There’s much to say about the supervaluationist response and whether it succeeds as a response to the Nihilist Argument.14 My contention here is that even if it succeeds as a response to the Nihilist Argument, it’s much harder to mount the same response to the Anti-Materialist Argument. Premise (c) of the Anti-Materialist Argument is on much firmer ground than its counterpart in the Nihilist Argument, for at least three reasons: two have to do with a difference in the predicate (‘x is conscious’ vs. ‘x is a tree’), the third with a difference in the subject (‘I’ vs. ‘Arby’).

Let’s start with the predicate. The predicate ‘x is conscious’ is meant to express the property of being phenomenally conscious—of being such that there’s some way it’s like to be that thing. Understood thus, it certainly doesn’t seem to be vague—and doesn’t appear to admit of multiple precisifications—in the way that ‘x is a tree’ does. On the face of it at least, for anything whatsoever, either that thing is definitely conscious or that thing is definitely not-conscious.15 Either it’s lights on inside, or it’s lights out. Even a very dim or fuzzy light is a light. Of course sometimes we get woozy, or lightheaded. But that’s not a case in which it’s indeterminate whether we’re conscious. It’s perfectly determinate that we’re conscious when we feel woozy. We feel woozy after all, and determinately so. It’s the character of our experience that’s fuzzy, not its existence.

We can further support the intuitive determinacy of phenomenal consciousness with a number of arguments. Some philosophers have pointed out that even after giving the matter a lot of thought we can’t imagine a situation in which someone or something is only borderline phenomenally conscious; usually we take such a failures of imaginability to be evidence that the situation in question is impossible.16

A much more sophisticated argument along these lines relies on the idea that a necessary condition for a predicate to have a borderline case is that sufficiently competent users of the predicate are positioned to understand what makes it a borderline case—but that in the case of ‘phenomenally conscious’ that condition doesn’t obtain.17 Thus, Simon (2017b: 2112) defends what he calls the ‘Positive Characterization Thesis,’ which says that “for every borderline case there is an explanation of why that case is borderline in terms of norms that apply to that case in light of what else is true about ‘it’.” And he further argues that (if zombies are conceivable, then) there can be no positive characterizations of borderline cases of ‘phenomenally conscious.’

Finally, we might note that for any vague predicate F it’s possible for something to be definitely F, possible for something to be definitely non-F, and possible for something to be neither definitely F nor definitely non-F; but then any vague predicate F must be gradable, in the sense that one thing can be more or less (of an) F than another thing. Thus, you can be more or less bald than another fellow. You might say to your child, while pointing at the Boab Prison Tree, “Believe it or not, that’s just as much of a tree as the one in our backyard.” And contrariwise, some shrub in the early evolutionary history of trees might indeed be less of a tree than the one in your front yard. But you can’t be more or less conscious.18 At least not if we’re using “x is conscious” to just mean “x is such that there is some way it’s like to be that thing.” Of course, a conscious being could be more or less aware of, and have greater or lesser access to, its own states or to the states of other things. But there’s no greater or lesser way it’s like to be something, in the relevant sense.19

So nothing is indeterminately conscious, in the intended sense of that term. (Of course that’s consistent with there being subject-predicate sentences, ‘A is conscious,’ which are only indeterminate in truth value, because the subject term that replaces ‘A’ might be vague.) Since nothing is indeterminately conscious, none of the Me_n’s is indeterminately conscious. If none are definitely conscious, then each one is definitely not conscious. But then it’s definitely not the case that there is a conscious being here. That’s not the result we want—and not a result that would allow us to reject (c). If, on the other hand, at least one is definitely conscious, then all of them are definitely conscious—because of the powerful thought, which I already mentioned, which even the supervaluationist wants to retain: anything that’s consciousness-indistinguishable from a definitely conscious being is itself definitely conscious. Again, that’s not the result we want—and not a result that would allow us to reject (c). Back to square one.

Second point about the predicate, ‘x is conscious’: even if it were vague, and admitted multiple precisifications, it’s not plausible that the needed penumbral connection exists. There’s nothing about the semantics of the term ‘conscious’ that precludes there being two or more distinct but massively overlapping conscious beings. Perhaps there are sortal terms, like ‘person,’ whose semantics precludes there being two or more distinct but massively overlapping persons.20 But ‘conscious’ isn’t like that. It’s relevantly like ‘bald’ and like ‘blue.’ Nothing in the semantics of those terms precludes massively overlapping things from all being bald, or all being blue. At least one sufficient reason for that is that each of those features (baldness and blueness) is very plausibly intrinsic, and so its instantiation makes no absolutely necessary demands on its environment. But it would make such demands if it were an analytic truth that no two distinct blue (bald) beings massively overlap. By the same token, consciousness is very plausibly intrinsic. Indeed, I can’t think of a clearer instance of an intrinsic property than the property, being such that there’s some way it’s like to be that thing.21 And so its instantiation makes no absolutely necessary demands on its environment. But it would make such demands if it were an analytic truth that no two distinct conscious beings massively overlap.

So the central predicate term in the Anti-Materialist argument is ‘special.’ But so is the subject term. ‘Arby’ was our name for that tree over there. According to supervaluationism, the name inherits the vagueness of the demonstrative term used to fix its referent. And the vagueness of the name ‘Arby’ blocks the inference of

from

If ‘Arby’ were perfectly precise—admitting of just one precisification—then we would be entitled to infer (C) from (A); and the supervaluationist semantics would vindicate that.

For, from (A) we’d be entitled to infer

According to the supervaluationist semantics, (A) is true only if, for every admissible precisification of the ‘Arby’/‘tree’ pair, the referent assigned to the former is a member of the extension assigned to the latter. Now suppose that ‘Arby’ has only one admissible precisification. Then it would follow from (A) (given the supervaluationist semantics) that for every admissible precisification of ‘tree,’ the (one and only) referent of ‘Arby’ is a member of it. But then it would follow that Arby is definitely a tree.23 (Indeed, it would follow that definitely, Arby is definitely a tree.) That is, (B) would follow from (A). And (C) follows from (B). Of course, supervaluationists wish to accept (A) but deny (C). They can legitimately do that only because ‘Arby’ is vague. If it were perfectly precise, then the conclusion would follow ineluctably.

But that’s exactly the situation I’m in regarding my being conscious. If anything is clear to me, it’s that:

I’m thinking and believing (A’) right now. But the first-person pronoun as it features in that thought admits of no precisification: when I think that thought, the function of the first-person pronoun is to allow for self-reference and self-predication. Whenever anyone thinks a first-person thought, the function of the first-pronoun they employ is to allow for self-reference and self-predication.

So then I am indeed entitled to infer (if I need to infer this at all)

From which I’m entitled to infer,

And now I’m back to square one again. Since one of us is definitely conscious, all of us are definitely conscious, again because of the powerful thought that even the supervaluationist wants to retain: anything that’s consciousness-indistinguishable from something definitely conscious is itself definitely conscious. If it’s true that definitely I am conscious, then there are very many definitely conscious beings where I am.

For all these reasons, premise (c) of the Anti-Materialism Argument is much harder to deny than premise (c) of the Nihilist Argument. Much harder, but admittedly not impossible. As I noted in §1, some philosophers might take physicalism about the mental to entail that phenomenal consciousness is vague and extrinsic. After all, it seems plausible that any physical property with which we might identify phenomenal consciousness (or to which we might ‘reduce’ it) is going to be both vague and extrinsic.24 And while the vagueness and extrinsicness of consciousness are widely acknowledged as counterintuitive and costly, some philosophers might also be prepared to bear those costs in order to buy a theory as elegant as physicalism.25 Likewise, some philosophers might take physicalism to entail the denial of determinate first-personal thought. And while they might acknowledge that the denial of determinate first-personal thought is counterintuitive and costly, they might also be prepared to bear that cost in order to buy a theory as elegant as physicalism.

Now, it’s worth first recalling a point I briefly mentioned in §1: physicalism (about the mental) is not entailed by materialism (about human beings). One can consistently think that mental features are irreducible (or not reducible to physical features) but that we human beings have only material parts. So, even if my argument assumes some things that no physicalist would reasonably grant—which, as I will argue presently, it doesn’t in fact do—that wouldn’t mean that my argument begs the question in any problematic way. The argument I’m defending is an anti-materialist argument, not an anti-physicalist argument.

But even more to the point, it’s not at all obvious that my assumptions (together with any substitutes that could work just as well) are in fact ruled out by physicalism.

Some physicalists have indeed been prepared to simply bite the bullet on the vagueness and extrinsicness of consciousness—without any concessions to the other side.26 But other, pretty ardent physicalists, have at least partially conceded—and their partial concession is good enough for my argument to succeed. Thus: Michael Tye (2021) argues on physicalist grounds that consciousness can be vague. But even Tye agrees that there is a non-vague property that is a central constituent of consciousness—which he calls “consciousness*”—that is just a matter of there being some way it’s like to be that thing. I won’t quibble about which property is picked out by our term ‘conscious,’ because I don’t need to. We could put the whole Anti-Materialist Argument in terms of consciousness*, and it would be just as persuasive as the original. Notice that if there are very many conscious* beings where I am, then we presumably all have the same powers, and all have the same interests. So there being so many conscious* beings where I am would have the same practical and moral implications as there being so many conscious beings. And remember, I’m spotting myself the falsity of Mental Manyism on the basis of the absurd moral and practical implications that Mental Manyism has been argued to have.

Likewise, Ted Sider (2003) argues on the grounds of microphysical supervenience that consciousness is extrinsic. But even Sider agrees that there is an intrinsic property that is a central constituent of consciousness—which he calls “consciousness*” (sound familiar?)—that is a matter of there being some way it’s like to be that thing.27 Again, I won’t quibble about which property is picked out by our term ‘conscious,’ because again, I don’t need to. We could put the whole Anti-Materialist Argument in terms of Sider’s consciousness*, and it would be just as persuasive as the original. At least it’s as persuasive given that I’m spotting myself the falsity of Mental Manyism on the basis of the absurd moral and practical implications that Mental Manyism has been argued to have.

When it comes to the assumption that the first-person pronoun is precise, the bearing of physicalism is even less clear. Some philosophers have indeed argued that if mental properties are physical properties—and so our token mental states are simply physical states—then massively overlapping human thinkers literally share numerically identical thoughts. And so they have further argued that any first-personal thought that an overlapping thinker has lacks a determinate referent, it referring ambiguously to all of the thinkers with whom she overlaps.28

But now: it’s far from obvious that overlapping thinkers do share numerically the same thoughts, even granting physicalism. Perhaps thoughts are individuated at least in part by thinkers. Distinct thinkers would automatically give us distinct thoughts. Whether that’s true presumably depends on what thoughts are, which presumably depends in turn on the nature of states and events more generally. If, for example, Jaegwon Kim (1976) is right that events and states in general are just property exemplifications—and that no two objects can be in numerically the same state—then no two thinkers could literally share a mental state, such as a particular thought. Contrary to the impression one gets from some of the literature on the thoughts of overlapping thinkers, the nature and identity conditions of states are open metaphysical issues.

It’s also far from obvious that first-person thoughts just as such have whatever referent they do. Perhaps, it’s thinker/first-person-thought complexes, or just thinkers (on a given occasion of having a first-person thought), who do so. Then there’d be no reason that each of the massively overlapping thinkers couldn’t use the same thought to refer unambiguously to herself—again, even assuming physicalism.

This suggests two places to get off the physicalist train that leads to massively overlapping thinkers having no determinate first-person thoughts. First, we might deny that they could share the very same thought. Second, we might contend that even if they do share the very same thought, each one can still think first-personally about herself and only herself. Neither of these two alternatives is obviously right, just as neither is obviously wrong. But a physicalist will be hard-pressed to deny both. If they do deny both, then they’ll be forced to deny that certain evidently thinkable thoughts are in fact thinkable. Suppose God tells me right now that he’s going to eliminate all of the Me_n’s except for Me₄₅ (and except for any Me_n, if such there be, that is a proper part of Me₄₅). That is: God is going to annihilate any particle P such that for some i ≠ 45, P is among the Me_i-particles but not among the Me₄₅-particles. God leaves every other particle (including all of the Me₄₅-particles) intact. Effectively, this turns Me₄₅ into an “unaccompanied” human organism (any humanoid object with which it overlaps is a proper part of it). It seems obvious that I could hope, in a way that’s not obviously empty, that I’m Me₄₅ (or one of the Me_n’s that’s a proper part of Me₄₅). It also seems obvious that I could have the worrying thought—in a way that’s not obviously misplaced—“Oh no, the probability that I am Me₄₅ (or one of the Me_n’s that’s a proper part of Me₄₅) is pretty low! I’m probably doomed!’.’ (Pretend God said that to you, and try this out.) But if the multitude in my chair all share the very same first-personal thoughts, and those thoughts ambiguously refers to all of us, then the only hopes and fears I can manage to have make little sense.

Moreover, the denial that overlapping thinkers can have determinate first-person thoughts would make one’s ability to think about oneself bizarrely extrinsic. Suppose we started with a situation in which the boundaries of human organisms were perfectly precise.29 Consider one such organism who was happily thinking about himself. And then suppose God decided to have some fun, and so sprinkled some atoms at the boundaries of human organisms, thereby making them all very fuzzy. Without touching or otherwise altering the parts of the fellow who was getting along just fine thinking about himself, God would have thereby rendered it impossible for him to do so. This seems incredible. How could one’s ability to think about oneself constitutively depend on anything but what’s going on with oneself?

The bottom line: mounting a supervaluationist response to the Anti-Materialist argument requires a bunch of commitments that are individually implausible—and none of which is straightforwardly entailed by physicalism, let alone by materialism. Taken together, these commitments amount to turning a blind eye to some of the most basic things we know about ourselves from the inside. In any case, what I claim is just this: it’s much harder to deny premise (c) of the Anti-Materialist Argument than to deny premise (c) of the Nihilist Argument. So much is clear, I hope.

Start with the hybrid vague object view. On this view, I am a vague object, and alongside me there are also all of the humanoid precise objects that I named in premise (b): Me₁, Me₂, etc. If this is to provide any relief to a materialist, then it’s going to have to be the case that while I am conscious, none of these precise objects is conscious.33 And you might think that this isn’t terribly implausible. Indeed, this claim about the ‘lack of consciousness of the many precise objects’ might be much more plausible than analogous claims regarding the lack of cloudhood, treehood, or humanity of the many precise objects. After all, as Lewis (1993) points out, it’s very odd to think that none of the arboreal precise objects overlapping Arby is in fact a tree. There’s nothing impossible about a precise tree—just imagine if the world had been much less fuzzy than it is. And it’s unclear how the presence of one vague tree could spoil the precise object’s treehood. So if alongside the vague objects there are also precise ones, you’ll probably still have the many trees, and human organisms too. But when it comes to consciousness, there could just be some contingent law that prevents anything but a vague object from being conscious. It’s not out of the question—at least if you’re dualist enough about consciousness. And so although we might all have to concede that there are many human organisms where I am, the materialist need not concede that there are many conscious beings where I am. Only one of the very many humans organisms here—the one that’s a vague object—will be conscious.

Unfortunately for materialism, I think this is out of the question. The reason it’s out of the question consists in the conjunction of a compelling principle about indeterminate identity, and the claim I made earlier, that consciousness is never vague.

Note first that if I am a vague object who exists along with all of the precise humanoid objects over here, it’s hard to avoid the conclusion that for each such object it’s indeterminate whether I’m identical with it. Consider Me₂₃, which is composed of the Me₂₃-particles. Now, it’s not definitely the case that I am composed of the Me₂₃-particles, but it’s also not definitely not the case that I am composed of those particles. If that were definitely not the case, it would have to be either definite that one of the Me₂₃-particles is not part of me, or definite that something overlaps me but doesn’t overlap any of the Me₂₃-particles, neither of which is the case. (I will return shortly to the argument contained in the previous sentence.) So it’s indeterminate whether Me₂₃ and I are composed of the very same particles. Setting aside the possibility of distinct objects composed of the very same particles—in other words, assuming mereological extensionality—it’ll be indeterminate whether Me₂₃ and I are identical.34 And the same goes for all of the Me_n’s. Each one is indeterminately identical with me.

But now, as van Inwagen himself says about the interaction between indeterminate identity and property possession:

Or as we might put it: if two things aren’t definitely distinct, then could it be that the one definitely has some property that the other definitely lacks? It seems not, as van Inwagen argues, for then they would be definitely distinct. At least suitably qualified, this seems as evident as Leibniz’s Law for determinate identity.35 Let’s call this claim ‘Leibniz’s Law for Indeterminacy’:

So for any property I definitely have, none of the Me_n’s definitely lacks it. It’s at least indeterminate whether it has that property. But now recall the claim I made above about the determinacy of consciousness, this time formulated in property-terms.36

There isn’t anything that’s kinda sorta conscious, and so there isn’t anything that only kinda sorta has the property, being conscious. But then it’s easy to see that we can derive that each of the Me_n’s is conscious after all—indeed, definitely conscious.

Trickle Down Mentality

The upshot is that there’s a trickle-down effect: if I, a vague material object, am definitely conscious, then all of the rest of the precise material objects over here are at least indeterminately conscious. But there’s no stable stopping point at indeterminate consciousness, and so all of the precise material objects over here are definitely conscious. Back to square one.

As I said, van Inwagen doesn’t accept the hybrid view. He doesn’t think there are any precise macroscopic objects. This leads us to wonder: Will salvation for materialism come from the pure view? Unfortunately for the materialist, I doubt it. The reason is that we can’t definitely do away with all of the precise macroscopic material objects—at least not while believing in the vague ones. If I am a vague material object, then for each collection, the Me₁-particles, the Me₂-particles, etc., it’s not definitely false that it composes me, and so not definitely false that it composes something. And not only that. I think we can show that it’s not definitely false that each of the collections composes something.

But all of the links for which I’ve argued, which together take us from the very many precise objects in my situation to the very many conscious beings in my situation, are themselves analytic or conceptual truths, and hence definitely the case. So then it’s at least indeterminate whether there are very many conscious beings where I am. Here’s the argument laid out more carefully, in two steps: