The Logic of Mind-Body Identification

2.1. Identification Problems

The ancients conceived of Hesperus and Phosphorus as distinct. At some point, someone—perhaps Pythagoras—suggested they were not. That person would have faced a problem: That Hesperus and Phosphorus appear to have different properties. Phosphorus seems to appear in the morning but not the evening, whereas Hesperus seems to appear in the evening but not the morning.

Any answer would have to contain, in addition to the declaration of identity, an explaining-away of the apparent differences. We can represent this as a list of corrections to the prior view, where those parts of the view that are not corrected (and are not affected by what is) are imagined to stay the same. I call this a “correction list” or “solution”. Here, in an abbreviated form, is the solution the ancients favored, where ‘H’ represents Hesperus, ‘P’ Phosphorus and ‘M’ and ‘E’, respectively, the properties of appearing in the morning and the evening:

Each element in this list represents one correction. The rightmost element is the principal correction. It represents that Hesperus and Phosphorus are now identified. The other corrections, to the left, facilitate this. ‘H+M’ represents that appears in the morning comes to be newly added to Hesperus, i.e., attributed as a property distinct from those that (when considered as Hesperus ) it was hitherto thought to have. I call a correction like this an ‘addition’. ‘P+E’ is also an addition, and represents that Phosphorus is newly thought to appear in the evening.

2.2. Subtraction

Lois has hitherto regarded Clark, but not Superman, as human. If we let ‘C’ abbreviate ‘Clark’, ‘S’ ‘Superman’ and ‘H’ ‘the property of being human’, Lois can identify Clark with Superman as follows:

‘−’ represents that the property to the right is subtracted from the bearer to the left. In other words, the solution above explains away the differences by denying that Clark is human after all.

We might have tried the same strategy with Hesperus and Phosphorus, subtracting E and M instead of adding M and E. But that would have meant denying that Hesperus appears in the evening and that Phosphorus appears in the morning, which is why this approach has not been favored. It serves to illustrate, however, that there are multiple ways to explain away the differences. And that one’s choice of solution depends on one’s knowledge of the world.

Where there is more than one difference to resolve they may each be treated differently. E.g., if Lois has hitherto regarded Clark, but not Superman, as both a human and a journalist, then (letting ‘J’ represent being a journalist ) a good solution is:

In advancing this solution, Lois ceases to regard Clark as human, but comes to regard Superman as having a day job.

2.3. Facilitatory Identifications

To adapt a case from Aristotle, how can we identify the road (A) from Athens to Thebes with the road (T) from Thebes to Athens when one (U) slopes uphill whereas the other (D) slopes downhill? The following looks right:

The justification is that, quite generally, the property of sloping upwards from x to y and the property of sloping downwards from y to x are the same one property. There are not two distinct states of affairs here, even if there are two ways of describing the matter.

But note that this solution contains two identifications: The principal correction, i.e., the identification of the roads, and the facilitatory identification U = D. This facilitatory identification, like an addition or subtraction, explains away an apparent difference.[3]

2.4. Higher Order Identifications

Facilitatory identifications add complexity to our scheme. In some cases, to identify x and y, you may have to make a facilitatory identification between their properties. And to identify those, you may need to make a further facilitatory identification between their properties. This may go on indefinitely, pushing the required corrections up to arbitrarily high orders.

Most identifications do not involve such higher-order facilitatory identifications, and we do not often have to think about them. When it comes to the mind-body problem, however, theorists may feel the need to advance to the higher orders. For example, suppose that an experiential state E is regarded as having the property P of being painful, and suppose that the neural state N that we want to identify with E is not. Then:

1. If the physicalist is to avoid property dualism, she must not add P as a new property of N over and above those discoverable from the third person. And if she is to avoid eliminativism, she must not subtract P from E thereby denying that the experience is painful. Suppose, then, that she makes a first order facilitatory identification between P and some third person property N′ of N. Then a problem is that P is regarded as having the property (U) of making the experience it modifies unpleasant, whereas no property of N (including N′) is regarded this way. So:
2. If she is to be a good naturalist, she must not add U as a new property of N′ over and above those discoverable from the third person. But neither does she want to subtract U from P, since that would mean denying that P makes E unpleasant. It seems better, then, to make a second-order facilitatory identification between U and some third person discoverable property N″ of N′. But then a problem is that U seems different from all third person discoverable properties, hence different from N″. If this is because it has different properties, it may take a third order identification to resolve these differences.

This is merely an example of where one might resort to higher-order facilitatory identifications. However, it also stands as a decent dress rehearsal for the deeper issues in sections 3 and 4, where it is shown that sequences of ever-higher-order identifications of the sort begun here are sometimes unable to ground.

Note something else that has happened in this section. We have gone from the problem of identifying particulars to the problem of identifying properties. Nothing changes, logically speaking, when we do this. Though it may be harder to think about the properties of properties, it remains the case that, if we are to identify x and y then, whether they are particulars or properties, we need to explain away their differences. And it remains the case that we can do that by either adding, subtracting or identifying the differences away.

3.1. Full and Semi-Solutions

Let me start by saying more about this notion of “quantifying out”. One way to think of this is as a fourth kind of correction, supplementing those of addition, subtraction and facilitatory identification. For example, let ^⌜(∃φψ)^⌝ be shorthand for the claim that there exists a property of φ that is identical to ψ, and suppose we want to identify heat (H) with molecular motion (M) but we do not know how to treat the property (R) radiates through empty space that H but not M appears to have. If this is the only difference we have to account for, we might propose the following:

‘(∃MR)’ says that some property of the molecular motion is identical to the property (R) of radiating through empty space. It does not say which. But that’s enough to permit the identification to proceed coherently. I call this kind of solution a semi-solution

Is this the same as adding R to M? No, since to add R to M is to continue to think of R as distinct from all the properties that M is hitherto held to have. But this semi-solution allows for R to be one of M’s previously known properties. In this way, (∃MR) is effectively a placeholder for either an addition or a facilitatory identification.

I use the term ‘semi-solution’ since, in not disclosing how exactly the differences are resolved, this solution does not provide us with all the information we would like. Semi-solutions may come in different forms, depending on how the question of interest is put off. One could, for example, include a maximally general element, using two quantifiers, that says that each property of H is identical to some property of M (and vice versa), but which offers no specifics. Rather than go through the various possible placeholders, I simply define a semi-solution as one that is not full, where a full solution is one that contains only additions, subtractions and identifications.

When might we offer a semi-solution? In two situations. First, when we are too rich— when there are lots of ways of adding, subtracting and identifying away the differences, and we do not know how to choose between them. Until we know which one is correct, we restrict ourselves to the quantificational claim that there is some way of explaining away the differences, going no further. Second, when we are too poor—when we have no plausible full solutions at all. If we have a powerful argument, perhaps from coincidence of time, place and causal role, that x = y, but no way to explain away the differences, we must tell ourselves that there is some way to do so and hope that, later, we think of one.

For an example of the latter kind of case, suppose once again that the physicalist is identifying (P) painfulness with some property (N) of a brain state. As before (i) she must deal with the fact that (U) qualifies its bearer as unpleasant is an apparent property of P but not N (ii) she refuses the dualist option of adding U to N as a new property over and above its third person properties and (iii) she chooses not to subtract U from P and deny that the pain makes the experience unpleasant. She must therefore identify U with some third person property of N, except that none of N’s properties look suitable. Hence she makes do with a semi-solution, assuring herself that U is identical to some property of the brain activity, without saying which.

There is, however, something odd about providing a semi-solution when one can think of no full solution. For it is effectively to insist that all is well while having no idea how all could possibly be well. This foreshadows how it is that how-possibly questions arise in the context of the problem of consciousness, and counts as a second dress-rehearsal for the problems to come.

3.2. Coherence

I stipulate that for a list to count as a genuine solution, it must be coherent, meaning that it does not identify any two entities without resolving their differences. In other words, if one’s correction list contains x = y where one has hitherto regarded x and y as having differences, then the list should also contain either a subtraction, addition or identification that explains those differences away, or a quantificational placeholder, of the sort discussed in the prior section, that removes the difference without providing the specifics. If, however, it has none of these things then it is not coherent and hence, the way I shall talk, not a solution at all.[4]

3.3. Preservative Solutions

Let a Preservative solution be one that contains no additions or subtractions. For example, suppose we wish to identify (L) light with a kind of electromagnetic radiation, which we will call ‘E’. Suppose the only difference is that L possesses (C) comes in many colors whereas E possesses (W) comes in many wavelengths. Then the following preservative solution looks good:[5]

After pursuing this solution, we are now inclined to say that L has W, where we did not say such things before. But, in doing so, we are not attributing a new property to L; we are identifying W with one of L’s old properties. Preservative solutions, then, are so-called because they are, in a certain sense, anti-revisionist. In containing no addition of new properties and no subtraction of old, they preserve our de re commitments about which entities have which properties.

We might have alternatively offered the following semi-solution:

This affirms that W is identical to some unspecified property of L, and that C is identical to some unspecified property of E. Despite being only a semi-solution, the list contains no additions or subtractions. Hence, by definition, it too is preservative, and will continue to count as such until the placeholder is replaced by an addition or subtraction.

3.4. Differentials and Discriminability

It’s time to get more precise about the notion of a “difference”. From here on, let entities count as discriminable if and only if they are distinguished by their differing properties. The properties that distinguish x and y will be referred to as their differentials.

Note that to say that x and y are discriminable is to say not only that they have distinct properties, but that they can be distinguished by those properties. What this requires, in addition to their properties being distinct, is that their properties themselves be discriminable. For unless the color or shape or size. . . of x is discriminable from the color or shape or size. . . of y, x and y themselves will be indistinguishable. (A precise non-circular definition is footnoted.[6])Accordingly, for a property x′ of x to be a differential with respect to its bearer and y, it must be discriminable from every property of the latter.

It might be thought that ‘discriminability’ is just another word for the more familiar notion of discernibility, where x and y are discernible if and only if they have distinct properties. It turns out that there are lots of interesting connections between the two notions, but I lack space to get into that here. Suffice it to say that the new notion does indeed reduce to the old if it is granted that, among properties, there can be no distinct indiscernibles.[7] Readers who are willing to grant that much may substitute ‘discernibility’ and ‘indiscernibility’ for ‘discriminability’ and ‘indiscriminability’ throughout what follows. Importantly, if it is granted, then where we said that if x and y are discriminable, their properties are discriminable, we can now say that if they are discernible, their properties are discernible. For if they are discernible they have distinct properties, and distinct properties, the reader is granting, must be discernible properties.

3.5. Representing as Discriminable

Though two elements cannot be discriminable without having differentials, two elements can be represented as discriminable without being represented as having differentials. A novel may inform us, for example, that Smith and Jones look quite different without telling us how. In a similar way, a viewpoint or theory may represent x and y as discriminable without providing the details.

In dealing with such cases, we will make reference to:

The motivation for this principle is pretty clear: If our view provides no specific differences to add, subtract or identify, then we cannot correct it by adding, subtracting or identifying specific differences. Since any solution containing x = y must succeed in removing the differences between x and y (see 3.2), it must do so by some other means. Hence it must be a semi-solution.

3.6. Principle (*)

We saw in 2.4 that, in explaining away the differences between identificanda it was possible to embark on a series of facilitatory identifications spiraling up to the higher orders. The following limit to this process is almost obvious:

Intuitively, if any part of the discriminability of x = y were explained away by facilitatory identification, then x = y would not be the highest ordered identification between discriminables after all. The facilitatory identification would be, since it identifies the differentials of x and y.[8]

3.7. Unfinishability

If we define a finite solution as one that contains only finitely many members, we can motivate the principal result of this paper:

To see why, suppose (arbitrary) x and y that are represented as discriminable. And suppose some finite preservative solution s containing x = y. Since s is finite, it cannot contain identifications at ever higher orders. It must therefore contain some element x*=y* (even if it is just x=y itself ) that is the (joint) highest ordered identification in s between discriminables. There are two cases:

1. x* and y* are merely regarded as being somehow discriminable, without any specific differential being provided. It follows by Absence of Differentials that any coherent solution containing x*=y* is a semi-solution.
2. Otherwise specific differentials are provided. s must explain these differentials away if it is to count as a solution at all. Since x*=y* is the highest-ordered identification in s of discriminables, we know by (*) that the differentials are not explained away by identification. And since s is preservative it does not explain them away using additions or subtractions. Hence s must contain an element that is neither an addition, a subtraction, nor an identification. Hence s is a semi-solution.

3.8. A Second Argument

A second argument better displays the regressive structure of the problem. First we show:

To see why, suppose the antecedent: That (arbitrary) discriminables x and y are identified in a full, preservative solution s. Since s is full, it must explain away the differences by some combination of (i) addition, (ii) subtraction and (iii) identification. But since s is preservative, options (i) and (ii) are excluded. Hence the solution contains at least one element of the form x′ = y′ for properties x′ of x and y′ of y, where one or both is a differential with respect to x and y. But to be a differential with respect to x and y, x′ must be discriminable from every property of y, including y′ (from section 3.4.) The same goes, with the appropriate changes, if y′ is a differential. Either way x′ = y′ is an identity between discriminables, hence we get the consequent of Regress.

Regress tells us that for every identification between discriminables in s there is another one at the higher order. It follows that if s contains at least one, it contains infinitely many. Since s was chosen as an arbitrary full, preservative solution in which discriminables are identified, it follows that all such solutions are infinite. Conversely, if a preservative solution identifying discriminables is not infinite then it must not be full. Thus we re-derive Unfinishability.

3.9. Remarks on Unfinishability

I stress the difference between the problem encoded in Unfinishability and the more obvious problem below:

This problem is obvious only to the extent that you forget the option of identifying the elements’ properties. That option gives us the prima facie possibility of identifying elements by identifying—and hence preserving—the properties attributed to each. The discussion above, in contrast, allows for this option, but notes that it can only be exercised at one order at the cost of a structurally identical problem at the next. This is what gives rise to Unfinishability.

One may fear that Unfinishability is too strong, because it may exclude full, finished identifications of the sort we make all the time. If so, then the arguments above overreach. I return in 5.4 to address this.

For now, let’s maintain our central course and apply these results to the problem of consciousness. I suggest that the physicalist problem of consciousness falls out as a special case of Unfinishability. For physicalists, I argue, in attempting to identify experiential and physical phenomena without revising our notions of either, are pursuing the kind of solution that, according to Unfinishability, cannot be had.

4.1. T, and its First and Third Person Parts

Let T be our current best picture of the world. I assume that T breaks down solely into a phenomenological, first person part and an objective, third person part. I take the former to include everything we have learned about consciousness through introspection, and the latter to include the whole of physical science, including everything we know about the microphysical facts and about what supervenes. I assume the physicalist wants to unify these two halves by identifying phenomena from the first person part with (supervenient) phenomena from the third person part.

There follow two restrictions on the inquiry into consciousness, first person preservativity and third person preservativity, each of which corresponds to one part of T .

4.2. First Person Preservativity

Goldman writes that “when a ... concept clashes with our first-person concept of consciousness... we should conclude that it isn’t a consciousness concept at all” (Goldman 2002: 122). Chalmers insists that we must “take consciousness seriously” by refusing “. . . to redefine the phenomenon in need of explanation as something it is not” (Chalmers 1996: x). First person preservativity is an attempt to model this idea. Stated within the framework we have developed, it forbids us from making the mind-body problem easier by adding and subtracting properties from the first person part of T ; i.e., by supposing that the types of phenomena we observe from the first person have properties that they seem to us to lack, or lack properties that they seem to us to have.

First person preservativity may seem rather strong. I will show how it can be weakened, without affecting the central point, in section 5.8. For now, simply note that first person preservativity follows, more or less, from commitments in the historical literature that are even stronger. I’m thinking of variants of the twin claims that conscious states are self-intimating —i.e., if one’s experience is F, it seems to one that it is F—and that our access to them is incorrigible —i.e., if an experience seems to one that it is F, it is. These claims are often justified by the observation that though other things can fail to appear as they really are, the appearances themselves cannot. To get first person preservativity, simply add that we ought not to revise our opinions about something—our own introspectible conscious lives—that we cannot be wrong about in the first place.[9]

However, you do not need to be attracted to such strong principles to be attracted to first person preservativity. For preservativity merely forbids us from adding and subtracting properties from the types of experiences we have, not the tokens. It does not ask us to deny that subjects in a change blindness experiment may sometimes be unaware of their alternating qualia (cf. Dennett 2005: 84); nor the possibility that dental patients may sometimes mistake a pressure for a pain (Goldman 2002: 126).[10] All that it requires is that whether we can be mistaken about a particular experience on a particular day, we are not wrong in thinking that, generally speaking, we have pains; that there is something it is like to have them; that a sharp pain is different from a dull ache; that pains appear in our somatosensory field—i.e., we do not see or hear pains—and that, like offensive flavors and experiences of nausea, pains are unpleasant. Similarly, we are not wrong to say that the type pleasure has a typically distinct feel from the type pain, that the type of experience associated with red differs in value from that associated with blue, and differs in kind from that associated with a tickle.

First person preservativity is relativized, moreover, to our reasons for making a change. It does not require that properties must never be added or subtracted, tout court. It merely insists that they not be added or subtracted, without independent motivation, just to make the mind-body problem easier. One may allow, consistent with this restriction, for additions and subtractions to be made in the light of appropriate independent evidence.[11]

The restriction, despite these caveats, may still be too strong for some. In the interests of an orderly discussion, though, I propose to stick with it for now. I’ll return to the question of how we may weaken it, without altering the central point, in section 5.8.

4.3. Third Person Preservativity

Ney (2008) writes that “physicalism is best taken. . . as nothing more than an attitude, a commitment to form one’s ontology according to whatever the physics of the day says exists”. This attitude is expressed, e.g., by (Lycan 2003: 13), when he suggests that the philosopher of mind ought not to second guess the ontology provided us by physics. In this spirit, the third person preservativist holds that if empirical science says a property is there, the philosopher of mind has no business denying it; and if it finds no property, the philosopher of mind has no business insisting upon it. In the framework we have developed here, this amounts to a prohibition against adding or subtracting properties within the third person part of T .

The most obvious operation forbidden by third person preservativity is the addition of qualia. We may not identify conscious states with brain states by supposing, in the manner of the property dualist, that qualia are new, ontically additional properties of the latter. The prohibition, despite this, does allow us to ascribe qualia to brain states, but only by identifying each quale with one of the brain state’s third person properties. In our framework, that means making a facilitatory identification, not an addition.

Some may think that third person preservativity is too strong. For the moment, it works as a reasonable idealization. I consider plausible ways in which it could be weakened in section 5.8.

4.4. Deriving a Problem of Consciousness

We might now suppose the following, where a ‘first person x’ and a ‘third person y’ are, respectively, elements from the first and third person parts of T:

(**) seems pretty obvious. If a solution is preservative (tout court ) then it contains no additions or subtractions. A fortiori, it can contain none from the first and third person parts of T , so it must be first and third person preservative. If, conversely, a solution does not add or subtract from the first or third person parts of T then since (we are assuming) there are no other parts, it does not add or subtract from T at all. In that case, the solution is preservative, tout court, with respect to T .

The principle (**) permits us to replace ‘preservative (tout court )’ with ‘first and third person preservative’ in Unfinishability to get:

Assuming no infinite solutions (I return to this in section 6), H1 tells us that if a solution between hitherto discriminable first and third person entities is preservative, it is not full. I.e., that when it comes to identifications between such things, there is no way to fully explain away their differences.

But this is where things get interesting. For if there is no way to fully explain away the differences, then the physicalist won’t be able to correctly conceive of one. The best she can do is to offer a semi-solution. Yet in offering a semi-solution where she can think of no full solutions, the physicalist (a) claims that though the identificanda appear to differ, there is some coherent way to explain away the differences, yet (b) can conceive of no specific way of explaining away the differences (for if she could then she would have at least one full solution to offer). The result is a how-possibly question: How could it possibly be the case that x and y are identical when there is no conceivable way to explain away their differences?

For this reason, H1 gives us:

Note that though Hardness was developed, by and large, from first principles, it predicts, to a reasonable approximation, the lay of the land in the investigation of consciousness. On the one hand, we have the contemporary physicalist who, wishing to take consciousness seriously, eschews the option, in Chalmers’ (1996, x) words, of “redefin[ing] [consciousness] . . . as something it is not”; but who, in respecting the authority of science, also refuses to revise the world that it describes. To the extent that this makes the physicalist into a first and third person preservativist, Hardness predicts, any solutions she offers will give rise to how-possibly questions.

On the other hand, Hardness tells us, the mainstream physicalist’s problem is in searching for a preservative solution. If she just gives up on that, these problems go away. So it’s not surprising, from this perspective, that we find theorists who have taken exactly that option. The property dualist, for example, succeeds in identifying mental states with physical states by adding the mysterious qualia as new properties, over and above those supplied by empirical science. The qualia eliminativist, meanwhile, subtracts the qualia from the mental state, removing the reason for regarding the two as distinct.

None of this is to say that, in being the approach that leads to the regress, the physicalist approach is incorrect. For it may in fact be that a = b, a’s property a′ is identical to b’s property b′, their properties a″ and b″ are, in turn, identical, and so on to infinity. If so, then the right solution would be an infinite one that captures this, not one that (say) adds a′ to b as a property over and above b′, nor one that (say) subtracts a′ from a. But the question of whether an infinite solution is correct is distinct from the question of whether we can provide it.

5.1. No Apparent Regress

One might object that the problem outlined here involves a regress, but one experiences no obvious regress when thinking about consciousness. Hence the problem outlined here, whatever else we might say about it, is not the problem of consciousness.

In answer, let us see how the regress might arise in the context of the problem of consciousness. Imagine a researcher tries to identify (say) pain with (say) lamina I neurons stimulating parieto-insular cortex. The problem is that they seem different, and they seem different because the pain has noxious properties that seem discriminable from any properties of the brain event. If he assures us merely that these noxious properties are identical to some unspecified properties of the brain event, he merely gives us a semi-solution, as Hardness predicts. If, on the other hand, he plows ahead and identifies some noxious property (N) with (say) (L) the lamina I stimulation’s tendency to cause activity in the anterior cingulate, the new problem is that N and L seem discriminable. If he is able to clearly articulate how they seem discriminable—i.e., by describing the properties that seem to distinguish them—he must now cross-identify these properties in turn. But these too will seem discriminable (or else they would never have distinguished N from L). Thus he has a new problem structurally identical to the first. Wherever the researcher stops, pending further empirical research, or wherever he can no longer articulate the differences, his legacy to us is a semi-solution.

This, of course, does not establish an infinite regress. But it does defend against the objection that there clearly isn’t one.

5.2. Mental and Physical States are Not Represented as Discriminable

A distinction I have ignored is between representing x and y as discriminable and not representing them as indiscriminable. One’s prior view may represent x as having x′ but remain silent on whether or not y has it, neither representing it one way nor the other. Since this is possible, one might suppose that our mental states and brain states, rather than being represented, according to introspection, science, etc., as discriminable, are merely not represented as indiscriminable, and that the principles Unfinishability and Hardness, being ostensibly about entities that are positively represented as discriminable, therefore fail to apply.

In the end, though, this does not significantly alter the problem. For the purposes of identifying x and y, all that matters is that x is represented as having a property x′ that distinguishes it from y. It does not matter whether y is represented as lacking it, or merely not represented as having it; either way, one cannot rationally identify x and y while ascribing x′ to x alone. This means that, as before, x′ must either be added to y, subtracted from x, or held identical with some known property y′ of y. But when options of the first two kinds are prohibited, the third leads to regress.[12]

5.3. Discriminability and Contrary Properties?

Objection: “When x and y are regarded as discriminable, they are either correctly or incorrectly represented as having contrary properties, which we can call x′ and y′. If they are correctly represented as contraries, there is no way to correctly identify x and y without subtracting at least one of them from its bearer. If, however, they are incorrectly represented as contraries, you can continue to assign x′ to x and y′ to y by merely revising your belief that they are incompatible. But it is unclear, in that case, that there is anything problematic here at all.”[13]

Suppose, taking the second horn, that they are not genuine contraries. Then, I agree, an option is to revise your belief to that effect. However, it’s a mistake to think that now your work is done. For if that is the only change, you still represent x, but not y, as having x′ and y, but not x, as having y′. Sure, you no longer regard them as contrary properties, but you still ascribe them unevenly. Since, as stressed in the prior section, one cannot rationally identify x and y while ascribing x′ to x alone (ditto, etc., for y′) you must either add x′ to y, subtract it from x, or identify it with some property of y. But that just brings you to the beginning of the problem.[14]

5.4. Counterexamples to Unfinishability? (I)

Unfinishability is a general restriction on identification, not pertaining specifically to the mind-body problem. One might worry that, in being so general, it is likely to predict problems, not just for mind-body identities, but wherever we try to make an identification.[15]

Does Unfinishability, for example, predict problems with identifying Hesperus and Phosphorus? No. The (correct) solution in 2.1 contained additions, and hence was not preservative. Unfinishability, however, only prohibits finite, full, preservative solutions.

Similarly, Unfinishability predicts no problems in identifying water (W) with H₂O (or heat with molecular motion, or light with visible electromagnetic radiation.) To see why not, suppose that the chief obstacle to identification is that H₂O instantiates the property (M) has a micro-particulate structure, whereas water does not. Then an appropriate solution would be [W + M, W = H₂O], i.e., we simply add M to our notion of water. But this is not preservative, and hence no counterexample to Unfinishability.

What’s the difference with consciousness? Simply that, with consciousness, we are reluctant to deploy regress-stopping moves like addition and subtraction, since it requires us to naysay either the scientist’s account of what there is or the individual’s account of what it’s like for her. In eschewing additions and subtractions, however, we must pursue a strategy of pure identification (or settle for a semi-solution). But the strategy of pure identification requires an infinity of operations.

5.5. Why Aren’t Other Semi-Solutions Puzzling?

It may be that, in identifying water with H₂O, I do not have much idea what gets added, what gets subtracted, etc. I just trust that the differences get explained away somehow, and leave the details to the chemists. But though I have to give a semi-solution I do not end up mystified about the identity of water and H₂O. So what’s the difference?[16]

The answer is that I can finitely discharge any quantificational placeholder in the water/H₂O semi-solution. E.g., when I leave a placeholder that covers for water’s lacking M, I anticipate that, later, I may discharge it by either (i) subtracting M from H₂O or (ii) adding M to water. And there are other options.[17] The fact that I do not yet know which option is right means I have how-actually questions to answer.

When addition and subtraction are prohibited, in contrast, attempts to finitely discharge a placeholder result in the reimposition of another placeholder. That’s because, given the prohibition, a placeholder can only be discharged by identifying discriminable properties. Yet those properties, in being discriminable themselves, must also have their differences explained away, which, given the prohibition, requires that their discriminable properties be identified, and so on. Sooner or later we must abandon the regress. But that means leaving a placeholder in lieu of the next identification.

In leaving a placeholder I promise that this can all be worked out somehow. But I can conceive of no finite way in which it could. So where, with water and H₂O, I had how-actually questions to answer, with consciousness and physical states, I have how-possibly ones. This is why, according to the present account, the latter problem leaves me mystified.

5.6. Counterexamples to Unfinishability? (II)

Objection I: “Suppose I wish to identify Cicero (C) with Tully (T), but I represent them to have no specific properties (this is unlikely, but it does not matter.) Would the finite, full, preservative solution [C = T] work? If so, isn’t this a counterexample to Unfinishability ?”

No. Consider both cases: Either I do not regard Cicero and Tully as discriminable, or I regard them as having (unspecified) differences. In the first case, since Unfinishability only prohibits finite, full, preservative solutions for things hitherto regarded as discriminable, [C = T] is no counterexample. In the second case, [C = T] does not address the (unspecified) differences between C and T. Hence it is not truly a solution (cf. 3.2) and hence not the kind of solution that Unfinishability prohibits.[18]

Objection II: “Suppose I represent Cicero and Tully to have, respectively, C′ and T′ but no other properties, and I do not represent any specific differences between C′ and T′. Then isn’t [C′ = T′, C = T] a full, finite, preservative solution, and hence a counterexample?”

No, since we get essentially the same dilemma. Either I do not represent C′ and T′ as discriminable, or I represent unspecified differences. In the latter case [C′ = T′, C = T] fails even to be a solution, since it does not resolve the (unspecified) differences. In the former, C′ and T′, being themselves indiscriminable, cannot act as differentials for C and T. Which means that, lacking other differentials, C and T turn out not to be discriminable either.

Note the way in which the indiscriminability of C′ and T′ cascades down. This happens no matter how long the list, and no matter how much it branches. If, for example, C′ has \(C_1^{\prime\prime}\) and \(C_2^{\prime\prime}\) whereas T′ has \(T_1^{\prime\prime}\) and \(T_2^{\prime\prime}\), then the list \([\mathrm{C}_1^{\prime\prime}=\mathrm{T}_1^{\prime\prime}, \mathrm{C}_2^{\prime\prime}=\mathrm{T}_2^{\prime\prime}, \mathrm{C}^\prime \!=\!\mathrm{T}^\prime, \mathrm{C}\!=\!\mathrm{T}]\) can be a genuine solution only if \(C_1^{\prime\prime}\) is not discriminable from \(T_1^{\prime\prime}\) and \(C_2^{\prime\prime}\) is not discriminable from \(T_2^{\prime\prime}\). But in that case (ceteris paribus) nothing distinguishes C′ from T′ and so nothing distinguishes C from T. Hence this is not a counterexample to Unfinishability either, since it does not contain an identification between discriminables. The same goes for any putative counterexample of this sort.[19]

5.7. An Appearance/Reality Distinction for Conscious States

Objection: “Why not deny first person preservativity? The idea that conscious introspection is infallible is a legacy of bad folk psychology. In fact, there is a coherent appearance/reality distinction for consciousness just as for anything else, and hence a coherent sense in which we may be wrong about our own conscious states.”[20]

I make four points in response: (1) The present paper is principally diagnostic. Infallibilist intuitions about phenomenal consciousness have long informed the philosophy of mind, and still exert a strong pull. I want to illuminate the connections between these commitments, however vaguely held, and the problem of consciousness. I do not need to subscribe to them. (2) Having said that, rejecting first person preservativity is a tricky business. Firstly, there is the enduring question of how one can possibly be wrong about what it’s like for oneself. Secondly, in allowing for mistaken representations of our own consciousness, we must be careful not to generate other problems. (To see a big one, ask yourself what it must be like to really have the conscious sensation of green but to misrepresent oneself, in the relevant way, as having the conscious sensation of red? See Dennett 1991: 132 and, especially, Neander 1998) (3) Thirdly, deviations from first person preservativity ought to be independently motivated, by which I mean that we should not abandon preservativity in order to avoid the regress since the regressive solution may be correct. Mental states may be identical with brain states, their properties identical to neurophysical properties, their properties identical in turn, etc. (4) And even if we do reject first (or third) person preservativity, that may not be enough. For it also matters how it is rejected. I argue next that, for most physicalists, it is unlikely to be rejected in the right way, and that, if it is not, the regressive problems will continue to arise.

5.8. Weakening Anti-Preservativity

My aim here is not to defend preservativity, but to use it to account for why how-possibly questions arise for physicalist proposals. The preservativity described in section 4, however, is stronger than what some physicalists may be willing to endorse. What explains the existence of a puzzling mind-body problem for those physicalists? I’ll answer by showing how weaker variants may lead to the same problems.

How might preservatism be too strong? Well, a reasonable physicalist, notwithstanding her reverence for the ontology provided by empirical science, may permit the occasional adjustment to that ontology if it makes the mind-body problem easier. And though she may generally resist e.g., denying that painful states are generally unpleasant, or that red and blue sensations are qualitatively different, she may allow herself to occasionally modify the image of consciousness provided by introspection. One further way in which preservativity seems too strong, moreover, is in forbidding the addition of third person properties to mental states, e.g., the addition of involving neural oscillations in range 7.5-12.5 Hz to the conscious state feeling relaxed. Couldn’t one justifiably add such properties to mental states while still taking consciousness seriously?[21]

I’m inclined to say yes. But even if physicalists permit such revisions, I would still expect the problem to arise. For though they relax their preservativity here and there, physicalists generally do not relax it enough, nor in the right ways, to banish the problem described in this paper. (Though I emphasize, recalling the end of section 4.4, that they may be right not to.)

The reason is that the typical mainstream physicalist is a realist about phenomenal consciousness.[22] She wants to explain it, not explain it away. Hence, whatever other violations of preservativity she is willing to tolerate, she does not abide the wholesale elimination of qualia. But that probably means that after she has made all the additions and subtractions she is warranted and willing to make, mental states are still ascribed properties—qualia— that appear to distinguish them from physical states.[23] This is sufficient to recover the problem. For once she has made all the revisions she is willing to, the physicalist is effectively a preservativist from now on. Which means that since her revisions did not remove the source of the discriminability, she is at the beginning of the problem, searching for a full, finite, preservative identification of things that seem discriminable. If the broad point of this paper is right, her search is forlorn. There is no conceivable solution that meets her requirements.