SCIENCE.......................................................................................................2The logic of science.................................................................................2

Undeniably true propositions..........................................................3Proofs...........................................................................................8False premises.............................................................................9

Theoretical knowledge, factual knowledge...................................11Falsification...............................................................................11Induction and history.................................................................12

Scientific progress.........................................................................13ORDER.......................................................................................................15

Natural orders.......................................................................................17Phenomenal aspects.......................................................................17

Phenomena................................................................................17Inorganic substances: process........................................................21Organic, inanimate substances: evolution.....................................27Animate substances: conscious behaviour.....................................29Persons: self-conscious action.......................................................31

Metaphysical orders..............................................................................36

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SCIENCE

THE LOGIC OF SCIENCE

‘Science’ literally means knowledge. “Scientific knowledge” is therefore a pleonasm. By extension, ‘science’ stands for the dedicated search for knowledge and connotes openness to criticism of methods used and claims made. With respect to this connotation, “secret science” is an oxymoron and “scientific knowledge” is not a pleonasm but refers to knowledge obtained by dedicated and public search. The search for knowledge, or truth, is not the search for consensus among experts, eminence in academia, headlines, book sales, research grants, peer recognition by people in search of similar things, or other signs of academic, social, economic or political success.1 A scientist is someone who searches for truth — he is a scientist only as far as that is what he is doing. Besides, no one is a scientist merely because other people call or believe him to be a scientist, or because he has the legal permission to call himself a scientist.

Here we are going to discuss only some of the main points in the logic of science as knowledge. The logic of research,2 or search for knowledge, is not on our agenda.

1 J. Ravetz, Scientific Knowledge and its Social Problems, (XXXX)2 Karl Popper, Conjectures and Refutations (London, 1963). Popper's main theme was “the logic of research / scientific discovery” (cf. his Logik der Forschung, 1934; The Logic of Scientific Discovery, 1959), with emphasis on the spectacular progress made in physics from the sixteenth to the twentieth century. Unfortunately, he tended to impute the characteristics of the quest for knowledge to the objective of that quest. “Science” became a set of “bold” theories (i.e. conjectures) awaiting refutation, while the facts needed for their refutation were “theory-laden” and therefore conjectural themselves. Thus, “science” became “conjectural knowledge”, which is not knowledge but conjecture. However, if science is conjecture, and if it takes a conjecture to refute a conjecture, then the movement of science ceases to be progressive and cumulative: it comes to depend on the relative strengths of the beliefs of various factions of “the community of scientists” in the merits of this or that conjecture. Popper's philosophy of science unintentionally opened the door to relativism, subjectivism, even nihilism, and to the substitution of the sociology and psychology of scientists for the philosophy of science — developments he watched in horror in his later years.

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Knowledge implies truth. For every proposition P, if you say that someone knows that P then you imply that P is true. Obviously, something may be true without anybody knowing it to be true, but nobody can logically claim “P is true but nobody (including me) knows it.” However, “He knows that P, but he does not know he knows it” is not necessarily false, although obviously “I know that P but I do not know that I know that P” is a necessarily false statement. Science is knowledge that is known to be knowledge. Because knowledge implies truth, what is false cannot be science; moreover, it can never be that one science contradicts another.

Knowledge is not the same thing as belief. It is not the same as having true belief(s). It makes sense to ask a person why he believes what he believes. He can adequately answer by giving his reasons, even if the questioner finds them unconvincing. In contrast, it does not make sense to ask a person why he knows what he knows. However, we can ask him how he knows. To answer that question, he must give evidence and arguments that ought to convince the questioners and others of the truth of what he claims to know. The evidence and arguments need not actually convince others, for they may be too dumb to understand them, too lazy to check them or too unconcerned to bother. However, whether the evidence and the arguments justify his claim to know is a question of logic, not of psychology. Every argument implies the claim that it ought to and does respect the laws of logic just as every assertion implies the claim that it is true and ought to be recognized as such. Without those implications, the speaker produces no argument or statement. Hence, as self-respecting persons, who mean to be serious and want to be taken seriously, we ought to respect the laws of logic. Indeed, we cannot argue that we ought not to respect the laws of logic in making arguments. If we did that, we would give ourselves permission to speak without logic — or rather, since speech (as distinct from babbling) implies commitment to logic, permission to pretend to speak without actually doing so. Moreover, and regardless of our conscious intentions, we would give our opponents permission not only to do the same but also to interpret our utterances as incoherent babbling. Similarly, every argument that relies on

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evidence implies the claim that the evidence is reliable and ought to be recognized as such. Without that implication, the speaker produces no evidence in support of his argument.

A claim to know how to do something can be made good by actually doing it or describing a step-by-step method of doing it in which each step is known or can be shown to contribute unequivocally to the production of the intended outcome. A claim to know that something is true needs to be made good with proof, i.e. a deduction from one or more true or undeniable propositions (the premises of the proof). Undeniably true propositionsA proposition is undeniable or irrefutable for a particular person if he would not know how to refute it or would not be able to try to do so without involving himself in a contradiction. The contradiction can be a formal one (claiming both P and not-P to be true). It can be a performative contradiction (claiming to do what one is evidently not doing, or not to do what one is evidently doing). It can be a lie (claiming to know that something is so and so while knowing it is not). Or it can be a mistake or a sign of ignorance (claiming truth for something that is known or can be shown to be false). Of course, the fact that some people cannot refute a proposition does not mean that no person can do so; it does not prove that the proposition is undeniable, let alone true.

An undeniable, irrefutable or necessarily true proposition is one that no person can prove false. Any attempt to deny or refute it involves one in a logical or a performative contradiction. Consider, for example, propositions or propositional forms like “A is true only if A is true”, “For any number x, there is a number that is greater than x”, “Eggs come twelve a dozen” or “Minutes before he died, he was still alive.” They are either formal tautologies or else analytical truisms that not even God could deny.

Some statements are analytically true (e.g., “A bachelor is not married”, “Until he died, he was still alive”). Other statements are analytically false (“An even number of eggs cannot be distributed among two persons so that the one gets as many eggs as the other”, “A hectolitre is 10 litres”). Their truth-value can be assessed a priori, without investigation of

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the things mentioned in them. We need only know, understand and analyse the meanings of the words used in making them and be able to make deductions from them. The relevant meanings should be looked up in dictionaries or in specialized vocabularies or terminological lists. However, these sources may not always agree, which means that the same sentence can express an analytical proposition under one linguistic convention but not under another. Some dictionaries may even include in their definitions elements that should be reserved for encyclopaedias. Compare “Whale: common name for big animals that spend their entire life in the sea” with “Whale: common name for big mammals that spend their entire life in the sea.” Under the first definition, “A whale is not a mammal” is false, but not analytically false. Under the second definition, it is still false but also analytically false — but that definition includes some knowledge about whales, not just about the common use of the word ‘whale’. A person may be able to use the word ‘whale’ correctly (e.g., he is infallibly able to pick out the pictures of whales from a miscellaneous collection of photographs), yet know zilch about what distinguishes a mammal from a fish.

Some statements are such that their truth-value cannot be assessed a priori. “This morning, a whale was found on the beach near Dunkirk” is an example. To assess its truth-value, we need to find out about the things mentioned in it (not just about the words used to make it). Statements of this kind are synthetic (not analytic). Their truth-value can be found only a posteriori, after an investigation of those things.

Not all synthetic statements are a posteriori, however. The truth-value of some synthetic statements can be known a priori. E.g., “All human beings are mortal.” This is undeniable, irrefutable and, in that sense at least, true (although there is no positive, constructive proof of it). It is not just that all the evidence we have confirms its truth. No matter how long a man lives, his living that long is not proof that he will live forever. Methuselah died eventually, but even his still being alive today would not prove his immortality. In fact, there will never be a moment when we have proof that some man is immortal. Hence, it is useless to say, “But the concept of immortal man is not contradictory in the way the

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concept of square circles is. It is not logically impossible that there will be at least one immortal man in the future.” Indeed, it is logically possible that at least one human being is immortal — which is why “All human beings are mortal” is not a formal tautology or an analytic proposition.

“Man is mortal” is an example of a synthetic statement that is true a priori: synthetic because “being mortal” is not part of the lexicographical definition of “man”, and a priori because mere thought can establish that no event in space or time can possibly prove it false. For the same reason, “No compound or complex material thing lasts forever” is undeniable. Again, there is ample evidence that supports its truth, and there could not ever be evidence that it is not true.

From the examples about men and physical objects, we cannot inductively infer that nothing lasts forever. Metaphysical things, such as numbers have no physical existence. There is no direct physical evidence of their existence,3 although there may well be physical evidence of the effect of their being. For example, a machine may be proof that its maker had access to mathematical knowledge, even if there is no physical evidence of its maker. No empirical evidence of metaphysical things going out of existence is possible — and of course, there can be no physical evidence to the effect that they will never cease to exist. Whether they can pass from being to not being (nothingness) is a question we cannot answer by referring to physical evidence. Indeed, as long as one of us is around to raise the question, such metaphysical things will have to be there, or the question will not be meaningful. For metaphysical things, to be is to be eternally or beyond time. This too is an undeniable, irrefutable truth. Mathematical being has no history, no development, no evolution; the only history of mathematics is the history of human discoveries of mathematical truths.

“Every existing physical thing can be the outcome of a coincidence of blind, unintentional or purposeless events or

3 Perhaps “elementary matter” should also be relegated to the metaphysical realm. Can we ever have physical evidence to prove that something is indeed, in an absolute existential sense, elementary, when for quantum-theoretical reasons we must acknowledge that there are limits to what we can observe without uncontrollably altering it?

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processes” is a synthetic a priori proposition. The coincidence may be extremely unlikely; but given the vast expanse of the universe both in its spatial and temporal dimensions, it cannot be excluded a priori. The famous “parallel roads” of Glen Roy, Scotland, which certainly look as if they were designed by man, are now deemed effects of natural forces (water and ice). Even a computer is nothing more than a particular physical arrangement. It is easy enough to prove that the computers we actually use are intentional products of intelligent design and purposeful manufacture; however, that does not prove that nothing that is physically identical or similar to a computer could come into existence by natural, unplanned, unintelligent coincidences. In fact, there can be no proof to the effect that such coincidences are impossible. This we know a priori, because what was put together on purpose was put together; it would have come about just the same if the physical process of putting it together had happened accidentally.

Consider for example the Darwinian “idea of evolution by natural, accidental variation and natural selection”. Darwin's idea was essentially an extrapolation from the intentional, artificial selection of animals and plants by humans. If farmers and breeders were able to produce new varieties of species in the short span of human history and on the limited area of land fit for human habitation and husbandry, think what natural variation and selection could accomplish over the full reach of time since the solar system came into existence! Thus, the Darwinian idea of evolution and the proposition that specimens of every kind of physical thing might have come about unintentionally by a coincidence of unintelligent factors are both synthetic a posteriori truths. However, although they are undeniable, there is no positive, constructive proof for them. In contrast, the Darwinian theory of evolution, which states that Darwin's idea actually explains the existence of every animate or inanimate organism, is not a synthetic a priori proposition. To appreciate the difference, compare “Accidental variation and selection might have produced X” (Darwin's idea) with “Accidental variation and

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selection did produce X — and did so without the assistance of any other factor” (the Darwinian theory).4

Other synthetic a priori truths are: “Human persons, such as you and I, can act”, “Being capable of acting, we have notions of past, present and future events or situations; of causal connections, regularities, means and ends, making choices; of better and worse, rights and obligations, being honest and pretending”. It is useless to try to demonstrate that they are not true. Every attempt to do so requires you to act, to consider what you hope to achieve by that action or how doing it will produce the intended effect, and to explain why others ought to accept that you have successfully refuted one of the above propositions. Yet, none of this you could do without presupposing their truth throughout your argument, which is itself essentially an intentional, purposive, claim-stating action.

“If you can choose, you must choose”, “Every choice has a cost” or “Choosing one thing entails giving up another” — these are synthetic a priori truths. So is “The utility of an additional unit of a good is lower than the utility of an already acquired unit of that good.” Yet another example “A person uses the means available to him to try to achieve his most highly valued ends for which he thinks them suitable, while postponing attempts to achieve ends he values less until additional means are available.” The undeniability of these propositions becomes clear as soon as we consider the plight of a person who would set out to argue that they do not apply to him.

It is of course possible to transform synthetic propositions (whether a priori or not) into analytical propositions by referring to a specialised list of definitions. This happens frequently in many sciences, when attempts at formalisation are made. Then so-called technical definitions are supplied not only to remove the ambiguities of natural languages but 4 Some people (Richard Dawkins, for example) claim “huge quantities of circumstantial evidence” for Darwin's theory, but circumstantial evidence is not proof and “huge quantities” is an expression of subjective opinion. Another argument is that the theory gives us the best available explanation. Again, this is not proof: the best available may not be (and in this case is not) enough. Evolutionists routinely call the theory “a fact” (which it may or may not be), perhaps because they confuse it with the idea (which is a fact, i.e. an undeniable truth, albeit one that concerns possibilities, not actualities).

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also to “pack” terms with essential knowledge. Such technical terms consequently refer not to a general dictionary based on common speech habits but to an encyclopaedia providing essential knowledge of a particular field. Recall the two definitions of the word ‘whale’ that were mentioned earlier. In a formal presentation of zoology (such as a textbook), “A whale is a mammal” will be an analytic proposition, if the text refers to a definition of ‘whale’ that already includes basic knowledge of whales, in particular, the knowledge that they are mammals. Still, that particular item of knowledge in the vocabulary of the text is synthetic. If the proposition about whales being mammals is analytic in the text itself then that is merely an artefact of the formalisation — not a qualification of that item of knowledge.

Note that the distinction between a priori and a posteriori is relative to the assessor of the truth or falsity of a proposition. On the one hand, we, humans, know a priori that the proposition that all men are mortal is undeniably true. On the other hand, gods, who are beyond time, might know that some humans are (or will be) immortal. They might even know that humans do not really exist or that they are actually incapable of acting or thinking. However, we could not know those things, since to assess their truth-values, we would have to engage in acting and, in particular, in reasoning, experimenting or otherwise marshalling the required evidence. In other words, our attempts to assess the truth-values of these supposed items of divine knowledge already presuppose our existence and our capacity of acting, thinking and speaking. If, in the eyes of the gods, we are merely deluding ourselves when we believe that we exist or can act, we can nevertheless never discover the illusionary nature of those beliefs. Thus, some propositions that are not necessarily true in themselves are undeniable for us. Because we are interested here in human science, not in scientia divina, we should accept that such propositions represent human knowledge.ProofsA proof can be direct, i.e. constructive: it leads by logically valid steps from true or undeniable premises to the

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proposition to be proven. The general form of such a proof is as follows:

P is trueProof

Q is undeniably true Q P [the actual construction]

Therefore, [arguing in modus ponendo ponens5]

P is true Q.E.D.

Alternatively, a proof can be indirect or non-constructive: without being constructive, it nevertheless shows that the proposition in question is undeniable or irrefutable, for example by a reductio ad absurdum of its negation. This kind of proof takes the following form:

P is undeniable (i.e. ¬¬P)

Proof1. Assume ¬P (¬P Absurdity) [the actual reductio] Therefore [arguing in modus ponendo

ponens] Absurdity2. But the absurd cannot be ¬Absurdity Therefore [arguing in modus tollendo

tollens6] ¬ ¬P Q.E.D.When using a reductio ad absurdum, one should take care

that the absurdity to which the reduction leads is really absurd. Merely showing that denying a proposition leads to some implausibility or other is not enough. A traditional way of putting this is that science must start from self-evident propositions — provided one understands “self-evidence” as a logical property of a proposition, not as a psychological effect 5 I.e. If (Q and (P follows logically from Q)) then P6 I.e. If ((P follows logically from Q) but P is not true) then Q is not true.

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of considering it.7 Obviously, every proof must ultimately rest on undeniable, non-constructively provable propositions, as it is impossible to give non-circular constructive proofs for every proposition used as a premise in an argument without going into an infinite regress.

A constructively provable proposition is undeniably true, but an undeniable proposition need not be constructively provable:

provable(P) undeniable(P)but not

[*] undeniable(P) provable(P).It is, of course, not the case that for every proposition P,

either it or its negation is provable/undeniable:[*] provable(P) or provable(not-P) [*] undeniable(P) or undeniable(not-P)

are not logical truths. However, provable(P) or not(provable(P)) undeniable(P) or not(undeniable(P))

are logical truths. So what about these formulas: true(P) or not(true(P))

true(P) or true(not-P) ?The classical “truth-functional” answer is that both have the

same meaning and that both are logical truths. Nevertheless, it is a fallacy to treat both formulas as equivalent to one another in the context of argumentation. For it would be wrong to interpret the fact that a person does not say that P is true as evidence that he says that its negation (not-P) is true. He may have no opinion either way. It would be absurd 7 A proposition is a logical, not a linguistic, object. It says something about something (i.e. it predicates something of some subject). Not every sentence expresses a proposition, even if it looks as if it does. Thus, the sentence “This is a lie” is perfectly good grammatical English, but if I were to pronounce it, intending ‘this’ to refer to the sentence I am pronouncing, then I would not make sense. Let S be that sentence. Assume it means something, viz. that S is a lie. Let L(x) be short for ‘x is a lie’. Then we have L(S), which, if it means anything, means L(L(S)), and so on, i.e. L(L(L(…))). We have a predicate (L) but never get to identify a subject. Hence, we have no proposition: something is said about nothing. Consequently, the assumption that I made a meaningful statement is untenable. It is sometimes said that the sentence expresses a necessarily false proposition, because even if we should suppose it truthful, it would still assert its own falsity. This invokes the logical principle (P ¬P) ¬P; but it also assumes that in pronouncing the sentence, I made a meaningful statement — which I did not.

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and bad form to insist that he provide arguments, let alone proofs, for what he does not say. However, in pure reasoning (which is, so to speak, an attempt to convince God), it is quite proper to assume “true(P) or true(not-P)” because then one's opponent is supposed to know and to be committed to the truth about everything.False premisesAlthough it is possible to derive (i.e. construct) a true conclusion from a false premise, a conclusion drawn from false premises cannot count as science. Given that the first premise is false, “Cats can fly, cats are mammals; therefore, some mammals can fly” has no scientific merit, although some mammals (bats) are capable of flying. Accepting a premise admitted or known to be false makes it logically impossible to deny any proposition that is alleged to follow from it — ex falso sequitur quodlibet.8 How would you provide a coherent justification for the view that a proposition is to be rejected because it is false when you have already admitted that the falsity of a proposition is not a reason for rejecting it? It is therefore pointless to try to prove something (anything) from false premises.

Knowingly reasoning from premises not known to be true (a fortiori known to be false) while calling the conclusions scientific knowledge is deception. A technician or engineer may be satisfied with a “model” that fits the observations, even if he has no clue about the realism of the assumptions built into the model. After all, he is interested only in what works as far as he needs it — that is to say, as far as he, his employer or the latter's clients need it. Neither he nor they need be interested in truth or knowledge. He should not therefore deceive others or himself into believing that he is a scientist. Technicians and engineers are disciplined by the profit-and-loss system of the market and the threat of liability claims if they try to pass off what does not work as something that does work. Scientists face no such threat; their discipline

8 Note that the ex-falso-quodlibet principle does not imply that any proposition can be constructed from a false proposition. From the false premise “My head is ten feet wide” one can construct neither the obviously false conclusion “The moon is made of cheese” nor the obviously true conclusion “London is a city”; however, one can construct the true conclusion that my head is less than ten meters wide.

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must be self-imposed respect for the logic of science. Although there is a market for ideas, it provides at best a test of the popularity of an idea, not of its value as science.

From a true premise, only true conclusions can be deduced. We must therefore continually check our premises against the conclusions drawn from them to weed out any untruth that might have escaped notice. If a conclusion drawn from a premise turns out to be not true, the premise must be revised (refined, qualified) or rejected. If the truth of a premise is either undeniable or provable, any false “conclusion” must be attributed to an error in its deduction from the premises. In other words, it must be admitted that the “conclusion” was not really a logical implication of the premise. However, although some truths are “given” a priori (i.e. from the very start of a search), most are not. The search for knowledge is the search for truths that, when found, can be used as premises in a later search.

Relaxing the standards of proof means giving up the requirement that a proof be provided: one settles for less than logically compelling reasons for believing something. Science, however, requires the highest standards of proof. Its intrinsic finality is to know, not to feel comfortable believing. Theoretical knowledge, factual knowledgeWe usually make a distinction between theoretical knowledge and factual knowledge. To the extent that we posses it, theoretical knowledge identifies what is, was and will be true for all men, regardless of time and place, whether they know it or not, because it is knowledge of one or other natural or metaphysical order (say, the order of mathematical things), none of which is man-made. Factual knowledge is knowledge of particular events in some order of things, which happened at particular times and in particular locations. Without theoretical knowledge, factual knowledge would be restricted to actually observed events; theoretical knowledge makes it possible to infer that an event of a particular kind must have happened, possibly before any form of human life appeared, or is bound to happen, possibly after mankind has disappeared. However, from our theoretical knowledge, such as it is, we cannot infer that it is complete. Therefore, inferences about facts come with a proviso, rebus sic

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stantibus (things remaining as they are known today) or ceteris paribus (no changes in things other than those mentioned).

Applying the laws of physics to available data about the universe, cosmologists can “calculate back” to a singular event, the Big Bang. They can do so on the assumption that there was no other singular event in the cosmos, i.e., that the known laws of physics have remained constant9 at all times throughout the universe. In other words, the Big Bang is a conjecture based on backward extrapolation from the present state of knowledge. We do not know if there was a Big Bang. If the laws of physics as we know them were valid only within our region or period of the universe, the conjecture might be false yet no human being would ever be able to refute it. We cannot just go to other regions of the universe to check. Obviously, because the data about the present state of the universe are numerous, heterogeneous and constantly changing, there is still room for other hypotheses. But there appears to be little interest in them. FalsificationIt is a fallacy to claim that a statement must be empirically falsifiable if it is to be a part of science.10 Our examples of synthetic a priori truths are not humanly falsifiable, but how much of the sciences of man or even the sciences of physical things would remain if they were ruled inadmissible? Is there no science of mathematics because mathematical propositions are not empirically falsifiable?

An unqualified general proposition, all a's are B's, is falsified when an a that is not B is observed or produced by a human person. The proposition is shown to be not true; it does not,

9 Occasionally, physicists will wonder whether the so-called constants of nature really are constant, and about the sort of evidence that would be needed to tell whether they are or are not. 10 Karl Popper (XXXX) suggested that “falsifiability” be used to demarcate science from pseudo-science. It is a useful criterion for distinguishing between 1) attempts to identify the conditions under which the theorems of a theory are true (or false), and 2) attempts to “immunise” a theory by invoking relations, entities, forces or processes the presence or absence of which cannot be verified empirically. However, just as science may use non-empirical unfalsifiable mathematical truths, it may use unfalsifiable truths with a different provenance. Science cannot be corrupted by truth of any kind.

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therefore, represent knowledge. However, if unknown to man, somewhere outside the range of human powers of observation or production, there is an a that is not B, it does not falsify the claim that the general proposition represents human (as distinct from divine) knowledge. That a proposition is not falsified obviously does not mean it is true. Nevertheless, knowledge of the fact that it has not been falsified may be significant, especially if strenuous efforts have been made to try to show it false.

Empirical falsification is scientifically important because, to the extent that it is successful, it leads to knowledge, if only negative knowledge: “This is not true in all cases.” However, the empirical sciences are on the look-out for theoretical knowledge, for what is true in all cases within their purview. Note that in the empirical sciences, the word ‘theory’ is now commonly used to identify a general conjecture or hypothesis, which is not a formulation of knowledge but of an idea to be checked by further research. Theoretical knowledge is one thing; a theory under scientific scrutiny is another. Induction and historyAs an inference of the form “some a’s are B’s; therefore, all a’s are B’s”, induction is formally invalid.11 However, the fact that it is formally invalid should not be used as the only reason to reject an inductive scientific inference if there are good reasons to accept it. Take this example: “In view of the overwhelming number of reports we have from a variety of independent sources in different periods of history and different places on earth, we have no fact- or data-based reason to doubt the truth of the proposition that all ravens are black.” It is true that we do not have reliable observations of all ravens that ever existed or will exist; so, the possibility remains that somewhere, at some time, there was, is or will be a non-black raven. Notice, however, that the claim made in the example was not that all ravens are black, but that, in so far as we know, or to the best of our knowledge, all ravens

11 For Karl Popper (XXXX), the formal invalidity of inductive arguments was a sufficient reason to rule them out as permissible scientific inferences. Contra Popper (and Hume, who inspired his anti-inductivist stance), we should say that scientific knowledge consists of ought-to-be-believed because provable or at least undeniable statements. There is no reason to exclude inductive arguments or generalisations a priori.

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are black. The appearance of a non-black raven would change the state of knowledge but it would still be true that before its appearance, we did not know of any non-black raven. Moreover, when we do say that all ravens are black, we usually do not claim that this is theoretical knowledge. We usually claim only that it just happens to be a fact that all ravens are black. Their blackness, albeit compatible with our theoretical understanding of the order of animal life, is not essential or crucial to it. Not every general proposition “all a's are B's” expresses theoretical knowledge about, or a natural law of, an order of things. Often, such propositions convey factual knowledge about things as they exist in a particular period or region.

Speaking loosely, we often say such things as “All ravens are normally black.” A non-black raven (if it were to appear) would be anomalous, for example because it was afflicted with a hitherto unknown disease. If all or some of its offspring (if it had any) were also non-black, the qualifier ‘normally’ could be expanded into something more explicit, e.g., “normally, except in the valleys of western Ruritania”. If non-black ravens eventually came to dominate or even to entirely replace black ravens, the proposition would have to be qualified with an indication of its temporal scope: “Before 2050, ravens were normally black.” In many, perhaps in all empirical sciences, such qualified truths are the best one can hope for. But a qualified truth is still a truth.

Unqualified general truths are rare in sciences that deal with phenomena that have “a history”. Human phenomena certainly have a history: to understand them we need to know about what happened earlier, but that knowledge is hardly ever sufficient to predict particular phenomena or even to assign a measure of probability to them. History is not development. Whereas a development is an unfolding of what was already there, even if it was not there in an empirically detectable form, history is marked by the intervention of unexpected, unforeseen events and happenings confronting the participants in the history with challenges for which they are not prepared. They face “new situations”, even though the novelty need not be anything physical — it may be a new idea or awareness. How they respond, given that they could have

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responded in various ways, is crucial to the course of their history. Scientific progressIt may happen that as more-stringent methods of proof (e.g., more powerful mathematical techniques) or means of observation and measurement become available, scientists need to revise their beliefs or assumptions about the scope of a theory. A scientific theory of limited scope is still a scientific theory; if true, it is still a formulation of knowledge. If scientists develop a more general theory from which the more limited theory can be derived, given a proper circumscription of its scope, the latter theory is vindicated as a special case — it is not refuted. It may be rendered obsolete by the more general theory, but even an obsolete scientific theory is still a scientific theory.

An empirical theory is refuted when it fails to predict the phenomena it seeks to predict, taking into account the scale at which phenomena of the relevant kind could be observed when the theory was formulated. If it fails to predict at higher standards of observation than were available when its original formulation was proposed but continues to predict according to the old standards, it is shown to be limited in scope but not refuted. Newtonian mechanics has not been shown false. It was not abandoned because it was false; rather the belief that it has universal scope has been proven false — but that belief was never scientific knowledge.

Of course, much of what we know is encapsulated in theories that are not empirical. Our understanding of the economic aspect of the world has progressed enormously since medieval theologians began to pay attention to it. However, the progress has little to do with economics becoming more of an empirical science. Empirical economics remains stuck in a universe where it is easy to show that not all observable a's have observable aspect B, and very nearly impossible to find any theoretical relation that holds good universally and can be tested empirically. That is not surprising, the order of the economic aspect of the world is an order of human actions, constrained but not made predictable by objective, observable or measurable physical conditions. Human agents react at least as much to other

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human agents as to their physical environment. They act as much in anticipation of what others will do as in anticipation of what will happen in their physical environment. Subjective factors abound: opinions, prejudices, hopes, fears, preferences, etcetera. The same observable happening may be a surprise to some people, a fully anticipated, either welcomed or feared, event to others. It may escape the notice of some people, induce others to revise their plans drastically and still others to sink in despondency, even lethargy. Although money prices are to some extent observable to outsiders, they are not measures of anything. They are results of actual transactions, indications of a willingness to sell (“ask”) or to buy (“bid”), or indications of a desire to control buying and selling (e.g. when a government institutes and enforces price controls or taxes). To understand the economic order of the world, we need to understand the order of the world in which human persons act and interact.

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ORDER

In the introduction, we noted several types of order: natural, artificial and metaphysical (or supernatural). In this chapter, we shall focus on the differences between natural and metaphysical orders. Artificial orders will be discussed later.

The main distinction between natural orders and metaphysical orders is that the former are orders of existing things, whereas the latter are orders of real things. In everyday English, this distinction cannot be expressed without substantial circumlocution, because ‘is real’ is often used as a synonym of ‘actually [or effectively] exists’. However, I shall frequently refer to it. Therefore, a short explanation of the words ‘real’ and ‘reality’ as distinct from ‘existing’ and ‘existence’ is in order.

Some languages make it easy to disambiguate two relevant meanings of ‘real’ and ‘reality’. For example, to translate them into German, we can use ‘real’ and ‘Realität’, or we can use ‘wirklich’ and ‘Wirklichkeit’.12 The words in the second pair obviously derive from the verb ‘Werken’ (to work) and refer to [the totality of] what works, i.e. produces tangible, observable, measurable effects. Often, ‘effective’ or ‘actual’ (in the sense of “actually existing”) will do to translate the adjective ‘wirklich’ into English, but the noun ‘Wirklichkeit’ has no commonly used English equivalent. In fact, it is usual to translate it as ‘reality’, which carries the risk that its distinctive meaning is lost in translation. Even worse is the fact that in English ‘real’ and ‘reality’ are used most of the time to convey the meaning of ‘wirklich’ and ‘Wirklichkeit’. This is the case, for example, when one speaks of empirical reality, the realities of war, a really sick person, and so on.

The words in the first pair (‘real’ and ‘Realität’) are based on the Latin ‘res’, thing (also object, action and much more). In a philosophical context, ‘res’ refers specifically to something that is, i.e. to something intelligible or capable of

12 To translate them into Dutch, we have ‘reëel’ and ‘realiteit’, or ‘werkelijk’ and ‘werkelijkheid’.

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being understood.13 I shall use the words ‘real’ and ‘reality’ accordingly. For example, mathematics is the study of the order of numbers; it would not be what it is if it were confined, say, to the study of how people effectively or actually (wirklich) count and measure. Similarly, the laws of logic are real, regardless of how people effectively reason or argue. Thus, neither the reality of mathematics nor the reality of logic is belied by the existence of widespread innumeracy and illogicality. If it is true that we all make mistakes, one might say that mathematics and logic do not exist or that only attempts to do math or logic exist. However, saying that is meaningful only because mathematics and logic are real orders of things (numbers, arguments, etcetera). These real orders provide the norm for every attempt at doing math or logic: we ought to respect the orders of mathematical and logical objects. We can identify and correct our mathematical and logical errors precisely because of the objective reality of those orders. We can imagine a flawless exposition of mathematics or logic; we cannot imagine an exposition of mathematics or logic consisting of nothing but errors, mistakes and fallacies. Although errors, mistakes and fallacies undoubtedly exist, they do not constitute an order of things: in themselves, they lack mathematical or logical being.

Thus, we have the philosophically essential distinction between being (what is and can be known to be) and existence (what can be observed, seen, heard, felt, touched, measured, manipulated, moved, torn, cut, dissolved, etc., at particular points in time and space). The common meaning of ‘A exists’ is that A can be located somewhere in space or time.14 The number pi cannot be located in that manner. Yet, there is a number pi. Thus, “The number pi does not exist” is not equivalent to “There is no number pi.” The distinctive 13 In this a sense, there are no realities of war, as war is not a reality. War is disorder. While we can recognize disorder when we see it, we cannot understand it as such, but only as a disappearance of order, the appearance of confusion. Ultimately, it is total confusion, total absence of order (consequently, of information), which is a situation we cannot understand at all. War is pure Wirklichkeit — in fact, a self-destructive, self-exhausting process that we can study only as long as it is not the only Wirklichkeit. 14 Sometimes an entity is said to exist putatively: although its existence cannot be proven. The assumption that it exists may render certain phenomena intelligible which would otherwise be inexplicable. But putative existence is not the same as existence.

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meaning of ‘A is [real]’ is precisely that A's being is undeniable. Of course, we can say that the number pi exists in the order of numbers, just as we can say that Hamlet exists in the imaginary world created in Shakespeare’s play. We then interpret “being” as equivalent to “existence in some, perhaps unspecified, order of things”; but then we have still to determine whether the order in question is another of actually existing things or not.

In addition, we have the distinction between necessary and contingent being, which turns on the difference between, on the one hand, things we can understand although we have no proof or evidence of their existence anywhere in space or time, and on the other hand, things we can understand only because we are aware of their present or past existence. Thus, while the order of mathematical things has necessary being, we should say that the order of human persons is contingently real because we can only understand it through our awareness of our own and one another’s existence.

It is, of course, proper to refer to mathematics, logic, also to health and natural law, as ‘ideal orders’ to emphasize that even when they are not existentially present, they are still accessible as ideas. However, unlike utopias, designs, story plots, and the like, they are not ideas in the sense of products of the human mind. Instead, they are realities understood or grasped by the human mind. Health is a reality (even though no organism may exist in a perfectly healthy condition) in a way sickness is not (even though no organism may exist without some sickness or other defect). We can imagine a living organism being and continuing to be perfectly healthy, but we cannot imagine it being and continuing to be perfectly ill, i.e. deficient in every possible way — for then it would no longer be able to function as a living organism at all. Similarly, we can imagine the world [of human interaction] being and continuing to be in perfect order, but we cannot imagine it being and continuing to be perfectly disordered — for then the idea of human interaction would no longer make sense. Again, we can imagine a person being and continuing to be perfectly good, but we cannot imagine it being and continuing to be perfectly evil. We can think of Satan as a fallen angel, who can do his devilish work only because he knows, but does not practice, goodness. We cannot think of

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him as absolutely, totally, unqualifiedly evil and still deem him a person.

NATURAL ORDERS

Phenomenal aspectsTo study phenomena we must distinguish between substances and happenings: a phenomenon is something observable that happens to something observable. We must also distinguish between appearance and reality, i.e. between phenomena that are and phenomena that are not resolved intelligibly. For example, when we observe a change in the colour of an object (the appearance), we still have to resolve whether the reality is that the object itself changed its colour, that there was a change in the light that allowed us to see the object, or that there was a change in ourselves, our eyes or our brains. There is of course no guarantee that we will always be capable of distinguishing between appearance and reality. Not only will there often be practical limitations (due to the actual state of technology and the costs of making and operating tools of observation and measurement); there may also be fundamental, unsurpassable limitations, which no advance in technology can overcome. The latter limitations come about because there is always a level or scale at which the act of observation or measurement risks interfering significantly and uncontrollably with the things we want to observe or with our instruments of observation. Unlike gods, who presumably have direct, immediate (“unmediated”, “pure”) knowledge, we can gain knowledge only by interacting with things, by acting on them and experiencing their effects on us. Human natural science is not scientia divina. PhenomenaLet us briefly consider the relevant concepts of substance and happening that are part of the definition of “phenomenon”.

(1) “Substance” refers directly to a definite form, which we can observe. A man lies in his bed, breathing; a moment later, the same man lies in the same bed, not breathing. It is easy to miss what happened, the change to the form. Some methods of observation may not register it at all. For example, taking photographs of the two forms may not show any difference

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between them; nevertheless, a momentous change happened: the man died.

“Substance” also refers to a range of possible modifications of the form. For a man asleep in his bed, this range is obviously different from what it is for a man who died in his sleep moments ago. The range of potential shapes is the condition of the form. We may think of it as a set of propensities or more or less probable changes. We cannot observe the condition directly, but its existence becomes obvious from the experience that a particular form can and does change, often in a variety of ways (but not in every conceivable way). Moreover, experience also teaches us that the form at the end of an observed episode usually still has the potential to change. In other words, the resulting form comes with its own condition, which may but need not be similar or even identical to the condition of the original or earlier form. Of course, the condition may go through a state-change: the condition of a living person is radically different from that of his bodily remains. Even if we were unable to detect the breathing of a sleeping man, even if, for a while at least, the observable form is similar, we would eventually notice the change in his condition brought about by his dying in his sleep: he remains still, does not wake up; his temperature drops; his complexion changes.

Thus, unlike a formal change, a transformation, of a substance, a material change, which is an alteration of the condition of a substance, is not directly observable. Nevertheless, we can often induce that, although no formal change was observed, something must have happened to a substance because subsequent observations reveal unexpected or abnormal behaviour. For example, a laboratory technician comes to suspect that there is something wrong with the condition of either his instruments or the batch of experimental samples that he was working with. His suspicion is aroused when he starts getting unexpected results. The combination of instruments and samples is the substance of the phenomena the technician undertakes to observe. To detect what went wrong (if anything did), he will have to analyse the substance, i.e. take it apart and check the parts. E.g., he may use the same machine with a different batch of samples or the same batch with a different but similar

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machine, or he may replace parts of the machine with reserve components. Of course, there may have been something wrong with his expectations or his handling of the machine or the samples. In the final analysis, the human observer and his condition is also a part of the phenomenal substance. The analysis of the substance amounts to setting up different experiments with different substances. For example, if the machine is sent to a repair shop, the engineers will check its various components in tests that are unrelated to the uses of the machine in the laboratory.

For many physical things, the condition is composed of certain (“deterministic”) potential changes, with a probability equal to one: if a1 then b1; if a2 then b2; and so on. For other things, that may not to be the case. Their movements seem “non-deterministic”, although repeated observations may show that they are not objectively uncertain or random but objectively probabilistic, with probabilities far from one: if a1

then b1a with a probability of 0.6 or b1b with a probability of 0.4; if a2 then b2a with a probability of 0.2 or b2b with a probability of 0.8; and so on. The concept of probability is mathematically well defined but its application to various sorts of phenomena raises many problems. The mere fact that we establish ex post fact that in 10,000 observations a1 is followed 6,000 times by b1a and 4,000 times by b1b does not always indicate the existence of an objective distribution of probabilities in the condition of the substance under observation. By itself, it does not warrant the claim that we are able to predict the probability of a particular change (to b1a or b1b) given that we know that a1 is part of the observed substance. However, the absence of a detectable objective probability distribution does not necessarily imply sheer randomness. It may imply uncertainty, which is irreducible if we cannot control the condition of a substance to analyse it systematically and to measure all of its components unambiguously.

As used here, the word ‘substance’ means the combination of form and condition as at least conceptually separable phases of a phenomenon. Other appropriate but somewhat ponderous terms would be ‘the phenomenal system’ (which does not exclude the observer as part of the substance) or ‘system under observation’ (which does exclude the

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observer). In the following discussion, I shall consider the substance without including the observer, assuming that the observers are competent, if not infallible. Indeed, in discussions of the science of particular classes of phenomena, it is quite common to assume that not only the observers but also certain parts of the system under observation are known to be reliable, e.g., the instruments used to make observations.

‘Substance’ does not necessarily denote something solid, although it often takes something solid (e.g., isolation material, test tubes, observation and measuring equipment) to produce phenomena that we can study systematically, under controlled circumstances. Light, sounds, smells, electromagnetic forces or fields, and the like, are not “solids”, yet they are involved in many phenomena. They may, therefore, be considered [components or elements of] substances in the intended sense. It is not relevant whether one thinks of physics as the science of “matter”, of “energy”, of “processes” or of “interacting events. Whichever one prefers, the phenomenal aspect is always the first to consider — and we cannot do so unless we can identify a substance that we can observe. When we make observations with a particular goal in mind, our purpose will influence our choice of the appropriate substance. Depending on the questions they seek to answer, scientists may treat an object (say, the sun) as a stationary or a moving solid ball, a massive quantity of particles in turbulent motion, an event, a process, or any other “substance” that is suitable for the task. Of course, in every case, the requirement that the answer be checked for truth and consistency with other known truths must be met.

(2) “Happening” refers to the actual change to the substance as we observe it. It implies that a potential form is selected and actually produced or triggered. Consideration of the happening itself reveals two additional, at least conceptually distinct, phases of a phenomenon: the selector and the trigger. The selector gives direction by reducing the number of potential outcomes, i.e. by acting on the condition of the original form; the trigger brings about a single outcome from within that reduced set.

Thus, we can think of a phenomenal object in terms of how it appears (form), what or where it might subsequently be

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(condition), what or where it “wants” to be (selector), and what makes it “do” what should take it there (trigger).15 The double quotation marks in the previous sentence indicate that the words ‘wants’ and ‘do’ are used metaphorically. A physical object, such a stone or a metal ball, need not want anything, nor need it do anything. Yet, in physical experiments, the human experimenter, who certainly wants and does things (if he is not just aimlessly fooling around), supplies both the selector and the trigger. In a laboratory, the “happening” would be the performance of an experiment on a substance or system: it involves making appropriate selections, releasing particular triggers and carefully noting the effect or outcome of the experiment.

It is fallacious to conclude that all physical phenomena must be explained by supposing they are experiments conducted by some possibly invisible experimenter, who supplies the selector (purpose) and the trigger (will). Rather, physical experiments are relevant to physical phenomena outside the laboratory to the extent that out there the selecting and the triggering might happen without wilful interference by a human person or any other conscious agent. For example, the selection might occur because of a change in the temperature or pressure in the environment of the substance under observation, or because another object with a strong gravitational field is approaching it. The trigger might be a collision or some other event, as when the environmental temperature reaches a critical value: e.g., water freezes, paper combusts.

It is equally fallacious to conclude that no phenomena ever need be explained in terms of purpose and will. Some people go on about science having disposed of “illusions” about mind, purpose, will, and the like, and in the same breath, without intending or realizing it, dispose of science itself. If no phenomena ever needed an explanation in terms of purpose and will then the phenomena of people preparing, conducting, evaluating and discussing experiments performed in laboratories would be reduced to mere happenings, without any scientific meaning or relevance. Experiments are 15 Cf. the Latin translation of the Aristotelian theory of causation. It refers to the form as causa formalis, to the condition as causa materialis, to the selector as causa finalis, and to the trigger as causa efficiens.

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scientifically relevant only because they are experiments conducted by people who know what they are doing, keep detailed records of why and how they do it, how the trials work out; and who are capable of assessing the consistency or inconsistency of the results with already acquired knowledge as well as with various beliefs or hypotheses. Without them, there would be no basic physics, hence no physical science at all. There would be no experimental science if the experimenters were not rational, purpose-driven free agents.

Let us apply the analysis of phenomena in terms of what happens to a substance — i.e. in terms of form, condition, selector and trigger — to a few paradigmatic cases. As we shall see, there are significant differences among phenomena involving inorganic, organic, animate or personal substances. There may well be many intermediate or borderline cases, which would require a separate discussion if our aim were to provide a full taxonomy of phenomena — but that is not the purpose of what follows.Inorganic substances: processConsider a simple physical experiment: striking a billiard ball moves it across the billiard table, most likely to a different position than the one it was in at the start of the episode. The position of the ball on the table is the form. Any position of the ball on the table is a potential outcome of striking the ball one way or another. Selecting the way one will move the ball, e.g., with a weak push to the right or a strong push to the left, amounts to selecting a range of potential outcomes, although the selection made may not be the selection intended — as any inexperienced billiards player knows. Moving the ball in that way will bring about an outcome within the selected range. The experiment has scientific relevance to the extent that it informs us what would have happened if the ball had been pushed, with or without reason or motive, by something else than the human experimenter, yet in exactly the same way as he did.

Note that the four phases of the phenomenon — form, condition, selection, trigger — can easily be identified because they can be arranged and re-arranged at will. The ball does not prefer one table rather and than another; and

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the table is indifferent to the size, shape or material of the ball. Neither the ball nor the table prefers any position to any other. The ball does not prefer being pushed this way or that, by a man, woman dog or a gust of wind. The selection is not dependent on the position of the ball, and the trigger is supplied externally. The mutual independence of the four phases in the phenomena investigated by the physical sciences determines the general form of laws of inorganic, inanimate things:

[L1] F & C & S & T E

Here, F stands for form, C for condition, S for selector, T for trigger and E for the observed effect. Such laws we call type-1 laws (L1). Note that the laws of physics, which scientists can discover and formulate with remarkable exactitude, are not themselves phenomenal substances. They are not physical things (matter or energy in one form or other) and neither are they processes. They do not exist in the order of matter, and they do not exist for any lump of dead matter or senseless energy. Yet, they are real. Without them, the idea of an order of inorganic and inanimate substances would be like an empty box. Non-artificial inorganic things have no function of their own and no humanly assigned functions; they exemplify but do not incorporate physical laws. The same is true for their parts, which moreover have no function in relation to the thing of which they happen to be parts — or rather, of which we see them as parts. The sun shines. We may be able to explain how its shining comes about; but it is pointless to ask what need or purpose would explain its shining. Still, as long as one is not carried away by metaphors and analogies, it may occasionally be useful to consider inorganic things as if they were machine-like systems, or even organic things. Thus, we speak of the birth, the life and the death of stars, without suggesting that we are dealing with biological phenomena.

Laboratory experiments in physics deal with “dead” substances,16 which a skilful, knowledgeable experimenter 16 Not necessarily with dead inorganic matter or objects: instead of a billiard ball, the experimenter might use a ball of living moss, or even (God forbid) a bunch of people tied up or glued together in the form of a ball. The experiment concerns only the phenomenal substance (a solid ball on a solid

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can carefully arrange to ensure that every phase of the experiment is well controlled. The experimenter can describe, measure and analyse the substance both before the experiment begins and after it terminates; he controls what happens to the substance by his choice of selectors and triggers. The high degree of freedom for the experimenter in conjunction with the very low degree or even absence of freedom for the physical substance on which the experiment is performed is characteristic of experiments in physics. As we shall see below, not all phenomena can be studied in that way. Substances that include their own selectors or triggers give rise to phenomena that would simply not occur if they were interfered with in order to replace or override their selective or triggering capacities with those supplied by the experimenter. Thus, there are limits to the knowledge we can gain from controlled experiments, and these limits become more obvious the freer the substance under consideration is relative to the purpose and will of the experimenter.

In physical experiments, the feasibility of exact or nearly exact replication of the experimental set-up is usually a requirement. Presumably, the experimenters know all the relevant properties of the substance as well as the selector and the trigger. Using the available data about various repetitions, scientists may determine whether factors not described in the original set-up may have an effect. For example, the results may differ depending on whether the experiment is conducted in the northern or the southern hemisphere; or with chlorinated or distilled water. If that is the case, these factors need to be taken into account when yet another replication is attempted.

Replication of trials is also essential for determining, by progressive approximation, constant values or frequencies (probabilities) in the distribution of the effects of triggering the production of a move or change in one way or another. Controlled variation of particular dimensions of the substance (e.g., larger or smaller balls and tables, for example, or balls and tables made of different materials) gives us the possibility to look for quantitatively constant relationships (“laws”). These are represented as mathematical formulas such as flat surface). The experimenters need have no interest in the material from which the components of the substance are made.

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y=f(a,x) with variables [x] for any aspect of the experimental set-up that we can manipulate and control, and constants [a] that allow us to calculate a value for the variables [y] describing the outcome of the experiment — a value to be confirmed by further actual performances of the experiment. For simple functional relationships, the constants are mere numbers. E.g., if the measured value of y is always equal to twice the measured value of x, the formula y=f(a,x) would be written as y=2x, where 2 is the constant. In some cases, the constants have a physical interpretation (e.g., speed of light in a vacuum, the gravitational constant). As physics advances, it may turn out that, for some formulas, the relevant constants can be calculated from laws operating at a deeper level of phenomena; but some constants can be determined only experimentally, from observation and measurement.

Getting the constants right is crucial. If a cannot be determined then y=f(a,x) remains a formula: no matter how accurate our measurements of x, we cannot calculate a corresponding value for y. If a cannot be reduced to a precise value but, say, only to a range of values [amin, … amax] then many observed values of y may be consistent with any value of x. Obviously, even a precise value of a may turn out to be wrong if the formula were applied to phenomena of a significantly different scale than those from which it was experimentally derived. We cannot take it for granted that the scale of things never makes a difference. Moreover, we should not expect to be able to detect universal constants if the phenomena we are dealing with are “historical” or “local” — which is invariably the case if our subject is human history, culture, economics, politics or religion, and on a different scale, biology. In fact, if the phenomena concern the substance “human person in action”, the search for universal constants is in vain, even if occasionally we discover regularities across large numbers of such phenomena in a particular place, at a particular time, or among a particular group. Such regularities may be due to prevailing customs, habits, fashions, taboos or enforced legal restrictions, but these are all local, temporary and at least to some extent non-natural, artificial things. There is not even an a-priori guarantee that the physical universe, as far as we can observe it, is truly universal (i.e. closed) and uniform. There

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may be inaccessible regions, or distant parts or ages, far removed from our place and time, where our constants and laws of physics do not apply.17 If that possibility is admitted, the question arises whether there are ways for us to test the validity of our interpretation (according to our laws of physics) of whatever signals or influences might reach us from out there. After all, we cannot go and see for ourselves.18

If one experiment is to be an exact replication of another, we must be able to measure all the relevant dimensions of their constituent parts. In particular, it must be possible to determine and replicate the initial conditions of the experiment. This may not always be possible. E.g., the techniques of observation or measurement may be inadequate or unreliable, leaving open the question whether the failure or success of the experiment tells us something about the hypothesis being tested or only about our inability to set up the experiment and determine its outcome with sufficient precision. Alternatively, our techniques of observation or measurement may be “invasive”: the act of observing or measuring may change the thing to be observed or measured in significant, uncontrollable ways. If this is the case, the form is not robust relative to the method or technique of observation or measurement employed. Then, we cannot precisely identify the form.

Thus, with respect to phenomena involving very small forms, e.g., at the level of atoms and electrons, the energy needed to

17 See e.g., W.J. Sidis, The Animate and the Inanimate (Richard G. Badger, Boston, s.d. [circa 1925]). The book is an analysis of a thought experiment. It starts from the hypothesis that the universe consists of regions where our second law of thermodynamics (the law of increasing entropy) holds and of regions where entropy decreases. The hypothesis eliminates the “anomaly” of the second law of thermodynamics (which, unlike other basic laws of physics, is not symmetrical with respect to time). 18 Assuming that our universe is closed and uniform, observations and calculations suggest that it began with a Big Bang and will end with a Big Crunch. Thus, it would appear that everything physical is situated between a low-entropy creational event and a high-entropy end-of-time gathering of black holes. It is well known (but not always appreciated) that modern science, particularly physics, was a product of Christian civilisation. Its basic presuppositions dovetail those of the Christian faith. Consider, for example, the relevance of mathematics — “but You have ordered all things in measure, and number, and weight“ (Wisdom 11:21); or the linearity and finiteness of time, which is the “narrative arch” that spans the whole story from Genesis to the Book of Revelation.

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make an observation may be enough to disturb and displace the electron. If it is, we can never actually observe an electron circling the core of an atom. Such experiments may still be consistent with the familiar model of the atom as a small-scale system of planets circling a star, but they do not give us sufficient knowledge to decide whether the model is true. Whereas we can actually see in one continuous observation that a billiard ball moves from one position to another in a continuous movement, we cannot do the same with respect to an electron. We can explain the phenomena of the experiment with the billiard ball in terms of the properties of the observable things that are involved in it: the ball and the table are things in themselves that we can produce and reproduce, use, handle and study successively in various non-damaging, non-destructive ways and from a variety of perspectives. Electrons are not things in themselves. Their properties do not explain quantum phenomena; rather, the phenomena are all we have. Consequently, the laws of quantum physics are irreducibly laws of phenomena, not of things. Electrons and other particles are intellectual constructs in terms of which we can express those laws.19 At some point, as we delve deeper into the finer structures of matter, “classical explanations” in terms of known things become impossible, because the “mechanism” (if indeed there is one) that transforms the substance in question cannot itself be isolated as an observable form or substance to which something observable happens.

Of course, not all physical phenomena are such that they can be mimicked reliably in laboratory experiments. The most obvious reason is that the scale (in terms of number of objects involved in a process, or in terms of spatial or time dimension) of some phenomena relative to what human experimenters can manage is simply too big or too slow, too small or too fast. The mathematical techniques of statistical mechanics may help to handle problems that arise when we 19 “In atomic physics, we can no longer uphold the idea of a behaviour of objects, independent of the circumstances under which the phenomena are observed. It is […] an aspect of the laws of nature, associated with the quantum of action, which sets a lower limit to the interaction between the objects and the measuring instruments.” N. Bohr, “Medical Research and Natural Philosophy”, Acta Medica Scandinavica, 1952, supplement 266, p.967-972

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move from observing a few objects to very many and then to too many to count. However, such techniques may not always suffice. The initial strategy will be to try to understand the observed phenomena in terms of known, well-tested principles of basic physics; but if that does not work satisfactorily, the specific aim of accurate, precise prediction may have to be relaxed or even given up. It is then tempting to substitute prognostications based on some model or other for predictions based on scientific understanding, but we should be aware that we are then leaving the domain of science and entering into that of more or less informed guesses.

Even for phenomena that cannot be mimicked in a laboratory (e.g., variations in the Earth's climate), scientists will rely on observations to gather as many data points in as many dimensions as they can. Then they will try to devise mathematical functions that fit the data within an accepted margin of error. They will test the reliability of prognostications based on the functions (“hypotheses”, “models”) as new data become available. The aim is to find the function that continues to fit the data, or at least to determine which function does so more consistently than others. However, because their ability to control enough of the variables involved in the phenomena is limited or absent, they are stuck with the problem of trying to find some kind of order in the appearances — which is different from the problem of resolving or accounting for appearances by laying bare the reality behind them. The paradox, if that is the right word, is that modern physics can often do little more than that. It tends to operate at the edge of our capabilities of measurement and observation, and to deal with phenomena on a scale that rules out replicating the phenomena in a controlled manner.

Resolving appearances is much easier in disciplines such as biology, economics or sociology. These are integrated by one or a few concepts (e.g., “life”; “wealth”, “coordination”; “status”, “mobilisation”) and therefore allow us to assess the functional or dysfunctional aspects of the things, events or processes we observe. What is not fit to live will not live; what impoverishes diminishes the means of action and so the capacity to deal with famines and other disasters; and so on.

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Physics, in contrast, is — and is designed to be — utterly blind to the functionality or teleology of the things it studies.

More complications arise if we do not have simultaneous values for all the variables that we need. Moreover, the input variables may not be sufficiently independent of one another: there may be positive or negative feedbacks; a variable may take its value at one moment from the value it had earlier. Then we can no longer assume that the observed phenomena (at the moment when the data are gathered) are independent of the history of what happened before, i.e. independent of the path that led the substance in question to where it was when it was observed. The observations are like a snapshot of an ongoing process, not a picture of a fixed set-up at the very beginning of a separate episode that can be re-created at will. Prediction may become impossible at the level of accuracy one would expect for a well-controlled experiment. One might be lucky to predict patterns, complex systems of relationships, without being able to determine specific values for the elements involved in those relationships. Or one might be not so lucky and realise that one is dealing with complex systems that defy mathematical resolution because the mathematics needed to resolve them do not exist. Possibly, the system under investigation exhibits chaotic behaviour: even slight variations in the initial conditions can lead to widely divergent outcomes, while existing techniques of observation or measurement are not capable of catching such variations. Still, knowing the limits of particular methods or the limits inherent in the nature of the substances under investigation is a considerable part of science.

If it is not possible or not necessary to manipulate or deal with form and condition separately then the type-1 laws have this form:

[L1*] FC & S & T E

The substance is seen or treated as an indivisible whole, although there is no question that it should be possible, at least in principle, to separate its form from its condition. For example, we may not be interested in how a machine (such as a car or a clock) works but only in how it behaves as a unit. Obviously, although a machine is a physical thing, it is not

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part of the physical order of nature. It is a contraption and already incorporates type-1 laws in its design and manufacture. More importantly, it is meant to serve human purposes. It is not just a functioning system but also and primarily a functional one. On the one hand, then, a machine resembles organic things, which are not only functioning but also functional units serving either their own or some other organism's vital needs — indeed, their functionality is a condition of their existence: they would not continue to exist if they were not functional.20 On the other hand, a machine differs from naturally occurring inorganic systems such as stars or clouds, which function as phenomenal units but are not functional units. Organic, inanimate substances: evolution When observing the phenomena of organic, inanimate life (such as those involving cells, multi-cellular organisms and, most conspicuously, plants), we cannot separate the form from the condition. We cannot separately control all the relevant properties or aspects of the plant as it is at a particular moment and those of the range of possible changes to its form. A plant is a living thing, growing or dying, seeding or multiplying in other ways — it evolves (develops, changes “of its own”) according to a characteristic pattern. It has, so to speak, its preferences built into it. Hence, tampering with the form (the plant as it is) will inevitably and in uncontrollable ways change its condition. In other words, the substance itself, not just its form will be affected. Left alone, the plant will grow or die. We can still control the selector and the trigger, e.g., by feeding or starving the plant, cutting it, regulating the amount of light or heat to which it is exposed. In this way, we can affect the range of possible outcomes (e.g., the plant's size, the colour of its leaves, and the like). But we cannot change its form and keep its condition constant, or vice versa.

20 Machines are typically designed to be functional for achieving a particular purpose. However, once a machine exists, people will often try to think of other functionalities, other purposes it may serve. The outcome is not always efficient: think of the inefficiencies introduced by those who believe “If a computer can do it, a computer should do it”, for example in communicating with people (clients, patients) or in assigning tasks to employees.

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Of course, we can treat a plant as a mere physical object, a lump of “dead matter”. However, if we do that, we are no longer trying to observe the phenomena of plant life. Most of the time, the plant used in the experiment will be more or less severely damaged, even killed. In this way, we can learn a lot about its cellular microstructure, its chemical make-up, and so on. However, even a full description of the physical or chemical properties of the matter found in an organism would not add up to a description of a living organism. A full description may not even be possible: to produce a physicochemical description of its matter, we must do various things to the plant that will make it impossible to do other things needed for a full description. That means that we will need to do many things either to the same plant at different moments of its life or to many different specimens of a particular species of plants. We do not get a full description of a single specimen as it is at any singular moment of its life, but a number of descriptions of non-simultaneous properties of a number of specimens. We can “collate” all information of this kind in a description that we then boldly declare “the physicochemical description” of plants of a particular species. However, that is not a description of any existing, living plant. Every element in the collation comes with the distortions produced by the method of obtaining particular bits of information. In short, we never see the physicochemical phenomena of plant life: either we see physicochemical phenomena or we see the phenomena of life. The study of the latter is not reducible to the study of the former. We may [want to] believe that such reduction is possible, but we cannot demonstrate that it is. This does not mean that we cannot know anything about the life of plants, how they germinate, how they grow, how they die. In fact, much of that knowledge was acquired long before anybody thought of systematically studying the physicochemical basis of anything. Farmers and breeders have known about such things and about laws of “evolution by variation and selection” for millennia, even if they never thought of systematically searching for truths about plant life.

Within the order of inanimate organisms, we can detect laws of life, but we cannot suppose that those organisms are even aware of them. However, the laws of physics do exist within

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the biological order. For example, the physical structure of plants is obviously in accordance with physical laws; it is also functionally adapted to the laws of life. While every organism is a physical thing, not just every physical object is or can be an organism. This determines the general form of the laws of organic, inanimate substances:

[L2] (FC)L1 & S & T E

(FC)L1 signifies not only that form and condition cannot be determined independently of one another but also that living substances functionally incorporate at least some type-1 laws. We see that in the order of organic (even if still inanimate) things, we have confirmation of the existence of laws of nature — indeed, nearly as much confirmation as we have in the order of artificial material things (machines, tools, computers, and the like). This contrasts with the order of inorganic things, with respect to which we can only say that there are laws of nature that we can detect, although we cannot find them among the substances that make up that order. Animate substances: conscious behaviourObserving phenomena of animal life and movement restricts our ability to separate their phases (form, condition, selector, trigger) even more. A rat is not a plant; it is an animal. It will not remain in whatever state it is until we give it a push; nor will it just grow or die. It will move of its own or change its condition. If we touch it, it might flee or turn and fight, become agitated or paralysed, but there is no way of telling which actual selector was a factor in causing the observed phenomenon. Form, condition, and selector are inseparable.

Within the limits of its natural capacities, a rat sets its own range of possible outcomes; it is a self-selecting substance. Thus, it is able to scan and search its environment for things of interest to itself, which will trigger a focussed goal-directed response when it becomes aware of them. It is, to some extent, conscious of its form and condition and of substances in its environment, hence of relations between itself and parts of its environment. Its behaviour lends itself

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to descriptions in terms of what it tries to do and hence of success and failure.

We can still to some extent control the actual outcome of an experiment by supplying a specific trigger. However, the trigger will not apply to the rat's condition as it is determined by us, but to the rat as a conscious substance. E.g., we can place food in one corner of the experimental set-up and a cat in another, or send an electric current to the segment of the floor where the animal rests. Yet, observing the effects of such triggers can only establish relations between conscious substances and triggers on one side and observed outcomes on the other. We cannot measure the conceptually separable but in fact inseparable component parts of the conscious substance. Hence, no strict replication of an experiment is possible, because there is no way in which we can ascertain that, with regard to form, condition and selector, the rat in one experiment is exactly similar to the one in another. Repeating an experiment with the same rat is virtually impossible, as the animal may remember and learn from earlier experiences. It may therefore change its condition from one experiment to the next merely because of its experiences in the first. Repeating an experiment with different rats may yield significant statistical correlations, but these inform us at best only about a non-existent thing, e.g., “the average rat”.

A physical interference with a living rat is likely to change its substance and its consciousness. We cannot compare the behaviour of an animal under observation with that of an unobserved animal. Even a weak ray of light, a faint smell, or a gentle stroke has the potential to turn the form-to-be-observed into a different form in an uncontrolled and uncontrollable way. An observer can take precautions to prevent the animal from detecting him, but he may not be able to prove that he has succeeded. In any case, he cannot directly access only the substance or only the consciousness of the animal, whether it is under observation or not. Physically interfering with an animal or with many animals of the same species and collating all the information into a description of the physicochemical or the psychological basis of animals of a particular species never gives anything other than the possibility of making qualitative pattern predictions.

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However, while the laws of matter do not exist for plants, or even for most conscious animals, they exist to some extent in the orders of living things. Living things, whether animate or not, consist of cells; they develop from seeds or cells that contain the necessary information for getting through the various stages of growth. If external conditions are right and no accidents happen, they reach a stage of maturity and then grow old or start withering away. They are not random heaps of cells, let alone molecules or atoms. Plants and animals, in particular, are complex material structures that physically embody laws of physics. Their body structure is such that they do not collapse under own weight, can disperse their seeds or sperm and catch their food. Animals can move about without being moved about. Complex organisms, such as animals, house large populations of microorganisms that are of vital importance for their health. Thus, they incorporate not only physical laws but also some laws of inanimate life. They would be marvellous pieces of mechanical and bioengineering but for the fact that they are not.

Some animals, moreover, show “insight” into the laws of matter when they use objects found in their environment as tools to get food (using a rock to crack shells or nuts) or to chase away rivals or predators (using sticks or stones as weapons). In some cases, they demonstrate their “understanding” of the laws of physics by bending branches, piling up stuff, digging tunnels, or pulling up ropes to get at food that would otherwise be out of reach. Of course, this does not mean that they know any laws of physics as such. It does mean that an animal can learn to discern functional relationships, which will be incorporated into its condition. When an appropriate trigger occurs while the animal's purpose is focussed on a goal for which such relationships are relevant, it will demonstrate its insight in its behaviour. Similar things can be said about the “understanding” of a conscious animal of law-like behaviour of plant life and of animal life, especially of course with respect to their own species and species that are directly relevant to them, e.g., as mate, prey or predator. Most spectacularly, some domestic animals, circus animals and animals reared in behavioural laboratories show a remarkable ability to learn skills about how to handle human artefacts: they open doors by pulling

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the handle; they play the piano, paint, or practice skateboarding.

The general form of laws of animate things is

[L3] (((FC) L1,L2)S)L1,L2,L3 & T E

Animals are substances that incorporate not only type-1 laws of mechanics, kinematics, heat transfer, and the like, but also type-2 laws of organic inanimate life, e.g., in relying on populations of organisms (cells, bacteria) that are functionally necessary to the life of the animals themselves. Thus, in the order of animate things, we have confirmation of the existence of type-1 and type-2 laws. Moreover, we have evidence of the consciousness of animals when we notice that their behaviour shows goal-directedness and functional adequacy, as if they have some knowledge of how things (including other animals) in their environment work — knowledge that allows them to discern means-ends relationships. There is of course no evidence that they have such knowledge in the sense in which ‘knowledge’ is a synonym of ‘science’. Nevertheless, they can and do learn about the properties of physical, inanimate and animate things in their environment. As a scientific project, the attempt to reduce animal life to plant life, a fortiori to the existence and collisions of dead matter or energy fluxes is therefore bound to fail. Persons: self-conscious actionFinally, when we turn to observing the phenomena of human personal life itself, we find that all their phases are inseparable. Form, condition, selector and trigger cannot be physically separated, although we can still conceptually tell them apart. Persons are not only self-selecting but also self-triggering — in a word, self-conscious — substances.

The unity of selector and trigger is sometimes called ‘the will’, which shares the selector, hence overlaps, with the conscious substance. Seeing how a person acts in response to what an experimenter intends to be a triggering event tells us next to nothing about how another person or the same person at a different time would react to it. We cannot physically distinguish a case where he reacts impulsively or instinctively

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from a case where he acts with a will to do as he does, for example, to satisfy or frustrate the experimenter's expectations, to keep his preferences from showing, etcetera.

Moreover, like many other animals, people are highly context-sensitive. They are likely to register higher values of blood pressure when a doctor rather than a nurse measures it, and much higher values than when they wear an unobtrusive bracelet that records their blood pressure. Thus, one would be mistaken to assume that even an “objective” condition such as blood pressure can be measured independently of a person's consciousness.

Supposing for a moment that lie detectors could be made perfect, it would still require the actual application of the lie-detector test to find out whether a person was lying or not — and there would be no way to establish whether or not his telling lies in the laboratory is different from his telling lies elsewhere. Even when a lie detector detects lying, it does not tell what the lie is. For example, a suspect is caught telling a lie, although he spoke the truth — but by telling his interrogator the truth, he was betraying the trust of a friend or relative. If it is possible to induce the symptoms of lying by means of drugs or physical stimuli, there cannot be “sure physical proof of lying”. The symptoms could have other causes than the telling of a lie. Moreover, it would be preposterous to conclude that externally inducing the symptoms that a perfect lie detector identifies as sure proof of lying would cause a person to lie.

Even with brain scans, we should not presume that the brain of a person who is conscious of being scanned reacts as it would otherwise. Nor should we presume that its reactions are the same or even systematically different if the scan is intended “just for the fun of it” or, on the contrary, to produce evidence that could have serious personal consequences for the subject. Monitoring the “higher” brain functions of a person is not as simple as monitoring lower, animal or vegetative functions — and drawing conclusions about persons from brain scans is and may remain an exercise in bluffing. A lie detector based on neuroscience may well give much better results in a laboratory than the primitive devices that record sweating, blushing, dilation of eye pupils, and the like, but it would still suffer from the same sorts of

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restrictions and limitations. Any symptom or pattern of symptoms could have been artificially induced or provoked by other causes. A person telling a lie is not the same thing as a brain showing neural activity conforming to a particular pattern.21

Conscious animals internally set their own purpose, but their control over triggers is either absent or minimal. For us self-control is natural to our constitution. We are not only conscious of our own current substance and our current environment; we are also capable of being conscious of our consciousness itself. This is not restricted to our being conscious of the current content of our consciousness. We are also conscious of our ability to retrieve such contents from memory and to perform mental operations on them. Hence, we can distinguish between current, past and even hypothetical contents (forms) of our consciousness and modify their condition, for example by looking at a particular form from a variety of perspectives, asking what-if questions, and the like. This enables us to seek things of interest to us without being triggered to respond to them merely because they enter into our consciousness. It also enables us to establish or discover connections between various contents, to compare forms of consciousness for similarities and dissimilarities. Being a person not only includes the ability to look at other things; it also includes the ability to put oneself hypothetically in the position of any of those other things and, conversely, to put it in one's own position. Thus, forms of consciousness are like formulas with variables rather than forever-fixed values. A content that entered consciousness under the operation of a particular purpose may be reconsidered for other purposes, e.g., now as an example of one thing, then as an example of something entirely different, or now as a means, then as an end in a scheme of action. Not only is conceptual abstraction possible, it can be performed selectively and purposefully. Thus, the self-conscious mind can intentionally abstract all physical features to arrive at metaphysical objects, which can then be treated as contents of consciousness in their own right.

21 See XXXX

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It is possible for persons to switch their focus back and forth between one form of consciousness and another to look at each one from the perspective of the other. This enables persons to become conscious of the absence, the not-being-there of something; to note that all the salient elements in one form are also present in another, even if the converse is not true; and to note that every salient element in one form is present either in this or in that other form. Thus, self-consciousness implies the ability to detect logical relations of identity and non-identity, inclusion and exclusion, compatibility and incompatibility, contrariness and contradictoriness among various forms of consciousness. Abstracting from particular contents, the self-conscious mind can achieve consciousness of formal logical structures. Because these metaphysical objects are independent of material content, they can serve to relate any form of consciousness to any other. Thus, self-consciousness implies the ability to think, in particular to think in hypothetical and counterfactual modes.

These logical faculties enable the development of linguistic faculties,22 which are in turn of great significance in increasing intellectual powers. Lower life forms and even inorganic things can “express” things about themselves (e.g., the look of soil is different depending on whether it is wet or dry, an animal may express its state of fear, hunger, desire to mate, etcetera, in specific movements or bodily reactions, including the production of characteristic sounds). They can also “signal” to other things (as when a the smell of a flower signals its location to insects, or a bird lets out a danger signal that alerts other birds to the presence of a threat). Human beings can do similar things, but they can also do them by using language. More importantly, humans can use their language for descriptive, analytical and argumentative purposes, for asking and replying to questions, making promises, relinquishing others from their obligations, and the like.

22 I consider only the language of speech. I suppose it is proper to think of other types of languages, e.g., the language of music (or even art in general), but I do not think they are as essential to understanding the concept of persons as the language of speech is.

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Language enables persons to keep track of their infinitely multipliable forms of consciousness by representing them symbolically, using names or short relevant descriptions. It provides the ability to represent any form of consciousness symbolically, which allows a lexicographical ordering of the representations (as words are ordered in a dictionary or references to words in an index). It also provides the ability to generate new forms of consciousness in a trivial and frivolous manner: by stringing words together into sentences. However, we need logic to sort out the forms of consciousness by means of concepts that are applicable to all of them: “testing for truth”, “consistency with truth”, “implication of truth”, and the like refer every actual or potential form of consciousness to the same concept, truth.

“Truth” makes it possible to distinguish between mere sentences, which are phenomenal forms of language, and statements, which combine the substance of language with personal purpose and will. A sentence is a means of expression; a statement is an expression of the person himself to which he commits his purpose and will. Hence, whereas it is meaningless to ask whether a sentence is true, every statement proclaims if not the belief of the person who makes it that it is true then at least his desire that others accept it as true. This implied claim immediately puts the statement in competition with other statements, which also have truth claimed for them, because not all statements can be fitted together under a single concept, if some of them directly or by implication deny the truth of other statements. Because every possible statement, regardless of its content or level of abstraction, implies it, the concept of truth is necessarily implied in every act of thinking. It is an irreducible, logically undeniable concept.23 To deny it, is to deny that one is making a statement, hence that one is saying anything at all (as opposed to merely uttering sentences).

Truth cannot be derived or abstracted from forms of consciousness or operations on such forms, as it is already presupposed in every derivation or abstraction. We cannot 23 Thomas Aquinas (Summa Theologica, I, qu.2, obj.3: “Further, the being of truth is self-evident. For whoever denies the being of truth grants that truth is not: and, if truth is not, then the proposition "Truth is not" is true: and if there is anything true, there must be truth.”

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think in terms of physical objects, only in terms of concepts. Unless we can distinguish between an object being a true or an illusory exemplification of a concept, we cannot even begin to think about objects. Moreover, thinking does not happen spontaneously. Dreaming is not thinking, nor is being unable to get something (whether a song, or a sentence) “out of one's head”. We need to focus on some question if we are to think at all; we need to want to think and be prepared to make the effort to go in search of the true answer to the question. If any answer whatsoever was satisfactory then that would mean that there was no question. Without an interest in the truth, there is no question.

Without the concept of truth, the multiplication of forms of consciousness would result in an ever-growing, eventually chaotic, mass of impressions of diverse origin — observations, memories, hallucinations, and artefacts of the imagination as well as of sound or unsound thinking. Only a retreat from self-consciousness would restore order; but the price would be the surrender of everything that makes a person different from a mere animal. E.g., instead of being able to activate, scan and search memory at will, we would be dependent on triggers in our currently perceived situation to be reminded of an earlier experience, without having the means to assess whether there was any logical connection between such psychologically associated ideas.

It is of course possible to treat persons hypothetically and counterfactually as dead matter or as mere animals, and perform experiments on their bodies to find out how they would behave if they were only matter or animals. Then we would not be looking at the phenomena of personal life, for example, thinking, speech, arguments, creative activities, commercial transactions and so on. Laboratory experiments regarding natural persons as persons cannot produce anything like the mathematical functions that made physics a hard science. At best, they can establish that, in some respects, human persons have much in common with other animal creatures, and that for some human beings — usually qualified as subnormal — the differences are relatively small. The laws of the order of persons cannot be reduced to those of the orders of non-persons.

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The general form of laws of natural persons as self-triggering conscious animals is:

[L4] (((FC) L1,L2)ST) L0,L1,L2,L3,L4 E

This formula captures not only the substantial similarity of natural persons and other forms of life, (FC)L1,L2, but also the self-triggering consciousness of persons, (((FC) L1,L2)ST), as well as its expanded range. The difference with animals is the appearance not only of type-4 laws but also and primarily of metaphysical or type-0 laws (of mathematics, geometry, ethics, and so on) as possible contents of consciousness.

The essential difference between the world (the natural order of persons) and other natural orders is that the objects in the latter have no knowledge, possibly even no awareness, of the principles of order that to us appear to “govern” them. We know or suspect that material things move and interact in a law-like manner — but the things themselves do not. We know or suspect that the development, growth and behaviour of plants and animals are law-like phenomena. We know or suspect that animals are to some degree aware of causal relationships and may demonstrate that awareness in their fitting their goal-directed behaviours to particular circumstances — but the animals themselves do not. In any case, they do not know that they know such things, or that they might be mistaken about them. Consequently, they do not know that there is a difference between knowing and not knowing; and they have no way of questioning their beliefs (if they have any) to find out what they know and what they do not know. In short, there are natural laws of inorganic and organic orders of things but those laws have no meaning to the things in those orders.

In contrast, human persons are aware and have knowledge of not only the other orders of nature but also the order of natural persons. For us, these laws are in the order of nature in which we live and act. This is evident from the fact that humans are skilled toolmakers, unlike merely tool-using animals that use a twig, a rock or some other object in their environment to get at food or to chase away a rival or predator. It also seems probable that humans learnt about the laws of the order of persons and various personal capabilities

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before they learnt anything about other orders of nature. They may seem primitive to us now, but anthropomorphic and teleological explanations of the universe and the natural environment were necessary, essential first steps on the road to what we now call scientific knowledge.

METAPHYSICAL ORDERS

Metaphysical orders are non-natural, non-artificial orders of non-physical things. The key to understanding them is the distinction between existence and being.24 This distinction is a requirement of thought. It arises because we cannot get very far without distinguishing between pure and applied theory. Pure thought, or pure logic, need not assume the existence of anything. The idea of a purely physical order of things is the result of assuming away the existence of persons, even those who “do physics”, as well as everything that is entailed by the existence of persons (in particular, physical science itself). Consequently, those who would claim that the universe is a purely physical order that contains everything that exists must consider themselves and other persons as illusionary phenomena without physical reality. They would be as illusionary as colours, sounds and other so-called secondary qualities were deemed to be in the universe as it was presented by classical mechanics in the age of Galileo and Newton.

Logically opposed to pure physics stands pure metaphysics: it results from assuming away the physical existence of things. Both exercises are complementary to one another and perfectly legitimate in their own right, as long as we keep in mind that they are human exercises in systematic thought. Obviously, the claim that the universe as presented by pure physics contains everything that exists is false from the human point of view — pure physics cannot account for the science of physics because it cannot account for the activities of the scientists who produce that science or the philosophers who came up with the idea of a purely physical universe. Nevertheless, the being of such a universe — its metaphysical reality — cannot be denied. Similarly, the claim that nothing exists is self-evidently false sub specie humanitatis; yet, it

24 See p.19 sq.

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cannot be denied that there are things that do not exist, and that many existents are of particular interest precisely because of properties that cannot be accounted for in physical terms.

The “existence” of a thing is always relative to other things that exist. To prove the existence of a thing requires proof of its interaction or interference with known existing things. Because we naturally, spontaneously assume our own and each other's existence, as well as the existence of the things we make, the primary everyday sense of existence is determined by the fact that we can detect stability in certain phenomena of change in ourselves and in the things we make. We can then extend the domain of “existents” based on phenomena of change in things the existence of which we have come to take for granted because of our primary experiences.

Numbers do not yield proof of their existence in this way, if by ‘existence’ we mean the same sort of relation we have in mind when we say that trees, mountains, molecules, clouds, tables, cars, apples, germs or people exist.25 Not being material things, they cannot be detected or located anywhere in space or time; no force, no matter how large, can destroy them; they do not evolve by random variation and natural selection; they do not interfere or interact with any substance. The language of mathematics has no means of expressing the existence of anything, including numbers. Yet, the language of mathematics would be meaningless if there were no numbers and no order of numbers. It would be nonsense to claim that there are no numbers. The same is true with respect to the laws of mathematics and of logic itself. They are not inventions or conventions, things made by influential or powerful people who have tricked or forced the rest of us to accept their products or edicts. The laws of

25 All sorts of paradoxes and contradictions ensue if we think of numbers and shapes as names of naturally occurring or manufactured things, of mathematics or geometry as sciences of natural orders, or of “the mind's eye” as a physical sense organ. Yet, although mathematical and geometrical objects are metaphysical objects that do not exist in the universe that answers to any theory of physics, they are real. They are certainly not useless. Indeed, physical science as we know it would not exist without the benefit of mathematics: we need mathematics if we want to have any scientific conception of the universe as an order of physical things.

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mathematics and of logic express objective relations, discovered by the more intelligent among us. They would still be what they are even if nobody had yet discovered them. It is of course truly remarkable that human minds are capable of making such discoveries; but that does not make them human inventions.

Mathematical and geometrical objects constitute indeed the best-known examples of metaphysical orders. We gain access to them by mentally stripping away the physical characteristics of material things as they appear to us. Surprisingly, this stripping-away does not leave us with nothing; it leaves us with things such as numbers, lengths, widths, directions and shapes. Moreover, these objects do not constitute, metaphorically speaking, a heap of disconnected things. Instead, they constitute orders of unimaginable complexity and, as those who have explored them invariably attest, overwhelming beauty. Apparently, material things as they appear to us are not simply matter; there is an authentic metaphysical side to them. Indeed, we have to abstract physical characteristics from phenomena to discover the orders of mathematical and geometrical objects, which would otherwise remain hidden behind the phenomenal veil of our perceptions. Few people doubt that those metaphysical orders are objectively respectable — that they are laws of things — if only because not respecting the laws of mathematics is as likely to cause avoidable harm as is not respecting the laws of physics.

Another type of metaphysical order involves supernatural persons. Like mathematical and geometrical objects, these are not natural, material things. However, supernatural persons are accessible by mentally stripping away the physical characteristics of natural persons.26 For this reason, I shall use the term ‘meta-personal’ to refer to this type of metaphysical order.

26 A more common move goes in the opposite direction: one obtains the concept of the “human animal” by abstracting all personal, person-related capacities and functions. This usually involves treating personal actions as instances of mere behavioural patterns or habits. If abstracting the rational part from the concept of a human person leaves us with the concept of a merely animal but still biologically human existence, abstracting the animal part leaves us with the concept of a rational being.

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A common use of stripping away the physical characteristics of natural persons is to flesh out anew non-physical person-specific characteristics in the shapes of fictional characters. These shapes may be human (Don Quixote, King Lear, Rip van Winkle) or not (Mickey Mouse, Reynard the Fox, the computer HAL in the movie A Space Odyssey 2001, or the tragic hero of Kafka's story The Metamorphosis).

Less common is the attempt to investigate those non-physical person-specific characteristics “in themselves”, unencumbered by any real or fictional physical constraints. This gives rise to the idea of a meta-personal order of supernatural persons and their relations, perfections and imperfections, to the ideas of demons, angels and gods, and eventually, the idea of God as the perfect metaphysical person. For a long time, the idea of an order of supernatural persons served to enhance the intelligibility of all sorts of moral and psychological phenomena, somewhat as mathematics serves to render physical phenomena intelligible. However, whereas mathematicians resisted the lure of magic in not claiming physical powers for their numbers and shapes, students of meta-personal orders were far less consistent in that area:

Only one God exists, the greatest of gods and of humans. Neither in mind nor in body does he resemble us mortals. Eye he is wholly and ear; and wholly thought. From afar, he is moving everything by his foreknowing mind; by his power of thinking.27

Moreover, the impressive triumphs of the physical sciences tempted many intellectuals in the West to believe that no metaphysical order deserved attention or even recognition. Mathematics would then have to be salvaged by redefining it as non-metaphysical, for example as an inductive generalisation from handling small objects (J.S. Mill) or as an essentially arbitrary set of conventions symbolically 27 Xenophanes (±500 B.C.), translated from the fragment quoted in Diels-Krantz (eds), Die Fragmente der Vorsokratiker (Berlin, 6th edition), B23-25. Xenophanes is often cited as one of the first monotheists, although the phrase “the greatest among gods” suggests that he was comfortable with the idea of there being “lesser gods” (cf. Christian monotheism and its beliefs regarding angels and demons).

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represented as a formal system (in a word, a game). This development arguably led to a lopsided view of all things and a difficult-to-resist temptation to declare illusory all facts and phenomena that do not fit a favoured physical theory.

Supernatural persons stand to natural persons as mathematical objects stand to physical things. No visible triangular object (for example, a drawing of three apparently straight lines, each of which intersects with the other two) corresponds exactly to a geometrical triangle. Yet, it makes sense to say that a particular drawing is a better approximation of a real, geometrical triangle than another drawing. Nevertheless, an approximation never coincides with the thing it approximates. Similarly, although no physical, natural person corresponds exactly to a supernatural person, it makes sense to say that one natural or fictional person is a better approximation to a supernatural person than another. We can imagine fictional persons to have as few physical characteristics, to be subject to as few physical constraints as we wish. However, when the last constraint is lifted, what we are left with is no longer a fiction. A fictional thing is a product of the imagination, a transposition, transformation, transfiguration of an image of a physical thing. Properties and relations are attributed to it that are not true of the physical thing that served as its model. Yet, some image must remain. From Mickey Mouse to Mighty Mouse to Almighty Mouse — we need the image of a mouse if we are to remain in the realm of fiction.

Supernatural persons are not fictional persons. To say otherwise would be just as wrong as saying that a geometrical triangle is a fictional triangle. A mathematical point is not a fictional dot, although for some purposes a dot may be interpreted as a graphical representation of a point. Likewise, a supernatural person is not a fictional person, although for some purposes, a fictional person may be interpreted as a representation (in speech or otherwise) of a supernatural person.

Like mathematical objects, supernatural or metaphysical persons too have their uses, even if they do not exist as persons in any order of nature, including the natural order of persons. We may need them to make sense of what makes us persons rather than mere objects, and to grasp the concept of

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an order of persons. Ethics would remain mired in the swamps of casuistry, if it were not possible to study the logic of ethical concepts and their integration into types of personal perfection and imperfection in isolation from contingent, always changing physical constraints.

To say that there is no proof that supernatural persons exist in the same way material (physical, natural) things exist, is trivial. It implies no negation of their being. Their relation to the world of natural persons is similar to the relation of numbers to the material universe — and the latter is not a cosy one, as numerous paradoxes, from Zeno’s paradoxes of motion onward, illustrate all too clearly. For the greater part of history, people have assumed that there are supernatural persons and that it is within the power of human minds to discover truths about them — and even today, the number of intellectual circles where their being as opposed to their existence is denied is still relatively small. Both assumptions may of course be wrong. Moreover, it is safe to say that most of what is and has been believed about supernatural persons is wrong (if only because it is always safe to say that, with respect to natural relations no less than with respect to supernatural relations). However, one should not dismiss the assumptions merely because one mistakenly believes that ‘being’ and ‘existence’ are perfect synonyms. They are not.

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