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PHENOMENAL EXPERIENCE AND THE MEASURE OFINFORMATION

ABSTRACT. This paper defends the hypothesis that phenomenal experiences maybe very complex information states. This can explain some of our most perplexinganti-physicalist intuitions about phenomenal experience. The approach is to describesome basic facts about information in such a way as to make clear the essentialoversight involved, by way illustrating how various intuitive arguments againstphysicalism (such as Frank Jackson’s Knowledge Argument, and Thomas Nagel’sBat Argument) can be interpreted to show that phenomenal information is notdifferent in kind from physical information, but rather is just more information thanwe typically attribute to our understanding of a physical theory. I clarify how thishypothesis is distinct from Nagel’s claim that the theory of consciousness may be

inconceivable, and then in conclusion briey describe how these results might suggesta positive and conservative physicalist account of phenomenal experience.

This paper defends the hypothesis that phenomenal experiences maybe very complex physical states. This possibility can be described in arigorous way using some tools from algorithmic information theory,

and some plausible assumptions about the physical bodies of con-scious agents. This possibility is remarkable for two reasons. First, itcan explain some of our most perplexing anti-physicalist intuitionsabout phenomenal experience. Second, it suggests a conservative viewof phenomenal experience: these experiences may be nothing buthighly complex physical states that are representations, or of whichthe agent is otherwise aware.

Fundamental facts about information are frequently ignored andcontradicted in philosophical discussions of information. It is typicalto overlook that information can be quantied, and that it takes upspace in any physical implementation. Rather, many wrongly assumethat any particular system – a modular system within a human brain,for example – can contain any quantity of information. Ignoringthese basic facts allows a host of illegitimate intuitions and invalid

Erkenntnis (2007) 66:329–352 Ó Springer 2007DOI 10.1007/s10670-006-9024-z



arguments to appear compelling. Most egregious of these are manyintuitions and arguments in which it is assumed that the information

in a phenomenal experience is no greater than the information in anyparticular theory or conception we might have about that phenom-enal experience. But until we know more about phenomenal experi-ence, it is possible and indeed plausible that phenomenal experiences,if they were physicals states, may be very complex physical states, andthat many of these states may be so complex that they cannot becomprehended by our theoretical abilities. This is not the commonclaim that a theory of consciousness might be too complex for us tocomprehend, but rather a claim about the historical, contingentphysical state that – if physicalism about phenomenal experience weretrue – constitutes a particular phenomenal experience. To myknowledge, this hypothesis has been overlooked as a possibility in thevast literature on consciousness.

My approach in this paper is to explain some basic facts aboutinformation in such a way as to make clear the essential oversightinvolved, by way of illustrating an example of such an oversight. Iwill do this using the most compelling and inuential argument that

physical theory will fail to account for phenomenal experience: FrankJackson’s Knowledge Argument, which aims to show that there issomething about phenomenal experience that cannot be captured asphysical information (Jackson, 1982). The inuence of this argumenthas not abated, even though Jackson now doubts its conclusion.However, this argument, and the related arguments of ThomasNagel, can be interpreted as seeming plausible because phenomenalexperiences are just more complex – they provide more information – than we typically attribute to our understanding of a physical theory.That is, we can both explain the intuitive appeal of these arguments,and show that they are invalid or based on false premises, with theclarication of the simple possibility that a phenomenal experience, if it were a physical state, might be a very complex physical state (whichcan be sufciently described in some way, that description beingphysical information). The intuitive appeal of these arguments reliesupon overlooking this possibility.

I will proceed as follows. First, I will clarify an ambiguity in

Jackson’s argument, with the aim of clarifying why it has the appeal itdoes. Jackson’s argument is amenable to several interpretations. Oneinterpretation yields a valid argument, but egregiously begs thequestion and as a result establishes nothing. Another interpretationseems to reveal compelling and surprising facts about consciousness,but it requires highly dubious empirical assumptions regarding our

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capacities. I will show that this compelling form of the argument failsto show physicalism is false. I show that this is true also of Nagel’s

bat argument, and the recently strengthened form of the KnowledgeArgument created by Graham and Horgan. I clarify how myhypothesis is distinct from Nagel’s claim that a true theory of phe-nomenal experience may be inconceivable, and then in conclusionbriey describe how these results might suggest a positive account of phenomenal experience.

The general notion of information I use is that the information insomething is given in a description of that thing. This is a very simplenotion: we pick a way to describe something (such as a particularscientic theory) and then we can measure the information in thatdescription in a rigorous way (roughly, a large description containsmore information and so is more complex than a small one, assumingboth are as pithy as they can be). There are of course different pos-sible descriptions of a thing and so different amounts of informationin a thing; but this is no more problematic than is the fact that thereare different possible numbers in a thing (one forest might be athousand acres and a million trees). What matters is that once we

pick a form of description (based upon considerations of the ade-quacy of that description for the purposes – such as serving in apredictive science – for which the description is required), and thatform of description is used for several things, we can then comparethe amount of information in those things as described. I will makethis more rigorous in section 4 below by use of the measure of information given in one branch of theoretical computer science,known variously as Kolmogorov complexity theory or algorithmicinformation theory.

I should address a common criticism of physicalism that couldarise at this point. Given that many anti-physicalist arguments aboutphenomenal experience conclude that phenomenal experience may just not be the kind of thing that we should think of as physicalinformation or that can be adequately ‘‘captured’’ as physicalinformation, it can seem that my argument is off on the wrong footby starting with a notion of physical information. (I do not believethat Jackson would offer this objection: Jackson formulates the

argument of his paper ‘‘Epiphenomenal Qualia’’ in terms of physicalinformation and what it leaves out.) However, given my notion of information as description, this would be simply to deny that we cangive an adequate physical description of phenomenal experience.Understanding that this is the very thing at issue, both Jacksonand Nagel do not stipulate that phenomenal experiences cannot be

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described physically, but rather offer valuable and compelling argu-ments to this effect. These arguments, and many others, share an

appeal to an intuition that we (as thinking humans) will be unable tograsp phenomenal experiences through theory. But physicalism couldbe true, and still we would have that inability, if phenomenal expe-riences could be fully described physically, but those descriptionswere sufficiently complex. Thus, it is necessary to develop some of thephysicalist apparatus that is ultimately rejected by anti-physicalists inorder to show that this same apparatus can explain the intuitions andinsights in the Knowledge Argument and related arguments.

1. HOW MUCH DOES MARY KNOW ?

The Knowledge Argument is now as familiar as it is inuential: fromthe premise that phenomenal experience gives a kind of informationor otherwise provides some kind of knowledge, and the premise thatthe relevant sciences cannot predict or do not entail this informationor knowledge, appears to follow the conclusion that these sciences areincomplete with respect to phenomenal experience. The rst explicitformulation, 1 and the most intuitively compelling form, of theKnowledge Argument was given by Frank Jackson (Jackson, 1982).Jackson illustrates the argument with a thought experiment:

Mary is a brilliant scientist who is, for whatever reason, forced to investigate theworld from a black and white room via a black and white television monitor. Shespecializes in the neurophysiology of vision and acquires, let us suppose, all thephysical information there is to obtain about what goes on when we see ripetomatoes, or the sky, and use terms like ‘red’, ‘blue’, and so on....What will happenwhen Mary is released from here black and white room or is given a color televisionmonitor? ... It seems just obvious that she will learn something about the world andour visual experience of it. But then it is inescapable that her previous knowledge wasincomplete. But she had all the physical information. Ergo there is more to have thanthat, and Physicalism is false. (Jackson, 1982, p. 130)

This argument leaves it ambiguous what it is that Mary is meant toknow before she leaves the room. We might read ‘‘all the physicalinformation’’ to mean at least three different things. First, it mightmean complete physical omniscience . Mary knows all physical facts,

including particular empirical facts about what was where and when.Since we might suppose that relations between natural kinds is anempirical fact, I ’m going to eschew the usual ambiguous term‘‘empirical’’ for particular empirical facts, and call a description of these ‘‘historical physical information,’’ to draw attention to the factthat these are particular events. Complete physical omniscience

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therefore includes complete knowledge of all historical physicalinformation. Second, we might take the Knowledge Argument to

ascribe to Mary sufcient physical theory competence. This is the viewthat Mary knows all the relevant true physical theories (any knowl-edge about physical theory she lacks is not relevant to understandingconsciousness). 2 Third, we might take it to mean Mary has augmented physical theory competence , that she knows all relevant true physicaltheories and she knows all relevant historical physical information.

Jackson offered a strengthened form of the Knowledge Argumentin a later paper, in which:

[Mary] knows all the physical facts about us and our environment, in a wide sense of ‘physical’ which includes everything in completed physics, chemistry, and neuro-physiology, and all there is to know about the causal and relational facts consequentupon all this, including of course functional roles. (Jackson, 1986, p. 291)

Thus, it seems Jackson’s intention was that Mary has completephysical omniscience. This formulation of the argument has twograve problems. The rst is that it describes a physically impossiblesituation. Even if the historical physical information in the universe iscompressible (I describe below what this means), it is still going to be

immense beyond imagining. Mary would need a brain billions, per-haps trillions, of times the size of a normal human brain in order tostore this information, under even the most optimistic of assump-tions. We should have grave suspicions about whether intuitionsabout a physically impossible situation can be relied upon to illustrateactual limits of physical theory.

Second, and more important, is that to grant Mary completephysical omniscience makes the Knowledge Argument valid butclearly trivially question begging. The suppositions of the thoughtexperiment include the assumption that the experience of color is nota physical fact, since it is by supposition not already known. Thethought experiment amounts to:

Knowledge Argument, Complete Physical Omniscience Form

Premise 1A: Mary knows everything that is in the set of physicalinformation, P;

Premise 2A: Color experience is not known by Mary and so no

sufcient description of color experience is in P;Requirement A for Physicalism (about phenomenal experience): a

sufcient description of each phenomenal experience (includingeach color experience) is in P;

Conclusion : Physicalism (about phenomenal experience) is false.




(In what follows, I use ‘‘sufficient description’’ and its cognates tomatch Jackson’s notion of nothing being ‘‘left out.’’ For example, if

there is a sufficient physicalist description of a phenomenal experi-ence, then there is nothing relevant to be known about that experi-ence that is not in that description already.) The suppositions of theargument explicitly and directly assume that physicalism is false.

My task is not to criticize the Knowledge Argument but rather toexplain its intuitive power as a way of illustrating the danger of overlooking fundamental facts about information. Thus, we shouldask, why do we nd the Knowledge Argument so compelling? Any-one who has taught the problem of consciousness in a classroom canattest that the Knowledge Argument is the one of the most compel-ling arguments, if not the most compelling argument, for anti-phys-icalism. But the argument would lack any appeal at all if delivered inthe form I describe above. Furthermore, we can condently assumethat no reader of the argument is omniscient with respect to allphysical facts, and so the reader has to make crucial assumptionsabout what it means to be omniscient about all physical facts in orderto be willing to accept anything like premise 2A. 3

The argument’s appeal lies in that we overlook that informationcomes in quantities, and as a result we read the argument quitenaturally as concerning physical theory competence or augmentedphysical theory competence, but notice no problem when itsdefenders shift the interpretation to complete physical omniscience.The problem with this, however, is that while the complete physicalomniscience form of the argument begs the question and has nointuitive appeal, the other two forms of the argument are invalid orinclude false premises. I will consider each in turn to show this.

2. HISTORICAL PHYSICAL INFORMATION AND RELATIONS BETWEEN

NATURAL KINDS

If we read the argument as supposing that Mary has physical theorycompetence, we can give the argument as the following enthymeme:

Knowledge Argument, Physical Theory Competence Form

Premise 1B: Mary has a complete (standard, scientic) theory of color vision and other necessary relevant sciences; call this T.

Premise 2B: When Mary sees colors she learns something notentailed 4 by theory T.

Conclusion: Physicalism is false.

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Here I am assuming that a standard scientic theory is one thatdescribes at least both natural kinds and natural laws that relate these

kinds. This is meant to be a very general notion of scientic theory,and is consistent with either a classical syntactic view of theory or thevarious richer semantic views (see Suppes, 1972; Gieri, 1994). Thenotion that a theory that describes natural kinds and the laws thatrelate them deserves to be called ‘‘standard ’’ might be challenged, butthe arguments that follow will only require that some theories are likethis to make the relevant points.

This argument has as an implicit premise that physicalism is falseabout some domain if the physical theory does not entail all of therelevant information. This is a strong assumption of a kind of com-pleteness for physicalism. Thus, to be valid, the argument needs ananalog of Requirement A above. This replacement for RequirementA is:

Requirement B for Physicalism: phenomenon E is explained byphysical theory T if and only if a sufcient description of E isentailed by T. 5

Most responses to the Knowledge Argument attack this notion of physicalism. One way to do this is to argue that the information orknowledge gained in phenomenal experience is somehow differentfrom the information or knowledge gained or described throughphysical theory, but different in a way that should not be seen asproblematic for physicalism, and so physicalism should not have toexplain all of phenomenal experience but physicalism can still besomehow sufficient. Thus, Churchland rejects the argument by usingthe distinction between knowledge by acquaintance and knowledgeby description (Churchland, 1985); Loar proposes that phenomenalexperience is knowledge that concerns objects under a differentdescription than they are given in theory (Loar, 1990); Lewis arguesthat phenomenal experience is a kind of knowing how, whereastheory is a knowing that (Lewis, 1999). These arguments aim to showthat there is an ambiguity in ‘‘information ’’ or ‘‘knowledge’’ (or both)such that this stronger notion of physicalism is true for one notion of information (e.g., knowledge by description or knowing that) but not

for another (e.g., knowledge by acquaintance or knowing how).We can assume that Jackson’s notion of information is unpro-blematic and still show that there is a grave problem with the physicaltheory competence interpretation of the argument. Imagine a thoughtexperiment in which Sue knows the complete theory of dynamics, butis locked in a closed environment where she never sees the moon and




is never told about the moon. One day she is let out and sees themoon, and so learns that the Earth does have such a satellite. The

analog to the rst form of the Knowledge Argument would then be:Dynamics Argument

Premise 1: Sue has a complete (standard, scientic) theory of dynamics.

Premise 2: When Sue sees the Terran moon she gains new informa-tion about a moving body.

Conclusion: The claim that dynamics is a sufcient scientic theory of motion is false.

But this is obviously invalid. We should not conclude thatdynamics were incomplete as a theory of motion. Most standardscientic theories will not entail all the relevant historical physicalinformation but will still be excellent physicalist accounts of the rel-evant phenomena. Dynamics does not entail what masses there areand where they are and how they are moving; chemistry does notentail how many kilograms of hydrogen there are or where and whenvarious chemical reactions take place; limnology does not tell us howmany lakes and streams there are and where they are; and so on.Most of our successful scientic theories tell us not all the relevanthistorical physical information but rather what one can derive fromthe relevant kind of historical physical information.

This distinction addresses one version of the Knowledge Argu-ment offered by George Graham and Terrence Horgan. They believethat their version of the Knowledge Argument escapes the standardobjections to Jackson’s formulations (2000). In their argument, there

is another Mary, whom they call Mary Mary, who in addition tohaving (at least) complete knowledge of physical theory and being forsome years unable to see colors, is also devoted to some particularform of physicalism (they use as their example Tye’s PANIC theory – see Tye ( 1995) – although they presume their point should general-ize). When Mary rst sees colors, she is surprised. But Graham andHorgan argue that there should be nothing like surprise, since thissuggests that the theory left something out:

But should Mary Mary, while still in her monochromatic situation, expect to besurprised by the new experiences and new knowledge she would acquire uponbeginning to have color experiences? Should she expect unanticipated delight at thenew experiences and new knowledge, over and above any anticipated delight that shemight expect to arise purely from the acquisition of new discriminatory and recog-nitional capacities per se? No, she should not. (Graham and Horgan, 2000, p. 71)

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the Chengjiang Laggersta tte rst, and gotten from it fossil specimensof the strange velvet-worm like organisms found there, we could

safely predict that specimens like these might be found in the BurgessShale. But that did not happen, we lacked the relevant historicalphysical information, and it was a surprise and delight to get thisinformation rst from the Burgess Shale Laggersta tte. Graham andHorgan’s version of the Knowledge Argument, interpreted as a claimabout theory competence, thus serves to well illustrate the funda-mental difference between theoretical and historical physical infor-mation, but provides no additional reason to doubt physicalism.

3. AUGMENTED PHYSICAL COMPETENCE INTERPRETATION

The physical theory competence form of the Knowledge Argumentassumes that Mary has a standard scientic theory about color vi-sion, which I described as at least being a theory that describes nat-ural kinds and natural laws. It is a reasonable hypothesis that somephysical theories are sufficient if they describe only natural kinds and

the laws that relate these. Dynamics appears, for example, to be likethis. On such a view, to predict some particular physical state, wewould need not only the relevant physical theory but also some rel-evant historical physical information. The Knowledge Argumentcould be read as recognizing this if we interpret it as giving Maryaugmented theory competence. I give this interpretation also as anenthymeme:

Knowledge Argument, Augmented Physical Theory Competence

FormPremise 1C: Mary has a complete (standard, scientic) theory of

color vision and other necessary relevant sciences; and she has allthe relevant historical physical information about any particularkind of visual experience she might have when she leaves the blackand white room; call this T+.

Premise 2C: When Mary sees colors she learns something not entailedby T+.

Conclusion: Physicalism is false.Implicit here is a weaker notion of physicalism, to replace

Requirement B:

Requirement C for Physicalism: phenomenon E is explained byphysical theory T if and only if a sufcient description of E is

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entailed by both T and the relevant historical physical informationof events antecedent to E.

Fortunately, we do not need to establish what makes a theoryphysicalist to illustrate the points being made here. We can keep thenotion of the physical primitive. Suppose that T is a complete stan-dard kind of physical theory of color vision; we now understand thisto mean that if we have a sufficient relevant description of a historicalsituation of color vision H t1 , T and H t1 together entail all the relevantfacts at some later time 2, H t2 . We do not need to explain what H t1

and H t2 are like, except to illustrate the concept: in the case of

physicalism, for example, each H tn might be a complete description attime tn of what is happening in someone ’s visual cortex during acolor vision experience. Many would deny that this is a sufficientdescription of a phenomenal experience, of course, but as the targetof the Knowledge Argument is physicalism we need address thepremises as they would be formulated for a charitable version of physicalism.

Note that theory T is a kind of information; it is the informationof the physical theory that describes natural kinds and their relationsthrough natural laws. H t1 is also physical information, but of aparticular phenomenon; that is, it is a description of the relevantvisual color information that the agent experiences at time t1. Onlyhistorical physical theories, such as for example one nds in someparts of paleontology, entail historical physical information about theenvironment at any time. There is then no a priori reason that atheory of color vision must entail any input to the theory. This wasmy point in section 2: T alone may not entail any H tn for any time tn,

just as, say, dynamics alone (without any historical physical infor-mation) does not entail that there is a moon in such and such aposition in orbit of the Earth.

But one could argue that a complete theory of color vision shouldinclude some , but surely not all, historically contingent information.This is to endorse the augmented physical theory competence inter-pretation of the Knowledge Argument. A defender of the argumentwould then hold that the physical theory of color vision would in-clude some historical physical information, and be of the form de-scribed above as T+; and so Mary should be able to derive H t2 forthat time t2 when she nally sees colors. Some plausible argumentscan be made that a theory of color vision should include at least somesuch information. After all, a theory of color vision must have sig-nicant connections to disciplines like ethology and paleontology,




8 looks like, sufficiently well for her to be able to recreate Number 8or to distinguish Number 8 from Pollock’s Full Fathom Five. Given

this intuitive understanding, it seems at rst that physicalism, evenwhen the complete theory is coupled with historical physical infor-mation, is false. The Knowledge Argument, in the claried aug-mented physical theory competence interpretation, appears to work.

Herein lies the intuitive appeal of the Knowledge Argument.Claried so that the premises are explicit, the complete physicalomniscience interpretation of the argument is blatantly questionbegging. The theory competence form is clearly inadequate in itscharacterization of physicalism and physical theories. But when weimagine ourselves in Mary’s shoes, we imagine learning theories likethe other theories that we have learned, we imagine that these theo-ries we learned are true, and then we imagine that we have not seencolor before but that someone or some text has described them for us,before we see them afterwards for the rst time. We put ourselves, inother words, in the very situation described by the augmented theorycompetence form of the argument.

In sum, the central intuition that makes the Knowledge Argument

compelling is the intuition that there is something in certain phe-nomenal experiences that is not captured in our everyday experienceof texts and conversation and theory. This would be true if physi-calism were false, and these texts and conversation and theory were just physicalist descriptions. But this intuition could be true for otherreasons. For example, those phenomenal experiences could be morecomplex than our everyday texts and conversations and theories, andeven more complex than can be grasped by us (given our contingentbiological abilities to hold and manipulate such linguistic informa-tion) through these channels.

4. THEORY AND MIND

The Knowledge Argument under the augmented physical theorycompetence interpretation contains an implicit and very dubiousempirical assumption. This assumption is that the amount of infor-

mation that we can manipulate with our theoretical understanding issufficient to include the kind of historical physical information that (if physicalism were correct) constitutes the phenomenal experience of color. But this is neither obvious, nor even plausible. Humans havevarious mental capabilities, and each of these will have some limitto the amount of information that it can store, recognize, and




manipulate. If we are physicalists, such limits are real and mustconstrain any account of the kind of information we suppose is in-

volved in some mental function. Furthermore, these limits may bedifferent for different capabilities, and these capabilities may not beable to fully share information. Most physicalists will suppose thatthese are various brain modules, which have varying degrees of interdependence with, and independence from, each other.

For the sake of a demonstration here, I will assume one verystrong formulation of physicalism: computational functionalism (theview that all mental states – and even phenomenal experiences – canbe sufficiently described as discrete states of a Turing machine, plusthe supposition that the brain instantiates something that can beinterpreted as acting like such a Turing machine). 7 My aim in usingcomputational functionalism as an example of a physicalist theory isconservative: I will show that even as unattractively simple a theoryof consciousness as computational functionalism escapes the bite of the Knowledge Argument.

Assuming computational functionalism, the information stored ormanipulated in mental modules can in principle be measured objec-

tively, using a standard called ‘‘Kolmogorov complexity.’’8

Kol-mogorov complexity denes a measure of the minimal size of descriptions. The Kolmogorov complexity of a description is thesmallest computer program that can generate (e.g., print) thatdescription. The size of the relevant program in bits is one metric of Kolmogorov complexity. This measure is then a kind of measure of how compressible some information is. Some very large descriptionswill compress down very signicantly. An innitely long string of ‘‘10101010... ’’, for example, compresses to a very small program. Theinnite extension of pi also compresses signicantly. We say then thatboth have a low Kolmogorov complexity. But some descriptionscannot be compressed any more. Information which cannot becompressed we can call Chaitin random ; a Chaitin random descriptionthat is 1000 bits long, for example, cannot be reproduced by a pro-gram that is less than a 1000 bits of information. The measure of Kolmogorov complexity can be standardized if we agree upon the useof some particular universal Turing machine as a standard. However,

the measure of Kolmogorov complexity is implementation indepen-dent, up to an additive constant; this follows directly from the factthat any universal Turing machine can perform the operations of anyother such machine, with some nite additional program. For thisreason, the measure is objective.

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We do not need to speculate too much about what is being mea-sured beyond that the measurement is of physical things, presumably

brain states, since we are supposing that physicalism is true for thesake of showing that the augmented physical theory competenceinterpretation of the Knowledge Argument is awed. There are manyphysical states that could be measured, but the basic guiding principleis that one would make the coarsest (that is, simplest) measurementsthat identify and distinguish those states that make a difference tobehavior (behavior here is construed broadly, as it must be, to includethings like perceptuomotor control and not just linguistic reports)according to the theory. We have been using visual perception andvisual experience as our example. If we measure the state of the visualcortex during some red experience, we would not measure moleculesand their placement if it makes no difference (if moving these mole-cules could not possibly alter behavior), but would measure, say, theconnectivity and ring patterns of individual neurons if altering themcould make a difference (that is, if it follows that simplifying such astate would result in the loss of behavior) according to the theory.This is something of a platitude, but pointing it out should clarify

that when we say that some kind of physical brain state is morecomplex than another, we are comparing similar physical kinds, usinga common metric based on functional role.

We know that human individuals have at least the following twocapabilities: they can understand, use, and manipulate theories; andthey can see objects and respond to them or otherwise deal with themin various ways. I make no claim about whether these are ultimatelythe same kind of capabilities (that is, whether knowing how andknowing that are ultimately interreducible). But we cannot assumethat these capabilities are the same token capability in Mary or inanyone attending to Jackson ’s thought experiment, nor that they arefully integrated with each other so that the information in one can befreely and fully manipulated by the other.

The kind of description that we might measure with Kolmogorovcomplexity could be a theory, such as the complete standard theoryof color vision T, or it could be a historical description (perhapsincomplete) of the functional state of an individual visual cortex at

time tn, H tn . Note that T+, the richer historical version of a theory of vision, is T plus some historical physical information of the same kindas H tn . Let I(T) be the Kolmogorov complexity of T. By suppositionof Jackson ’s thought experiment, our subject can at least know T, soI(T) is less than or equal to the amount of information that the agentcan recognize and manipulate with the cognitive capabilities that




constitute the relevant theoretical understanding. Call the upper limitof the information that can be manipulated by theoretical under-

standing N (in this case, N can be the storage capacity of the theo-retical understanding of Mary). Let H t1 be a description of all therelevant features of the state of the brain (presumably, the visualcortex) of Mary at time t1 that are required to fully describe therelevant (physical features of the) color experience at time t1. LetI(H t1 ) be the Kolmogorov complexity of H t1 .

Given these denitions, note that there is no reason to believe thatI(H t1 ) £ I(T), nor that I(H t1 ) + I(T) £ N, nor even that I(H t1 ) £ N. Infact, it is highly plausible that I(H t1 ) is signicantly greater, perhapsvastly greater, than N. For example, the portion of the human neo-cortex devoted to visual processing is very large, and appears to besignicantly larger than those regions of the temporal cortex thoughtto be devoted to mathematical or linguistic reasoning. We are able tostore and manipulate and use visual information in various ways, andsuch manipulations could well exceed our abilities to manipulate suchinformation in the form of theoretical information or to describe itlinguistically. Thus, it could be that (1) T and H t1 are a fully sufficient

physical account of color vision because together these entail therelevant subsequent state of the agent in question (T and H t1 entailsH t2 ); and (2) T and H t1 explain H t2 in such a way that if we did have atheoretical grasp of both T and H t1 we would nd no reason tobelieve that something was ‘‘left out ’’ of the theory (that is, we wouldnot accept the conclusion of the Knowledge Argument); but (3) I(T)< N << I(H t1 ), and so N << I(T+). In such a case, the agentcould have a complete standard theory of color vision T, but theagent could lack the theoretical form of the information that con-stitutes the actual having of the experience of color vision (namelyH t1 ), because in practice she cannot manipulate the information H t1

with her theoretical understanding.This is consistent with the claim that the subject can herself

experience color vision and thereby learn something new (i.e., gainnew information), since being aware of some information, being ableto recognize it, being able to act in particular ways with that infor-mation, and so on, do not require that the agent’s ability to theorize is

sufficient to be able to grasp that visual information as part of atheory. This is not to deny that they might be the same kind of information (‘‘physical information’’) but rather just to deny thatevery system of the mind has the same mental capacity, and to denythat all information that enters the mind is available to every systemof the mind.

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There are good reasons why our brains might have separatemodules that generate and use sensory, autonomic, and other kinds

of information that exceeds in complexity the information capacity of our theoretical abilities. First, if there is benet to having the abilityto recognize and otherwise use a great deal of complex sensoryinformation, there may be some evolutionary pressure to increasethat information capability or at least keep it large. There is noobvious reason that we would have a signicant or even equal benetfrom having theoretical information handling capabilities that canmanage that same information. If we are realists and assume theenvironment is shared, for example, then there is likely a great deal of parsimony to be had in letting the world speak for itself. We can leaveour theoretical abilities not for describing in complete detail shades of red but rather, based on the assumption we both see the red before usas we talk, we can use our theoretical abilities instead to make andcommunicate relevant inferences. Second, it seems unlikely thatlanguage could ever manage to convey the information in a visualexperience, for example, in a timely way. Given the bandwidth con-straints of this medium, which we inherit and do not choose, it is

likely that it is better used for other purposes. Such purposes arefacilitated, again, by the assumption of realism and the consequentassumption that we share the relevant sensory experiences.

An analogy may help. The Kolmogorov complexity of Peanoarithmetic is obviously small enough for human beings to memorizeand work with this theory, but there are large numbers that areChaitin random that a mathematician will not be able to memorize orpractically manipulate. 9 Suppose now that Jane knows a version of Peano arithmetic, Zermelo-Frankel set theory with the Axiom of Choice, and how to construct the natural numbers using set theory;let us call this combination of theories, basic arithmetic theory. AKnowledge Argument that arithmetic were not reducible to basicarithmetic theory would go something like this. There are very largeChaitin random numbers that Jane cannot memorize, recognize, ormanipulate, even though she knows basic arithmetic theory; thisfollows simply from the facts that Jane must have a nite theoreticalmemory, and that there are innitely many numbers of Kolmogorov

complexity exceeding the information capacity of that memory. Let Rbe such a number. Even though Jane knows basic arithmetic theory,she cannot ‘‘in her head ’’ add R to itself. Therefore, R and itsproperties are not expressible or derivable in basic arithmetic theory.Namely, basic arithmetic theory is incomplete in respect to addition




with R. The analog of the augmented physical theory competenceinterpretation of the Knowledge Argument then is something like:

Basic Arithmetic Theory Argument

Premise 1: Jane knows basic arithmetic theory and she has the abilityto store, recognize, and manipulate many numbers in which shemay have an interest.

Premise 2: Jane cannot predict the relevant properties of R (e.g.,R+R).

Conclusion: Basic arithmetic theory is not a sufcient theory of numbers and their arithmetic properties.

This argument has obviously gone badly wrong. The problem iswith premise 1, which mixes human capabilities with the limitationsof theory. All of the properties of R that interest us may beexpressible or derivable in basic arithmetic theory. But R is just toolarge for Jane to handle, and so numbers she may have an interest inmay be beyond her theoretical abilities to remember and manipulate.Just so, there is no reason to believe that the information in our visualsystems, which we use effectively to guide ourselves through theworld, can be compressed enough to be manipulated with thosecapabilities (a physicalist might suppose, with those brain modules)that enable theoretical reason, nor to be communicated in thebandwidth of human speech. But this does not show that thisinformation is not the kind of information that could be fully ex-pressed and used in predictions by a physical theory of color vision, just as Jane the mathematician’s limitations show nothing about therelative completeness of basic arithmetic theory.

More explicitly, in the augmented physical theory competenceinterpretation of the Knowledge Argument, premise 1C allows forambiguity about what Mary ‘‘has’’ and how she ‘‘has’’ it; premise 2Callows for ambiguity about what she ‘‘learns’’ and how and where she‘‘learns’’ it; and Requirement C for physicalism addresses mereentailment, but the argument invites us to consider instead whatMary ‘‘knows’’; and the notion of ‘‘knows’’ is ambiguous.

The mere possibility of the kind of modularity of mind I havedescribed, and of these kinds of information capacity differencesbetween human capabilities, means that the historical physicalinformation of a particular visual experience may be beyond thetheoretical scope of an individual working with a successful completetheory of vision. We should no more expect Mary to have all theinformation of a red experience than we should expect a great

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mathematician to be able to remember and divide ‘‘in her head’’ twoincompressible (Chaitin random) numbers that are 1000 numerals

long.Thus, the Knowledge Argument under the augmented theorycompetence interpretation does not show that phenomenal experi-ence cannot be fully captured with a physical description. Theplausibility of the augmented physical theory competence interpre-tation of the argument rests upon an unexamined and dubiousempirical assumption about the mind: a naı ve conception of a single,homogenous mental capability with unbounded storage capacity. Itappears, however, that the mind is highly modular, and no physicalistcan allow that any such module has unbounded storage capacity. Wecannot then assume, as does the Knowledge Argument, that theinformation in one such module is available to or could even ‘‘t’’ inanother.

5. COMPLEXITY OF THEORY VERSUS COMPLEXITY OF EXPERIENCE

The claim that the information in a phenomenal experience could bemore complex than can be grasped by the relevant theoretical capa-bilities that we have should not be confused with the claim that asuccessful theory of phenomenal experience is, or could be, beyondour grasp. The latter claim is entertained in Nagel ( 1974). Nagelargued that we intuit that we cannot know what it is like to be a bat,and he recognizes that his intuition may have something to do withhuman limitations:

My realism about the subjective domain in all its forms implies a belief in theexistence of facts beyond the reach of human concepts. Certainly it is possible for ahuman being to believe that there are facts which humans never will possess therequisite concepts to represent or comprehend. (Nagel, 1974, p. 441)

The talk about concepts here is ambiguous. We can easily have aconcept like that-which-humans-will-never-understand, and so have aconcept of the phenomenon in question. Nagel seems to mean thatthe theory will contain laws or other kinds of theoretical descriptionsthat are beyond our capacity to comprehend. We can make more

sense of such limitations if we recognize them as regarding theory andour abilities to hold and use such theories. To use the notation above,this would be to entertain that the information of a standard physi-calist theory T of a kind of phenomenal experience, perhaps even if just a standard scientic theory without reference to historical states,may be greater than our theoretical grasp can handle: N < I(T). This




would not show us anything about whether T was an adequate theoryof phenomenal experience; it would, however, explain perhaps some

of our intuitions about the mysteriousness of phenomenal experience,and might mean we would never understand physicalism aboutphenomenal experience even if it were true.

Nagel thus recognizes that the relevant theory may be incompre-hensibly complex. But this is distinct from the idea of phenomenalcomplexity: the view that a sufficient description of a particularphenomenal state (given within a successful theory of consciousness)will be much more complex than we can comprehend with our the-oretical abilities. It is possible that a successful physical theory of phenomenal experience will be more complex than we can grasp; butit is far more likely that the relevant historical physical information isgoing to be beyond our theoretical grasp, rather than the theoreticalinformation. The wonder of good theories, after all, is that they arerelatively simple, whereas historical facts are not (uncompressedhistorical physical information is not theory for the very reason thatit is uncompressed). Thus, it is a more conservative position to as-sume that the intuitions that underlie the Knowledge Argument and

Nagel’s intuitions about bat experience are best explained not bytheory complexity, but rather historical complexity.Thus, Nagel’s intuition (that bat echolocation experience is

beyond our grasp) can be explained though the distinction betweentheoretical and historical physical information: a complete theory of echolocation experience may also require the historical physicalinformation of a particular echolocation experience Hb t3 in order toentail another echolocation experience Hb t4 , and this historicalphysical information may well be beyond the capabilities of ourtheoretical abilities. Thus, it could be that we cannot know what it islike to be a bat, but that there could be a complete physical theoryand physical description of this phenomenal experience.

6. CONSERVATIVE NATURALISM ABOUT CONSCIOUSNESS

The hypothesis that phenomenal experiences are very complex physical

states explains the intuitions that underlie Jackson and Nagel’s argu-ments; the hypothesis is plausible given our best current understandingof the modularity of mind; and the hypothesis is more conservativethan Nagel’s alternative that a physicalist theory of phenomenalexperience may itself be too complex for us to comprehend. The mostobvious consequence of my arguments is negative: if correct, they prove

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that the Knowledge Argument and related subjectivity arguments failto provide any evidence that phenomenal experience is irreducible to

physical states. However, these arguments suggest also a positiveconsequence, in a novel positive account of consciousness: we mightconclude that phenomenal experiences are nothing but physical states,given in representational states or other kinds of states of which theagent is in some sense aware, that are very complex. This is to reducephenomenal experience to something like access consciousness (Block,1995), or the hard problem to the easy problem (Chalmers, 1995).

The internal states of some human having a red color experience,or a bat having an echolocation experience, are likely extremelycomplex. It is even possible that the information in a particularphenomenal experience of human vision or bat hearing is a unique setof information in the physical history of the world. Thus, it could wellbe that some future standard physical sciences of mind will provide asufficient theory of phenomenal experience, but be unable to predictany particular phenomenal experience, in the same way that weexpect that a successful ecological science will fail to predict theprecise composition of a wetland at any place or time. Such a con-

clusion has on its side parsimony, in that it gives a simple, conser-vative interpretation of the difficulty that the Knowledge Argumentand related arguments struggle to articulate: subjectivity is history. 10

ACKNOWLEDGMENTS

Thanks are due to Gabriele De Anna, Carla Fehr, Malcolm Forster,Lilia Gurova, Nikolay Milkov, John Norton, Athanassios Rafto-poulos, Wang Wei, and Brad Wray for helpful observations. Thanksalso to the Center for the Philosophy of Science at the University of Pittsburgh, where I did some work on this paper. Finally, I amgrateful and indebted to two anonymous reviewers for Erkenntnis .

NOTES

1 Arguably some of the presuppositions of Jackson’s Knowledge Argument werearound for some time. For example, see Carnap (1967: 19ff); Feigl (1958: 450ff).2 The simpler formulation, and one that seems more in line with Jackson’s way of describing the case, would be that Mary knows all true physical theories. Since it issufficient to suppose instead that Mary knows all true relevant physical theories,I will assume this instead. This might avoid some possible objections to this




interpretation of Jackson’s view that are not relevant to my argument (such aswhether anyone could know all true physical theories).3 It is here that Daniel Dennett attacks the Knowledge Argument (1991: 398ff). Heobserves that we really cannot imagine what it is like to have complete physicalomniscience, so our intuitions about it are unreliable. The argument that I makebelow could be read as consistent with this point, but it is far more conservative: I amclaiming not only that we cannot imagine and therefore rely upon intuitions aboutcomplete physical omniscience, but also that there may be more information in asingle phenomenal experience than we can ‘‘imagine’’ (read: model, properlyunderstand, manipulate through reasoning) using those mental capabilities thatenable theoretical thought.4 I mean here semantic entailment: true given the theory. The argument would bemore intuitive if I used ‘‘predicted’’ instead of entailed, but I aim to avoid problemsarising from the fact that some information might be entailed by physical theory butnot predictable by it (a standard notion best illustrated by Turing’s Halting Prob-lem). Nonetheless, some of the intuitive appeal of the Knowledge argument reliesupon prediction, not entailment, as will be clear below.5 A more natural way to phrase this notion of physicalism might have been to saythat all relevant phenomenal information must be reducible to physical information.However, some might object that phenomenal experiences cannot be described, andso cannot be information. (Thanks to one anonymous reviewer for Erkenntnis forthis observation.) I nd it hard to grasp how something could fail to be informationbut could still be knowledge (as the Knowledge Argument requires it to be), but it issufcient to my argument to keep with Jackson’s general (if vague) formulation thatsomething is ‘‘left out’’ of the physicalist account, since my approach here is to showthat something could be left out of some kinds of physicalist accounts (e.g., purelytheoretical accounts, or accounts limited by our ability to comprehend them) even if physicalism were true.6 If we read Terrance and Horgan’s argument as concerning total physical omni-science, it adds nothing new to the defense of the Knowledge Argument (theassumption of total physical omniscience allows for a valid but trivially question-begging argument like the one above). If they mean for something like the aug-mented relevant physical theory omniscience, then the arguments below will apply totheir argument.7 If one adopts an alternative view of mind to computational functionalism butremains a reductive physicalist, the arguments that follow should still work. How-ever, the application of standard notions of descriptive complexity might requiresubstantial additional mathematical work to generate relevant measures for con-tinuous states. Since this is not necessary to make the points of this essay I will notextend the argument to other kinds of views of mind. Regarding non-reductivephysicalism, however, I cannot say whether the arguments that follow will apply,since in general the forms of non-reductive physicalism are not sufficiently clearabout the nature of the physical states that constitute mental states for one to be ableto speculate about the appropriate description of them (and thus the amount of information in those appropriate descriptions).8 ‘‘Kolmogorov Complexity’’ is a common name for this measure of descriptivecomplexity, but the measure was independently developed by three mathematicians:G. J. Chaitin, A. N. Kolmogorov, and R. J. Solomonoff. See Chaitin (1966, 1982),Kolmogorov (1965), Solomonoff (1964).

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9 A simple counting argument shows that there are many Chaitin random, orincompressible, numbers of each size. Suppose for simplicity we are using a binarycoding of numbers, and have xed a universal Turing machine to use as a concretemeasure. At most about half of the strings n bits long can be compressed, since thereare 2 n such strings and at most 2 n ) 1 shorter strings that they could be compressedinto.

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Department of PhilosophyState University of New York, Oswego,Piez Hall, Oswego, NY, 13126, USAE-mail: [email protected]

Manuscript submitted 15 March 2006Final version received 8 December 2006

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