I am Joe's Explanatory Gap

A longer version of a paper presented at the American Philosophical Association symposium on Color Vision and the Explanatory Gap, Pacific Division Meeting, Los Angeles, 31 March 1994.

Austen Clark
Department of Philosophy U-54
University of Connecticut
Storrs, CT 06269-2054

Suppose that sitting in front of Joe is a greenish-looking coffee mug filled with some hot steamy liquid--water, say. The problem of the explanatory gap is, roughly, that some of the aspects of this tableau can be given a full and satisfying explanation, while others cannot. We can explain in a full and satisfying way why the water in the mug is identical with H2O, why its liquidity is identical with a state of its molecular bonds, and why its heat is identical with its molecules being in motion. But we cannot explain in the same way why the neural processes which Joe undergoes when he looks at the mug are such as to make the mug look green, and not red. The latter explanations have gaps.


It is important to lay out the structure of the full and satisfying explanation we can purportedly give for water, liquidity, or heat but which we purportedly lack for experiences of color. Simple descriptions of the explanatory gap will not distinguish explanations of why the mug looks green from explanations of why the mug is hot. For example, a first intuitive formulation of the explanatory gap might be something as follows:

Let P be the complete story as told by physics of what goes on in the mug and in Joe when Joe looks at the coffee mug. The problem is that appeal to P does not explain the qualitative character of the experience Joe has when he looks at the mug. P does not explain why the mug looks green because it is equally consistent with the claim that the mug looks red, not green. So any attempt to deduce "the mug looks green to Joe" from P will not succeed.

To this I think the physicalist should say: of course, of course, but the reason is simply that the terms "red" and "green" are not found within the physical story P. If no sentences in P contain those terms, then all those sentences are consistent both with "the mug looks green" and with "the mug looks red". In exactly the same way, unless the physical story P contains the terms "steamy hot" and "tepid", the entire physical story P is consistent both with the claim "the mug contains a steamy hot liquid" and "the mug contains a tepid liquid". In both cases the explanatory gap is just a gap in vocabulary; we need "bridge principles" connecting terms in the physical story to terms such as "red", "green", "hot" or "cold".

As bridge principles the physicalist will naturally incline toward identity sentences of the form

process R = the process of sensing something which looks red
process G = the process of sensing something which looks green

Many anti-physicalist arguments are aimed at denying the truth of such identities. Kripke, Jackson, and Nagel all deny the truth of such identities, and wind up arguing for the existence of "subjective facts" or of facts outside the physicalist ken. Levine's initial (1983) version of the explanatory gap also implied some degree of skepticism about the truth of such identities. What is interesting--and I think unique--about the current formulation of the explanatory gap argument is that it does not dispute the truth of our identity claims. It is perfectly consistent with Levine's position that process G in the brain is identical with the process of sensing something which looks green. What the various "conceivability" arguments show is not that the identities are false, but rather they cannot be explained. They retain an arbitrary character. We cannot explain why process G is associated with one particular qualitative content instead of some other one.

Levine is quite explicit about the connection between conceivability and explanation:

if citing the relevant mechanisms really does explain how the psychological capacity in question is instantiated, then it would be inconceivable that some creature should possess these mechanisms and yet lack the capacity. (Levine 1993 p. 130)

Levine says that in the water/H20 case and heat/kinetic energy case we get a kind of "bottom-up necessity" that is lacking in the case of opponent processes and green qualitative contents (Levine 1993 p 132). "There is an apparent necessity that flows from the reduction of water to H20, a kind of necessity that is missing from the reduction of" sensing greenly to process squiggle-squiggle. (Levine 1993, p. 128). Suppose that there are various superficial macro properties by which we identify something as being water. While it is perfectly conceivable that something other than H20 manifest those properties, Levine suggests that if we take the physical story P as a premise--if we "keep our chemistry constant"--then there is a sense in which it is inconceivable that H20 fail to manifest those properties (see p 128). The apparent contingency of the identity statement works in only one direction. Whereas with sensing redly and process squiggle-squiggle, it is conceivable both that sensing redly not be identical with process squiggle-squiggle, and--more importantly--that even if you take the physical story P as a premise, it is perfectly conceivable that process squiggle-squiggle be a process of sensing greenly, and not redly.

The conceivability of assigning different qualitative contents to the same physical process does not show that our identities are false, but rather that they not been adequately explained. If we can explain the identity then there is a sense in which we cannot conceive of alternatives. "We can see why, given the facts cited in the reductions, things must be the way they seem on the surface. I claim that we have this with the chemical theory of water but not with a physical or functional theory of qualia." (Levine 1993 p 129).

One might complain here that Levine is setting up requirements so onerous that no purported explanation could ever reasonably be expected to meet them. One version of this complaint might run as follows:

No scientific explanation can ever meet the requirement of "bottom up necessity". Nor is it reasonable to expect that the denial of the explanandum should be inconceivable. The explanandum is almost always an contingent empirical truth, to which no variety of necessity attaches. Similarly, most of the premises in the explanation will also be contingent empirical truths. To require necessitation from the explanation is to set a requirement that few if any scientific explanations ever meet.

I think this complaint rests on a misunderstanding, and it is important to see why it is a misunderstanding. An explanation can yield what Levine calls "bottom up necessitation" even though all of the claims that make it up are mere contingent truths. It is clear that the physical story P need not contain any necessary truths, and I will show below that Levine's account has the implication that the identity statement is not a necessary truth either. The only claim that need be necessarily true is the claim "if P then I" and its necessity may be mere logical necessity. One revealing passage is as follows

The basic idea is that a reduction should explain what is reduced, and the way we tell whether this has been accomplished is to see whether the phenomenon to be reduced is epistemologically necessitated by the reducing phenomenon, i.e. whether we can see why, given the facts cited in the reduction, things must be the way they seem on the surface. (Levine 1993, p. 129).

The necessity here does not attach to the reducing theory or to the reduced theory, but rather to the claim: given the reducing theory, it follows that things are as described in the reduced theory. This is even clearer in "Cool Red":

explanation is essentially a matter of removing alternatives. ... An explanation is satisfying if it becomes intelligible why this event occurred, and not some other, why the object in question manifests this property, and not some other. In order for this explanatory feat to be accomplished, the alternative to be ruled out must be incompatible with the explanans, and the sense of incompatibility is epistemological. That is, we must be able to see why if the explanans is true then the alternative events could not have occurred. (Levine 1991, p. 38)

One way--perhaps not the only way, but one way--in which this epistemological necessitation could be provided is by straightforward logical necessitation: the alternative to be ruled out is logically inconsistent with the explanans, and the epistemological necessitation is nothing more or less than logical derivation. As Levine says

While there is obviously a lot to criticise in the D-N model of explanation, I think it contains a kernel of truth in its emphasis on the role of deduction, which is one way of capturing the element of necessity that must be present in any adequate explanation. (Levine 1991, p. 38)

An explanans should epistemologically necessitate the explanandum. This relation can also be expressed in terms of "conceivability". Suppose something is "conceivable" if it is "epistemologically possible" (see Levine 1991, p. 37). Now if P epistemologically necessitates Q, then the conjoining P with the denial of Q should be epistemologically impossible, or "inconceivable". This gives Levine a second test: in a successful explanation, the conjunction of the explanans and the denial of the explanandum should be inconceivable. If such a conjunction is conceivable, then the explanation fails:

consider Block's China-head. Even if I cannot definitely rule out the possibility that ... it does not experience qualia, I certainly can clearly conceive of the possibility that it does not. But if the functional description provided a genuine explanation of the qualitative character, such a situation would not be conceivable; for I would see what it was about satisfying such a functional description that necessitated--all else being equal, of course--the presence of an experience with just this qualitative character. (Levine 1991, p. 38)

Similarly, if, even given a complete functional story, the inverted spectrum is conceivable, then the functional story does not explain why states therein have the particular qualitative character that they do. Whereas given a sufficiently detailed chemistry and physics, it is inconceivable that H20 fail to manifest the various superficial properties by which we identify water, or that H20 fail to boil at 212 degrees fahrenheit at sea level (see Levine 1993, p. 129).

One might challenge this latter claim. It seems I can conceive of water at sea level failing to boil at 212 degrees fahrenheit. Here's how:

I accept all of chemistry and physics as a given. I imagine myself at the beach, a pot of H20 sitting on a burner, with an accurate fahrenheit thermometer stuck in it. Impatiently I wait for the pot to boil. But this time something odd happens. I clearly and distinctly see the mercury rise past 212 with no sign of boiling. It gets all the way to 224 before finally we get the first signs of steam. The subsequent mussels indeed tasted a bit overdone.

Have I succeeded in conceiving that, given contemporary chemistry and physics, H20 still might fail to boil at 212 degrees fahrenheit at sea level? I think Levine would have to say no, appearances to the contrary, this thought experiment does not show that the conjunction is conceivable. Why not? Well because contemporary physics and chemistry logically imply that at sea level H20 boils at 212 degrees fahrenheit. (Endnote 1) Even though a clever thought experiment may make it appear as if it is conceivable that one conjoin that chemistry with a different boiling point, in fact it is not conceivable--because that conjunction is logically inconsistent. Here the touchstone for epistemological necessitation becomes: logical necessity. If we can get a deduction of the explanandum from the explanans then we have all the epistemological necessitation that can ever be required. The fact that some people might not be able to follow the deduction, or that some people might believe they have "thought experiments" in which they conceive of the possibility of conjoining chemistry with a different boiling point does not show that this conjunction is conceivable. Thought experiments can be an unreliable guide to epistemological necessitation.

Put it another way: logical necessitation trumps all bids. If we can deduce the explanandum from the explanans, then we should not allow ourselves to be deceived by the blandishments of thought experiments, no matter how seductive. I think this is exactly the situation with arguments about color qualia. We will I think be able to achieve a logical derivation of the explanandum, but it may never become intuitively obvious to us, and we will always be pestered by seductive thought experiments which appear to show something is conceivable which in fact is not conceivable.

So how do we get the appropriate kind of necessitation in one case but not the other? We first carry out what might as well be called an "analysis" of the concept. This stage "involves the (relatively? quasi?) a priori process of working the concept of the property to be reduced "into shape" for reduction by identifying the causal role for which we are seeking the underlying mechanisms." (Levine 1993, p 132). In the case of "water", we analyse the concept of water, and come up with some characterization of the superficial macro properties by which we identify water. Some of these will specify causal roles. As Levine puts it "our very concept of water is of a substance that plays such and such a causal role". (Levine 1993 p131). The "analysis" stage of a reduction will specify such a role. So to physical story P we add an analysis A, as follows:

Levine accepts a causal/functional analysis for terms such as "water". If "water" applies to whatever fills that niche, then the term "water" is a non-rigid designator; in other possible worlds other sorts of stuff might do the job. (Endnote 2.)

If all goes well, from these two sorts of claim we can deduce a third claim. In the physical story P we can identify a substance satisfying all the characteristics required by our analysis A. The analysis specifies a causal or functional role; if P is sufficiently detailed, we can in it identify a unique occupant of that role. So from P and A we deduce statement O: (for Occupant)

This just says: given the physical world as it is, the substance which in fact occupies that causal niche is H20. One could of course imagine some other substance occupying that niche in some other possible world, but that is not to the point: one rule of the game is that no changes to P are allowed.

Given specification of a causal/functional role, identifications of occupants follow logically from knowledge of physics and chemistry. Consider heat and molecular motion:

our knowledge of chemistry and physics makes intelligible how it is that something like the motion of molecules could play the causal role we associate with heat (Levine 1983, p. 357).

and later

If someone asks why the motion of molecules plays the physical role it does, one can properly reply that an understanding of chemistry and physics is all that is needed to answer that question. (Levine 1983, p. 358)

I think this is right: given an analysis, O just follows from P.

But now from claims A and O we can derive the identity statement "water = H20" and this derivation explains the identity. We have no explanatory gap, because to the physical story P all we need to add is the analysis A, and identity claims logically follow. "We can see why given the facts cited in the reduction, things must be the way they seem on the surface" (Levine 1993 p 129). This means: we see how they follow from those physical facts. The "bottom up" necessitation is a matter of the necessity of the claim "if P then I". Given the analysis A, that claim in turn is a simple logical truth. The necessitation is simply this: once we analyse our concepts, we will see that such identities follow logically from chemistry and physics. It is perhaps not so much "bottom up necessitation" as "bottom up derivation".

So let us return to our opening tableau. If we had a complete physical story of the scene, we could give a full and satisfying explanation of some of its aspects: that there is water in the mug, that it is liquid, that it is hot, that it is steaming. All we need add to the physical story P is some account of our concepts--the analysis A--and the identities which license these descriptions will all logically follow from P. This is why "there is an apparent necessity that flows from the reduction of water to H20". We can see why, given the facts stated in P, the H20 in the mug must be water, its molecular motion must be what we mean by "heat", and the fast moving molecules near its surface which escape the intermolecular attractive forces within the liquid must be what we mean by "steam".

But the mug also looks green to Joe, and this aspect of our tableau cannot be explained in the same full and satisfying way. It seems equally consistent with available analyses and the physical story P that the mug looks red to Joe instead of green. The alternatives cannot be ruled out. So there is an "explanatory gap" in the application of our terms for qualia, which is not found for the terms "hot steamy water".


Now at this stage one could quibble at the requirements imposed on reductive explanations, carp about concepts, throw rocks at D-N explanation, and generally carry on; but I don't propose to do that. I think we can admit that our reductive accounts of water, liquidity, and heat have a certain full and satisfying character, and that it would be nice to have explanations of that sort for other phenomena. I think it is a reasonable to ask: why is it that given the physical story P, the mug looks green to Joe, and not (say) red? and that if we cannot answer this question we have in some sense failed to explain a qualitative feature of our tableau. We might want to avoid the dangerous talk of "necessitation" and just say: give us an analysis which when conjoined with P implies that the mug looks green to Joe, and not red. I accept this challenge and will proceed to describe how I think it will be met. But first I want to make a few preliminary comments about the gap.

1. The crux of the reductive account of water is to provide an analysis of the concept of water which, when conjoined with the physical story, implies the various identity statements. The latter fall out as implications of the analysis, provided that this is a successful case and in our physical story P we find a unique occupant for the causal/functional role dubbed "water".

Described this way, the account ought to sound familiar, since it bears a striking resemblance to the position articulated by David Lewis in his "Psychophysical and theoretical identifications" (1972), and "An argument for the identity theory" (1966). Recall that in those articles Lewis argued that given a correct analysis of psychological terms and sufficient psychological and neurophysiological details, identity statements are in no ways optional--not something we might choose to endorse merely in order to simplify our ontology--but rather fall out as mandatory logical implications of claims already endorsed. The irony is that Lewis was arguing the case precisely for psychological terms. So we find Levine is arguing that the Lewis account is exactly right for terms such as water, heat, and liquidity, but exactly wrong for its target: the terms we apply to certain famous yellowy-orange after-images.

2. Levine's epistemological reading of the conceivability arguments yields a problem which persists even when all the ontological questions are settled. The ontological readings--the objections of Nagel, Jackson, and Kripke--raise doubts about the very truth of the identities, while the epistemological reading asks for an explanation of identities that are acknowledged to be true. Here is a sacrilegious way to make the point. Suppose someday a big booming voice comes out of the sky, and GOD simply tells us what the identities are, and tells us that they are necessary truths. Provided the speaker is indeed omniscient, this would settle the ontological question, and pretty definitively deflate the ontological reading of the conceivability arguments. But it would not satisfy Levine. Levine would still be standing, asking "Why, Lord, why?" The epistemological problem persists.

We can imagine an act II. The big booming voice from the sky peals out an explanation for the various identities. One interpretation of the explanatory gap argument is that such an act II is impossible: even GOD could not explain why process squiggle-squiggle in the brain is identical with sensing green, and not red. There is some conceptual or logical impossibility associated with explaining these identities, to which even the deity would be subject. This is a very strong reading of the gap. A second, slightly weaker interpretation is Colin McGinn's. GOD could indeed boom out the explanations, but we humans could not follow them. We would invariably get muddled and confused, or find the terms impossible to understand, so that even though GOD was as clear as He could be, we could not follow His reasoning. GOD could explain the identities to Himself, but not to us. McGinn finds this prospect somehow reassuring (see McGinn 1991). It lets the fly out of his flybottle.

The arguments advanced for the gap do not support either of these two interpretations. One argument is: we believe we can imagine a case of inverted qualia, the possibility of inverted qualia would defeat a functionalist analysis of qualitative terms, there are no other viable analyses available, hence we have an explanatory gap. A second argument is: absent qualia seem to be conceivable, the possibility of absent qualia defeats a functionalist analysis, there are no other viable analyses available, hence we have an explanatory gap. Apart from the worries about showing that what seems to be conceivable really is conceivable, the main flaw in both arguments is obvious: that we currently have no analysis of qualitative terms which meshes in the appropriate way with the physical story P does not show that no such analysis is possible--or that the gap cannot be closed.

So we might ask: is the claim merely that we currently have this explanatory gap, or is it rather that this gap is permanent and inevitable?

3. The conclusion of the explanatory gap argument is that physicalist theories of mind cannot explain why particular brain states have the particular qualitative contents that they have. There is an interpretation of this claim which a physicalist can find perfectly congenial: right now we do not have an explanation. But for any phenomenon for which there is currently no explanatory gap, one can pick an historical period for which there was a gap. (As will emerge shortly, "water" and "heat" are both funny examples in this respect.) Explanatory gaps exist wherever we currently lack explanations with the structure sketched by Levine. So we have explanatory gaps about gravity, the causes of cancer, the top quark, and so on. Indeed, even the identity of water with H20 has its problematic side, in that we are not entirely sure of the composition of the quarks that compose protons.

Unless the explanatory gap is tied in some deeper way to physicalism, one might be tempted to shrug it off as nothing more than an accurate description of our current state of ignorance. The gap exists today, but this is no argument that it must exist tomorrow. Perhaps tomorrow a journal will arrive in the library with an article containing the requisite derivation.

4. An explanatory gap exists if the physical story P conjoined with available analyses A fails to imply the requisite identities. The fault may lie with either party. We may today say: we cannot see how this gap could be closed, but even this is not much of an argument that it cannot be closed. The existence of an explanatory gap is an historical phenomenon.

It is ironic that the examples cited by Kripke and Levine--water and H20, liquidity and molecular bonds, heat and molecular motion--are all ones whose explanation is remarkably recent. Locke's Essay contains some early formulations of the explanatory gap:

We are so far from knowing what figure, size or motion of parts produce a yellow Colour, a sweet Taste, or a sharp Sound, that we can by no means conceive how any size, figure, or motion of any Particles, can possibly produce in us the Idea of an Colour, Taste, or Sound whatsoever; there is no conceivable connexion betwixt the one and the other. (Book IV, ch. III, 13; all quotations are from the Nidditch edition)

And a strikingly modern version:

the Ideas of sensible secondary Qualities, which we have in our Minds, can, by us, be no way deduced from Bodily Causes, nor any correspondence or connexion be found between them and those primary Qualities which (Experience shews us) produce them in us... (Book IV, ch. III, 28)

To understand the connexion, he says, "we are fain to quit our Reason, go beyond our Ideas, and attribute it wholly to the good Pleasure of our Maker" (Bk. IV, ch. III, 6); the particular connexions are attributed to "the arbitrary Determination of that All-wise Agent, who has made them to be, and to operate as they do, in a way wholly above our weak Understandings to conceive" (Book IV, ch. III, 13). Note that this anticipates McGinn by three hundred years. But it is important to point out that Locke also thought there was an equivalent explanatory gap for water, liquidity, and solidity. As he says:

The little Bodies that compose that Fluid, we call Water, are so extremely small, that I have never heard of any one, who by a Microscope (and yet I have heard of some, that have magnified to 10,000; nay, to much above 100,000 times,) pretended to perceive their distinct Bulk, Figure, or Motion: And the Particles of Water are also so perfectly loose one from another, that the least force sensibly separates them. Nay, if we consider their perpetual motion, we must allow them to have no cohesion one with another; and yet let but a sharp cold come, and they unite, they consolidate, these little Atoms cohere, and are not, without great force, separable. He that could find the Bonds, that tie these heaps of loose little Bodies together so firmly; he that could make known the Cement, that makes them stick so fast one to another, would discover a great, and yet unknown Secret: And yet when that was done, would he be far enough from making the extension of Body (which is the cohesion of its solid parts) intelligible, till he could shew wherein consisted the union, or consolidation, of the parts of those Bonds, or of that Cement, or of the least Particle of Matter that exists. Whereby it appears that this primary and supposed obvious Quality of Body will be found, when examined, to be as incomprehensible, as any thing belonging to our Minds, and a solid extended Substance, as hard to be conceived, as a thinking immaterial one, whatever difficulties some would raise against it. (Book II, ch XXIII, 26)

The problem of understanding solidity, liquidity, and extension is described in several places, and described as equivalent to the problem of understanding how primary qualities produce sensations (see book II, ch. XXIII, 23; book II, ch. VI, 6; book IV, ch III, 14). Locke thought there was an explanatory gap both for sensations and for Water. He thought it was just as difficult to explain how particles cohere as to explain how particles produce a sensation of yellow. We might say: well, he was wrong about one of the gaps. In fact there is no barrier to explaining the Cement that holds those heaps of loose little Bodies together. But this line should shake our confidence that philosophical argument is a reliable indicator of the existence of explanatory gaps. Pronouncements of the a priori have had an embarrassing track record. We think there is an explanatory gap for sensations, but how do we know we are not in Locke's shoes?

The other response is to say: well, Locke did have an explanatory gap both for sensations and for water. At the time we lacked an analysis of the notion of water which would mesh with a suitably detailed physical story in such a way as to explain how water solidifies. But, some three centuries later, voila! the gap is closed. This line should give us grounds for optimism: even problems that seem beyond the bounds of human comprehension, like what holds ice together, might, with time and patient investigation, yield. Human experimental psychology has had barely a century to get underway. Despair seems premature.

5. One final preliminary point. The progress that occurred in the three centuries it took to close Locke's explanatory gap about water cannot be described simply as progress in physical science. Our notions of water also changed, and they had to change in certain ways to make the completed explanation possible.

Consider the schematic analysis of "water" I gave above:

water = the substance which is found in all liquids that quench our thirst; which flows as the predominant ingredient in all inland springs, streams, and rivers; which freezes into ice, condenses into clouds, and falls from the sky as rain and snow ...

Any such analysis has to betray an acquaintance with modern chemistry. The operative notion of "substance" cannot be anything other than "molecular compound." We certainly no longer think of water as elemental. But it took a remarkable feat of imagination to conceive of water as a compound which could be converted into two gases, and back again into a liquid.

Even the notion that liquid water, ice, and steam are all the same stuff--differing only in the amount of kinetic energy--is remarkably recent. There is, for example, a passage in Locke's Essay in which he intimates that water and ice are members of different species. (Endnote 3.) The caloric theory of heat was still alive and kicking even in the 1850's. On its terms steam differs chemically from water--it has more caloric in it. It is not a crazy idea. The change in the properties of water as it boils or freezes are, after all, quite similar to changes that are chemical. Recall that Lavoisier's 1787 textbook of chemistry listed heat as the second element (after light). The analysis given above of the notion of "water" could only become current after the caloric theory was finally abandoned. We needed a notion of "substance" under which water and steam could be described as exactly the same substance. This in turn required a notion of energy (and the transformation and conservation of energy) that is really quite recent. Our great grandparents could have known some of the disputants.

So perhaps there is a sense in which Locke's notion of water--or even Lavoisier's--had an explanatory gap, and it was one that could never be closed, because that notion could never be rectified with the emerging physical story. It embodied concepts of substance and energy that were just wrong. Here the reasonable response was not to berate the physical sciences for failing to mesh with our notions in such a way as to render reality comprehensible; rather it was to change those very notions. The earlier game looked unwinnable, so we changed the definition of success. Prior explananda were simply abandoned. And this was the reasonable thing to do. I suggest that there might be elements of the pre-theoretic notion of qualia that could suffer a similar fate. We should not mourn their passing, any more than we should mourn the passing of medieval notions of substance.


So how will the explanatory gap be closed?

I think the first step is one that vision science has already made. Forego the frontal assault on particular, singular qualities, and focus attention instead on the relationships of qualitative identity and qualitative similarity. Studies in color vision do not proceed by studying the conditions under which some solitary stimulus presents red; rather the focus is almost always: what are the conditions under which one stimulus matches another? Under what conditions does Joe find two stimuli to be indiscriminable? What explains his judgements of the relative similarities among qualities? These are all cognate notions. They all describe relations between qualities.

One attraction of these two termed relations is that they are physicalistically tractable. Take the notion of indiscriminability, which is probably the strictest of the lot. It indicates an absolute inability to pick up any difference between two stimuli. The notion is potent because quite often we can explain its application in terms of the physical effects of stimuli on transducers. For example, we might have a split field experiment. In one half of the field is light all of the wavelength 589 nm. In the other half is a mixture of two wavelengths, 535 and 670. (These are the wavelengths used in the Nagel anomaloscope. See Hurvich 1981, p. 227.) Perhaps the mixture was initially selected by Joe, who adjusted the relative intensities of the two wavelengths until the apparent chromatic border across his visual field disappeared. I want to insist on two points. First, what Joe is matching are the qualities presented by the stimuli, not the stimuli. That is, the stimuli differ physically, but to him in his state of adaptation they present the same color. Second, we can often explain why the qualities presented by those physically disparate stimuli match in terms of the physical effects of those stimuli on transducers. Joe has three different classes of cones in his retina, and the combination of wavelengths x + y effects each of those three classes of cone in exactly the same way as the single 589 nm wavelength. We have found a pair of metamers. Their study is the royal road to understanding color vision.

Often we can give explanations free of gaps for facts of the form: Joe finds stimulus x to be indiscriminable from y. Once his actual physical structure is granted, then we can explain why Joe cannot discriminate 589 nm light from a mixture of 535 and 670, appropriately adjusted. The bundle of wavelengths affects his retina in exactly the same way as the monochromatic light, so no difference between the two can be detected. Furthermore, with the addition of a "conceptual analysis" of the notion of qualitative identity, (see Clark 1993 ch. 3.) I think we can go on to give a bottom up necessitation for the claim that Joe will find the two to be qualitatively identical. Particular qualitative contents--that Joe sees 589 as yellow--may be problematic, but I assume that indiscriminability and qualitative similarities can be given the appropriate sorts of explanation. We can explain why Joe sees this the same way that he sees that.

Much of color science can be summarized under this heading: describe the conditions under which stimuli match, are indiscriminable, or are qualitatively similar. If we know the precise absorption spectra for the cones found in Joe's retina, predictions of color mixing and matching can be quantified. They can be applied to broad-band stimuli and mixtures of many wavelengths. We can predict how those matches will change if the background illumination is shifted in wavelength, if it is shifted in intensity, if Joe adapts, or if his body temperature changes. We can explain why color anomalous individuals make slightly different matches than Joe, and why dichromats make radically different matches. We can give viable gap-free accounts of contrast effects, hue constancy, brightness constancy, the effects of illumination changes on hue matches, and simultaneous contrast effects. None of this seems problematic; we just detail conditions under which the qualities presented by two stimuli match, and never try to identify exactly what the quality is.

A natural extrapolation is that the time will come when we can give satisfying explanations detailing all those conditions under which Joe's experience of stimulus x is qualitatively identical to his experience of stimulus y. (We can do this for some stimulus domains and some conditions already.) We detail the relations of qualitative identity but do not mention what the particular qualities are.

Here now is the defining question: if we can explain all that, will there be anything left to explain about qualia? I believe--and will argue that--the answer to that question is "no", and that any appearance to the contrary is a sophisticated illusion. If you have a precise grasp on qualitative identity, then you have grasped qualia. Part of this claim is trivial: once you have defined the relation of qualitative identity, then particular qualia can be extracted as equivalence classes, a la Frege. But part of the claim is more substantive: that this domain is not a heterogeneous unstructured hodge podge of monadic properties (or simple ideas), but is rather structured by those relations of qualitative similarity.

Here is one way to unearth that structure. The relations of indiscriminability and of matching are non-transitive. That is, you may find stimuli x and y indiscriminable, and find stimuli y and z indiscriminable, yet somehow manage to discriminate between x and z. The pair x and y then cannot present you with the same qualia (even though you find them indiscriminable) since x can be discriminated from something that y cannot. To assure qualitative identity, we need something stronger than indiscriminability, namely global indiscriminability. For stimuli x and y to present the same quale, there must be no item z discriminable from one but not the other.

Whatever similarity relation you choose, its non-transitivity allows us to place qualia in an order. We can construct a map whose guiding principle is that qualia that are more similar to one another are to be placed closer to one another than those that are less similar. With our three items x, y, z, we can deduce immediately that the qualia presented by y must be placed between those of x and z, since y is indiscriminable from both x and z, but those two are discriminable from one another. In Carnapian terms, the overlapping of similarity circles yields an ordering relation. Or perhaps you are willing to plonk immediately for a triadic predicate: x is more similar to y than to z. With it we can briskly generate an ordering of qualities. That x is more similar to y than to z immediately places x closer to y than x is to z. A few such judgements (eg, is y also more similar to x than to z?) and the ordering of qualities is soon constrained to a unique solution (for details see Clark 1993, ch. 4.)

The resulting "quality space" represents the relative similarities among the qualities presented by stimuli. Typically we represent those similarities spatially, so that qualities more similar to one another are closer than qualities that are less similar. Fortunately, and not fortuitously, the sensory domain in which the ordering is best understood is human color vision. Even in a restricted stimulus domain such as surface colors (presented in controlled illumination in a 2 degree foveal field), we require three dimensions of variation if we are to place colors in an order such that nearer ones are always more similar than ones further apart. Two dimensions are required for the familiar hue circle. Hue is the angular coordinate, saturation the radius. Hues are minimally saturated (or closed to achromatic) at the center of the "circle", and maximally saturated at the periphery. These hue planes are stacked one on top the other in terms of their varying brightness, from black to white.

Quality space is one way to detail the structure of a sensory modality. One can imagine this changing minutely as one ages, but by and large these structural facts endure over time, are true of all humans with normal sensory capacities, and are given innately. An example of the sort of structural fact I have in mind is that orange is between red and yellow. That is true of any human trichromat, is not affected by learning or by aging, and is presumably due to the way that humans are innately constituted to sense colors. As Quine put it:

Without some such prior spacing of qualities, we could never acquire a habit; all stimuli would be equally alike and equally different. These spacings of qualities, on the part of men and other animals, can be explored and mapped in the laboratory by experiments in conditioning and extinction. Needed as they are for all learning, these distinctive spacings cannot themselves all be learned; some must be innate. . . . it can be said equally of other animals that they have an innate standard of similarity too. It is part of our animal birthright. (Quine 1969, p. 123)

Indeed, one can detail the structure of qualities in other sensory modalities and in other animals. We should be prepared for some surprises. What members of species x innately sense as relatively similar, members of species y may readily discriminate. Different species have visual quality spaces that have a very different structure--even a different number of dimensions--than do humans (see Thompson, E., Palacios, A., and Varela, F., 1992). If we consider modalities that humans do not share--such as echolocation or electroreception--we will find orders that seem even more alien.

Consider the fact that orange is between red and yellow. I am not sure how to characterize this fact. It is not a straightforward physical fact. Nor is it a fact about causal or functional roles. Call it a fact of "qualitative structure". It is facts of this sort that will link the physical story P to the appearances presented to Joe.

The sense of similarity that structures the human visual quality space is presumably innate. Hence facts about the structure of quality space are not derived from conventions. They do not derive from the meanings of our words; we could not alter them by altering our speech habits. These structural facts include all the ones that Wittgenstein struggled over in Remarks on Colour; just as orange is between red and yellow, so, if we understood human color quality space sufficiently, we could see why there cannot be a transparent white or a luminous gray. But these facts do not derive from grammar; they derive from the operations of our sensory systems, specifically from the innate possibilities for resemblance or difference provided by those systems.

I hope that to this point developments have seemed relatively unproblematic, and that they have not begged any questions. Now comes the tricky part. I think the problem of the explanatory gap arises in part from myopia, from focusing exclusively on particular identities. Suppose we are trying to explain why process squiggle-squiggle in the visual system is identical with the process of sensing greenly. Viewed locally, this identity does indeed seem arbitrary. There is nothing particular about process squiggle-squiggle, or about neural processes that are similar to squiggle-squiggle, or about sensing greenly, or about hues similar to green, which explains why sensing greenly should be identical with process squiggle-squiggle, instead of some other squoggle-squoggle. These identities cannot be justified or explained in local terms, or one by one. Viewed in that fashion each particular identity seems utterly arbitrary.

But although there seem to be no individual necessities--no particular necessity in attaching this quale to that neural process--given the structure of our quality space, there is only one way that the two can fit together. If you had full knowledge of the opponent processes--of Joe's Y-B, R-G, and Wh-Bl systems--and of the phenomenal structure of color quality space, then you would see that there is only one possible mapping. Outputs from the Y-B system could not be associated with red or green. It is not a matter of these two classes of phenomena being "stuck together" in an arbitrary way. Given their structures, they could only fit together in one way. With enough knowledge of the structure of color quality space, you could deduce the labels to be attached to the chromatic response functions.

Why think the color space can be mapped in only one way onto the nervous system? Since it is a biological product, it would be remarkable if the space had the structure of a perfect sphere (or of any of the Platonic solids). That is to say, it seems overwhelmingly likely that the color quality space is asymmetrical. It is a lumpy, anisotropic, asymmetrical ovoid. These asymmetries give the clues needed to hook the structure up with neural hardware.

Human color quality space is not isotropic; in some parts of the spectrum it is much easier to discriminate wavelength differences than in other parts (see Boynton 1979, pp 256, 281; Hurvich 1981, p. 296). So using physical coordinates the space will vary in "density". We go on to ask: why do surface color qualities have this structure? Why are the qualities presented to sense similar to one another in just this way, and not some other way? In asking this question we are really asking how it is that we actually go about making the discriminations and sensing the similarities that order the qualities as they are ordered (see Clark 1993, section 5.6). Presumably there is something in us--more particularly, in our nervous systems--whose operations account for those discriminations. When they are found and described those operations will account for the similarities in question. We hunt for the actual axes in terms of which discriminations are made.

The only viable theory around is those axes correspond to opponent processes: red-green, yellow-blue, and white-black. These three opponent processes generate the three dimensions of variation found in the human color order system. Furthermore, once we know enough about the structure of color qualities and about the opponent processes, we can deduce that the R-G opponent process could only be the axis which runs through color space from red to green.

For example, given the difficulties in finding any biologically viable photo-sensitive pigments--much less three different ones, with differing peak sensitivities--one of them turns out to be much less sensitive than the other two. Outputs of the short wavelength cones are perhaps a tenth as vigorous as the others (see Boynton 1979, p 153). Given this, and given the linkages from receptors to opponent processes, slight variations in the density of middle wavelength cones can have a proportionally greater effect on qualitative similarities. The genes coding the mid-wavelength photopigment hence turn out to be critical. Perhaps one kind of color anomaly or color blindness is more likely than other kinds. Perhaps it is a sex-linked trait, so that males are more likely than females to get it. (In fact, of course, all these are the case!) (Endnote 4.)

So the link from the physical story P to occupant statements O will proceed, not via an analysis of our concepts, but rather via a detailing of the structure of quality space, Q:

  1. The structure of qualities presented by stimuli is not a Platonic solid, but is asymmetric, anisotropic, and of varying densities.
  2. Givn these asymmetries, there is only one neural model for Q. Q cannot be mapped onto visual processing in two equally successful ways.

The asymmetry in the quality space is not at all apparent to introspection or causal observation. Nor is it revealed by any analysis of our color terms or by reflection on the meaning of "red". That does not matter; we just need a derivation of the identity. It need not be one that is introspectively obvious, anymore than the identity of heat with molecular energy is introspectively obvious.

We can explain why particular identities seem so arbitrary--as if the two phenomena are just arbitrarily stuck together. If one examines a particular identity in local terms, it is arbitrary. There is nothing in the concept of red or in the neighborhood of red, or in squiggle-squiggle or neural processes similar to squiggle-squiggle, which serves to explain the identity of sensing redly with process squiggle-squiggle. It can only be justified in global terms. It is only the overall fit of the structure of similarities to neural mechanisms of discrimination which justifies the particular identities. Indeed sensing redly may well have been process squoggle-squoggle if there had been compensatory adjustments elsewhere in the nervous system. One could imagine a nervous system in which sensing redly is subserved by squoggle-squoggle. (This would take large scale changes in lots of places--basically a redesign, from cones upward--but it is conceivable.) To do this we would need to change the physical story P, and the need for such a change demonstrates that the gap has been closed.


The tricky part of the argument is to show that there is just one way to map the structure of our quality space onto processes in the nervous system. It might be useful to elaborate how this mapping takes place.

I said above the human color quality space for surface colors has three dimensions, typically coordinatized as hue, saturation, and brightness. The number of dimensions of a quality space is simply the number of independent variables needed to describe an observer's abilities to discriminate. If we simply try to catalog human discriminatory abilities in the domain of surface colors, we find we need three dimensions to describe the data. Any explanatory model of these abilities must posit internal states that vary in at least three dimensions.

When we turn to the nervous system we are looking for those axes along which the system actually makes its discriminations. It is just a datum that we can discriminate one stimulus from another, but then we can go on to ask: how do we manage to make this discrimination? What differences are actually picked up and employed to differentiate the two? There are various ways in which the points in a lumpy lop-sided ovoid could be distinguished one from another. One system might use precisely the coordinate scheme we use for our color order systems: polar coordinates for hue and saturation (with hue as the angular component, and saturation as radii), and a vertical dimension for brightness. One would need to find some neural mechanism which yields angles around the hue circle, and another which yields radii.

Such a mapping of quality space to neural mechanisms is quite implausible. It would require some system which responds purely to hue, independently of saturation and lightness; and another which responds purely to saturation, independently of hue and lightness. It is hard to imagine a biophysical system responding to saturation independently of hue.

We need some other way of registering three dimensions of variation so as to yield the structure of qualities presented by surface stimuli. The raw materials are not promising: we have three photosensitive pigments, which differ only in the wavelengths to which each is optimally sensitive. The output of any receptor to any particular wavelength can be reproduced by other wavelengths, simply by adjusting intensity appropriately. So any one of the three kinds of cone can be "fooled" by stimuli of differing wavelengths. The solution is elegant: generate outputs from all three kinds of cone, and then compare the results. These comparison processes are a matter of adding or subtracting signals of one type of cone from those of another. They give us the so called "opponent processes". The best available theory is that the visual system encodes differences among stimuli in three opponent processes, which I will label R-G, Y-B, and Wh-Bl. These yield the three axes in terms of which the visual system actually makes the discriminations among surface colors.

Now how do we associate processes R-G, Y-B, and Wh-Bl with the color quality space? Wh-Bl is the simplest: it adds outputs from all three cones, and is quiescent in the dark. We can derive the identity

outputs from the Wh-Bl channel = the properties upon which discriminations of brightness depend.

That is, the Wh-Bl channel provides the differences which the visual system actually uses in order to detect differences in brightness. Change the Wh-Bl outputs and you will change how bright a stimulus appears to be. This identification seems unproblematic: If it is too dark, you can not see anything. No discriminations are possible. Unlike particular color names, darkness can be analyzed in terms of causal role, and there is no particular problem finding the states that play that role in the visual system.

The other opponent processes do not correspond to our mathematically pristine "hue" or "saturation" but instead yield non-orthogonal axes running from red to green and from yellow to blue respectively. We need to derive identities of the form

activity above baseline in the R-G channel with baseline activity in the Y-B channel = sensing unitary red.

Why is this activity associated with sensing that quality? Why is it not rather associated with sensing unitary green?

I think we can answer that question, but not in local terms. That is, there is nothing about red in isolation or about the neural processes R-G per se that explains why unitary activity in channel R-G yields unitary red. Instead the identity is explicable only as part of a global package. We need a mapping of one structure onto another, and in this particular neighborhood, that is how the map fits. For example, as mentioned above, the axes defined by the unitary hues are not orthogonal to one another. Some unitary hues are more similar to one another than others. Intuitively, yellow and green are more similar to one another than are yellow and red. This constrains possible mappings to two.

We add other constraints. In moonlight we are all monochromats, but as rosy fingered dawn approaches, reds and greens become visible first, followed by yellows and blues. (Endnote 5.) The red-green process has a lower threshold than does the yellow-blue process (see Hurvich 1981, p. 72). Hence at the dark end of the color ovoid, hues start bumping out in the red and green directions before much happens in the way of yellow or blue. We can note other asymmetries. Some hues can become more saturated--less similar to white--than others. The most saturated yellow still seems more similar to white than does the most saturated red. (If saturation is a radius, the most saturated red will be further away from the achromatic center of the hue "circle" than will be the most saturated yellow.) Furthermore, hue discriminations differ tremendously in different parts of the spectrum. The "density" of discriminable points is higher in some places than others. The "color solid" is not a Platonic solid. It is a lumpy product of our biology. (Endnote 6.)

We turn to the neurophysiology of opponent processes, and find first that some photopigments work better than others, and respond betters to changes in wavelength than others. None of the response curves are not perfect bell-shaped curves. The optimal points are not spread uniformly over the visible spectrum (see Boynton 1979, p. 153). Subtract or add their products and you will not find an isotropic continuum, but rather just the sort of noisy, asymmetrical, anisotropic outputs that could yield a lumpy asymmetrical color solid. The lumps can only line up in one way. Given our visual system as it is, and given the structure of color qualities as it is, there is only one way to line up outputs of the visual system so as to produce that structure. We find a unique instantiation. This is completely analogous to finding just one physical process that could serve as heat in our tableau: namely the motion of molecules.

It might be handy to formalize the argument. The qualities in a quality space are ordered by relations of relative similarity. The resulting structure specifies distance and betweenness relations, so that qualities closer to one another are always more similar than qualities further apart. In color quality space we will also get relations such as matching and mixing of colors. Orange is "between" red and yellow because it has red and yellow "components". Complements are hues which when mixed yield white, so the relation of complementarity will also drop out as a consequence of the quality space for colors.

If we are pick out the reference of "green" using the resources available in the quality space, we can mention all and only these relations. So for example we might have

Unitary hues can be defined: they are the ones that are mixtures of no hues but themselves. To abbreviate

Ux: x is unitary
xMyz: x is a mixture of y and z
xCy: x is the complement of y
xSyz: x is more similar to y than to z

The "analysis" phase for green generates a pure structural description of the relations of green to yellow, red, and other qualities:

We then apply the same strategy to all the hue names in the analysans. We are left with a pure structure description, of almost unimaginable complexity. (Endnote 7.) All of the color terms vanish from the analysis, leaving something like

Note that this is a structural definite description. Given the asymmetry in the color quality space, this structural description is true of just one place in the order. For example, green and yellow are the two unique hues that are relatively most similar to one another. This fact about their relative similarity yields a landmark that can help to identify green and yellow relationally. But that structural fact is hidden from view; it is not introspectively obvious.

This "analysis" is not an a priori conceptual analysis. We are not analyzing the meaning of the word "green". Rather the description is based on an empirical investigation of the real nature of the referents of our speech. This is the approach of a "psycho-functionalist" about qualia instead of an "analytical functionalist" (see Block 1978). Insofar as people are talking about something real when they talk about their sensations, they are talking about states which will be described in more detail by empirical psychology. Those states will wind up as referents of the theoretical terms of models of discrimination. The "analysis" above is a product of such as description. I think it is true of qualia, and it reveals much of their real nature, but it is not true in virtue of the meaning of our words.

It is logically possible that we could have had a symmetric quality space, and in such a world the assignment of colors to stimulus classes would not be constrained as it is in our world. There is no necessity attaching to the fact that yellow and green are, among the unique hues, the two that are relatively most similar. But remember the rules of the game: we do not need to establish the necessity of any claim in the deduction, but merely that given the facts as they are, the conclusion follows logically from the premises.

Next we give the "physical" story of stimuli impinging on three types of cones, outputs being added and subtracted from one another, opponent processes, and so. We describe the structure of discriminations, but no color terms are allowed. The account can include all the facts about what matches what, how mixtures match, which wavelengths can be mixed to yield a target, and so on. We might identify a region P in the structure with a pure structure description of the form

Furthermore, we can identify processes in the nervous system in terms of this structure description. Given our nervous systems as they are, there is only one way that the discriminations and similarities mentioned in (A) can actually be mapped onto them. We get something of the form

But then given the actual asymmetry of the color solid, we can derive an identity. Instantiating a sensory state which is in the appropriate place in the order of brightnesses, the order of hues, and the order of saturations is just the process of sensing greenly. We get

which yields

So "green" can be attached to neural processes in just one way. Given the ordering of color qualities, there is only one area in it that could be green. This is exactly analogous to Levine's description of heat or liquidity: given the way the physical world actually is, you can see that molecular motion has to be heat, or that such and such a molecular characteristic has to be liquidity.

Now of course there is a sense in which the mug could have presented a different color; it could have looked red to Joe, not green. And there is a sense in which he could have had a visual system which works in the appropriately different way. He also could have had a symmetrical quality space. But this possibility does re-open the explanatory gap. Necessity does not attach--and need not attach--to any particular premise in the explanation. We do not say that heat has to be molecular motion. (Endnote 8.) In some possible world, heat might have been caloric. (Endnote 9.) Similarly, in other possible worlds, green might have been subserved by process R instead of by process G. But to make such a change we would also need to change the physical story. In our world process G is the only place for green. We should not confuse the lack of necessitation for our structure for a lack of necessitation of identities, given that structure. Given (A) and the actual structure of the color solid, process G has to be the process of sensing something green.


A few concluding comments need to be made about the account I have proposed. It differs a bit from the bill of requirements that Levine laid out, and the differences might be important. If he insists on all the particulars of those requirements, this route to a solution fails, and I would agree with Levine that it is hard to see how the explanatory gap could be closed.

The big difference is that I propose that we replace the analysis of color concepts with a detailing of the structure of qualitative similarities among the colors. Quality space replaces the analysis of concepts. Recall that "stage 1" of Levine's solution to the explanatory gap is to pursue the "quasi" or "relatively" a priori process of analysis of concepts. To the physical story P we are to add only claims that are relatively unproblematic, conventional, or of the sort once thought to be analytic, so that deductions from P using those added premises confer a sense of "necessitation".

The problem is to generate some explanation of the identities. Levine naturally supposes that this is to be done by analysing concepts. We analyse the concept "water" to the point where we can see how, given the way things are, it must be H20 that is water. From the analysis and statements of atomic theory we can derive identities, hence explain them.

This strategy seems quite unlikely to succeed with color terms. There just does not seem to be enough of a conceptual "stuffing" for a term like "red" that mere conceptual analysis and neurophysiology combined will allow us to see "ah, squiggle-squiggle in the brain must be a redly-sensing". It is hard to see how analysis of our concepts would enable us to differentiate the squiggle-squiggles that are redly-sensings from the squoggle-squoggles that are greenly-sensings.

But there is another way of "linking technicolor phenomenology to soggy grey matter" (see McGinn 1991). We focus on relations of qualitative similarity, and construct an entire "quality space" for colors, using those relations. The study of similarity relationships and the quality space replaces the analysis of concepts. It does not yield analytic truths or truths justified by analysis of the meaning of our words. (If that is the only style of solution that is acceptable, then I agree that the problem remains intractable.)

The account still confers an element of necessitation, but it does not arise from analytic truths or from necessary truths about our concepts. Instead it is of the form: given the way the human visual system is constituted, we are born with certain standards of visual qualitative similarity. As a consequence of that heritage, orange must be between red and yellow. For this to be false for us, we would need to be equipped with a totally different structure of qualitative similarities, which in turn would require a new sensory system. This account replaces the necessary truths yielded by analysis of concepts with qualitative similarities yielded the operation of our visual system.

There are two implications of this shift. One is that it gives us a new model for how qualitative terms might function--of how they manage to latch onto an extension. The old model is that we learn some analyzable reference-determining concept of "red", and then can apply the term to just those things which satisfy the concept. It turns out to be difficult to analyse what that concept is; behavioral, physical, and functional analyses all go off the tracks in various counterfactual situations, yielding faulty verdicts as to what is or is not red. If there is a concept of "red qualitative contents", it seems to be a metaphysically elusive, subjective, funny kind of concept. I suggest that color terms latch onto an extension in a different way. If we have an innate sense of qualitative similarity, shared across speakers and across generations, then we can pick out the extension of "red" quite simply by pointing to a few exemplars---a few objects acknowledged to present a red qualitative content--and saying "red things are whatever present an appearance similar to the one presented by that." As long as we have a determinate application of the standards of qualitative similarity, this works, even across the weird counterfactual situations of inverted qualia.

To fix the extension of qualitative terms we require a determinate application of a sense of qualitative similarity, and we require an indexical. Call this an "indexical" account of how qualitative terms attach to an extension. It has some similarities with a "natural kind" analysis of terms such as "gold" or "lemon". Recall that Putnam and Kripke deny that we can provide "Lockean definitions" for terms such as "gold" or "lemon", but rely instead on two things: a notion of theoretical similarity (sameT) and ostension to paradigms. The term "gold" is attached to an extension as follows: we ostend some paradigms, and say gold is whatever is the sameT as that stuff there.

A very similar maneuver works for our qualitative terms, except that instead of relying on some theoretical notion of similarity--some notion whose unpacking requires extended empirical investigation--we can use one that is built-in. The constitution of the sense modality provides standards of qualitative similarity. Add ostension to some paradigms, and the extension of "red" ceases to be problematic.

The second implication of this approach is a bit speculative: perhaps qualitative terms simply lack reference-determining intensions, and rely essentially on indexicals. Bluntly, perhaps we have no concept "red"; perhaps there is no concept "red". What I mean by this is that there is no analyzable intension learned when we learn the term "red" which suffices to determine its extension. Instead we have innate abilities to determine similarities in color, and a selection of historically ostended paradigms. That is all we need, and I suggest that there is nothing more there.

We feel an explanatory gap because we feel we ought to have an analysis of the concept which suffices to explain why this particular physical state is identical with sensing redly. Perhaps we are feeling, not the lack of an analysis for this particularly elusive and troublesome concept, but rather the fact that there is no concept there to be analyzed.

Qualitative terms apply in a determinate way just so long as we find determinate application of a shared sense of qualitative similarity. Someone in whom the operation of those innate standards is somehow blocked--as in a dichromat, or poor Mary--cannot gain our skill in applying the term "red" to all and only red things. It seems implausible to think that dictating any sort of conceptual analysis could confer this skill. They are unanalyzable not because the concepts are metaphysically elusive, but rather because there is no concept there at all. The terms work in a different way. This idea lets the fly out of my flybottle.

If you accept any part of the Putnam-Kripke account of "natural kind" terms such as "gold" or "lemon" then you have accepted the possibility that some terms might function without reference determining concepts. If you think we cannot give Lockean definitions for these terms, then you have accepted what I mean by saying that those terms lack reference-determining concepts. They function in a different way.

The indexical account for qualitative terms shows how terms could function without reference-determining concepts at hand. Terms for qualia do not have much conceptual stuffing; they rub up against stimuli in a more direct and brutish fashion. These are, after all, raw feels. To figure out how terms for them function, we might need to do something other than classical analysis.

The indexical view provides an answer to one obvious objection, which runs as follows. While the structure of our color qualities may in fact be asymmetrical, it seems quite unlikely that that fact is reflected in the meanings of our words. It may be, for example, that reds and greens stay brightest longest as the lights dim, or that red is the hue that can become the most saturated, but it seems quite unlikely that these relational facts are part of the meaning of the terms "yellow", "green", or "red". But to the physical story P we are allowed to justify identities only by adding an analysis of our concepts. If the asymmetry of color quality space is not reflected in the meanings of our concepts, then adding the analysis to the physical story P will not suffice uniquely to identify yellow, green or red.

In an odd way I agree with this objection. I do not think we have concepts of "yellow", "green", or "red" which suffice to determine their extension. But this is not because they are somehow peculiar qualitative or subjective concepts which elude analysis; rather it is because there are no concepts there to be analysed at all. The terms function in a different way.

The structure of color quality is not learned, but innate. It is not determined by our concepts. Although our concepts reflect that spacing, they do not yield its entirety. The quality space could not be derived purely by conceptual analysis. Furthermore, much of the structure of the modality fails to be reflected in our concepts. It is (probably) no part of our concepts of purple and blue-green that we are much weaker discriminating among purples than among bluish greens. Is it part of our concept of yellow or red that a saturated red is more saturated than a saturated yellow? I doubt it. But if we allow the delineation of a quality space to replace the analysis of concepts, this is no problem.

Instead of giving analytically true necessary and sufficient conditions--conditions which need to be stated using other predicates--we need to describe how the terms rub up against some stimuli and not others. Instead of a semantic account we need something closer to a mechanical account. These after all are the only psychological states whose causes are exclusively non-psychological. They are triggered by physical events outside the skin. Figure out how the trigger works, and you will have figured out how the term works.

Now Levine might actually require a classic "analysis" as part of any explanation which closes an explanatory gap. That is, perhaps it is essential to his project that to the physical story P all we add are "analytic truths" about our terms. Otherwise the explanations may lack the element of "epistemological necessitation" that Levine seeks.

If so, then I agree with Levine: there is an explanatory gap, and I am very skeptical that it could ever be closed. I do not think this because I think the concepts that underlie our qualitative terms are metaphysically elusive and refined; rather it is because our raw feels are brutish, and lack conceptual refinement altogether.


1. This isn't really true. We are talking statistical mechanics, after all, so for a particular pot of water there is small but non-zero probability that it will fail to boil at 212 degrees. The theory does not imply that a particular pot of water will boil at a particular temperature. We need to talk about averages of pots of water--but then a similar thought experiment could be run on those averages. (Back)

2. This is why, as I alleged above, the eventual identity "water = H20" will be merely contingent. It might be necessary if both terms were rigid designators, but according to Levine's analysis the term "water" functions more like a description. The identity states the merely contingent truth that in this world it is H20 that satisfies such and such a causal role. (Back)

3. "If I should ask any one, whether Ice and Water were two distinct Species of Things, I doubt not but I should be answered in the affirmative; And it cannot be denied, but he that says they are two distinct Species, is in the right." (Book III, ch. IV, 13). But Locke held that Species were purely nominal, and did not necessarily reflect the "real internal Constitution" of things. (Back)

4. Red-green color anomalies are sex-linked and are much more common that yellow-blue ones. See Hurvich 1981, ch. 17; Boynton 1979, ch. 10. (Back)

5. This is the "Bezold-Bruecke phenomenon". The apparent brightness of hues changes as illumination changes. Although red may be the first visible hue, yellow things are soon visible and many will eventually surpass the red items in apparent brightness. The yellow-blue process requires more illumination to get going in the morning, but then accelerates more quickly. (Back)

6. Two other asymmetries are worth noting. The first is that hues presented by a given package of wavelengths typically shift as the light increases, but there are exceptions, provided solely by unitary hues. See Hurvich 1981, p. 73. The combination of curved and straight hue contours at different illuminations provides an asymmetry. Second, red-green and yellow-blue processes are not equally or symmetrically distributed across the retina. They are correlated with size. Yellow-blue discriminations fail for very small objects, even though others of the size can be seen as red or green. This is called "small field tritanopia". See Hurvich 1981, pp. 21, 162. (Back)

7. The maneuver here is similar to "Ramsifying" a theory and removing all of its theoretical terms in one swoop. Here though the relations among these terms are not straightforward causal/functional relations, but relations of qualitative similarity. See Lewis 1970, 1972; Block 1978. (Back)

8. I am here agreeing with Levine that "heat" can receive some sort of causal/functional analysis, and that in other worlds "heat" names whatever satisfies that analysis. This makes it a non-rigid designator. (Back)

9. At least there is no conceptual incoherence to the supposition. It seems conceivable that in some possible world the superficial macro properties by which we identify heat are subserved by caloric and not molecular kinetic energy. This world would differ physically from own, in ways some of which would be observable. It is certainly inconsistent with the physical story P for our world. There might be some sense in which it is not physically possible. (Back)


The explanation of the uniqueness of the mapping needs more work. We need to derive identities of the form

sensations of red = brain process b

or if we are talking about sensations of a particular shade R,

sensations of R = brain process b.

Even better: we need to derive whatever "bridge principles" connect the vocabulary of qualitative terms to a neurophysiological vocabulary. These may not be type-type identities, but whatever principles suffice to give a neurophysiological explanation of color perception.

The key idea is that the structure needed to do this is not found directly in particular individuating causal roles. Sensations of red do not seem to be associated with any particular causal niche. Instead sensations of red are associated with a particular qualitative niche. This coheres with the idea that qualitative terms, to the extent that they can be defined, can only be defined by their relations to one another. No stimuli can be mentioned. Sensations of red are picked out by their relations to sensations of green, sensations of yellow, etc; not (directly) by a particular unique causal role.

Step 1. Using relations of matching, indiscriminability, and relative similarity, construct an ordering of stimulus classes: a quality space. A stimulus is an instance, a presentation; the terms of the matching relation are such stimuli. Indiscriminability however requires an assessment over repeated trials, and its terms are hence classes of stimuli. All the members of such a class M match one another and are mutually indiscriminable. In a very strict sense they all "look the same"; they might all look red, for instance.

One can label a point in quality space with such a class, but one cannot define a place in the ordering of qualities with any such finite listing. Physically the same stimuli might under other conditions of adaptation present a different quality. And whatever class of stimuli one uses to tag a place in the ordering is not extensible or projectible in any easy way: it will include a motley bunch of metamers, for instance.

Step 2. Treat each point in quality space as a singular phenomenal property: a property of appearance. It is the property that all the stimuli in class M present. They all look a particular shade of red, R, say. The physically hodge podge class M of stimuli all cause sensations of the same red R.

A place in quality space is best construed as a particular sensory quality, one that every member of the class M of stimuli presents. It is a phenomenal property; the property that all the sensations caused by those stimuli are sensations of. Relations of indiscriminability, relative similarity, mixing, matching, complementarity, etc which obtain among places in the ordering of qualities are relations among these qualities.

Now we cannot use any particular stimulus to identify the property, since physically the same stimulus might present different qualities at different times. So this is where we have to use a structure description to identify the particular quality that all those stimuli present. The "niche" for this particular red R is identified by relational facts of the form "the quality which stands in such and such relations to other qualities." For example, red is the complement of green, the quality that must be added to yellow to get orange, the quality more similar to purple than to blue, and so on.

Red(x) º (x C green) & (x M yellow orange) & (x S purple blue)...

Here the variable is ranging over places in the ordering of qualities. We can Ramsify the entire relational structure. We would get something like

($x1)($x2)... ($xn)( x1Cx2 & x1Mx3x4 & x1Rx5x6 & ...)

To simplify the presentation a bit, we can abbreviate the string of initial qualifiers as a vector


Then a "Ramsey correlate" for a particular quality might be

R(y) º ($x)(( x1Cx2 & x1Mx3x4 & x1Rx5x6 & ...) & X1y)

Interestingly, only such structure descriptions generalize across people and across viewing situations. There is no stimulus that looks unitary green to everybody, but for everybody (who is not color blind) there is some stimulus that looks unitary green; and that in virtue it looks unitary green is that it satisfies a structural definite description of the form given above.

Step 3. Make the tiny step from phenomenal properties to qualia. The idea is that distinct phenomenal properties require distinct qualitative characteristics: distinct properties of sensation. The step depends on an account of the notion of qualitative identity.

The stimuli in class M all look the same; each causes a sensation of exactly the same red. Now

a sensation of x is qualitatively identical to a sensation of y º x presents exactly the same qualities as y.

So from the latter we can get to the former. Or it can be put this way: the qualitative character of a sensation is that in virtue of which the stimulus presents the appearance that it does. Since all the stimuli in class M present the same appearance, the sensations they cause are qualitatively identical to one another. In any case this is the move that gets us from the properties that stimuli appear to have to talking the qualitative properties of sensation.

So suppose y is the same place as before in the quality space. Now that place identities a particular qualitative character of sensation: it is the qualitative character that any visual sensation has when it is a sensation of that particular red.

Q = the property of sensations in virtue of which they are all sensations of R

And our Ramsey functional correlate can be used to identify this particular qualitative character of sensation:

Q(y) º ($x) (( x1Cx2 & x1Mx3x4 & x1Rx5x6 & ...) & X1y )

Here we are identifying a particular qualitative character that various sensations can have. It is the particular qualitative character in virtue of which they are all sensations of that same shade of red. So we have gotten to the point where we are talking about the qualitative character of sensations of red R, as needed in the identity.

Step 4. Find the unique neurophysiological realizations. It turns out that the structure just detailed is anisotropic, asymmetric, has bumps and irregularities. So if it has a neural realization at all, it will be a unique realization

($!x)( x1Cx2 & x1Mx3x4 & x1Rx5x6 & ...)

And suppose eventually we find brain states b1, b2, bn such that

b1Cb2 & b1Mb3b4 & b1Rb5b6 & ...

But then, as in Lewis, we could derive the connection between Q and the corresponding brain process. Since we would have established a unique realization, we would have

Q(y) º ($x) (( x1Cx2 & x1Mx3x4 & x1Rx5x6 & ...) & X1y )
($!x)( x1Cx2 & x1Mx3x4 & x1Rx5x6 & ...)
b1Cb2 & b1Mb3b4 & b1Rb5b6 & ...


x = b, (that is, x1 = b1, x2 = b2, ... xn = bn) and
Q(y) º B1y

So the having of sensations with the particular qualitative character Q could only be the having of brain process B1. The connecting principles are logically derived. The structure description is generated not by causal relations but by qualitative ones. That particular sensation of red doesn't have to have any particular and unique causal role, but it wouldn't be the sensation that it is if were not related as it is to the other qualities of sense. The key to closing the gap is not a causal niche, but a qualitative one.


Block, Ned (1978), `Troubles with functionalism', in C. Wade Savage (ed.), Perception and Cognition: Issues in the Foundations of Psychology, Minnesota Studies in the Philosophy of Science, ix. Minneapolis: University of Minnesota Press, 261-326. Reprinted with revisions in Block (1980).

--- (ed.) (1980), Readings in the Philosophy of Psychology. Cambridge, Mass.: Harvard University Press.

Boynton, Robert M. (1979), Human Color Vision. New York: Holt, Rinehart and Winston.

Clark, Austen (1993). Sensory Qualities. Oxford: Clarendon Press.

Hurvich, Leo M. (1981), Color Vision. Sunderland, Mass.: Sinauer.

Kaufman, L. (1974), Sight and Mind. New York: Oxford University Press.

Levine, Joseph (1983). Materialism and qualia: the explanatory gap. Pacific Philosophical Quarterly 64: 354-61.

--- (1988). Absent and inverted qualia revisited. Mind and Language. 3(4): 271-87.

--- (1991). Cool red. Philosophical Psychology. 4(1): 27-40.

--- (1993). On leaving out what it is like. In Martin Davies and Glyn Humphreys, (eds), Consciousness: Psychological and Philosophical Essays. Oxford: Blackwell.

Lewis, David (1966), `An argument for the identity theory', Journal of Philosophy, 63(1): 17-25.

--- (1970), `How to define theoretical terms', Journal of Philosophy, 67: 427-44.

--- (1972), `Psychophysical and theoretical identifications', Australasian Journal of Philosophy, 50(3): 249-58.

Locke, John (1689:1975). An Essay Concerning Human Understanding. Edited by John Nidditch. Oxford: Clarendon Press.

McGinn, Colin (1991). The Problem of Consciousness. Oxford: Blackwell.

Quine, W. V. (1969), Ontological Relativity and Other Essays. New York: Columbia University Press.

Thompson, E., Palacios, A., and Varela, F. (1992). Ways of coloring: Comparative color vision as a case study for cognitive science. Behavioral and Brain Sciences 15: 1-74.

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