3) the epistemological assumption:"An epistemological assumption that all knowledge can be formalized, that is, that whatever can be understood can be expressed in terms of logical relations, more exactly in terms of Boolean functions, the logical calculus which governs the way the bits are related according to rules."3

and,

1 1 Dreyfus 1992

2 2 He makes a very strong case in the third edition.

3 3 If a biological machine can do it, so, presumably, can a silicon one!

1 1 op cit P.156

2 2 ibid

(4) the ontological assumption:"Finally, since all information fed into digital computers must be in bits, the computer model of the mind presupposes that all relevant information about the world, everything essential to the production of intelligent behavior, must in principle be analyzable as a set of situation-free determinate elements. This is the ontological assumption that what there is, is a set of facts each logically independent of all the others.4”

Dreyfus raises serious doubts about the first assumption, based on the results of current neurophysiology -neurons are no longer understood as simple binary switches, for instance. He concludes a broader inquiry more strongly: "In fact, the difference between the 'strongly interactive' nature of brain organization and the noninteractive character of machine organization suggests that insofar as arguments from biology are relevant, the (biological) evidence is against, (my emphasis), the possibility of using digital computers to produce intelligence".1

He makes substantial arguments against the second assumption based on a survey of research in Psychology and Cognitive Simulation and comes to the same conclusion I reached in chapter 1: "the assumption of an information-processing level is by no means so self-evident as the cognitive simulators seem to think; ... there are good reasons to doubt that there is any information processing going on"!2

The third and fourth assumptions involve more fundamental issues:"But this still leaves open another ground for optimism: although human performance might not be explainable by supposing that people are actually following heuristic rules in a sequence of unconscious operations, intelligent behavior may still be formalizable in terms of such rules and thus reproduced by a machine. This is the epistemological assumption."3

He argues that human behavior, (understood as the input and output of physical signals), though presumably completely lawful in the sense that "formalists" require, does not support the epistemological assumption as made by Turing and Minsky. They do not simply claim that man is a physical system describable by natural law, (as are boats and planes), they claim that man is a Turing machine.

"...When Minsky or Turing claims that man can be understood as a Turing machine, they must mean that a digital computer can reproduce human behavior ... by processing data representing facts about the world using logical operations that can be reduced to matching, classifying, and Boolean operations ... All AI research is dedicated to using

3 3 ibid

4 4 ibid

1 1 ibid P.162

2 2 ibid P.163, my emphasis

3 3 ibid P.189

logical operations to manipulate data representing the world, not to solving physical equations describing physical objects ... (however) considerations from physics show only that inputs of energy, and the neurological activity involved in transforming them, can in principle be described and manipulated in digital form".1

But even the weaker form of the assumption -the use of the laws of physics to calculate in detail the function of human bodies, (and brains)- may be physically impossible. There are theoretical limits to processing density! Therefore "the enormous calculations necessary may be precluded by the very laws of physics and information theory such calculations presuppose."2

Nor, Dreyfus argues, does research in language translation and semantics support Turing's or Minsky's interpretation. It raises, instead, insurmountable problems of context and heuristics. This empirical objection is not sufficient to dismiss the assumption, however. Its supporters can "offer the platonic retort ... that we have not fully understood this behavior, we have not yet found the rules.. "3

He bases his central argument on Wittgenstein's. Wittgenstein provisionally assumed "that all nonarbitrary behavior must be rulelike, and then reduce[d] this assumption to absurdity by asking for the rules which we use in applying the rules, and so forth."1

"For the computer people the regress ... stops with an interpretation which is self-evident, but this interpretation has nothing to do with the demands of the situation. It cannot, for the computer... generates no local context. The computer theorist's solution is to build a machine to respond to ultimate bits of context-free, completely determinate data", (my emphasis), "which require no further interpretation in order to be understood. Once the data are in the machine, all processing must be rulelike, but in reading in the data there is a direct response to determinate features of the machine's environment... so on this ultimate level the machine does not need rules for applying its rules. ...So human behavior, if it is to completely understood and computerized, must be understood as if triggered by specific features of the environment."2

The third assumption is thus logically dependent upon the fourth:"A full refutation of the epistemological assumption would require an argument that the world cannot be analyzed in terms of context-free data. Then, since the

1 1 ibid p. 196

2 2 ibid p. 197

3 3 ibid p.202-203

1 1 ibid P.203 He elaborates: "It is a question of whether there can be rules even describing what speakers in fact do. ... one must ..have further rules which would enable a person or a machine to recognize the context in which the rules must be applied. Thus there must be rules for recognizing the situation, the intentions of the speakers, and so forth. But if the theory then requires further rules in order to explain how these rules are applied, as the pure intellectualist viewpoint would suggest, we are in an infinite regress." (ibid P. 203). Wittgenstein resolved the problem in terms of the "practical demands of the situation". For the computer, however, this is not possible. "The computer is not in a situation." (my emphasis)!

2 2 ibid P. 204

assumption that there are basic unambiguous elements is the only way to save the epistemological assumption from the regress of rules, the formalist, caught between the impossibility of always having rules for the application of rules and the impossibility of finding ultimate unambiguous data, would have to abandon the epistemological assumption altogether. This assumption that the world can be exhaustively analyzed in terms of context-free data or atomic facts", (my emphasis), "is the deepest assumption underlying work in AI and the whole philosophical tradition. we shall call it the ontological assumption..."3

The ontological assumption is the profoundest presupposition of AI researchers. It is a fundamental assumption of western philosophical and scientific thought in general:

"As in the case of the epistemological assumption, we shall see that this conviction concerning the indubitability of what in fact is only an hypothesis reflects two thousand years of philosophical tradition reinforced by a misinterpretation of the success of the physical sciences."1

Computers are characterized, (even by the proponents of AI), as accepting a "task environment" defined in terms of discrete objects which are organized into the data structure "which makes up the computer's representation of the world." "Every program for a digital computer must receive its data in this discrete form. ... When one asks what this knowledge of the world is, the answer comes back that it must be a great mass of discrete facts."2

"the data with which the computer must operate if it is to perceive, speak, and in general behave intelligently, must be discrete, explicit, and determinate; otherwise it will not be the sort of information which can be given to the computer so as to be processed by rule. Yet there is no reason to suppose that such data about the human world are available to the computer and several reasons to suggest that no such data exist"3, (my emphasis).

He cites Minsky's attempt to specify the magnitude of the mass of knowledge necessary for humanoid intelligence. Minsky estimates the number of facts required as on the order of one hundred thousand for reasonable behavior in ordinary situations, a million for a very great intelligence. If this doesn't satisfy us, we are to multiply this figure by ten!4 But this immediately leads to the "large database problem" -how could one find the information required in a reasonable amount of time?

"When one assumes that our knowledge of the world is knowledge of millions of discrete facts, the problem of artificial intelligence becomes the problem of storing

3 3 ibid P.205

1 1 ibid P. 207

2 2 ibid P. 208

3 3 ibid P. 206

4 4 Dreyfus argues that the "facts" required may well be infinite!

and accessing a large data base ...and ... little progress has been made toward solving the large data base problem."1

The same problem arises when he considers the problem of disambiguation, (and "context"), in linguistics:

"... finally, human activity itself is only a subclass of some even broader situation -call it the human life-world- which it would have to include even those situations where no human beings were directly involved. But what facts would be relevant to recognizing this broadest situation? ... Well then, why not make explicit the significant features of the human form of life from within it? Indeed, this deus ex machina solution has been the implicit goal of philosophers for two thousand years, and it should be no surprise that nothing short of a formalization of the human form of life could give us artificial intelligence. But how are we to proceed? ... Without some particular interest, without some particular inquiry to help us select and interpret, we are back confronting the infinity of meaningless facts we were trying to avoid."2

He comes to the conclusion that the only way out of the dilemma is to conceive of "facts" as "a product of the situation". "There must be some (other) way of avoiding the self-contradictory regress of contexts, or

the incomprehensible notion of recognizing an ultimate context, as the only way of giving significance to independent, neutral facts....then the only alternative way of denying the separation of fact and situation is to give up the independence of the facts and understand them as a product of the situation."3

His final judgement is severe. Artificial Intelligence research has revealed fundamental flaws in the assumptions we make about mind, brain, and, I propose in consequence, -about our access to the world itself: "Recent work in artificial intelligence (is) a crucial experiment disconfirming the

traditional assumption that human reason can be analyzed into rule-governed operations on situation-free discrete elements -the most important disconfirmation of this metaphysical demand that has ever been produced."1

Dreyfus' is quite convincing in many respects. I specifically disagree with the scope of his objection to the third (epistemological) assumption, however. In the particular form in which he stated it, though, it is unobjectionable:

"that all knowledge can be formalized, that is, that whatever can be understood can be expressed in terms of ... Boolean functions, the logical calculus which governs the way the bits are related according to rules."

1 1 ibid P. 209

2 2 ibid P. 221-222

3 3 ibid P.224

1 1 op cit Pps. 303-304

Neither Boolean functions nor "atomic bits", (context-free "facts"), will suffice -as his arguments ably demonstrate. But Dreyfus extends his legitimate objections to this form of the assumption to an argument against the general platonic case "that whatever can be understood can be expressed in terms of logical relations". But Boolean functions and atomic facts do not exhaust the possibilities either for "understanding" or for "logical relations"! In Chapter 2, (The Problem of Logic), I argued an alternative formal concept, Cassirer's "functional concept of mathematics" and the alternative logic which is its consequence. Aristotelian (and Boolean) logic is the harvest of the Aristotelian (generic) concept! Classical logic -and its modern extensions- consist in the abstraction and manipulation of ultimate, context-free "atomic bits"! They are the calculus-of-abstraction of "marks". They are themselves purely digital, (i.e. discrete), processes, and therefore valid heirs to all the arguments Dreyfus makes against mind, (and thought), in a digital computer. They are not the logic of mind, nor, I argue, of the brain!

Dreyfus' arguments have nothing to do with silicone or copper.1 His arguments are arguments against discrete logic itself, and applicable to any instantiation of the mind-body relationship grounded in it, even a physiological one! The large database problem, the heuristics problem, the context problem, (and the digital computer itself), are all, as problems, products of classical digital, (i.e. discrete), logic, and, ultimately I argue, of its formal concept.

Dreyfus characterized the fourth (ontological) assumption as presupposing that : "all relevant information about the world, everything essential to the production of intelligent behavior, must in principle be analyzable as a set of situation-free determinate elements ... -that what there is, is a set of facts each logically independent of all the others." I would extend his characterization, however. The fundamental presupposition is that "the world" itself consists of such situation-free determinate elements! Dreyfus argues against analysis, I argue against reference.

Finally, I strongly disagree with Dreyfus' "finesse" of perceptual and physical phenomenology into distinct and mutually disjoint domains:

"(This) is not to deny that physical energy bombards our physical organism and that the result is our experience of the world. It is simply to assert that the physical processing of the physical energy is not a psychological process, and does not take place in terms of sorting and storing human-sized facts about tables and chairs. Rather, the human world is the result of this energy processing and the human world does not need another mechanical repetition of the same process in order to be perceived and understood."2

He quotes Neisser:"There is certainly a real world of trees and people and cars and even books. ... However, we have no direct, immediate access to the world, nor to any of its properties."1

but argues contrarily:"Here... the damage is already done. There is indeed a world to which we have no immediate access. We do not directly perceive the world of atoms and electromagnetic waves (if it even makes sense to speak of perceiving them) -but the world of cars and books is just the world we do directly experience. ... 'the human

1 1 He never even mentions them in any significant way!

2 2 ibid P. 268, my emphasis

1 1 ibid

world is the brain's response to the physical world.' Thus there is no point in saying it is 'in the mind,' and no point in inventing a third world -between the physical and the human world -which is an arbitrarily impoverished version of the world in which we live, out of which the human world has to be built up again."2

His evisceration of the problem, (the exact parallel of the eliminative materialist's, for instance), fails to answer important questions: "How perception?", "How mind?" "How is the human world 'the brain's response to the physical world?'" The answer, (on both sides), is that both the problem and the question are the result of semantic confusions. I don't think they are. I believe the platonic ideal can be achieved. The explication of both the mind and the physical world can be encompassed in a comprehensive set of rules, but not by the sort of rules, (or logic), currently envisaged. The dream of one comprehensive knowledge is attainable, but it need not be simple -this book supplies my answer. "If there could be an autonomous theory of performance, it would have to be an

entirely new kind of theory, a theory for a local context which described this context entirely in universal yet nonphysical terms. Neither physics nor linguistics offers any precedent for such a theory, nor any comforting assurance that such a theory can be found."1

My hypothesis of "implicit definition, (Chapter 2), coupled with the "schematic object" , (Chapter 1), supplies the formal beginnings of such a theory. It is an autonomous theory of performance, "a theory for a local context (describing) this context entirely in universal yet nonphysical terms."!

2 2 ibid Pps. 269-270

1 1 ibid P.202

Appendix D: (Roger Penrose)

Roger Penrose categorized scientific theories based on a number of criteria. To the extent that they satisfy these criteria, he classified them all the way from, (his caps), SUPERB down to MISGUIDED, (SUPERB, USEFUL, TENATIVE, MISGUIDED): 1. Scope: -range and variety of phenomena explained, and hitherto unexplained. The scope of the theories Penrose classifies as "SUPERB" is, of course, well known. They explain the whole range of facts of our scientific view of reality: “the actions of the mold on a piece of bread, the dynamics of a violin, the workings of a transistor, and the explosions of supernovas.”

Newton's theory, Maxwell's, the special and general relativities, and quantum mechanics explained vast ranges of phenomena. Their fecundity was startling. 2. Consistency: "Always constrained by logical argument and known facts." (P.422) This is, of course, fundamental. An inconsistent logical system proves, (trivially), both everything and nothing. A theory incompatible with known facts, of course, has no relevancy as a theory of reality. 3. Accuracy: Need not be perfect, but extremely accurate over many orders of magnitude! (Degree of accuracy is a value criterion, however, and is a decision factor in deciding between theories.) The degree of accuracy of the "SUPERB" theories is astounding:

A. Euclidean geometry: "Over a meter's range, deviations from Euclidean flatness are tiny indeed, errors in treating the geometry as Euclidean amounting to less than the diameter of an atom of hydrogen!" (P. 152)B. Galilean and Newtonian dynamics: "As applied to the motions of planets and moons, the observed accuracy of this theory is phenomenal -better than one part in ten million. "The same Newtonian scheme applies here on earth -and out among the stars and galaxies -to some comparable accuracy". (P.152) C. Maxwell's theory: "Maxwells theory, likewise is accurately valid over an extraordinary range, reaching inwards to the tiny scale of atoms and subatomic particles, and outwards, also, to that of galaxies, some million million million million million million times larger!" (P.152)D. Special relativity: "Gives a wonderfully accurate description of phenomena in which the speeds of objects are allowed to come close to that of light -speeds at which Newton's descriptions at last begin to falter." (P.153)E. General relativity: "Einstein's supremely beautiful and original theory ...generalizes Newton's dynamical theory (of gravity) and improves upon its accuracy, inheriting all the remarkable precision of that theory...In addition, it explains various detailed observational facts which are incompatible with the older Newtonian scheme. One of these (the 'binary pulsar'..) shows Einstein's theory to be accurate to about one part in 10 to the 14th power." (P.153)F. Quantum mechanics: Explains "hitherto inexplicable phenomena...The laws of chemistry, the stability of atoms, the sharpness of spectral lines...the curious phenomenon of superconductivity.. and the behavior of lasers are just a few amongst these." (P.153) "No observational discrepancies" (at all) "with that theory are known."

4. Mathematical elegance:

"Both relativity theories -the second of which subsumes the first -must indeed be classified as SUPERB (for reasons of their mathematical elegance almost as much as of their accuracy)." (Page 153) (This relates both to easy utility and to aesthetics!) Again: "It is remarkable that all the SUPERB theories of nature have proved to be extraordinarily fertile as sources of mathematical ideas. There is a deep and beautiful mystery in this fact: that these superbly accurate theories are also extraordinarily fruitful simply as mathematics." (P. 174)

5. Experimental support: -to establish the unique relevance of a theory to reality -to establish correlation to experience. 6. Substantial advance to understanding: -- i.e., it must be a "conceptual organizer". This criterion relates to the mathematical elegance of criterion 4, to future applicability, -and to overall world-view. 7. Simplicity:

"Ptomemaic theory of planetary motion became more and over-complicated as greater accuracy was needed" (P.155). Copernican theory simplified the data of astronomy. "'Tidyness' -quark and lepton theories "are, for various reasons, rather more untidy than one would wish". (P.154) (This criterion is cross-related, clearly, to #'s 9, 8, and probably to #6.)

8. Provides a predictive scheme:"Kepler's and Mendeleev's theories, while accurate, did not provide a predictive scheme and later were subsumed into Newtonian dynamics and quantum theory respectively!" (P.155) It is a criterion of usefulness.

9. Aesthetics:"A beautiful idea has a much greater chance of being a correct idea than an ugly one"..."...The importance of aesthetic criteria applies ...to the much more frequent judgments that we make all the time in mathematical (or scientific) work." ("Always constrained by logical argument and known facts.") (P.421) Also, see his comment on the Relativities. This criterion is transparently a purely artistic one. #'s 1, 4, 6, and 8, (at least), clearly have artistic components as well

Any physical theory satisfying these definitive criteria qualifies as "SUPERB". I believe that the satisfaction of these criteria constitutes a necessary and sufficient definition of a viable "theory of reality" in the general sense as well -i.e for world-views! The adequacy of their fulfillment, taken as a balanced whole, constitutes the actual basis of choice between theories of reality, and, ultimately, between world-views.

Nowhere are these criteria themselves based in a particular conceptual scheme of reality or in specific metaphysical assumptions, however! Any conceptual system of whatever nature actually meeting these criteria, (to include correlation = #3, redundantly), qualifies that system as "SUPERB"! But all these criteria involve solely "relational" aspects of a theory -its internal structural relationality and its relationality to the perceptual model, (and the phenomena). The ranking of a particular theory, -and its believability-, derives from the extent of their fulfillment alone.

Though I dearly love the book, I do not value the "Emperor's New Mind" as a theory of mind-brain. I value it as a wonderful and succinct synopsis of the state of modern physics and as

what I believe is a meaningful formulation of the actual criteria by which we evaluate theories -all theories. To paraphrase one of his reviewers: even if Penrose's ideas are correct, they don't explain consciousness, only how the brain works!382 Penrose's is a theory of physics -and specifically a theory of the physics of brain function. The problem of self-reference, (sometimes referred to as "the mind's I”), which both he and Hofstadter, for instance, treat in terms of Goedel's Theorem is not the most important part of the problem of mind. Though they may well be correct in their resolution of the difficulty, my opinion is that the problem itself, and their proposed solution is an internal one only, i.e. it is an internal, model-model complication of the calculus. I believe it is a problem of ordinary logic, ("associationist logic" in Dreyfus' terminology –or “objectivist logic” in Lakoff’s), rather than of the constitutive logic of implicit definition. That ordinary logic, I believe, stands to our constitutive logic in the same role that diophantine, (integer), arithmetic stands to continuous arithmetic. I believe it is a limited and partial, (though valid), calculus; it is not the continuous and universal logic of mind. Its very concepts are built on the special, limiting case of abstraction, not on (Cassirer's) functional rule of connection, for instance, nor would they countenance my own Concept of Implicit Definition. (Cf. Chapter 2) -i.e. they represent the limit case of a general function and inherit the difficulties of that genealogy.

Appendix E: Dogmatic Materialism and Reality

At the basis of ordinary Naturalism are two fundamental assumptions: that perception (somehow) embodies externality, and that rational thought can utilize the "facts" of perception to discover the actual nature and ground of that externality. It is seriously committed to only one possibility for that ground, moreover, and it is "substance".

I argued the error of the first assumption in my first two chapters. I argued that perception does not embody externality; that its objects are schematic artifacts, embodying the relationality of brain response only. But the brain does not embody metaphysical externality either! It is, following Maturana and Varela, only in "structural coupling" with it. Lacking a metaphysically simple referent for our perceptions, however, (metaphysical) "substance" is no longer an obvious or immediate hypothesis.1 And yet no one can seriously question either the validity or the utility of science!

Why do we believe the things we do? Why, specifically, do we believe in "matter", or "objects" -as absolutes? What else could science, (and physics specifically), concern?

Naturalism, in its modern essence, assumes that the reduction of the whole of reality into biology, chemistry, and physics will be successful. It further presumes that biology and chemistry themselves will reduce, finally, to just physics. History in general supports these conclusions, and this is taken as a conclusive substantiation of the materialist hypothesis.

There are two profound weaknesses in this argument, however. The first is its assumption that physics itself is capable of a further reduction to "substance" -which is certainly not confirmed in recent science but rather contravened.383 The second weakness is its tacit incorporation of a limited logical possibility -i.e. that reduction/replacement is inherently an asymmetrical process! This limited conception of relational possibility, implicit in Naturalism's reductionist argument and leading to the "material" conclusion, is, from a mathematical standpoint, profoundly naive! From

382 This, in my opinion, succinctly sums up the case for Edelman’s hypothesis as well.1 1 Its actual enticement was always sensory anyway: the world had to be "solid"!

383 In the twin-slit experiment, for instance.

the standpoint of abstract algebra, for instance, it is simplistic. Mathematical disciplines are constantly, (and almost at the whim of the author), regrounded, reoriented, and recast. Theorems become axioms and axioms theorems. And yet the discipline retains its integrity!

That one system of relationality, (theory), is capable of embodiment in another is not therefore a convincing argument that converse, -or other transformations, equally viable- are not possible or significant.1 It would be considered mathematically naive to presume that, because of the existence of one orientation, that other "reductions", (transformations), are consequently, (or even probably), impossible, less important or irrelevant!2

But materialism makes exactly that assumption. It assumes that, since the whole of our cultural world is reducing, historically, to biology, chemistry, and physics, that this is a necessarily asymmetric reduction, and that the essence of reality is therefore physical,- and presumably material. From the broadened perspective of the "schematic artifact", however, it is an unnatural and unjustified assumption. The structural coupling of the brain is the embodiment of response -it is the whole of the relationality between "perturbation" and action. Its very "objects" are not metaphysical, (nor "substantial"), but procedural1 -nor are they referential! What is important is not a particular organization, a particular perspective on that structure, but its relationality as a whole!

Theories, as orientations of "data", (and pictorial perceptual "theories" as well), are organizational structures. They are, I believe, transformations mapping the "perceptual space", (the schematic perceptual model), back onto itself.2 As such, following Quine, they are always amenable to profound translation and reorientation -no matter the precision of experimental correlation! What is unique and permanent are the invariants of the system of possible transformations, (including even those which might redistribute the objects themselves) -which embody its relationality as a whole. (See the discussion of hierarchy and mathematical ideals in the “Afterward: Lakoff, Edelman and Hierarchy.

Materialism is profoundly committed to a physical theory of reality.3 It is thereby committed to the best picture that actual physical theory, (not its experimental data), can present - to a succession of theoretical approximations4 refining closer and closer to a picture of its presumed actual objective physical -and material- reality.

1 1 Quine's argument is absolutely conclusive here.

2 2 If we assume that Maturana and Varela's arguments for ontogenic coupling and structural drift are viable, for instance, then the whole of the physical world co-reduces to biology -and to its ontogenic hypothesis specifically! Behaviorism then becomes a "Quinean ladder".

1 1 Nor is a simple correspondence with externality implicit in them.

2 2 They map historical experience/experiment onto future experience/experiment.

3 3 -and to the conclusive evidence of its technology as well! This is materialism's strongest coherent argument.

4 4 This is not to say that successive physical theories refine a particular approximation of the object, but rather that successive theories are believed to be in closer and closer overall correlation to reality- i.e. that successive theories better approximate reality.

"We have only to look about us to witness the extraordinary power that our understandings of nature have helped us to obtain. The technology of the modern world has derived, in good measure, from a great wealth of empirical experience. However, it is physical theory that underlies our technology in a much more fundamental way..." (Penrose, 1989, P.150)

But what sense do materialism's metaphysical assumptions of "object" or "substance" make

to modern physical theory? What sense do they make in the relativistic universe, or in the quantum theoretical one? What is "the object" to modern science? What does "matter", conceived non-reductively as "substance", have to do with modern physics? Physics, as a discipline, has always been ready to question its presuppositions!

Appendix F: "Dennett and the Color Phi"(Towards a Working Model of Real Minds: Dennett, Helmholtz and Cassirer)

I really like Daniel Dennett's "Consciousness Explained"1. It is not because I can agree with his conclusions, (except in a certain sense), that I like it, but because it is a brutally candid and forthright exposition of the Naturalist position, proceeding with compelling logic, and without hedging. It is, moreover, a phenomenologically pure position. I think it is, (agreeing with his own parenthetical question), really "Consciousness Explained Away" however, rather than "Consciousness Explained" because, at the end, "we are all zombies".2 There is one crucial argument he makes against the existence of mental states, (i.e. "figment"), however, in which I think he has correctly identified a profound antinomy -and, I believe, a necessary and major modification to our ordinary conception of mind. He has argued it from "the color phi".

"The color phi" names an actual experiment, suggested by Nelson Goodman, wherein two spots of light are projected in succession, (at different locations), on a darkened screen for 150 msec intervals with a 50 msec interval between them. The first spot, however, is of a different color, (red, say), than the second, (green). Just as in the case of motion pictures, (the "phi phenomenon"), subjects report seeing the continuous motion of a single spot, but interestingly, they report that it changes color, (from red to green), midway between the two termini!1 Dennett bases a very interesting, (and, I feel a very important), argument against the very possibility of a "Cartesian Theatre", against a unity, (and "figment" = substance), of consciousness on this well documented and reproducible experiment. Dennett's argument, in brief, is this:

Mental states, the "Cartesian Theatre", if they exist, are subject to the laws of causality, of time precedence. For one event to affect another, it must occur before it. Let me, for discussion's sake, label the events described. Let E1 be the ("heterophenomenological"2), perception, (hereinafter to be called by me "h-perception"), of the first, (red), spot. Let E2 be the h-perception of the red-changing-to-green, and let E3 be the h-perception of the final green spot.

1 1 Dennett, 1991

2 2 I know, I know! I must, in threat of disingenuousness, quote his footnote to this comment: "it would be an act of the utmost intellectual dishonesty to quote this statement out of context."

But the context he demands is 470 pages of careful redefinition and argument against all the normal senses of mental function and existence -qualia, figment, the "substance of mind". The upshot is that it is O.K., (i.e. socially correct), to be a zombie! But the sense in which his statement would normally be understood out of context is essentially what it still means. He attempts to make any objection, (or any comment on its own prima facie unintuitiveness), unraisable. There is another cult, (besides the Feenomanists!), in the jungle, you see! :-)

1 1 and not, for instance, that it is red all the way till its terminus, with a final and sudden change-to-green.

2 2 Dennett introduces the criterion "heterophenomenological" to describe "mental events", which he does not believe in, to describe whatever-it-is that is named by them, i.e. to talk about them as they are (linguistically) used by real bodies and brains, (which he does believe in), but with a neutral metaphysical commitment.

Dennett argues, based on the principle of causality, that E2 cannot occur until after E3. Since there were only two actual, (physical), events, (the first and second projected spots), he argues that the h-perceived midpoint, (the "mental event", i.e. red-changing-to-green), cannot occur until after the reception of the second actual event, (green projection), as it was that which provided the very sensory data necessary to the h-perception of change. Other than a (mystical) hypothesis of "projection backward in time", there remain for Dennett just two possibilities for an internal, "Cartesian Theatre" consistent with the experiment: the "Stalinesque" and the "Orwellian" hypotheses.

The first involves the creation of a "show trial" staged by a subterranean "central committee", (after the fact of both real events, of course, and involving a "delay loop"), wherein the complete, (and partially fabricated), sequence, (red ->red-changing-to-green -> green), is "projected", (i.e achieves sentiency). Under this hypothesis, the whole of our sentiency, our consciousness, occurs "after the fact". The second possibility, the "Orwellian" hypothesis, is that the actual events are received by our sentient faculty as is, but that our memory then rewrites history, (just as the thought police of Orwell's "1984" did), so that we remember not two disjoint and separate events, but the connected, and pragmatically more probable sequence red -> red-changing-to-green -> green.

Dennett argues that ultimately neither theory is decidable -that either is consistent with whatever level and kind of experimental detail science may ultimately supply, and that, therefore, the only pragmatic distinction between them is purely linguistic, and therefore trivial. He argues that there is no "great divide", no actual moment, (nor existence), of sentiency, but only the underlying brain process, (which all theories must countenance), itself. Based on the "spatial and temporal smearing of the observer's point of view", he expounds his thesis of "multiple drafts" wherein there is no "theatre", only brain process -and its various "speakings", (drafts).

And yet the observer himself has absolutely no problem with these events! His perspective is very clear: E1 -> E2 -> E3. It is our interpretation, (and rationale), for this sequence that causes the problem.

I think Dennett has a very strong argument, but I want to refocus it. Nondecidability is all very well and good, but it is a much weaker line than the one he started out with- on the possibility of synchronization! In a very real sense, I feel it is very similar in intent and consequence to Einstein's "train" argument against simultaneity.

Consider, (with Einstein), an imaginary train moving (very fast)1 down a track, with an observer standing midway on top of the moving train and observing two (hypothetically instantaneous) flashbulbs going off at either end of the train. The train goes by another (stationary) observer standing (hypothetically infinitely) close by the track as the bulbs go off. Suppose that the moving observer, (OT), reports both flashes as simultaneous. He argues that since both photon pulses reach him simultaneously, (granted for all frames on the local, infinitesimal scale, and thus agreed on (?) by both observers who are assumed infinitely close -i.e. side by side), that therefore the pulse from the rear of the train, having to "catch" him, must have left its source sooner than the pulse from the front which added his velocity to its own and so must have left later. Relative to OS, (stationary observer), however, the two sources travel the same distance to a stationary target, (himself). Since OT and OS are momentarily adjacent to each other, (i.e. within a local frame), they should be able to agree that the two pulses arrive there simultaneously. What they cannot agree on, however, (in that instance), is whether the events, (the flashes), occurred simultaneously -nor that the other could have thought, (i.e. could have observed), them so! Time, in Dennett's

1 1 nearing the speed of light

words, is "smeared"!2 We could, of course and significantly384, vary the parameters to make either event "earlier" and the other "later".

The argument is that from the standpoint of one observer, he must maintain that the other cannot see them as simultaneous, and vice versa! Thus from OS's standpoint, if he sees them as simultaneous, then, since he is stationary, they occurred simultaneously. But if they occurred simultaneously, and since OT is moving, then OT cannot, (OS argues), see them as simultaneous, (and conversely). And yet both observers pass through an infinitesimal local frame of reference, (side-by-side). Time is "smeared"!

Just as Einstein's two observers, near the limits of physical possibility, cannot agree whether the two lights were simultaneously flashed at the ends of the train or not, (i.e. cannot establish a common temporal frame of reference), nor that the other could observe them locally as such, neither, given Dennett's pointed argument, can we establish a common temporal frame of reference for "the world" and "the mind" at the limits of cognition.1

I agree with Dennett that "the color phi" identifies a legitimate and critical aspect of the mind-body problem. The spatial and temporal "smearing" of the percept and the non-explicit reference of qualia that he demonstrates forces a profound extension to our traditional conception of the "theatre". But his dimensional "smearing" actually fits very well2 with the model I am proposing. I submit that it is more plausible in terms of the "focus" and "function" of an operational object than in terms of his "multiple drafts", "demons" and "memes" in the "real world". His objections to the ordinary "Cartesian theatre" are admittedly valid, but so were those of Cassirer and Helmholtz before him:

"For example, if we conceive the different perceptual images, which we receive from one and the same 'object' according to our distance from it and according to changing illumination, as comprehended in a series of perceptual images, then from the standpoint of immediate psychological experience, no property can be indicated at first by which any of these varying images should have preeminence over any other. Only the totality of these data of perception constitutes what we call empirical knowledge of the object; and in this totality no single element is absolutely superfluous. No one of the successive perspective aspects can claim to be the only valid, absolute expression of the 'object itself;' rather all the cognitive value of any particular perception belongs to it only in connection with other contents, with which it combines into an empirical whole.

...In this sense, the presentation of the stereometric form plays 'the role of a concept'", (my emphasis), "'compounded from a great series of sense perceptions, which, however, could not necessarily be construed in verbally expressible definitions, such as the geometrician uses, but only through the living presentation

2 2 Are the observers, (and the experimental apparatus), then "heterophenomenological"?

384 ? i.e. -relative to Dennett's problem1 1 For macroscopic science, these limits are at the scale of the speed of light. For atomic physics, they are at the scale of Planck's constant. And for the brain, I suggest, they are at the scale of minimal biological response times, i.e. in the 100 msec. range.

2 2 when taken "heterophenomenologically" -i.e. with a neutral ontic commitment. Heterophenomenology works both ways!

of the law, according to which the perspective images follow each other.' This ordering by a concept means, however, that the various elements do not lie alongside of each other like the parts of an aggregate, but that we estimate each of them according to its systematic significance...." (Cassirer, 1923, pp. 288-289, citing Helmholtz)

But Cassirer's reformulation of the formal concept itself must be considered for an understanding of his meaning here. The concept, for Cassirer, is a function. It is "the form of a series", independent and distinct from what it orders. This is the "systematic significance" which he purports. I urge, extending Cassirer's insight and in the sense of my conclusions of Chapter 2, that the stereometric form itself, the percept,1 then plays the role of, (is), a function.

From the standpoint of (relativized) Naturalism,2 if we take the mind to be schematic, but specifically a "predictive" and "intentional" schematic model, (which extension I will suggest shortly), rather than a static and "representative" one385, then the temporal and spatial "smearing" of the percept do not have the implications against the "theatre" per se that Dennett attributes to them. I have argued that the percept itself is conceptual, (albeit specialized, invariant and constitutive), and therefore, following Cassirer, functional. It is an entity of order and process -and it is "smeared". That is the normal nature of functions -they are smeared! What Dennett explains by "multiple drafts", (and the "demonic" process he envisions beneath them), I explain by "focus". We focus the percept, (via implicit definition) according to operational need.

An Extension of the Schematic Model: A Brief SketchLet me frame the following in the language of ordinary Naturalism, (this will be a short

appendix). I want to sketch a very large canvas very quickly.1 In "the color phi", I think that Dennett has identified a very important difficulty in our ordinary conception of mind. It suggests an enlargement and a more sophisticated perspective on the schematism I have argued heretofore. Though I think I have successfully laid the solid foundation, let me now sketch the design of the cathedral itself, i.e. the design of real minds!

I have dealt, previously, with the schematic object. I argued that the object of perception is a schematic artifact of reactive brain process, specifically "designed" to optimize a simple and efficient "calculus" of response. But the converse side to that argument is that an actual calculus was enabled! What are the (Naturalistic) implications of that calculus, and of the schematic model?

Follow me in a thought experiment! Keeping your eyes fixed to the front, you perceive, (in your perceptual model), this paper in front of you, the wall behind it, and, perhaps, the pictures of

1 1 This, the percept as concept, is clearly at odds with, but, (I have argued), a legitimate extension of, Cassirer's ideas. He did not have the perspective of the schematic object.

2 2 cf. Chapter 4

385 ? i.e. vis-à-vis current process1 1 I could, of course, try to footnote every misconception and every possible claim of inconsistency, but we have already done that, haven't we? I think I have paid my dues. "Predictivity", "intentionality", et al are, under my thesis, perfectly valid conceptions within the Naturalist "form" - and I may consistently use them as such without self-contradiction! Within the context of my larger perspective, they are model-model correlations, synthetic a priori "slices" across the phenomena.

your family. There may be pens and pencils, books. You may hear music from the stereo next to you, (and perhaps still in peripheral vision). There may be a window, and the lights of the neighbor's house beyond it. But there is no wall behind you! There is no car in the driveway outside of your house -indeed, there is no "house" at all. There is no city, no taxes, no friends. The sun does not exist in this model. There is no government, no "universe", -no tomorrow! The (purely) perceptual model is incomplete as a model of "reality" and it is, (Naturally!), inadequate even to keep you alive! There is something else necessary for completeness of the model detailed in this book, i.e. a new perspective on it. It is an intentional aspect. It is necessary to supply the object behind your back and the reality "over the hill"! It supplies the connection to "tomorrow" and "yesterday". It supplies "causality". It is necessary for the completeness of a model of "the world". It is necessary, (specifically following Dennett!), even for the individual "objects" of perception itself, (E1 and E3 for instance). This model, I suggest, is where E2, (the object of Dennett's perplexity), lives. It cohabits there very comfortably with E1 and E3 which, I argue, are also predictive and schematic objects. There is a seamless integration, (above the scale of 100 ms, let us say), of what we normally think of as our pure percepts and the intentional fabric within which they are woven.386 This model, I believe, is the actual "home" of mind, and the legitimate purview of a truly scientific psychiatry.387

"Now what is a phenomenal space? Is it a physical space inside the brain? Is it the onstage space in a theater of consciousness located in the brain? Not literally. But metaphorically? In the previous chapter we saw a way of making sense of such metaphorical spaces, in the example of the 'mental images' that Shakey, [a robot], manipulated. In a strict but metaphorical sense, Shakey drew shapes in space, paid attention to particular points in that space, based conclusions on what he found at those points in space. But the space was only a logical space. It was like the space of Sherlock Holmes's London, a space of a fictional world, but a fictional world systematically anchored to actual physical events going on in the ordinary space in Shakey's 'brain'. If we took Shakey's utterances as expressions of his 'beliefs', then we could say that it was a space Shakey believed in, but that did not make it real, any more than someone's belief in Feenoman would make Feenoman real. Both are merely intentional objects.... So we do have a way of making sense of the ideas of phenomenal space -as a logical space." Dennett, 1991, pps.130-131, my emphasis.

386 But let us turn Dennett's argument around. Dennett argues strongly and convincingly that "figment", (mental states), are logically inconsistent with our, (his), ordinary (naïve) views of cognition and reality. If, instead of accepting his conclusion however, we choose to accept the reality of that figment -E1, E3, and E2, -if we believe that E2 is actually perceived, (whatever it may be), then his argument takes on a different import and works against the very ground in which it was framed: i.e. his ordinary view of cognition and the Naturalism, ("objectivism"), in which he embedded it. The "color phi", he says himself, embodies a precise and reproducible experiment -you and I would both expect to "see" it!I consider the "phi phenomenon" itself more interesting than the "color phi", however. The credibility and intentional depth of a series of oversized, rapidly sequenced still pictures, (a movie), is quite suggestive. Its potential for an uncanny parallelism with our ordinary experience suggests that the latter, (i.e. ordinary experience), is itself a predictive and integrative phenomenon grounded in a schematic, intentional model in precisely the same manner as I propose the "color phi" to be.

387 ? Consider the world-views implicit in paranoia or schizophrenia, for instance, or in bipolar orientations

But this is my exact conclusion of Chapter 2. Dennett and I are not so very far apart after all -save in our metaphysics, (wherein we are very different). Mind is a logical entity -i.e. its "space" is a logical space. But Dennett's "mind" is based in associationist logic (after Dreyfus' usage388), and dead, and mine is based in a functional logic, (the constitutive logic of Kant), and live. We are not zombies!

On the issue of metaphysics, on the other hand, Dennett specifically argues that "nature does not build epistemic engines."1 Why, then, does he think that he, either as a physical engine of process, (and the "demons" of process), or as a linguistic engine of "memes", -is epistemic, (i.e. metaphysically so)?2 I don't think that he, or I, are. This was my exact conclusion of Chapter 4.

388 ? Or "objectivist" logic after Lakoff's1 1 Dennett, 1991, P.382

2 2 Or that his book is so?

Appendix G: An Outline of the Semantic Argument, (For Philosophers)

This appendix is the logical outline and synopsis of my argument I promised in the Introduction. Though the line it traces is complex, I think it reflects the actual complexity of the mind-brain problem itself and defines a plausible solution for the first time.

Outline of Argument:1. Chapter 1, (the presentation of my first hypothesis), is not, in itself, primarily

argumentative in form. It is, rather, the constructive exhibition of what I believe is a more plausible evolutionary alternative, (and a specific counterproposal), to the representative model of cognition. This, the schematic operative model, is my hypothesis about the origins and the organization of the brain. I propose that "cognition" and human reality, (viewed from a contemporary Naturalist perspective), is a purely schematic, (i.e. internally organizational rather than representational), artifact of (reactive) evolutionary process. The plausibility of this first thesis is argued on the basis of innate design constraints for the control of specifically -and especially- complex and dangerous processes. This, I propose, was exactly the "engineering problem" that evolution was faced with in the design of control systems for complex metacellular organisms. The primary argument for this model, and against representation, (even behavior isomorphism/representation), is made elsewhere -at the conclusion of chapter 2, in chapter 3 and appendices A and B. The only argumentative, (per se), aspect of this chapter lies in what I believe is its stronger evolutionary plausibility vis a vis representation.

2. Chapter 2 approaches the mind-brain problem from the other side, (i.e. mind-brain |div|1

mind). It presents my hypothesis for the origin and the organization of the mind. This chapter too is primarily constructive, (rather than argumentative), and constitutes a totally independent line of investigation from that of chapter 1. It investigates the nature of logic and specifically of the formal logical concept, (/category). It expands Cassirer's insight that the logical concept, (category), is a "new form of consciousness" profoundly distinct and independent from those of perception and abstraction. I expand on Cassirer's highly original and mathematically oriented, (and generally overlooked), logical results,2 plausibly extending them in terms of (one of) Hilbert's pivotal and purely mathematical revelation(s), i.e. "implicit definition"389, to conclude that mind itself is a single (higher order and, like Cassirer's, a rule-based) concept, the (constitutive) "concept of implicit definition". This, I argue, is the only "form of consciousness", subsuming all the others. But this concept, like the axiom systems of abstract mathematics, internally, (rather than referentially or oppositionally3), resolves its very objects. Nor are they local, but global. It supplies thereby, for the first time, a plausible rationale for the "Cartesian theatre", i.e. awareness. 1 1 divided by

2 2 Throughout his later writings, Cassirer constantly refers back to "Substance and Function" wherein he developed the logical ideas which are their basis. cf, e.g. "Einstein's Theory of Relativity", "Symbolic Forms", "Determinism and Indeterminism", etc.

389 ? as strongly distinguished from Hilbert’s “formalism” which was specifically a theory of proof and quite distinct

3 3 i.e. as opposed to presentation vs. attention/abstraction

For how, in Leibniz' formulation, could the many be expressed in the one? How could this part of even a "mental substance" know that part? This is a purely logical problem -the problem of the "homunculus".

Implicit definition390 permits knowing, (as a whole -i.e. "the one"), what are, in some real sense, our distinct and separate parts, ("the many"). This is because those parts, (objects), are in fact non-localized and virtual (logical) expressions of the whole, (the rule). It opens a genuine possibility, therefore, for the resolution of this essential requirement of "naive" consciousness.

"Implicit definition" takes on a new significance in light of Cassirer's reinterpretation of the formal logical concept, and a new, (and very different) application to the mind-brain problem in view of my first thesis. If the function of mind and brain is primally organizational rather than referential, then "interpretation" as an assignment of meaning -and reference- is no longer the crucial issue -other than as it applies internally to the model itself. (Chapter 4 deals specifically with the problem of reference. Appendix B is also directed to this issue.)

3. Combining the conclusions of the second chapter with that of the first, I conclude that if we identify the mind as the single (higher order and constitutive) “concept” defined by the primitive logical, (i.e. logically behavioral), rule of the brain, (legitimized under the new formal concept), then a perfectly natural and plausible physical definition of "mind" is possible: i.e. that the mind is the concept1 of the brain! But here both "concept" and "logic" are themselves interpreted reductively -biologically and operationally, (i.e. materially). This, I propose, is the physical, (i.e. Naturalist), answer to the mind-body problem.2 But the combination of the first two hypotheses creates a staggering epistemological problem, and involves moreover, (so it seems), an obvious self-contradiction. If both our perceptual and intellectual objects are solely artifacts of biological coordination, then on what ground can knowledge, (and my own argument), stand? If the very language, (to include the very "biological coordination" and "evolution" of my argument), in which I describe the problem, (being part of that self-same human reality), is only internally organizational and not referential, then what is it that am I describing? How can I even discuss the problem itself? Doesn't my theory contradict itself? How, then, could there be science at all?

4. Chapter 3 makes the first thrust towards the resolution of this epistemological problem, (created by the combination of the first two theses). It also lays the groundwork for a solution of the metaphysical problem of existence -i.e. "Where could a mind exist?". Framing my argument in the context of Maturana and Varela's "Tree of Knowledge", (and specifically in their concept of "structural coupling"), I argue an initial Kantian conclusion of "substantia phaenomenon" confirming what I consider to be the two minimal and necessary (Kantian1) realist assumptions: the "axiom of externality" and the "axiom of experience". (These will also lay the foundation for my solution of the problem of existence.)

390 ? and the concept of implicit definition1 1 alternatively, the behavioral rule

2 2 Please note that I am not just saying that we can have a conception of the mind, but rather that mind itself is a single (functional) concept (== rule) of a "higher dimension".

1 1 who, I argue, was very much a realist!

5. Building on the groundwork of chapter 3, chapter 4 tackles the epistemological difficulty head-on. Building on -and delimiting- Cassirer's thesis of "symbolic forms", (itself rigorously based in actual scientific methodology), I argue that knowledge is not referential, but organizational. With Cassirer, I argue that the essential flaw in the referential conception of knowledge, ("scientific realism"), lies in its confusion of a particular "frame of reference", i.e. "symbolic form", (and its assumption that there is only one comprehensive frame possible2), with the invariant relationality of experience in the abstract, (i.e. under all consistent frames). This, we argue, is the heart of the issue. It results in a confusion of a specific organization of experience with the experience itself,1 which is organized. It results in an (improper) assignment of (unique) metaphysical reference rather than a (legitimate) judgement of empirical, (i.e. experiential), adequacy for the primitives of the theory. I believe that Cassirer was, in fact, very much a modern "antirealist"2, (though I question the ultimate scope of his conception), and argue that his essential solution is, in Van Fraassen's terminology, "coordinate-free". His reformulation of the formal logical concept, (/category), allows a new logical possibility and an escape from the dilemma.

Just as Einstein relativized measurement and disembodied the ether, so did Cassirer argue for a scientific relativization of knowledge, and a disembodiment of direct reference. But Cassirer's is not a frivolous, laissez-faire relativism, (nor is it solopsism); it is an explicit and technical -I might well say "mathematical" epistemological relativity rigorously grounded in the phenomenology of science.3

I argue beyond Cassirer however that "experience" itself may be defined as precisely the relativistic invariant under all consistent and comprehensive worldviews, (forms). The relativism that I argue is a rigorous one grounded in the principles of science; its invariants are experience. This conclusion, I maintain, resolves the epistemological problem created by my first theses.

Nowhere does Cassirer, nor do I, question the profound effectiveness or the legitimacy of modern science. His orientation is wholly and profoundly scientific. Rather, the various sciences are preserved as perspectives, as organizations of phenomena. Cassirer has provided the tools necessary to resolve the epistemological dilemma created by the combination of my first and second theses.

For even though my thesis assumes the validity of the Naturalist organization, (at least on the human scale), it does not assume the metaphysical reality of Naturalism's primitives thereby. In questioning our actual, (referential), cognition of metaphysical reality, it is not, therefore, innately self-contradictory! Though stated in Naturalist terms, (as a legitimate but relative organization -and its terms as "focal points" of that organization), my thesis can consistently and

2 2 i.e. Naturalism

1 1 to include scientific experiment as an extension of ordinary experience

2 2 a word I consider to be a total misnomer

3 3 Why is Einstein not saying that any measurements, (at all!), are valid? Why is Einstein's itself not a laissez-faire physical relativism? It is because there is a rigid structure at the core of his assertion -i.e. the specific, (and precise), invariant equations of relativity. It is the rigid and invariant "equations", (alternatively "the topology"), of experience that structure valid theories. These "equations", this "topology", must be retained as invariant(s) under all viable theories. This is why neither mine, nor Cassirer's, is an irenic relativism. Also see my discussion of the “ideals” of Abstract Algebra.

legitimately question the actual (metaphysical) existence of, (and even the possibility of knowledge of), absolute referents of those terms!

Repeating my conclusion of chapter 4: the results of my first two theses are therefore consistent under this epistemological rationale. The resolution lies in the scientifically and mathematically, (but most certainly not arbitrarily), conceived relativization of knowledge itself. Relational implications, predictive systems, (to include scientific theories), are not, (with Quine), epistemologically determinate. Rather, their essence, (which is their predictivity), can be isolated, (following Cassirer), as relational invariants, (in a mathematical sense), over the field of consistent hypotheses in a sense parallel to that in which Einstein's equations of special relativity were isolated as invariants from the "ether" in which they were originally grounded by Lorentz. Or, rather, relational implications are invariant, but predictive organizations, (i.e. theories), even comprehensive ones, are not! They are the (better or worse), "SUPERB" or "MISGUIDED"1

"forms" which organize those implications.It is in Cassirer's sense of the organizational,1 rather than the referential relevance of

theories that I propose that the relations of ordinary Naturalism -and my own thesis as well- can be, (must be), retained in a deeper realism.6. Building on the results of chapters 3 and 4, chapter 5 proposes an actual solution to the problem of the "substance", (the "figment" in Dennett's mocking characterization), of mind. But the problem has now, (by virtue of the perspectives gained in chapters 3 and 4), been considerably simplified.

I propose that the actual and metaphysical basis for mind is already presumed under any and all realist, (i.e. not idealistic), conceptions of reality. And that presumption is that of the interface itself -i.e. the connectivity necessarily, (a priori), presumed, (howsoever it may be reduced/explanatorily-oriented under any particular conception), between a cognating entity and the external reality in which it exists. It is that minimal interface itself, conceived in its most abstract and minimal sense, (as a limit) -the intersection of necessity of all realist theories- which I maintain, (as a realist), therefore metaphysically exists! It is apodictic, (by definition), under all realist worldviews.

But I maintain furthermore that this minimal, (and analytically conceived), interface is sufficient to the problem of the substance of mind as well. If it is assumed that this (minimal) interface (metaphysically) exists,391 and if it is furthermore assumed that it is structured as postulated in my first two hypotheses, then mind itself (metaphysically) exists! It fully and internally defines -and knows2- its objects! This is my third hypothesis. I conclude that we, as minds, are (metaphysically == truly) real! We do (metaphysically == actually) exist! We are sentient!

The problem of substance was caused, I argue, by Naturalism's overstrong metaphysical presumptions which left no room for, and concealed the possibility for a (metaphysical) reality of mind. To repeat myself, the problem was that (Van Fraassen's) "egg" of Naturalist metaphysics was just too full and left no room for anything else. Or, rather, we were ignoring the shell!

1 1 cf Penrose "The Emperor's New Mind" (his CAPS!)

1 1 i.e. as organizations of phenomena

391 which, as realists, we must2 2 i.e. it does not just "account for" them

End of Outline.

In a serious, (and regrettable), way I suppose that the form and the order of my argument is in itself confusing -it is certainly complex. But it is complex, necessarily I think, because I am proposing a very different paradigm wherein even the simplest questions demand new answers. On the most general level of organization, I argue backwards, (analytically). rather than forwards, (synthetically), but I feel the nature of the subject, and the demands of comprehension compel me to do so. Each of the three steps reorients and reevaluates, (and to some extent invalidates), the one before it. They are each, as Kant calls such a move, a "Copernican revolution", and this disorientation is in the very nature of such moves. There is good precedent for such a plan, however. They have constituted the most effective and the most critical strategies of our intellectual history and are the actual record of our scientific advance. It is also the way we necessarily learned in school. Before we could adopt more sophisticated perspectives, we were required to "learn our facts" in more simplistic settings.

Do not be confused. I have, for the most part, talked the language of ordinary Naturalism -as I must and should. It is good language. We must accept the reality of the experience which we necessarily (?) describe in Naturalist terms. But we needn't thereby accept the absolute reference which Naturalists demand. I argue, ultimately, that our naive, human-scale world stands to the ultimate reality beyond it in the same relationship that modern physics does, i.e. that of ontic indeterminism.

8. I equate the ultimate worth of my theory with the practical and pragmatic results it will, (or will not!), ultimately generate. Though I, (personally), feel it is innately beautiful, it is certainly a large meal to swallow. But just as the (beautiful and esoteric) theories of modern physics damage our naive psyche, so do they produce immediate, practical, and unarguable results, impossible without them. So do I propose that my thesis will produce the immediate and pragmatic results vis a vis neuroscience, (amongst other things), that we so desperately need. The mind-body problem is the key to the whole of human culture, and I believe that I have supplied its first truly plausible solution.

Question: on what basis did we ever presume that the foundations of biology, philosophy and psychology were necessarily more simplistic than those of modern physics? If the solution to the mind-body problem were that easy, would it not be a long settled question?9. Mine is a realist theory. It is not idealism, no more than was Kant's. Rather, (repeating Kant's claim), it bridges the gap between realism and idealism and resolves their differences. It resolves the mind-body problem and is eminently compatible with contemporary science.

Appendix H : Extended Abstract This book presents a tentative but comprehensive solution to the mind-body problem. The

approach is classical rather than merely technically innovative, and triangulates the answer between three distinct but related theses: one biological and evolutionary, one logical, and one epistemological. Though individually controversial, I argue that together they constitute the first plausible and truly adequate answer to the mind-body problem.1. My first hypothesis, (in agreement with Maturana and Varela, Freeman and Edelman, for instance), asserts that the brains of organisms, (human or otherwise), do not embody representations of their environment as realists generally assert. I propose further, however, that the "objects" of those brains embody schematic and virtual organizations of reactive biological process instead. I propose that their primary evolutionary purpose was to enable an internal operational and calculational simplicity uniquely empowered by a virtual object. I argue that this simplicity and its implicit efficiency was necessary for the adroit functioning of profoundly complex metacellular beings in a hostile environment. This purpose, I argue furthermore, was actually antithetical to a representative role. (The apparently self-defeating epistemological implications are resolved in my third thesis.)2. Contrary to Dennett, Hofstadter, Churchland, et al, my second hypothesis asserts that the problems of sentiency –of consciousness: the "homunculus" problem, the "mind's eye", "the Cartesian theatre",... are capable of solution, (and I have proposed an explicit one). Indeed they must be if mind in our ordinary sense of the term is to exist at all. But they are not solvable within the confines of classical Aristotelian logic or its modern embodiments. Current logic, still based essentially in the Aristotelian, (i.e. "generic"), formal concept, is inadequate, I maintain, for the specifically logical problems implicit in the mind-brain problem. Building on Ernst Cassirer's innovative rule-based, (rather than property-based), reformulation of the classical concept itself, (his "functional concept of mathematics"), and a new application of David Hilbert's brilliant logical reorientation of mathematics onto purely axiomatic grounds: "implicit definition", (as strongly distinguished from his "Formalism"), I propose a further extension of Cassirer's technical Concept, (and its subsequent logic), largely equivalent to the complex rule of an axiom system. It is the “Concept of Implicit Definition”, (CID). Following and extending Cassirer's cogent arguments, dualism and opposition, (innate in classical logic and themselves the basis of the “homunculus”, I argue), are then no longer innate in this new Concept. As Cassirer argued for his own “Functional Concept of Mathematics”, CID no longer derives from presentation vs. attention and abstraction in cognition- which latter is generally accepted as the theoretical basis of the classical Concept, but is unary and internally, (i.e. logically), resolving of its objects in the sense of modern mathematics. The extended Concept, (CID), is no longer confined to intellectual cognition, (i.e. logic and concepts), however, but is adequate to perceptual cognition, (i.e. "objects"), as well. It is part of a constitutive logic in the sense envisaged by Kant. In concert with the first hypothesis, (non-representation == "not presentation"), it allows a solution of the logical problem by permitting cognition and "objects" without presentation and the latter's implicit oppositional "cognator" -i.e. without a homonculus. Reconceiving brain function as organization rather than representation allows mind and cognition in our ordinary, unified sense.

A significant corollary of this hypothesis is that it allows mind to be productively defined as the biologically logical, (i.e. operative), "concept", (as an expression of the behavioral rule), of the brain. (But here "logical" itself and "concept" itself are taken in a reductively materialist sense.) This is an important result since I have argued that it is only in taking our objects as

specifically logical objects that the homunculus problem can be solved, and it shows the relevance of that conclusion to the biological problem. But the "logic" just mentioned is biological logic in the sense of the first hypothesis. It is the “calculus” of our biological “schematic model”.3. My third hypothesis is epistemological, an extension of Kant's, and ultimately of Cassirer's epistemology. Its purpose is to reconcile the apparent self-contradictions of the first two hypotheses and to supply, as well, a plausible answer to the "what" of mind. Expanding on, (and modifying), another of Cassirer's original conceptions, his theory of "Symbolic Forms", it resolves both the problem of reference raised by my prior theses and that of their seeming inconsistency as well, (their being stated in the very language of reference). Arguing from Hertzian grounds, Cassirer maintained that our knowledge is organizational, (as an organization of the phenomena), rather than metaphysically referential. There is, he argued therefore, a plurality of alternative and equipotent (symbolic) "forms", (and their concomitant "objects"), corresponding to different possible organizations of the phenomena and different organizational intents.392 It is the confusion of (the "objects" of) a particular form with the invariant relationality of the phenomena which it organizes, he argued, which leads to an unwarranted assertion of metaphysical reference for its objects. His is, as Swabey stated it, a genuine "epistemological theory of relativity". I argue that it is "coordinate free", (and non-referential), in Van Fraassen's sense as well. It allows my first and second hypotheses to stand as consistent, though relativistic, organizations of the phenomena using the language of naturalism, but without the latter’s commitment to reference. I further argue an essentially Kantian position consistent with Cassirer's to reduce the de facto metaphysical presumptions of naturalism to their legitimate and necessary minimum. This, surprisingly, leaves room for the actual existence of a "substance" of mind for which I propose a specific and plausible answer. There remain, of course, significant problems. The most obvious of which still remains "reference". But I argue that there is a categorical difference between metaphysical reference and the internal, model/model automorphisms of what I maintain is our logically closed human cognitive world. (cf Quine). It is the latter which constitute the problem of science, and I have suggested a particular kind of automorphism between the brain and the world. (See Appendix B).

392 This is clearly parallel in many respects to the function and intent of Lakoff’s “Idealized Cognitive Models”!

However totally "antirealistic" it may sound, I will argue that my thesis is more compatible with contemporary science than any alternative currently proposed. It preserves science and ordinary experience as well.

184

Afterward: Lakoff, Edelman, and “Hierarchy”

As I mentioned in the Introduction, I had not seen George Lakoff’s “Women, Fire, and Dangerous Things” nor Gerald Edelman’s “Bright Air, Brilliant Fire" until very recently. It was remarkable to me, therefore, to see how closely Lakoff’s logical and epistemological conclusions resembled those of Cassirer393, (considered as the combination of Cassirer’s dual theses: his logical thesis of “the functional Concept of mathematics" and his epistemological thesis of “Symbolic Forms”), and how closely Edelman’s biological and philosophical answers, based in Lakoff’s and his own original work, resembled my own conclusions. There is an uncanny parallelism of structure, (though not of consequence), between the paths we have followed to arrive at our conclusions.

Our structural differences are differences of degree –but important differences. I believe that Lakoff, (and Edelman), have gone too far in the case of logic, and not far enough in the case of epistemology. They fail394, crucially thereby, to provide the grounds for an answer to the ultimate problem: i.e. how can “mind” or “consciousness”, (normally taken) coexist with the existence of the brain? Lakoff:

Lakoff grounds his work in logical reflections of Wittgenstein395 which questioned the adequacy of the classical logical Concept and in the work of Rosch and a host of modern empirical researchers which further challenged that classical Concept by demonstrating exceptions in actual human usage of language and concepts across cultures and even within our own legitimate contemporary usage. From these grounds and his own original work, Lakoff drew strong conclusions about the nature of logic396 –and the human mind- itself.

The Classical ConceptThe classical concept397 is defined “by necessary and sufficient conditions” -that is, by set

theoretic definitions on properties. It is an elementary theorem of logic that the whole of the operations of sentential logic, for instance, may be grounded solely in the primitive operations of intersection and complement.398 More generally, logical sets and categories, (concepts399), are defined on presumed “atomic properties” and are commensurable wholly based on the set-theoretic possibilities of those sets –i.e. union, intersection, complement, etc.

Concept-sets, (within this classical perspective), express a hierarchical “container schema” moreover, (using Lakoff’s language). Though Lakoff frames his discussion to the same

393 Of which Lakoff, apparently, was unaware394 -innocently for Lakoff who never promised such an answer, but more pointedly for Edelman

who did395 E.g. Wittgenstein’s “family resemblances”396 compare Cassirer: "... Every attempt to transform logic must concentrate above all upon this

one point: all criticism of formal logic is comprised in criticism of the general doctrine of the construction of concepts." –cited at the beginning of my Chapter 2.

397 Lakoff is concerned with primarily with categories, but the distinction is technical and not necessary to this discussion. Cassirer dealt specifically with concepts, but he covered essentially the same ground.

398 Or on other subsets of set operations as well399 See prior footnote: categories vs. concepts

185

end slightly differently, by this I mean that whenever we classically specify a genus, we do so by eliminating one or more of these atomic properties, (by intersection of the properties of species), at the same time thereby specifying an expanded extension, (union) –i.e. the set of “objects” which the genus concept encompasses. The delimitation, (by property containment), of the genus category is contained within, (is a subset - an intersection of), that of the species category while the extension of the species category, conversely, is contained within, (is a subset of), the extension of the genus category. In specifying a species category on the other hand, we do so by adding one or more properties –ultimately “atomic properties” to the properties of the genus concept and this species concept encompasses a diminished, (intersectional), extension of the extension of the genus.400 This classical categorization therefore expresses an absolute, rigid and nested hierarchy of levels and containment. In Lakoff’s terms it expresses a hierarchical “container schema”.401

Ultimately, (because they are nested), at the limits these processes specify (1) a largest concept: “something”, (defined by no atomic properties), whose extension is “everything”, and (2) a smallest concept: a particular “object” in reality, (or possible reality), defined by all its atomic properties402. Given the classical paradigm then, reason necessarily begins with “something”, (the most general concept), and points, inexorably, to some ”thing”, i.e. a specific object.403

But Lakoff plausibly argues that concepts404 in legitimate human usage are actually determined by any rule, (to include the classical rules of set operations on properties as just one special case of a rule), or even by no rule at all ! Thus metaphorically based categories, such as the Japanese concept of “hon” are generated, (determined by), a metaphoric rule of extension and metonymically based categories are generated by a rule of metonymy. (Metonymy is the case where one instance of a category is made to stand for the category.) “Don’t let El Salvador” become another Vietnam” is an example Lakoff uses of a metonymically based category.405

Here “Vietnam” stands for the concept of all hopeless, unending …. wars.In the case of “radial categories”, such as the concept of “mother”, (to include birth

mother, adoptive mother, foster mother, surrogate mother, etc.), or of “Balam”406 in the Dyirbal aboriginal language in Australia, they are determined by simple historical accident –they are not generated from the central model by general rules .. [but] .. must be learned one by one.”407

(Extensions from the central model are not “random” however, but are “motivated”, his emphasis, “by the central model plus certain general principles of extension.”)408

400 “Cross categorization”, the “other . . . classical … principle of organization for categories” refers to the various possibilities at any stage of genus or species categorization – on the particular choices of which “atomic properties” are to be eliminated or added. Cf Lakoff pps. 166-167

401 ibid402 to include spatio-temporal properties403 or the exact converse –i.e. beginning with some specific object or objects in reality or possible

reality and ending with everything!404 he would say “categories”405 P. 77. Actually I like his “ham sandwich” better, but it was pre-empted by Edelman!406 The category which is the source of his title and includes, among other things, women, fire, and

dangerous things.407 Lakoff, P.91408 As I will repeat later, this discussion of Lakoff’s thesis is woefully inadequate, but it will have

to do for the purposes of this appendix. He states as the “main thesis of [his] book .. that we organize our knowledge by means of structures called idealized cognitive models, or ICMs, and

186

He argues his case rigorously and scientifically by exhibiting myriad examples that are not compliant with the classical Concept and analytically by demonstrating the degradation of concepts in actual bi-cultural environments –i.e. where a culture and language is being overrun by another, (“language death”), as is the case with the Dyirbal aboriginal language in modern Australia.409 The degradation is characterized by the loss of blocks of suborganizations, not of random individual elements.

Lakoff’s logic is not trivialized by this “free formation” of concepts however, (as it might seem it would be410- logic being [paraphrase] “mostly concerned with categories”), as he bases logic and the relevance of concepts ultimately in a preconceptual context rather than in the concepts themselves. Concepts, (categories), he argues, are not created in a vacuum, but within preconceptual schemas: “idealized cognitive models”, (ICMs). The latter are ultimately determined, (he argues), by the function of the body in the external world–all describable from “body in the world”.

“There are at least two kinds of structure in our preconceptual experiences:A. Basic-Level structure: Basic-level categories are defined by the convergence of

our gestalt perception, our capacity for bodily movement, and our ability to form rich mental images.

B. Kinesthetic image-schematic structure: Image schemas are relatively simple structures that constantly recur in our everyday bodily experience: CONTAINERS, PATHS, LINKS, FORCES, BALANCE, and in various orientations and relations: UP-DOWN, FRONT-BACK, PART-WHOLE, CENTER-PERIPHERY, etc.”411

These schemas, however, being at the basis of our reasoning412, are necessarily mutually relativistic and equipotent and we utilize them on a “best fit” rationale. The concepts that arise within them need not be commensurate across them. Thus he arrives at a relativism of logic and concepts.

that category structures and prototype effects are by-products of that organization.” Ibid, p.68409 See Lakoff, pps. 96-102410 If, according to Lakoff, (1) legitimate concepts may be formed on any principle or no principle,

and if, also according to Lakoff, (2), most of the business of logic is concepts, (categories), then it would appear, (at first glance), that (3) logic could prove any conclusion. But if logic can prove anything, then it can prove nothing! Thus it would appear, on the face of it, that his purported impossibility of a rigorous, comprehensive structure for categories in general would imply the invalidation of logic in general.

411 Lakoff, p.267.412 rather than categories

187

Lakoff’s Concept/category in many ways resembles Cassirer’s413 and he rejects, (as does Cassirer), the classical “necessary and sufficient conditions”, (as he phrases it), which ground set theoretic abstraction and the Aristotelian generic Concept. His logical and ultimately epistemological relativism, (in his “idealized cognitive models”), is also very similar to, (though it is not as abstract and comprehensive as), Cassirer's “Symbolic Forms” which is described in my Chapter 4.

Cassirer and Lakoff’s Logic

Cassirer rejected the logical sufficiency of classical categorization as does Lakoff, but he did not reject the possibility of any absolute, comprehensive structure for categories, (which Lakoff does). Instead Cassirer retained an overall formal structure for categorization in the notion of a mathematical functional rule or series.

Cassirer did not question the legitimacy of the classical schema, but he did question its necessity and sufficiency. (Which is pretty much where Lakoff and myself stand as well.) He argued that it is, in fact, a special and limit case of the Concept and of the possibilities of logic. Cassirer maintained that many concepts –and specifically the very concepts of mathematical and physical science414 –demonstrate another mode of concept formation and specification than the classical scheme, (this is the subject of my Chapter 2). Both concept formation upward, (genera), and downward, (species), can obey another rule-based law, i.e. the properties of their extensions can embody a series other than the specific series of identity. As a crude example, one member of the extension of a concept, (using an example drawn from numeric sets), might contain the numeral “2”, another the numeral “4”, another “8”, “16”… rather than the numeral “2” being in all of them. Thus the concept would express, (and be formed on the principle of), the series 2,4,8,16,… across its extension rather than being based in the series of identity: 2, 2, 2,…. , (the classical schema). The extension of a category, therefore, may be defined based upon the possession of some property belonging to a series or function on properties rather than on the possession of some identical property(ies). Concepts can be specified by a function other than identity. 415

413 There is an uncanny parallelism of argument throughout between Lakoff’s and Cassirer’s treatment of logic. Consider, as an example, the following:

“Category cue validity defined for such psychological (or interactional) attributes might correlate“, (his emphasis), “with basic-level categorization, but it would not pick out basic-level categories; they would already have to have been picked out in order to apply the definition of category of category cue validity so that there was such a correlation.” (Lakoff: P.54, my emphasis) This is almost an exact parallel to one aspect of Cassirer’s argument against the classical concept, and the “theory of attention”, (see my Chapter 2), –and for a “new form of consciousness”. Discussing Erdman, Cassirer writes: “…instead of the community of ‘marks,’ the unification of elements in a concept is decided by their ‘connection by implication.’ And this criterion, here only introduced by way of supplement and as a secondary aspect, proves on closer analysis to be the real logical prius; “ (his emphasis), “for we have already seen that ‘abstraction’ remains aimless and unmeaning if it does not consider the elements from which it takes the concept to be from the first arranged and connected by a certain relation.” Cassirer, “Substance and Function”, p.24414 Cf Cassirer, “Substance and Function”, “Einstein’s Theory of Relativity”. Incidentally, the

original title for “Substance and Function” was “Substanzbegriff und Funktionsbegriff”, i.e. Substance Concepts and Function Concepts!

415 Cassirer's "series" could be ordered by radically variant principles, however: "according to equality", (which is the special case of the "generic concept"), "or inequality,

188

Cassirer has supplied a clear counterexample and an alternative to the classical schema, (which I explained at length and further extended as the subject of Chapter 2). Simplistically, (and as crude illustration), we may have three pieces of “metal” in front of us for instance, wherein none of their properties are the same! The first is a one pound piece of gold, (color: yellow, specific gravity: a.aaaa…., conductivity: b.bbbb…., etc.), the second a two pound piece of lead, (color: gray, specific gravity: l.lll…, conductivity: m.mmm…., etc), and the third a three pound piece of tin: (…, …., …., etc.) None of these properties need be identical however. They are related as “metal”, (and are specified as “metal objects”), because the color of each, (for instance), is a value of the function COL(x) {yellow, gray, silver,…), the specific gravity of each is a value of the function SG(x) {lll…, ggg…, …}, and so on. These objects, (the objects called “metal objects”), can “cross party lines”, so to speak –i.e. they are not the product of strict set-theoretic intersection of atomic properties. In the illustration their intersection across these properties is null! The extension of scientific and mathematical concepts, (specifically, Cassirer argues), need have no atomic properties in common416 . Repeating a short citation from my Chapter 2:

"Lambert pointed out that it was the exclusive merit of mathematical 'general concepts' not to cancel the determinations of the special cases, but in all strictness fully to retain them. When a mathematician makes his formula more general, this means not only that he is to retain all the more special cases, but also be able to deduce them from the universal formula."417

But this possibility of deduction does not exist in the case of the scholastic, (Aristotelian), concepts, "since these, according to the traditional formula, are formed by neglecting the particular, and hence the reproduction of the particular moments of the concept seems excluded."418

"The ideal of a scientific concept here appears in opposition to the schematic general presentation which is expressed by a mere word. The genuine concept does not disregard the peculiarities and particularities which it holds under it, but seeks to show the necessity of the occurrence and connection of just these particularities. What it gives is a universal rule for the connection of the particulars themselves.... Fixed properties are replaced by universal rules that permit us to survey a total series of possible determinations at a single glance."419

Consider “the ellipse as a simple mathematical example of a genus” for instance. Its species are functionally related –and fully recoverable- in the defining equation of ellipses in general.

number and magnitude, spatial and temporal relations, or causal dependence"? -so long as the principle is definite and consistent. But please remember that these are principles of category construction rather than properties of categories. see my Chapter 2416 ? Compare Wittgenstein’s “family resemblances”.417 ? Cassirer, “Substance and Function”, P.20-23

418 ? ibid P.20-23, my emphasis

419 ? ibid P.20-23189

Conversely in the specification of species and subspecies, (“downward”), the process does not necessarily lie in the addition of (identical) atomic properties either, (the members of the extension of a subspecies, which is also a category, need not contain (any) identical atomic properties by the same reasoning), but can be accomplished instead in the identification of the value of a sub-function whose possibility is implicit within the genus.420 Ultimately, (and recursively), the question proposes itself: need there be a lowest, “bottom” level concept at all?421 Speciation is no longer necessarily intersection or containment,422 (it is no longer necessarily nested), so there is always the possibility of another, further rule of assembly for a subspecies of any species –at any level!423 There is thus no longer a necessary logical focus on an ultimate “thing”.

Cassirer argues that the ultimate “objects” , (the “theoretical objects”), of mathematics and physical science are “implicitly defined” by, (and express), the fundamental laws of the science itself. He argues that they are instances of complex speciation based in the general functional rules, (the laws), of the sciences themselves and not objects “in reality”.

Some of Lakoff’s categories, it is true, are also rule based, (other than the classical rule), but in the case of his “radial categories”, they may be formed by historical accident. Lakoff concluded that categories may be formed by classical rules, other rules or “no rule at all”! But this characterization divorces him from the possibility of any universally comprehensive categorical structure.424 Cassirer includes this special latter case as an ad hoc rule, (series), however, rather than as an example of “no rule”. It would correspond to the special case in mathematical set theory wherein a set is defined by the explicit listing of its members. Cassirer’s conception may be likened to a line segment bounded on one end by the classical criterion of identity of properties across members, (a “unity”), with the central section composed of any and all functional rules, (i.e. rules of series/regular functions on those properties), and bounded at the other end by the rule of explicit listing, i.e. no other rule, (a “zero”). This view reconciles the

420 ? Since we can build a genus without commonality, so can we build a super-genus. Turning our perspective around, then, we may speciate downward from that super-genus without the utilization of commonality!

421 2The other pole is clearly impossible. There is clearly no Concept, (category), of all concepts under Cassirer’s vision as it would necessarily be defined on “the rule of all rules”. But some, (most), rules are obviously inconsistent with other rules –disallowing the concept.

422 ? Since there is no longer a necessary presumption of nesting, the implication that there must be a “least member” is no longer justified.

423 Remember that under Cassirer's Concept, we do not eliminate properties to speciate, but rather functions.

424 Cf: the discussion of the crucial role of comprehensiveness vis a vis mathematical ideals near the end of this Afterword.

190

two conceptions, I think, and might be acceptable to Lakoff.425 What it does besides, however, is reveal a comprehensive structure across the whole of categories/concepts.

I have suggested a further extension beyond Cassirer’s “Functional Concept” and sets of n-tuples however in my arguments of Chapter 2. Just why is the color of “gold-metal” yellow instead of gray? Why is “gold” a particular n-tuple rather than some other mix of possible place-values? Physical scientists will never agree with Lakoff, for instance, that it could be just an (accidental) property of a “radial category”, nor, possibly even with Cassirer, that it is simply an element in a multi-place series. They will insist that it must be a necessary property determined by physical law. Cassirer apparently glimpsed this connection in his conception of the “ideal objects” of the sciences, but he never fully exploited it. (I have pursued it in my “Concept of Implicit Definition”.426)

Both Lakoff and Cassirer followed the paths of their logical conclusions to see the essential flaw in “naïve realism”, (as Cassirer termed it), and “objectivism”, in Lakoff’s words, (I have used the term “naturalism”). If the classical logical schema of strict hierarchical containment were legitimate, and, more importantly, if it were necessary and sufficient, then the only possibility of science, as the resolution of experience and reality with logic, would lie in the absolute objective existence, (however reduced), of our ordinary objects. If valid logic and conceptualization is broader than that, however, then the possibility of reality is considerably enriched. Valid conceptual, (or utilitarian cognitive), “objects” need not then express “membranes” around spatio-temporally contiguous properties of ontological, (i.e. metaphysical), objects or groups of such objects!427 They can “cross party lines”!

425 Compare Lakoff, p.146 : “in the classical theory, you have two choices for characterizing set membership: you can predict the members (by precise necessary and sufficient conditions, or by rule), or you can arbitrarily list them, if there is a finite list. The only choices are predictability (using rules or necessary and sufficient conditions) and arbitrariness (giving a list). But in a theory of natural categorization, the concept of motivation”, (his emphasis), “is available. Cases that are fully motivated are predictable and those that are totally unmotivated are arbitrary. But most cases fall in between –they are partly motivated.”

Cassirer suggested another, (and more classical), “middle ground” wherein the principle of “necessary and sufficient” is not grounded in an identity of properties, but in a functional relationship between them. The relationship between their proposals is more complex than is possible to describe here, but as a thumbnail sketch of my opinion, the deficiencies in the classical category that Cassirer resolves in his “Functional Concept of Mathematics”, Lakoff attributes to his Cognitive Models whereas the deficiencies in classical metaphysics are resolved by both of them very similarly in the epistemological relativity of “Symbolic Forms” by Cassirer and of “ICM’s” by Lakoff. Cassirer’s is the more general of the two solutions to the latter problem, however, as it is not framed within a specific image of the world, but within the constraints only of abstract epistemology as Kant definitively iterated them.426 Cf my Chapter 2

427 This discussion constitutes my answer to one of the more difficult objections to my first thesis wherein it is objected that “schematism” is “just a level of abstraction”, (Richard Reiner, private communication). The discussion above shows why it need not be!

191

Cassirer had no problems with such an implication. It was implicit, of course, in his neo-Kantian origins. Lakoff did. In his laudable commitment to realism, he was forced to consider the minimal necessary requirements of such a (scientific) realism.428

He lists Putnam’s requirements of “internal realism”429

as:(1) “A commitment to the existence of a real world external to human beings(2) a link between conceptual schemes and the world via real human experience; experience

is not purely internal, but is constrained at every instant by the real world of which we are an inextricable part

(3) a concept of truth that is based not only on internal coherence and “rational acceptability”, but, most important, on coherence with our constant real experience

(4) a commitment to the possibility of real human knowledge of the world.”430

He has extended and refined Putnam’s position somewhat from this basis, (his “basic realism”), to be able to answer certain further questions that arise, but this is a reasonably concise rendition of his stance vis a vis realism. I have discussed his position, (as reiterated by Edelman), briefly in the preface to my Chapter 2, wherein I agreed with (1) – (3), but strongly qualified (4). I had argued the equivalent of his essential conclusions as the subjects of my chapters 3 and 4, i.e. the (bare) “axiom of externality”, and the (bare) “axiom of experience” respectively. Because of his conclusions, Lakoff was further forced into a position of epistemological, (as well as logical), relativism –against what has been called a “God-eye view of reality”.431

Lakoff’s relativism, necessary because of his logical conclusions but challenged in his own mind, (admirably, I maintain, as I consider myself a strong realist as well), by his fervent commitment to science and realism, is ill-defined however. Though he talks about relativism at length, he never clearly defines it. He begins by noting the anathema which “relativism” is considered by the scientific world, but argues that there are, in fact, many different forms of relativism. (Neither he, nor I, advocate a “relativism of everything”.) The most cogent interpretation I can give to it, (Whorf aside), is that he advocates a cognitive and logical relativism based on bodily function, (in the world), which leads to a relativism of contexts, (ICM’s), which employ different categorical, (conceptual), schemas. Within each of these ICM’s, there does exist a structure consistent with rigor, however,432 but ultimately the ICM’s themselves are relativistic.

I like what Lakoff has done, (hugely!), but his ICMs, the relativism in which he has based them, and his epistemology are deficient insofar as they are all derived from, (grounded in the concept of), the human body and the functions of that body in the world. This is his overview, and

428 The criteria of Putnam’s, Lakoff’s and Edelman’s basic realism are, I have argued in my chapters 3 and 4, essentially the same ones definitively identified by Kant. Kant is grossly mischaracterized as an “idealist”. He was, in fact, the penultimate modern realist in just the sense demanded by these thinkers. See chapters 3 and 4.

429 Which he uses as the jumping off point for his own “experiential realism”. Edelman, incidentally, has adopted Putnam’s definition pretty much “as is”.

430 P.263431 cf my chapter 4 for a discussion of Cassirer’s arguments on the same subject and of my

extension of them.432 ? “The main thesis of this book is that we organize our knowledge by means of structures called idealized cognitive models, or ICM’s, and that

category structures and prototype effects are by-products of that organization..” Lakoff, 1987, p.68, his emphasis.

192

this is the context within which they are framed. That very body in the world is conceived in the primary set theoretic sense, (he would call it the “container schema” ICM), however! But if they all may be described within the container schema, (the body in the world), then ultimately all of his ICMs and his epistemology are theoretically reducible to a container schema! This is a contradiction of his own position against a “God’s eye” picture of the world.433 It is the generality of Cassirer’s solutions434and of my extensions of them, (founded ultimately in a neo-Kantian perspective), which allows the solution of the general logical and ultimately of the epistemological problems.

Though Lakoff rejects the view that “anything goes” –that any conceptual system is as good as any other, nowhere does he approach the possibility of a scientific, mathematical relativism which would give rigor to his conceptions –save within a tacit objectivist context.

It is the possibility of a general and comprehensive structure of the Concept which allows the true relativity of the essential forms/ICMs. I will argue shortly, in the context of mathematical “ideals”, that the various “generators” of such an ideal must each be capable of generating the whole of the “space” of that ideal –to include all possible alternative generators as well. Thus each (legitimate) structure must be comprehensive to be translatable, (i.e. capable of itself being generated by another set of generators). But its concepts/categories/objects may be distributed in the translation.435 This is intelligible only outside of the classical conception of logic, and is the essence of my conclusion of chapter 4. Lakoff’s “Concept” is certainly broader than the classical concept, but he takes his arguments too far –against any rule of concept formation.

Please do not misunderstand me. I loved Lakoff’s book. It is brilliant, far reaching, and, I believe, essentially valid. He develops and documents his arguments solidly, but I think his strongest point is in his clear and cogent examples from our own normal usage436, (as well as from extensive anthropological studies), which makes his essential case almost unanswerable. His conception is considerably richer than it is possible to describe within the confines of an appendix, nor is it as simplistic as I have characterized it. We have huge areas of agreement and possible interaction, (his and Rosch’s “basic level categories” have a natural correlate in my “schematic perceptual objects”, for instance.)

Lakoff’s ICMs are biologically based –on the human organism. Human cognition and human reason consists, for Lakoff, in the application of the best fit of these inbuilt ICM’s, (and their respective categories), to a given problem or situation. They constitute an “embodied logic” deriving from the nature of the human organism itself. There is an obvious parallel between Lakoff’s “embodied logic” and the more general case I have argued. I have argued that logic is indeed embodied, but at the primitive level of cellular process! This more general characterization allows the crucial epistemological move,437 (which Lakoff’s does not), beyond the “God’s eye view” he disclaims.

The distinction is important because at the cellular level of phenomenology biology becomes a pure form, (in Cassirer's sense and compatible with Cassirer's Hertzian premise). This is especially transparent in Maturana and Varela's book, for instance, (see chapter 3), i.e. in its explicit constructiveness and the subsequent purity of their phenomenology.

433 I.e. all his arguments against it are reducible within it. I will have more to say on this subject shortly and will suggest a way out of his dilemma.

434 and their origins in science and mathematics435 cf my Chapter 4436 ? Cassirer’s case was grounded primarily in scientific examples.437 Through what Maturana and Varela call “structural coupling”

193

Citing a few pertinent examples quoted earlier in chapter 3:"Our intention, therefore, is to proceed scientifically: if we cannot provide a list that characterizes a living being, why not propose a system that generates all the phenomena proper to a living being? The evidence that an autopoietic unity has exactly all these features becomes evident in the light of what we know about the interdependence between metabolism and cellular structure."

"Autopoietic unities specify biological phenomenology as the phenomenology proper of those unities", (my emphasis), "with features distinct from physical phenomenology... because the phenomena they generate in functioning as autopoietic unities depend on their organization and the way this organization comes about, and not on the physical nature of their components."

"Ontogeny is the history of structural changes in a particular living being. In this history each living being begins with an initial structure. This structure conditions the course of its interactions and restricts the structural changes that the interactions may trigger in it", (my emphasis). "At the same time, it is born in a particular place, in a medium that constitutes the ambience in which it emerges and in which it interacts. This ambience appears to have a structural dynamics of its own, operationally distinct from the living being. This is a crucial point. As observers, we have distinguished the living system as a unity from its background and have characterized it as a definite organization. We have thus distinguished two structures that are going to be considered operationally independent of each other, (my emphasis), "living being and environment."

These are purely constructive and operational definitions, (or capable of being made so within "structural coupling"), in the precise sense of Hertz and Cassirer and clearly mesh with the substance of my chapter 4. They are Hertzian "images" with a definite, predictive logical structure.

At the level of cellular biology therefore, biology becomes a pure form, and, as such, it, (and the logic I posit within it), is capable of legitimate embodiment438 within the now viable scientific epistemological relativism espoused by Cassirer and myself. It is this deeper placement, (and not as reductive physics), which allows an escape from the inconsistent "God's eye view" implicit in Lakoff's and Edelman's theses, and enables a truly consistent relativism.

It is because of Lakoff's Wittgensteinian origins, I think, that he has gone too far, (-and not far enough). Had he started from Cassirer instead, the case might have been different. I will return to Lakoff presently to suggest a “cleaner” solution to his problem consistent with his apparent needs –in the mathematical notion of “ideals”. There is a way to save it, but I think it is too limited and inconsistent with the dictates of modern biology as espoused, for instance, by Edelman.

Edelman:Gerald Edelman has adopted Lakoff’s, (and Putnam’s), logical and epistemological

conclusions as the philosophical underpinning to his own theories of “Neuronal Group Selection”, (TNGS), and “re-entrant topobiological maps”. He proposed the combined result as an actual

438 i.e. as a legitimate, fundamental "symbolic form"194

answer to the problem of mind-brain. Though Edelman's is a very plausible theory of brain development and function, it is limited to dealing with “mind” only reductively -i.e. as strictly biological and therefore physical process and falls to the same objections that I, (and the preponderant Naturalist camp as well), have raised. “Mind”, normally taken, is therefore superfluous therein! Edelman explicitly denies the “homunculus”, (as do I), but his “Cartesian theatre” is specifically a physical and spatial one. It is spatially and temporally distributed. Though he does not explicitly deny the existence of “mind” as ordinarily taken, he tacitly reinterprets it and reduces it to a description of process. He fits very comfortably, I feel therefore, within the naturalism, (and “objectivism”), which Dennett, Churchland, et al espouse.439 I do not question the insightfulness or the importance of Edelman’s work –it is profoundly important and very solid –but, because of its limitations, (derived from Lakoff), it falls short of an answer to the problem of consciousness, retains internal inconsistencies, and does not resolve the mind-body dilemma.

Starting with the nature and limitations of embryology, Edelman makes a case for a very different concept of “recognition systems”. His exemplar “recognition system” is the immune system. The immune system, he argues, does not depend on information about the world –i.e. we do not create new antibodies from informational templates resident in newly arrived antigens. Rather, science finds that the body randomly generates a huge diversity of antibodies before the fact and reactively selects from this pre-existing diversity “ex post facto” as he phrases it. This, the immune system, is a system of process, not of information.

“A recognition system … exists in one physical domain”, (for the immune system it is within an individual’s body), “ and responds to novelty arising independently in another domain, (for the immune system it is a foreign molecule among the millions upon millions of possible chemically different molecules) by a specific binding event and an adaptive cellular response. It does this without requiring that information about the shape that needs to be recognized be transferred to the recognizing system at the time when it makes the recognizer molecules or antibodies. Instead, the recognizing system first generates a diverse population of antibody molecules and then selects ex post facto those that fit or match. It does this continually and, for the most part, adaptively.” Edelman, P.78

439 Save on the issue of “information”195

Cognition, our ultimate “recognition system”, he argues, is a parallel case and must be reconceived accordingly. Because of the sheer size, and the place and time sensitivity of embryological neural development, the neural system, (he argues), is progressively “pruned” ex post facto from random preexisting variety over the stages of its development in like manner to the immune system.

“given the stochastic (or statistically varying) nature of the developmental driving forces provided by cellular processes such as cell division, movement, and death, in some regions of the developing nervous system up to 70 percent of the neurons die before the structure of that region is completed! In general, therefore, uniquely specified connections cannot exist.”

“the principles governing these changes are epigenetic –meaning that key events occur only if certain previous events have taken place. An important consequence is that the connections among the cells are therefore not precisely prespecified in the genes of the animal.” Edelman, pps. 23- 25

Of the great diversity of (preexisting) neural connections generated at any stage, particular connections are reinforced and kept, or pruned and deleted, in tune with place and time dependent events the scenario of which is too complex “by several orders of magnitude” to be embodied in the human genome. This pruning is achieved operationally, not informationally. Embryological development is too complex, too dependent on place and time to be prespecified. His argument in some ways parallels my own of appendix A wherein I argued that there simply hasn’t been enough time in evolutionary history, (nor ever will be), to create such an information engine.

In his “ex post facto” adaptive “TNGS”, Edelman argues a criterion of competence , (as, indeed, did Darwin –and as did I in my first chapter), rather than one of information in the evolution and development of organisms –and specifically of the human organism.

“The immune selective system has some intriguing properties. First, there is more than one way to recognize successfully any particular shape. (my emphasis) Second, no two individuals do it exactly the same way; that is, no two individuals have identical antibodies. Third, the system has a kind of cellular memory.” Edelman, P.78 (These comments are directly relevant to my discussion of bounds and limits and the “parallel postulate” of cognitive science.)

He too disclaims the possibility of a “God’s eye view” by an organism of reality.440 But competence, as I have argued, does not imply parallelism. It is the question of bounds and limits that I have argued previously,441 and Edelman falls into the same epistemological trap as does Lakoff, (and Maturana and Varela as well). Other than this failing, however, I believe his overall position and arguments are very strong.On “Presentation”

440 cf: my “Axiom of Externality” and “Axiom of Experience”, (Chapters 3 and 4).441 Let me repeat a footnote of my Chapter 1: The question, of course, is whether "information" is

necessary to competence. I will argue, (in Chapter 3), that it involves a distinction between "bounds" and "greatest lower bounds" of biologic survival. A given organism, (to include human beings), must reflect a lower bound of competence in the world. But "information" requires that it reflect a greatest lower bound, and this is inconsistent with the fundamental premises of evolution. It is the "parallel postulate" of cognitive science.

196

Edelman challenges ordinary logic and ordinary epistemology, (the classical, “objectivist”/”naturalist” views), for some of the same reasons that I do. In his TNGS, he has framed the same problem, and reached largely the same conclusion that I did under the issue of “presentation”.

“some of the reasons for considering brain science a science of recognition", [under his special definition of "recognition systems" cited above]. " The first reason is almost too obvious: brain science and the study of behavior are concerned with the adaptive matching of animals to their environments. In considering brain science as a science of recognition I am implying that recognition is not an instructive process. No direct information transfer occurs, just as none occurs in evolutionary or immune processes. Instead recognition is selective.”

“a potent additional reason for adopting a selective rather than an instructive viewpoint has to do with the homunculus. …the little man that one must postulate ‘at the top of the mind’, acting as an interpreter of signals and symbols in any instructive theory of mind…. But then another homunculus required in his head and so on, in an infinite regress… selectional systems, in which matching occurs ex post facto on an already existing diverse repertoire, need no special creations, no homunculi, and no such regress.” Edelman pps. 81-82

Presentation, in any sense other than an eliminative one, requires a homunculus, and this is the problem that Edelman believes he has solved- in essentially the same way that I did. But, in doing so, he believed he had solved the whole of the mind-body problem.

Re-entrant Maps

To this point, (his theory of “TNGS”), his argument is very plausible and compatible with my own conclusions. His rationale from that point onward, however, bears examination.

His theory of re-entrant topobiological maps, (reactively linked cortical surfaces), is quite plausible and highly interesting, but, ultimately, it is tied to a truly topological correspondence of those maps with the “real” world, (contrary to his conclusions of the first part of his thesis). “Maps… correlate happenings at one spatial location in the world without a higher-order supervisor…”442 These maps themselves do, therefore, embody a “God’s eye view”, (contrary to the implications of TNGS). I have suggested a different orientation of Edelman’s schema in the discussion of my Chapter 1, wherein I suggested we step back from our human (animal) cognitive prejudice and consider the larger “global mapping” also described by Edelman, (which relates “non-mapped” areas of the brain to the topobiological maps), as the primary focus of biological process. Under this perspective, the “objects” of our topobiological maps may be reconceived, not as God’s-eye renditions of ontology, but rather as organizational foci, (efficacious artifacts), of process.443

442 Edelman, p.87, my emphasis443 An aside: While I hope it should be clear by now that I have no affinity for traditional idealism,

I think it is worth quoting a short passage from Edelman as it talks about levels of “strangeness” in theories:

197

Edelman rationalizes his biological solution to the problem of the brain and the mind upon Lakoff’s, (and Putnam’s), answer. To him that answer is important because it allows a rationale for the brain which is not based in information as, in fact, he has concluded that it is not, (inconsistently with his theory of re-entrant maps, I maintain). He therefore reaches a conclusion very similar to my own. But again, like Lakoff’s, his conception is too limited and incorporates an inherent contradiction. His concept of the world, like Lakoff's is based in a container schema. We, you and I and Lakoff and Edelman, are organisms too after all. But then “TNGS” requires that even our brains are not informational!444 It is the generality of Cassirer’s solution –and of my extension of it –the generality of the Concept and the generality of the scientific relativism which allows a consistent and meaningful solution445 to the problems of the brain, mind and epistemology.

The Cartesian TheatreWhat Edelman has not solved is the other problem, the problem of the “Cartesian

theatre”446, (i.e. “mind”, ordinarily taken), and this is the most important problem. It is that which we normally mean when we use the terms “consciousness”, “sentiency”, etc. Its comprehensive solution is the subject of Chapter 2: the Concept of Implicit Definition and its integration with biology as the unified rule of ontogenic coupling. Edelman’s solution remains an essentially naturalist, (objectivist), one itself however and is, I argue moreover, epistemologically inconsistent. It is compatible with the rest of the eliminativist camp in that ultimately all his correspondences, (his stated epistemology to the contrary), are from topobiological maps, themselves topologically corresponding to “the (real) world”! His “mind” is purely process, spatially and temporally localized –and known! His is “a God’s eye view”.

“and Berkeley’s monistic idealism –suggesting that inasmuch as all knowledge is gained through the senses, the whole world is a mental matter –falters before the facts of evolution. It would be very strange indeed if we mentally created an environment that then subjected us (mentally) to natural selection.” Edelman, p. 35

Berkeley aside, Edelman seems very put out with the very strangeness of the (recursive, re-entrant?) complication of such an idea. The complication, he implies, boggles the mind! But much of modern science is even more mind-boggling. My thesis proposes an even greater “boggle”, but results in an integration of epistemology and an actual solution to the mind-body problem.Modern epistemology is radical at both the extremely small and at the extremely large (and fast) scales. It is only as algorithms they are comprehensible. And yet everyone, (read this as “most realists”), seems to accept that at the middle scale epistemology must be simple. Consider instead the truly mind boggling possibility I propose that the middle scale is algorithmic as well! Does this not explain “the prototype” which Rosch demonstrated and which ground Lakoff’s and Edelman’s very logical theses. Prototypes and the logical relations between them would, under this view, represent the “objects” and the “calculus” of algorithmic biology. If this thesis be accepted, then continuity, temporarily removed from epistemology by modern science, is restored across the board. This is a major epistemological and scientific result and worth the price we must pay for it. So was quantum mechanics!

444 I think that Edelman would comment here, as he did on another occasion, that this conclusion would “boggle the mind”! Maybe so, but I think we’d better get used to such a state. Modern physics? Edelman’s own conclusions? …

445 by allowing a reorientation of the problem to a consideration of forms rather than of information446 after Dennett

198

Edelman is very derisive of Penrose’s “Emperor’s New Mind”,447 but I think he has missed a major aspect of it. Penrose, (though he doesn’t say so explicitly), and the “quantum people” are trying, (Goedel aside), I think, to supply a “non-localization” –i.e. a spatial universality to the brain’s perceptual and cognitive objects- to make headway on the problem of knowing. They are trying to conceive an answer to Leibniz’ problem of the “one and the many” within a physical space. The “chaos theory people” stand in a similar motivation I think, but attacking the logical problem of the object from a perspective of localized process, conceiving our objects as “attractors”. But even were such solutions meaningful, (and they are interesting), they would miss the requirement of a self-standing logical space in depth which the Concept of Implicit Definition, as combined with the schematic model of biology, supplies and which furnishes the foundation of “meaning” and “knowing”. Dennett glimpsed such a possibility448 for a Cartesian theatre based in logic in Shakey the Robot’s program, (as I cited previously449), but his naturalist/objectivist metaphysical prejudice enervated the concept before it could bear fruit.

But ordinary logic,450 (Shakey’s program for instance), is inadequate to the problem. It is essentially dimensional: linear, planar, multi-dimensional, missing the integration in depth –missing the autonomy and (logical) self-sufficiency which is necessary to knowing and to meaning. 451 452

That aspect of ordinary mind we call the “Cartesian Theatre” does not work as a linear, a planar, or even as a multidimensional space453 -even as a logical space. As I argued in chapter 2, each requires “presentation”, either physical or logical. Nor do such conceptions supply “knowing”, “meaning” or “motivation”, except as unnatural and gratuitous appendages.

C.I.D. and the schematic model focus logic and cognition in biology. Biology has innate depth and structure –derived from the single principle of efficacy as coupled with Darwinian survival –of ontogenic coupling, and these necessarily pass to the logic and the cognition which are embedded in it! The Concept of Implicit Definition as coupled with the schematic model454

supplies an integration and a rationale in depth –and an autonomy- implicit in its biological roots.455 Edelman got very close to this answer, but his efforts were frustrated by his epistemological beginnings.

Cassirer, (“symbolic forms”), Rosch, (“prototypes” and “basic levels”), and Lakoff, (ICM’s), demonstrate that dimensional logic is not adequate to the realities of the human mind. Nor, even putting aside the problem of “information”, (Maturana and Varela, Freeman, Edelman), 447 “Penrose’s account is a bit like that of a schoolboy who, not knowing the formula of sulfuric

acid asked for on an exam, gives instead a beautiful account of his dog Spot.” Edelman, P.217448 but using an inadequate logic449 cf the "Dennett Appendix" - "the color phi"450 “associationist logic” in Dreyfus’ term451 Wittgenstein’s objection is clearly pertinent here. He raised the question of the necessity for one

to have another rule: i.e. another rule to apply any given rule. C.I.D./biology, however, supplies a consistent rationale. “One” is a rule, “one” doesn’t apply the rule. “One” is the single, “ex post facto” and unified rule of ontogenic coupling!

452 and which could provide the enrichment necessary to the possibility of future scientific development moreover. All the other proposals yet presented are essentially just explanatory –i.e. logically reductive- and hold little promise for further exploitation.

453 cf Wlodek Duch for instance454 i.e. the “concordance” mentioned in the Introduction455 It supplies “the rule which we need to apply the rule which we need to apply the rule …”

demanded by Wittgenstein. Ultimately it is a constitutive rule. But one doesn’t “apply" this rule. Rather, “one” is a rule –namely the constitutive rule of ontogenic coupling as the term is used by Maturana and Varela.

199

can such a logic supply meaning or motivation except in a very unnatural and perverted sense. It is biology itself which supplies this aspect –in the concept of a schematic model and an enlarged logic. This is my argument of Chapter 1 as culminated in Chapter 2. On Epistemology:

But let me be more generous to Lakoff and Edelman. In basing their conceptions on our ordinary world, or, to call a spade a spade, on our ordinary naïve realistic conception of the world, (people, baseballs, cars and all the things they do), they are trying to preserve experience! This they identify with realism. They seek to preserve their logical and biological conclusions with the objects of that ordinary realism,456 and their relativism is a laudable and understandable attempt at a reconciliation. I have explained my answer to the same problem in terms of the multiple possible axiomatic foundations of mathematical systems, but another line of understanding is possible. Consider the notion of a mathematical “ideal”.

The mathematical definition of an ideal is technical,457 but the example given by Birkhoff and Mac Clane458, while rather “longish" is more easily understood and is clearly directly applicable, (by its substance), to the immediate problem.459 It illustrates a very different and very concrete notion of “relativism”. While encompassing a scope much wider than simple geometry, that example provides a very clear illustration of the concept:

“The circle C of radius 2 lying in the plane parallel to the (x,y) plane and two units above it in space is usually described analytically as the set of points (x,y,z) in space satisfying the simultaneous equations:

(16)x2 + y2 –4 = 0,

z – 2 = 0.

These describe the curve C as the intersection of a circular cylinder and a plane. But C can be described with equal accuracy as the intersection of a sphere with the plane z = 2, by the equivalent simultaneous equations:

(17)x2 + y2 + z2 – 8 = 0,

z – 2 = 0.

456 cf Lakoff’s discussion, (p.262) of the “objects” of our experience –his chair, for instance. “It is important not to read Putnam out of context here, especially when he talks about objects. An ‘object’ is a single bounded entity…. Putnam, being a realist, does not deny that objects exist. Take, for example, the chair I am sitting on. It exists. If it didn’t, I would have fallen on the floor.” (my emphasis). Compare this reference with my modification of Kant’s position on “objects” which I advocated in the footnote in Chapter 5.

457 “Definition. An ideal C in a ring A is a non-void subset of A with the properties(i) c1 and c2 in C imply that c1 – c2 is in C;(ii) c in C and a in A imply that ac and ca are in C”

Birkhoff and Mac Clane, “Modern Algebra”, 1953, pps.372458 ibid, pps.380…459 i.e. it deals with well defined "objects"

200

Still another description is possible, by the equations

(18)x2 + y2 – 4 = 0,

x2 + y2 – 2z = 0.

These describe C as the intersection of a circular cylinder with the paraboloid of rotation:

x2 + y2 = 2z.

Therefore the only impartial way to describe C”, (my emphasis), “ is in terms of all the polynomial equations which its points satisfy. But if f(x,y,z) and g(x,y,z) are any two polynomials whose values are identically zero on C, then their sum and difference also vanish identically on C. So, likewise, does any multiple a(x,y,z)f(x,y,z) of f(x,y,z) by any polynomial a(x,y,z) whatsoever.”, (my emphasis). “This means that the set of all polynomials whose values are identically zero on C is an ideal. This ideal then, and not any special pair of its elements, is the ultimate description of C.

In the light of this observation the special pairs of polynomials occurring in equations (16)-(18) appear simply as generators”, (my emphasis), “ of the ideal of all polynomials which vanish identically on C. Any polynomial obtained from the equations of (16) by linear combination with polynomial coefficients, as

(19)h(x,y,z) = a(x,y,z)(x2 + y2 – 4) + b(x,y,z)(z – 2),

will be in this ideal. Conversely, it can be proved that any polynomial equation h(x,y,z) = 0, which represents a surface passing through our circle, can be represented in the form (19). But the set of all these polynomials (19) is simply the ideal (x2 + y2 – 4, z – 2), generated by the two original polynomials (16) in the ring R#[x,y,z] of all polynomials in x, y, z with coefficients in the field R# of real numbers. The polynomials of (17) generate the same ideal, for these polynomials are linear combinations of (16), while those of (16) can conversely be obtained by combination of the polynomials of (17). The polynomial ideal determined by this curve thus has various bases,

(20) (x2 + y2 – 4, z – 2) = (x2 + y2 + z2 – 8, z – 2) = (x2 + y2 – 2z, z – 2)…”

The mathematical “ideal” just described opens a door to a better conclusion to Lakoff’s and Edelman’s arguments, and a simpler understanding of my own. None of these generators stands prior to any other, nor does it “create” the figure comprehended. Each stands, rather, as an

201

equipotent and relativistic “logical”, (i.e. explanatory), basis fully exhausting the actuality of the figure.

But we must consider this example in the larger context of mathematics. Not only can such descriptions be relativized in relation to a fixed coordinate system, but the very coordinate systems themselves stand in like case. Axes need not be orthogonal, nor need they be rectilinear, (e.g. polar coordinates are possible). Nor need they be fixed. They may be in translation –e.g. relative motion, (which translates to special relativity), and they need not be Euclidean, (nor Hyperbolic nor Spherical). Russell, for instance, further argued460 that our descriptions of phenomena might even be based in projective geometry. But need they be even spatial? Can we not conceive of such explanations being framed as abstract transformations, which latter are not defined on spaces, but on abstract sets! Abstract sets, however, fall naturally within the scope of axiomatics wherein I grounded C.I.D.Such a relativism of descriptions, combined with a scientific relativism of logic and epistemology themselves as argued by Cassirer, Lakoff, and myself, (superceding the traditional “container schema” and broadening the very ideas of “set” and “object” themselves), points to the further possibility for such an “idealistic”, (in the mathematical sense), foundation of logic itself. Need mathematics, or logic, be necessarily grounded in objectivist sets, (ultimate “atomic” –i.e. least objects -and a fixed "Universe" of such objects), or could it not pick itself up by its own bootstraps, (following the cue of mathematical “ideals”461 and the findings of Cassirer and Lakoff), and stand without them?462 This is a question –not an easy one to be sure- for abstract mathematics and the future of logic.

If we think of “experience” in the abstract –i.e. as the “axiom” without interpretation, (i.e. “impartially” in the sense of “basic realism”), – then I think an “ideal” in this sense is a very reasonable way of understanding it – beyond any particular “generator”, beyond any particular interpretation.463 But it is not necessarily a spatial interpretation either. Ideals are broader than this.On a narrower focus, the possible generators of an ideal rigorously parallel the explanatory

possibilities which can absolutely preserve the objects of ordinary experience and naïve realism, (conserving shapes, boundaries, etc.). As such, the ideal they ground is entirely commensurate with Lakoff’s and Edelman’s conceptions and logically validates their (limited) relativism.

Within the perspective of that same “basic realism”, the “experience“ we deal with need not be taken as ultimately informational however,464 but can be taken as specifically organizational and operative instead465 as I have argued in my Chapter 1 and consistently with Edelman’s “TNGS”. Though connected with externality, (as representative of successful- .i.e. adequate process466), it need not be further taken as conveying information about that externality. It need not be taken as paralleling externality. The latter presumption, I have argued, goes far beyond the needs and the implications of Darwinian biology.

460 Russell, “Foundations of Geometry”, 1956461 though presently itself conceived in set-theoretic terms462 This would be the truly transcendental logic after which Kant sought.463 “context-free” in Van Fraassen’s term464 This my qualification on Putnam’s 4th requirement of basic realism465 contrary to Putnam’s 4th requirement466 “ex post facto”, in Edelman’s words

202

The deeper issue is that of an adequate definition of “experience” itself. Need we identify it with the absolute and necessary preservation of ordinary objects? Or, might we not, consistent with the foundations of their own conceptions and the work of Rosch upon which it is grounded, consider even our ordinary perceptual objects as “prototypes” of a larger experience? Prototypes are objects of utility, of efficacy, after all, they are not foundational objects.467 Could not our ordinary objects be considered, (as I have argued), as prototypes, (“schematic perceptual objects”), of a biological calculus?

“Experience” in a modern sense must be broadened to include the experience of the results of scientific experiment, and that experience, at least insofar as modern physics is concerned, is not commensurate with the preservation of objects, nor is it commensurate with ordinary spatiality. Without even considering the deeper implications of QM or of Relativity, one need only consider results of the “twin slit” experiment or the implications of its multiple execution to see the point. Not even cardinality is preserved!468 Similarly, consider Penrose’s “most optimistic" view of quantum mechanics, (most optimistic for objectivism/naturalism, that is):469

"I shall follow the more positive line which attributes objective physical reality to the quantum description: the quantum state.

"I have been taking the view that the 'objectively real' state of an individual particle is indeed described by its wavefunction psi. It seems that many people find this a difficult position to adhere to in a serious way. One reason for this appears to be that it involves our regarding individual particles being spread out spatially, rather than always being concentrated at single points. For a momentum state, this spread is at its most extreme, since psi is distributed equally all over the whole of space, (my emphasis),...It would seem that we must indeed come to terms with this picture of a particle which can be spread out over large regions of space, and which is likely to remain spread out until the next position measurement is carried out...."

The particle -this smallest part of our "object"- is not included, (spatially, reductively, nested), within the spatiality of the atom or within the molecule -or even within the human scale object of which it is the theoretical (and supposed material) foundation. Naturalism/objectivism can no longer support, therefore, even a consistent hierarchy of spatial scale!470 At the human 467 see Lakoff for a discussion of Rosch, prototypes, and the logical significance of the latter. It is a

very illuminating discussion.468 In answer to a question I asked on this point, a physicist correspondent of mine replied that

“Yes, you can have many slits one after another, (it is better with Mach-Zehnder interferometers than slits, with the same result that one doesn’t know if the photon went through or was reflected by a mirror…. We can say that one photon may be in an arbitrary number of places at once.” (Wlodek Duch, private correspondence) My point was that even the cardinality of this basic object, (the photon), was purely arbitrary –it could be 1 or 2 or 3 or 1,000,001 or …, depending on the branching structure of successive slits and the design of the experiment. But innate cardinality is perhaps the most basic “property” we ascribe to ordinary objects, so I think the conclusion is significant.

469 Repeating a section of a prior appendix470 Compare Lakoff, p.195: “In the case of biological categories, science is not on its [objectivist

philosophy’s] side. Classical categories and natural kinds are remnants of pre-Darwinian philosophy. They fit the biology of the ancient Greeks very well….but they do not accord with phenomena that are central to evolution. … Objectivist semantics and cognition and, to a large extent, even objectivist metaphysics are in conflict with post-Darwinian biology. I’d put my

203

level, of course, it is a very useful tool, and that is just what I propose it is -constructed by evolution! Science and logic suggest other, non-scaled and non-hierarchical organizations -i.e. they support any other efficacious organization. It is a simple matter of utility.

Conclusion

To conclude this appendix, let me repeat that I truly admire Lakoff’s and Edelman’s work. It is both profound and crucial to the resolution of the ultimate problem. But then I really like the work of all the authors I have cited –even those most contrary to my own conclusions. (I would not cite or spend much time on anything of lesser quality –the problem is too huge and too difficult to be distracted.) Dennett’s work, for example, is very beautiful to me in his honorable and perceptive pursuit of the hard implications of naturalism. P.S. Churchland, as another example, has a “clean” mind and frames the problem wonderfully from the perspectives of biology and philosophy. None of them has resolved the fundamental problem, however, though all have come very close in different aspects of it. This is a hard problem, the hardest one, I maintain, that the human mind has ever dealt with. To solve it requires an intellectual ruthlessness, and specifically, a ruthless realism!

money on biology.”204

Appendix I: a few Illustrations

I. EDELMAN'S COGNITIVE ONTOLOGY: TOPOBIOLOGICAL MAPS AND A GOD'S EYE PARALLELISM

II. A METACELLULAR PERSPECTIVE: COGNITIVE OBJECTS AS ORGANIZERS OF PRIMITIVE PROCESS THROUGH A BLIND INTERFACE

III. UPPER AND LOWER BOUNDS OF A BIOLOGICAL ORGANISM'S PERFORMANCE / RESPONSE

205

206

GOD'S EYE REALITY

I.E. ONTOLOGY

EDELMAN'S COGNITIVE ONTOLOGY: TOPOBIOLOGICAL MAPS AND A GOD'S EYE PARALLELISM

GLOBAL MAPPING

NON-MAPPED PROCESS IN THE BRAIN

INTERFACE: A TOPOLOGICAL PARALLELISM

INTERFACE: A TOPOLOGICAL PARALLELISM

THE BRAIN AS A CORRESPONDENCE MACHINE

207

GOD'S EYE REALITY(I.E . ONTOLOGY)

A METACELLULAR PERSPECTIVE: COGNITIVE OBJECTS AS ORGANIZERS OF PRIMITIVE PROCESS THROUGH A BLIND INTERFACE

GLOBAL MAPPING

NON-MAPPED PROCESS IN THE BRAIN

TOPOBIOLOGICAL MAPS: :SPECIFICALLY AS COORDINATORS OF PRIMITIVE PROCESS

THE BRAIN AS A 3-D GRAPHIC USER INTERFAC

A BLIND INTERFACE :

BASED IN APPROPRIATENESS RATHER THAN INFORMATION

HOW COULD A BIO/MECHANICAL ORGANISM KNOW REALITY?

208

UPPER AND LOWER BOUNDS OF A BIOLOGICAL ORGANISM'S PERFORMANCE /

1

2

3

(1) AND (3) REPRESENT THE BEST AND THE LEAST POSSIBLE PERFORMANCE FOR AN ORGANISM OVER THE DOMAIN OF ITS BEHAVIOR IN ABSOLUTE (ONTIC) REALITY. LESS THAN (3) RESULTS IN LESSENED SURVIVABILITY OR DEATH; GREATER THAN (1) IS IMPOSSIBLE AS IT IS PERFECT PERFORMANCE IN ACTUAL REALITY. BETWEEN THE TWO BOUNDS, ACTUAL PERFORMANCE, ( (2), (2'), (2''),…), NEED NOT MATCH, NOR EVEN PARALLEL THESE OUTER BOUNDS. ANY CURVE WITHIN THEM IS CONSISTENT WITH EVOLUTION. EDELMAN, FOR INSTANCE, TALKS ABOUT THE MULTIPLE, NON-COMMENSURATE ANTIBODY RESPONSES TO A GIVEN ANTIGEN. THE SAME MUST SURELY APPLY TO COGNITION, ANOTHER "RECOGNITION SYSTEM". (NOTE: 2' AND 2'' PARLLEL 1, BUT 2 DOES

2

2'

RANGE OF NECESSARY RESPONSES AXIS

ADEQUACY AXIS

BOUNDS OF SURVIVAL

Appendix J: (An elaboration of the possibilities of the discussion)(Hyperlinked to Chapter 1)

The acceptance of even the possibility of such a free formation of an interface, (calculus plus objects), and the further possibility of a fluid correlation, (i.e. one not constrained a priori –denotationally- by classical logical categories), from a substrate to that interface is difficult, admittedly. There are two primary difficulties.

The first sticking point is that an interface must correlate to "experience", (to have any value), and experience already has objects, it seems. "Experience" can be taken in a wider, more scientific sense471, however, to include the experience of the results of scientific experiment. Most generally, it can be taken as that which must be dealt with, (incorporated), in any comprehensive theory of reality.472 (Remember the Marxist's problem with the royalist's "God" in section A.1) I argue, (in Chapter 4), that it is the invariants, ("that which must be dealt with", taken in the most general sense- to include experience of the results of empirical science), that define “experience” in its widest sense and it need not, (as in fact science does not), necessarily conserve the objects of our normal naive realism as objects.

The second difficulty has to do with logic itself. Within the classical, Aristotelian conception of categories and logic, (which still underlies the whole of modern logic), all logical operations ultimately come down essentially to the intersection, union and complementarity of sets, (of properties for instance). Even "relation" is defined as a set of n-tuples. How then can a cognitive object viable473 in the world, (even a conceptual object), be conceived except as a collection of properties collected into like sets –preserving hierarchy474, spatiality and ultimately the real contiguity of properties in ontological objects, (their extension), in the world therefore?475

How can it relate to other objects except in terms of a commonality or disjunction of those primitive properties? It is a question of logical possibility. I will deal briefly with this question here and expound it more fully as the subjects of Chapter 2 and Chapter 4.476

Modern cognitive theorists, (Lakoff for example), arguing from extensive and generally confirmed empirical data on how human beings, cultures and languages actually do categorize, (as opposed to a priori, philosophical and logical conclusions as to how they must categorize!), and the biologist Edelman suggest a very different constitution of our categories and concepts -and, in consequence, a very different constitution of the logic built upon them.477

Based in Rosch’s empirical researches demonstrating “prototype effects” and extensive other linguistic and anthropological findings, Lakoff argues478 for the existence of "metonymic", 471 ? cf Chapter 4472 ? See Chapter 3 for a definition of “experience”, and Chapter 4, (the “King of Petrolia”), for an elaboration.

473 ? correlating to and existing in it in some manner

474 ? See "Afterward: Lakoff & Edelman for a detailed discussion of "hierarchy"475 ? cf Lakoff, 1987, pps. 157-184. Lakoff has outlined this overall problem and the

foundations of what he calls “objectivism” with great precision and lucidity. In spirit I think he is correct though I do not agree with the whole of his answer. See Afterward: Lakoff and Edelman

476 ? also see Afterward: Lakoff / Edelman477 ? As Lakoff noted, “most of the subject matter of classical logic is categorization”. Lakoff,

1987, p. 353, (my emphasis)478 ? with lucid concrete examples and case studies

209

“metaphorical”, and “radial” categories which are not commensurable with classical set-theoretic categories, (though the latter are maintained as a special case –the “container schema”). These new categories are established by “association”, “similarity” and “motivation” rather than on the set theoretic intersection of properties. In the case of “radial” categories, they may be built by historical accident!

Lakoff’s “category” illustrates a conceptual “free formation” of a sort, (these criteria encompass any rule479), but I question aspects of it because it appears to be an anthropological blank check, losing credibility as the ground for an extension of scientific logic thereby. 480 Lakoff makes a good case, but it is too strong! Association, similarity and motivation –and the logic Lakoff grounds in them establish categories and a consequent logic with no bounds. They encompass whatever we can imagine!

In chapter 2 I will argue a similar but more constrained case from the more classical and formal logical position proposed by Ernst Cassirer481 over three quarters of a century ago and, sadly, largely overlooked. Cassirer's reformulation of the formal logical concept, (category), was based firmly in the actual history of modern mathematics and physical science themselves. Mathematics and physical science have already expanded, (tacitly, he argued), the classical, Aristotelian Concept. Cassirer’s "Functional Concept of Mathematics", (which is a broadening of the general logical “concept” based in mathematical considerations and not a specifically mathematical entity), is broad enough to encompass the essence of Lakoff’s “category”, (concept) -and that of classical logic as a completely plausible and natural limit case as well. It does so in a more comprehensive and cogent manner I feel however, one from which a new working logical “calculus” could more plausibly be expected.482 Cassirer's category is “freely formed” as well, based on any (consistent) rule, any rule of series. It is "a new 'object' ... whose total content is expressed in the relations established between the individual elements by the act of unification... [But it is] a peculiar form of consciousness”, (and therein supplies a unique clue to the nature of consciousness incidentally!), “such as cannot be reduced to" [i.e. set theoretically abstracted from] "the consciousness of sensation or perception", (i.e. sensory objects).483 But please note that it is specifically an act, i.e. an independent (internal) construction, and by implication I will argue eventually, a biological act, (an act of the organism)- rather than a passive, (i.e. informational), derivation or abstraction from perception. Cassirer's case is made solely for intellectual concepts, (conceptual categories), however.

479 ? Lakoff argues against rule basing in general. But what are “association” or “motivation” … themselves? It is the classical, (set based rule), that he questions, I think. Cassirer, (see Chapter 2), would call it the rule of identity.

480 ? It is a triviality that if logic can prove anything, then it can prove nothing! Lakoff’s case is considerably better than this I admit, (ultimately it is logically grounded in ICM’s -idealized cognitive models), but still involves a fundamental epistemological contradiction as I will discuss in the preface to Chapter 2 and in the Afterward: Lakoff/Edelman.

481 ? Lakoff bases his logical stance in the ideas of Wittgenstein and Putnam who also question the classical concept.

482 ? The reasonable prospect of such a calculus is, of course, crucial. It is the existence of powerful, simple and highly pragmatic algorithms based in classical logic, (formal logic, mathematical set theory, and the digital computer for instance), -and the lack of the prospect of any viable alternative –that severely challenges the credibility of any counterproposal for fundamental logic.

483 ? my emphasis. He argues that the rule of a series, -with which he equates the actual scientific “concept” -cannot be derived from any finite exhibition of its instances. It is, therefore, an independent act –a free creation- of the mind, and, by extension, of the brain.

210

Lakoff and Edelman make an explicit distinction between perceptual categories and conceptual categories, (as does Cassirer between percepts and concepts). From an operational standpoint, (from the standpoint of biology for instance),484 this is clearly an artificial distinction however. These are simply the parts of operative categorization by a biological organism –i.e. non-verbal vs. verbal motor function.485 They are just the aspects of biological categorical function vis a vis environment. The extension of the formal logical "Concept" which I will eventually argue486 encompasses them both: both ordinary concepts, (conceptual categories), and, in Kant's usage, "constitutive" concepts, (perceptual categories), as well.

There is a last issue involved in "free formation". Under the classical perspective, under the set-theoretic operations of intersection, union, complement,… of properties, what I will call "hierarchy"487 must be maintained at some level. It describes the requirement for the preservation of contiguous logical properties, (in a logical category), into contiguous physical, (really metaphysical), properties in ultimate reality: i.e. properties of logical488 objects, (categories), must correlate hierarchically to properties of objects in the world. Logical objects must be constituted as topology-preserving collections, (vis a vis properties), of their “objects”.489

Even Gerald Edelman, (though acknowledging Lakoff), preserves this kind of hierarchy in his thesis of the connectivity between the brain's myriad "topobiological maps"490. Given Cassirer’s extension of the category however –or even Lakoff’s, (which Edelman incorporates into his own thesis), hierarchy is not an a priori requirement of categories or of function, however. Indeed, Edelman himself speaks of the existence, (besides the massive, topology-preserving connectivity between his multiple “topobiological maps” in the brain), of the existence of another kind of connectivity in the brain -of the connectivity of a "global mapping ... containing multiple reentrant local maps ... that are able to interact with non-mapped , (i.e. non-topological), parts of the brain..".491

Though framed in a different context and for a different purpose, (and getting ahead of myself a bit), I think this non-topological connectivity from Edelman’s topobiological maps, and specifically the connectivity from the "objects" of those maps to the non-mapped areas of the brain,

484 ? Or from the critical perspective of Kant, for instance485 ? This clearly ties in with Lakoff/Edelman's "embodied" concepts.

486 ? In Chapter 2487 ? Lakoff would call it a preservation of the properties of the “container” ICM. See the

Afterward: Lakoff and Edelman for a fuller discussion of “hierarchy”.488 ? or operational

489 ? cf Afterward: Lakoff-Edelman490 ? -which themselves are supposed to preserve the property-topology, (i.e. the contiguity of the properties in real discrete objects), of reality as sensory maps. This is an epistemological error, supplying the very "God's eye view" against which he argues so strongly. To move beyond it requires a fundamental reevaluation of epistemology itself. That is the subject of my Chapters 3 and 4. Lakoff's and Edelman's, (and Putnam’s upon which they are based), Maturana’s -and indeed any thesis denying a "God's eye view" -requires some version of or alternative to the scientific relativistic epistemology I will propose, (in Chapter 4), in order to maintain internal consistency.

491 ? Edelman, 1992, P.89, his emphasis211

(the "global mapping"), -the general case492 -supplies a fortuitous illustration the kind of potential I wish to urge for a GUI, and ultimately493 for the brain itself. It allows "...selectional events”, [and, I suggest, their “objects” as well], “occurring in its local maps ... to be connected to the animal's motor behavior, to new sensory samplings of the world, and to further successive reentry events."494 Edelman, however, correlates the topobiological maps, (as sensory maps), directly with "the world" -inconsistently supplying thereby the very "God's eye view" whose possibility he emphatically denies.

But what if we take the converse perspective?495 What if we take Edelman’s stated epistemology seriously and blink our "God's eye"?496

Instead of adopting the perspective, (Edelman’s), wherein we look from the objects of the topobiological maps back towards the distributed process of the brain, let us step back from the prejudice of our human (animal) cognition and consider the converse perspective: beginning instead with the non-mapped areas of the brain, (distributed process), and proceeding to the "objects" of the topobiological maps themselves. Consider the converse perspective wherein "the objects" and the topobiological maps they operate in are taken as functions of, (organizing nexuses of), distributed process, and not the standard perspective wherein the distributed process is presupposed to serve the objects497. What if the maps and their objects both were taken, instead, as existing to serve primitive process? This is the case I wish to suggest as an illustration of the most abstract sense of the GUI, (and which I will argue shortly).498

492 ? retaining hierarchical mapping as a special case

493 ? epistemologically reentrantly

494 ? ibid

495 ? I will supply my answer to this epistemological problem in Chapter 4.

496 ? An aside: Edelman seems very put out with the very idea of “mentally creat[ing] an environment that then subjected us (mentally) to natural selection”. (Edelman 1992, p. 35 ). The complication, he implies, boggles the mind! But much of modern science does likewise. I wish to suggest an even greater complication- we might as well face it right now.I wish to suggest a conception wherein the visual cortices, (for example), do not receive a (metaphysically) topological correlate of their surroundings. I wish to look at a case wherein the cortex we view and the world which maps upon it are both aspects of (the same) internal process and not “God-given”!Modern epistemology is radical at both the extremely small and at the extremely large (and fast) scales. It is only as algorithms that they are comprehensible. And yet almost everyone, (read this as “most realists”), seems to deny even the possibility that at the middle scale epistemology can be other than simple. Consider instead the possibility that the middle scale is algorithmic as well! Does this not fit better with the “prototypes” which Rosch displayed and which ground Lakoff’s and Edelman’s logical theses. Prototypes and the logical relations between them would, under this view, represent the “objects” and the “calculus” of practical algorithmic biology and epistemology would therein regain continuity across the board!

497 ? which would mirror the objects of ultimate reality. For Edelman this is an epistemological error.

498 ? This reorientation of perspective suggests an interesting possibility. It suggests that evolution’s “good trick”, (after P.S. Churchland’s usage), was not representation, but rather the

212

We have here a concrete model, (in Edelman's "global mapping"), which illustrates the more abstract possibility of a connection of "objects"499, (in a GUI), to non-topological process, (distributed process) -to “non-objectivist categories", (using Lakoff’s terminology). Edelman's fundamental rationale is "Neural Darwinism", the ex post facto adaptation of process, not “information”, and that rationale is consistent with such an interpretation. It does not require “information”. It does not require “representation”. Mathematics illustrates the general case in abstract transformations -whose ultimate biological application would be competence -i.e. survival, not information.500 What we are dealing with here, ultimately, are transformations, and transformations are defined on abstract sets, not on spaces!

For the GUI I urge, similarly and in the general case, that the "front end" of a GUI, (an interface), may be freely constructed, (ad hoc), based on pragmatic considerations which boil down, ultimately, to operational efficacy. It can be formulated, for all intents and purposes, in any consistent way we desire. The real trick, then, (because of the requisite simplicity of rules), is in the conception, (correlation), of the "objects" of the interface themselves so as to accomplish what is intended. But the example above suggests that the definition, (correspondence/linkage), of "an object" itself can, in a real sense, be freely formed as well. It may be linked to whatever "things" or processes -or parts of things or processes- we choose. We, (or evolution), can, therefore, freely construct a "GUI", a calculus-plus-objects to efficiently organize, (control), profoundly complex process. It is made good in the correlations, (connectivity), of the "objects" themselves –in the “global mapping”. ( Click here for a few drawings illustrating the concept: GRAPHICS).

[RETURN TO CHAPTER 1]

organization of primitive process in a topological context. It suggests that the “good trick” was in the evolutionary creation of the cortex!

499 ? in the brain's spatial maps

500 ? The question, of course, is whether "information" is necessary to competence. I will argue, (in Chapter 3), that it involves a distinction between "bounds" and "greatest lower bounds" of biologic survival. A given organism, (to include human beings), must reflect a lower bound of competence in the world. But "information" requires that it reflect a greatest lower bound, and this is inconsistent with the fundamental premises of evolution. It is the "parallel postulate" of cognitive science.

213

APPENDIX K : An Elaboration on an Objection to my Use of "Implicit Definition"

April, 1999. Let me make an important correction and elaboration here. Saunders Mac Lane, an old instructor of mine and a recognized expert in the field, kindly consented to inspect this chapter. He commented that "the idea that axiomatics amounts to an 'implicit' definition is no longer generally accepted. It fits well with class axiomatics (e.g. for geometry) where there is just one intended model. It doesn't fit for axioms for groups or space, where there (sic) are many models."I discussed his response with another mathematical correspondent of mine, a semi-retired professor of mathematics at the University of Maryland who has followed my writing for years, and he responded: "maybe its just the idea that a set of axioms can have many models which may differ in properties not covered by the axioms".These responses caused me to think deeply about this chapter. My conclusions are reflected in my response to the latter mathematician- I am including the whole of the letter:

"D_,

I have been thinking about Mac Lane's response and your comment on it. This feedback is very valuable to me, short as it is. I have long suspected that I must rework Chapter 2, (on which it was based). It seems that my first and third hypotheses are more easily understood, but the gist of this one seems to bypass everyone. The form and cohesiveness of the chapter have never really satisfied me either. I had already attempted to refer to the problem that you and Mac Lane raised, (your comments were almost identical!), in a footnote in chapter 2, (I'm not sure of the version you are dealing with, but the footnote is on the page following the subsection: "The Concept of Implicit Definition" which goes:

"I am concerned here with the object of implicit definition only insofar as it is a logical object, only insofar as it is a mathematical object. This is the actual object of implicit definition. I am not concerned with the (different) objects of models with which it may be made to correspond, i.e. with the objects of its possible realizations. This is quite a different case and quite a different object. It is the logical object per se, I will argue, that solves the homunculus."

At this point it seems pretty clear that I must elaborate my thinking on this issue, (I have considered it -and would, very much, appreciate feedback on it) -and integrate it into the main text of the chapter. The larger organizational problem raises itself once again, though, of confusing the flow of the whole of the book -which is already huge in scope. This has always been a problem. Also, I must consider whether I have taken my arguments, (re: mathematicians themselves :-) ), too far.

Let me "ramble" a bit - I would appreciate your detailed feedback if you would be so kind:

214

1. The argument I am making is that the element of an abstract axiom system is meaningful and capable of standing as a legitimate logical "object" -as a real object- in itself! This is what its axioms refer to, ("create"), I argue, and why I believe Wilder labeled their Domain as "permissive" rather than "referential".

Consider the abstract Group: i.e. that which is defined / specified by the axiom system which characterizes the general "Group". That there are many viable models, -the integers under "+" or "*", biological organisms under some operation, (I know you have seen examples like this), etc., -differing in some, even a possibly "infinite number" of properties is, of course, trivial. Indeed, even abstract axiom systems, (as distinguished from their models -i.e. taken as abstract systems), may be different instances, (models), of more basic, also purely abstract axiom systems. For instance: the abstract axiom systems of the general integral domain, the general field, etc. may be considered as different, abstract instances of the abstract axiom system of the general "Group" -i.e. they may be considered as models of the abstract Group under some specific operation. Even the purely logical objects, (which are specifically the objects of "implicit definition", I argue), of those general systems may differ in their (logical) properties. But the "elements", the "objects" of the axiom system which defines the abstract Group, (i.e. that which the axioms deal with), are not the same as the elements, the objects of its models. This, I argue, is the thrust of "implicit definition". "Definition", (in "implicit definition"), need not translate to "specification in a model" but can be taken instead, rather, as logical specification or "focus" of an abstract object within the system in which it is framed. I suggest that that "definition" can be taken in the sense in which it is used visually or photographically -as "resolution"!

It is the resolution of the most general "permissive" object!* [Note-added later: This is clearly the sense in which Schlick understood the concept and most probably Hilbert's original conception as well.]

This is the model and the case I propose for the objects of logic -i.e. "objects" as purely logical and abstract elements of equally abstract axiom systems. I maintain that these are truly legitimate logical objects, (as objects), furthermore, but objects of a different kind of logic. This is my ground for introducing Cassirer's critique of the classical logical "concept" which he argues, (and Lakoff affirms for "categories"), necessitate a change, (an enlargement), in the nature of logic itself. His arguments, I believe, are profound and right on the mark. My extension of Cassirer's conception, (the "concept of implicit definition"), is at the least consistent with the line Cassirer followed, and, if the argument above be accepted, cogent.

An immediate problem arises, however: why are our conceptual / mental objects unique? Why would we not then have just a homogenous world, (a "domain"), of elements/objects -as the mathematical context would seem to suggest? In the case of an abstract field, however and for instance, unique and special elements can exist. Transcendental numbers: "e", pi, et al. are unique and special elements of the field of reals, and, it seems, would have abstract, implicitly defined correlates in any axiom system reflecting any significant part of the nature of the reals. If cognition is indeed embedded in axiomatics, then those systems must be profoundly complex - I realize this- they would seem to need many "transcendental numbers", i.e. special, unique logical elements. That our cognitive objects would therefore have to be taken as profoundly abstract -this

215

I also realize. But I propose that this fits the whole sense of the operative system and of the objects of Chapter 1.

2. There is another "Why bother?" question, (see Chapter 6), that comes up here. Why attempt to go against theflow of current interpretation of such systems in modern mathematics? My answer was stated inthe "plain talk" section of chapter 2:

"Implicit definition, virtual existence -and logic as biology- this is the only example within ourintellectual horizons that seems to hold even any promise for sentiency in this our ordinary sense ofit. It suggests the only scientifically plausible solution to "the mind's eye" and the "Cartesiantheatre" and the only non-eliminativist, (for "mind"), answer to the homunculus problem -answers which must exist if mind in our ordinary sense is, in fact, to be real. Implicit definition permits knowing, (as a whole), what are, in some real sense, our distinct and separate parts -precisely because those parts, (objects), are in fact non-localized and virtual (logical) expressions of the whole. It opens the first genuine possibility, therefore, for a resolution of this essential requirement of "naive" consciousness." Otherwise stated, it is the only alternative presently on the table. If we believe that "mind"

taken in the sense of the "Cartesian theatre" truly exists, (and I think most of us do), then this possibility must be explored. Given its tight "fit" with my first, biological thesis, I think it has considerably more than bare credibility.

(RETURN TO ORIGIN)

216

Bibliography

1. Asimov, Isaac. "Asimov on Numbers". Pocket Books, 1977.

2. Barrow, John D. "Pi in the Sky: Counting, Thinking and Being" Little, Brown & Company. 1992

3. Birkhoff, Garrett and Mac Lane, Saunders. "A Survey of Modern Algebra". The Macmillan Company. 1955

4. Cassidy, David. "Uncertainty: the Life and Science of WernerHeisenberg". New York. W.H. Freeman. 1992

5. Cassirer, Ernst. "Substance and Function" and "Einstein's Theory of Relativity". (Translation by William Curtis Swabey). Open Court, 1923

6. Cassirer, Ernst. "Spirit and Life". An essay included in"The Philosophy of Ernst Cassirer", New York. Tudor, 1949

7. Cassirer, Ernst. "The Philosophy of Symbolic Forms". (Translation by Ralph Manheim). Yale University Press. 1953 8. Cassirer, Ernst. "Kant's Life and Thought", (Hayden

translation). Yale, 1981

9. Cassirer, Ernst. "The Problem of Knowledge", (Woglom andHendel translation). Yale, 1950

10. Chalmers, David. "Facing Up to the Problem of Consciousness". Journal of Consciousness Studies. 1995

11. Churchland, Patricia. "Neurophilosophy". Bradford Books. 1986

12. Churchland, Paul. "Matter and Consciousness". MIT Press. 1990

13. Dennett, Daniel. "Consciousness Explained". Little, Brown,and Company. 1991

217

14. Dreyfus, Hubert. "What Computers Still Can't Do". MITPress. 1992

15. Edelman, Gerald M. "Bright Air, Brilliant Fire". BasicBooks. 1992

16. Einstein, Albert. "Essays in Science". PhilosophicalLibrary. 1934

17. Einstein, Albert. "Ideas and Opinions". Crown Publishers. 1954

18. Fine, Arthur. "The Shaky Game". University of ChicagoPress. 1986

19. Flannagan, Owen. "Consciousness Reconsidered". MIT Press. 1992

20. Freeman, Walter. "Societies of Brains". Lawrence Erlbaum Associates, Inc. 1995

21. Gleich, James. "Chaos". Penguin Books. 1987

22. Gould, Stephen Jay. "The Evolution of Life on the Earth"Scientific American. October, 1994. Volume 271, Number 4

23. Hilbert, David. "The Foundations of Geometry". (Translationby E.J. Townsend). Open Court. 1910

24. Hofstadter, Douglas. "Goedel, Escher, Bach". Vintage, 1979

25. Iglowitz, Jerome. "The Logical Problem of Consciousness". Presented to the UNESCO "Ontology II Congress". Barcelona, Spain. March, 1996.

26. James, William. "The Principles of Psychology". Encyclopedia Britannica, Inc. 1952 (1890)

27. Kant, Immanuel. "Prolegomena to Any Future Metaphysics",(Muhaffy translation). Liberal Arts Press, 1950

28. Kant, Immanuel. "Critique of Pure Reason". (Norman KempSmith translation). St. Martin's Press, 1961

28.5 KUHN ////GET REFS

218

29. Lakoff, George. "Women, Fire and Dangerous Things". University of Chicago Press. 1987

30. Lara, Blaise. "Semantics and Factor Analysis: an approach to the interpretation of factors semantics and factor analysis: an approach to the interpretation of factors". http://www.hec.unil.ch/people/blara/lara/factors0.htm

31. Maturana, Humberto and Varela, Francisco. "The Tree ofKnowledge". Shambala Press, 1987

32. Minsky, Marvin. "The Society of Mind". Touchstone, 1985

33. Penrose, Roger. "The Emperor's New Mind". Penguin Books. 1989

34. Quine, Willard Van Orman. "From a Logical Point of View"Harper Torchbooks, 1953

35. Quine, Willard Van Orman. "Word & Object". The M.I.T.Press, 1960.

36. Reid, Constance. "Hilbert". Springer-Verlag, 1970.

37. Resnik, Michael "A Structuralist's Involvement withModality", MIND, 101.104, 1992

38. Russell, Bertrand. "An Essay on the Foundations ofGeometry". Dover, 1956

39. Schlick, Moritz. "General Theory of Knowledge". (Translation by Albert E. Blumberg). New York: Springer-Verlag,1974

40. Searle, John. "Is the Brain's Mind a Computer Program?" Scientific American, January 1990. Volume 262

41. Stewart, Ian. "Fibonacci Forgeries". Scientific American, May, 1995. Volume 252, Number 5

42. Stich, Stephen. "What is a Theory of Mental Representation?"MIND, 101.402, 1992

43. Van Doren, Carl. "Benjamin Franklin". Viking. 1938

219

44. Van Fraassen, Bas C. "Laws and Symmetry", Clarendon Press. 1989

45. Van Fraassen, Bas C. "Quantum Mechanics, an Empiricist View", Clarendon Press, 1991

46. Weyl, Hermann. "David Hilbert and His Mathematical Work". Bulletin of the American Mathematical Society 50, 1944.

47. Wilder, Raymond. "Introduction to The Foundations ofMathematics" John Wiley & Sons, 1967.)

////////////////////////////////////////////END 3-END INSERT/////