Merricks on universalism and composition as identity

My earlier request for comments on my revised version of my Phil Studies paper ‘The Contingency of Composition’ recevied a grand total of no results, so I’m going to post the argument I particularly wanted reactions on and see if that provokes any response. If it doesn’t, I will take this as tacit consent from the entire philosophical community that I am right!

In the paper I claim that composition as identity is compatible with restricted composition. What I would like comments on is my response to Merricks’ argument to the contrary. Merricks has us assume, for reductio, that composition as identity is true and that mereological universalism is false. From the latter assumption, there are some things, the Xs, that don’t compose. But, says Merricks, they could compose. So there is a world, w, in which there is something that is composed of the Xs, call it A. Composition as identity, if true, is necessarily true, so A is identical to the Xs in w. Hence, from the necessity of identity, A is identical to the Xs in the actual world (@). And so, from composition as identity, the Xs actually compose in @, contrary to the initial assumption.

Now, I’m not sold on the necessity of identity at the best of times, but I think it’s particularly problematic here. There are two ways in which we might try and use the Barcan/Kripke argument for the necessity of identity to show that if A is identical to the Xs in w then it is identical to the Xs in @. Firstly, we might argue as follows:

A is necessarily self-identical in w. So in w, A has the property being necessarily identical to A. So, since A is identical to the Xs in w, the Xs has the property being necessarily identical to A. Hence, in the actual world, the Xs has the property being identical to A. Hence, A is identical to the Xs in the actual world, and hence the Xs compose A in the actual world, contrary to the hypothesis that there is nothing that the Xs actually compose.

This argument doesn’t work, however. A familiar complication with the Barcan/Kripke argument is that we must bear in mind is that we are dealing with contingent existents. If A is not a necessary existent then it is not self-identical in every world; all we can say is that it is self-identical in every world in which it exists: that is, that is has the property necessarily, being identical to A, if A exists. So all we can say about the Xs in w is that it has this property; and so all we can conclude is that in the actual world the Xs has the property being identical to A, if A exists. But, of course, proving that the Xs has this property in the actual world doesn’t tell us anything about whether or not the Xs actually compose. All we can conclude is that they actually compose if A actually exists – but, of course, whether or not A exists is precisely what is up for debate.

The argument only has a hope at succeeding if we start not from the necessary self-identity of A but from the necessary self-identity of the Xs. In that case the contingent existence of the Xs is not a problem. We can argue as follows. In w, the Xs is necessarily self-identical, by which we mean that the Xs is self-identical in every world in which the Xs exist. Hence, the Xs has the property necessarily, being identical to the Xs, if the Xs exist. Hence, given Leibniz’s law, A has the property necessarily, being identical to the Xs, if the Xs exist in w, and therefore has the property being identical to the Xs, if the Xs exist in the actual world. Since we know, ex hypothesi, that the Xs exist in the actual world, we can conclude that A is actually identical to the Xs, from which it follows, given composition as identity, that the Xs actually compose A, contrary to the hypothesis that they don’t actually compose anything.

But while there is no problem in this version of the argument due to the contingent existence of the entities involved, there is a further problem that faces this version and not the earlier version. The problem is that, while I am happy to grant the assumption that A is necessarily self-identical in w, I am not happy to grant the assumption that the Xs are necessarily self-identical in w.

My claim is that it only makes sense to ascribe a property like being self-identical to a plurality of things if there is some thing that the plurality is identical to; i.e. if there is a one that the many are identical to. (We can say that each of the Xs is necessarily self-identical, but that won’t help: we need the strong claim that the many are self-identical, and that only seems to make sense if there is a one that the many are identical to.) One can only infer that the Xs have the property of being self-identical at a world if we know that the Xs are identical to some thing at that world – i.e. if we know that they compose at that world (since, we are assuming for the sake of argument, what it is for a collection to compose is for them to be identical to some thing). So one cannot simply assume that the Xs are necessarily self-identical; to make this claim we would need to have a reason for thinking that they are necessarily identical to some thing or other. But that is simply the claim that they necessarily compose, which just begs the question. My contention – the claim Merricks is attempting to argue against – is precisely that the Xs compose in w but not the actual world: that there is some thing in w that they are identical to but that there is no thing in the actual world that they are identical to. In that case I deny that the Xs has the property being necessarily self-identical in w. All that we can say is that in w the Xs has the property being identical to the Xs, if identical to anything as a matter of necessity; but all that will prove is that A actually has the property of being identical to the Xs if identical to anything. And as before, that won’t tell us anything at all about whether A is composed of the Xs in the actual world, since whether or not A is identical to anything at the actual world depends on whether or not A actually exists, which is what is up for dispute.

So I don’t think there is any version of the Barcan/Kripke argument that can prove that A is actually identical to the Xs because A is identical to the Xs in w. We cannot start from the premise that the Xs is necessarily self-identical in w: that begs the question, because it assumes that there is necessarily a one that the Xs is identical to, which is just to assume that they necessarily compose. There is only something which is identical to the Xs if the Xs compose; so, since I take it to be contingent that the Xs compose, I also take it to be contingent that there is some thing that is identical to them, and hence I reject the first premise of the argument that they are necessarily identical to A. If Merricks appeals (on the assumption of composition as identity) to the necessity of the self-identity of the Xs in order to show that the Xs must actually compose then he assumes, I argue, that the Xs necessarily compose; and that is simply to beg the question against me. We can start from the assumption that A is necessarily self-identical – that is unproblematic provided we are careful to mean by this only that A is self-identical in every world in which it exists: but while the resulting argument has true premises, the conclusion is far from what Merricks wants – we cannot conclude that A is actually identical to the Xs, only that A is actually identical to the Xs if it (A) exists. Since the existence of A at the actual world is precisely the issue of disagreement between Merricks and myself, this argument obviously isn’t going to persuade me.

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15 responses to “Merricks on universalism and composition as identity

  1. Hi, I’m not totally familiar with this area, so if I make a blunder, I apologise. I agree with your overall argument, but I think you can deal with the second version of the Barcan/Kripke argument without having to argue that a plurality can only be self identical to a singular thing, but rather by repeating, slightly rehashed, your objection to the first formulation. (It may well be true that a plurality can only be self identical to a singular thing, but perhaps it is more controversial than your other arguments, so if you can get away without you would only have to defend yourself on one front.) The ‘familiar complication’ that you mention in the first argument I take to be the claim that if an object is a contingent existent it is not necessarily self identical – i.e. it is not self identical in every accessible possible world, because it is not self identical in those worlds where it does not exist. Accordingly, your opponent cannot make the move from A being necessarily identical to A in w to Xs being necessarily identical to A in w to Xs being identical to A in @. (Have I got you right so far?)However, if the above argument goes through, if A can only be identical to A when A exists, surely it is also the case that A can only be identical to Xs when A exists. Now if we start with the self-identity of the Xs, as you do in the second formulation:“Hence, the Xs has the property necessarily, being identical to the Xs, if the Xs exist. Hence, given Leibniz’s law, A has the property necessarily, being identical to the Xs, if the Xs exist in w, and therefore has the property being identical to the Xs, if the Xs exist in the actual world.” It would seem that we should rather say that given Leibniz law, A has the property necessarily, being identical to the Xs, if the Xs exist, and if A exists. Or alternatively, perhaps we should say that given Leibniz law, A has the property necessarily, being identical to the Xs, if A exists. If this seems like a violation of Leibniz, then perhaps the original property should be understood as containing an indexical referent: so the property becomes: necessarily, being identical to Q, if [the possessor of the property] exists. When Leibniz’ law is used to attribute the property to A, the contents of the square bracket changes to ‘A’.So again, all we have is that A is identical with Xs in @ if A exists, which is no problem. (As an aside, does this argument work if the Xs are necessarily existent?)

  2. Thanks Geoff. I toyed around with that thought for a while myself. The reason I go the way I go and not this way is as follows. You say”It would seem that we should rather say that . . . A has the property necessarily, being identical to the Xs, if the Xs exist, and if A exists”This is the claim I don’t want to rely on. It seems that (if we ignore the worry I raise) we can say of the Xs that they are necessairly identical to the Xs, if the Xs exist. So by LL we can say this of A, since A is the Xs. Why should we only be able to say of the Xs that they are necessarily identical to the Xs if both the Xs and A exists?Compare how your point goes in the more germane case of one-one identity. Would you be willing to say that Phosphorus can exist but fail to be identical to Phosphorus provided Hesperus doesn’t exist? That sounds odd to me – surely the conditions for Phosphorus being identical to Phosphorus are just that Phosphorus exists. (And hence, by Leibniz’s law, the conditions for Hesperus being identical to Phosphorus are just that Phosphorus exists – by which we prove that Hesperus must exist and be identical to Phosphorus in every world in which Phosphorus exists.)Likewise, surely the conditions for the Xs being the Xs are just that the Xs exist (modulo my other concern). And so, by LL, the conditions for A’s being the Xs are just that the Xs exist – by which we prove that A must exist and be identical to the Xs in every world in which the Xs exist.So I think either you have to commit yourself to some stange sounding results in the germane cases, or rely on my point for the many-one case. I find the latter more palatable, which is why I rely on that rather than the argument you offer.But it is a really tricky issue. I’m far from confident that your point isn’t correct (in both the many-one case and the one-one case). And if it is – well, that’s just one more potential nail in the coffin for Merricks’ argument, and that doesn’t sadden me!

  3. Thanks, yeah, I see your point. My mistake was to say the property was:”necessarily, being identical to the Xs, if the Xs exist, and if A exists”However, my thought was that it is plausible that property had by an object P is not:“identical with something (Q), provided that that something (Q) exits.”But rather:“identical with something (Q), provided that the holder of the property, object P, exists.”So in the case of Phosphorus and Hesperus, Phosphorus is identical with Phosphorus, provided that Phosphorus exists. And by LL Hesperus is identical with Phosphorus, provided that Hesperus exists. So we wouldn’t have to say that “Phosphorus can exist but fail to be identical to Phosphorus provided Hesperus doesn’t exist.” But we would say that Hesperus can fail to be identical to Phosphorus provided Hesperus doesn’t exist, and this sounds fine to me (?) – to be honest though, I am pretty convinced by the one-many identity problem that you go for, so perhaps I am just asking unnecessary questions.One more point (then I’m sure I have a thesis somewhere I should be attending to) is there anything wrong with arguing like this?:No version of the Barcan/Kripke argument can work as it would prove too much. Take an example of normal contingent identity. In w Blair is identical with the King. Also, in w Blair has the property ‘necessarily, identical with Blair, if Blaire exists’. Then by LL, in w The King has the property ‘necessarily, identical with Blair, if Blaire exists’. So in @ The King has the property identical with Blair, if Blair exists. This is obviously screwy, but I can’t see any difference between this line of reasoning, and the one involved in the second version of the Barcan/Kripke argument. Anyway, Ross, feel no obligation to reply, I’m sure you are busy, and as I said this isn’t my area so I am no doubt a little confused. But I like the blog, I’m thinking it would be good to start one up here in Manchester.

  4. So the Xs have the property of being identical to the Xs if the Xs exist. But do you want to say that A only has the property of being identical to the Xs is A exists and deny that it has the property of being identical to the Xs if the Xs exist? That sounds like a denial of Leibniz’s law.I think there isn’t really a problem in the “screwy” version of the argument provided we’re careful. ‘The King has the property ‘necessarily, identical with Blair, if Blair exists” is perfectly acceptable provided it is understood de re – as attributing a property of the object that is in fact (in w) the King.Of course, the *sentence* ‘Blair is the King’ doesn’t actually say something true. But the falsity of this sentence is compatible with the person who we picked out with the term ‘the King’ in w being Blair in @. It’s just that ‘the King’ is a non-rigid designator (i.e. one that changes its reference from world to world).A Manchester blog would be a good idea – especially given the imminent influx of excellent young philosophers!

  5. What is your reason for thinking that a plurality is self-identical only if it it is identical to some one thing?

  6. I just can’t understand what it is for a many to be self-identical unless the many are a one that they can be self-identical *to*. I can understand what it is for *each* of the many to be self-identical – but that’s not what’s being claimed. It’s being claimed that these things – the Xs – satisfy the predicate *is self-identical*: the very same predicate that is necessarily satisfied by every one thing. I can only make sense of something satisfying this predicate if it is *some thing* – i.e. an individual.That’s not really an argument, I guess – just a statement of my conceptual limitations. Do you think the plurality of the Xs could satisfy the predicate ‘is self-identical’ even if there is no one that the Xs are identical to?

  7. Pretty cool. But I still think that you’re refusing to really take on board the assumption that composition is identity — a very weird view, and I empathize with the resistance! But you have to really take the premise seriously — that they are the same relation, and that it’s a relation that can hold both one-one and many-one. After all, your claim is not supposed to be that composition as identity is a bad idea, but rather that it’s consistent with the contingency of composition. Which I don’t think it is…Argument 1: the point about contingent existence seems like a good one. But I’m not sure it really blocks the argument… consider a parallel case where it’s just identity at stake. Samuel Clemens is not a necessary existent, so he “is not self-identical in every world; all we can say is that [he] is self-identical in every world in which [he] exists: that is, that [he] has the property necessarily, being identical to [Mark Twain], if [Mark Twain] exists. So all we can say about [SC] in w is that [he] has this property; and so all we can conclude is that in the actual world [SC] has the property being identical to [MT], if [MT] exists.” That all sounds good so far. But it’s hard to see what’s supposed to happen when we move back to the actual world. Is it really the case that proving that SC actually has this property doesn’t tell us anything about whether Mark Twain exists?Ooops — I just read your reply to Geoff, and it sounds like you agree. Though thequestion I am asking is not whether you would endorse “Phosphorus can exist but fail to be identical to Phosphorus provided Hesperus doesn’t exist” but rather whether you would endorse “Phosphorus can exist but fail to be identical to Hesperus, provided Hesperus doesn’t exist”. BOTH sound odd to me… And someone who really endorses strong composition as identity is going to say that the composition case is just the same. What it is for A to exist is for the xs to exist. Period. Argument 2: Bradley’s question. Whence the assumption that pluralities are not identical to themselves? (Sorry, I just really wanted to use the word ‘whence’!) IF your assumption is right, Trenton’s argument looks question-begging.. But it’s hard for me to see how YOU’RE not begging the question. What’s the non-question-begging justification for the assumption? To assume it seems tantamount to denying that composition is not identity.

  8. My concern is the one stated (much better than I would have stated it) by Dr Bennett in Argument 2. I don’t think that someone who can conceive of a plurality being self-identical will grant your assumption that it makes no sense. And if it does make sense, then it seems that we can start with the necessary self-identity of the Xs and conclude that they compose A. So you may need to argue that1) A plurality is self-identical only if it is identical to some one thing.From there, you can modus tollens (for by hypothesis the Xs are not identical to A in @, and to say they are is question-begging), and thus the plurality is not self-identical. From there your argument continues.Does that sound right?

  9. Hi Karen, (and this addresses Bradley’s last point as well, I think),I may well be begging some questions against Merricks. But dialectically, I think the burden of proof is on him and not me, so I think I can get away with it (of course!).My guiding method, remember, is to take something to be possible unless given good reason to take its negation to be necessary. Now maybe that’s wrong. Maybe we should take something to be necessary unless given reason to think that its negation is possible. If so, then I’m perfectly happy to accept the necessity of composition etc. I haven’t argued for the ‘possibility first’ approach – merely assumed it.But on that assumption, I think the ball is in Merricks’ (or the necessitarian in general) court to argue that what I claim to be possible isn’t – it’s not on me to give some positive reason to accept it as a possibility.Now, I’m being generous and assuming that it makes sense to speak of a many being identical to a one. I personally can’t make sense of that – but hey, let’s run with it. It also seems to make sense to me, however, to speak of a many not being identical to any one – in fact, isn’t that what almost all of us think is true of *every* many? Prima facie, then, both are possibilities. There should be worlds (like @, I claim) where there is no one that the many Xs are identical to, and worlds (like w, ex hypothesi) where there is a one (A) that the many Xs are identical to. Ex hypothesi, the former will be a world where the Xs don’t compose and the latter a world where they do.Do I beg the question in assuming that there is the first world? Maybe. Just like I beg the question against the dialetheist when I rely on the law of non-contradiction. So it comes down to who has the burden of proof in their favour. I think I do, becuase of my ‘possibility first’ methodology. We can focus the argument on whether that’s a good methodology if you want – but I’m really concerned with the conditional: if this is a good methodology, then there’s no reason to hold that composition as identity entails univeralism.Karen – you claim I’m not taking seriously the thought that composition and identity are one and the same relation. I think I am. In w, the Xs *really are* identical to A, and that *really is* just what it takes for them to compose A.But to say that they *really are* the same realtion only implies, surely, that, necessarily, whenever we have one we have the ‘other’. In any world, if we have the Xs being identical to something then we have them composing – because it’s the same relation!Fair enough – but how can this tell us anything about @? My contention is that there is nothing the Xs compose and nothing that they are identical to. I can see how I would be denying that composition and identity are one and the same relation if I held that there is something that they are identical to but nothing that they compose, or held that there is something that they compose but nothing that they are identical to. I can’t see how I am denying the identity of the relations if I deny that they ‘both’ obtain.You say “To assume [that some pluralities are not identical to some thing] seems tantamount to denying that composition is identity.” I don’t see why. I can see why it would be to assume that if we added the assumption that universalism is true – but that would be to beg the question against me again.I assume that pluralities are identical to some thing if and only if they compose. Isn’t *that* what the thesis of composition as identity *is*. Whence (you’re right, that’s fun!) the assumption that, necessarily, every plurality *is* identical to some thing? Given composition as identity, that’s just the assumption that univeralism is necessary. Again – question begged.Since there’s no obvious incoherence in claiming that some many is *not* identical to any one (after all, that’s what they vast majority of us think about *every* plurality!), we should accept that there could be such pluralities, unless given reason to deny such a possibility. The burden, I claim, is on the CAI theorist to show me why this is impossible.

  10. No, no, I like the methodology. Except of course when there’s something *I* want to insist is necessary. !This bit seems right: “I can see how I would be denying that composition and identity are one and the same relation if I held that there is something that they are identical to but nothing that they compose, or held that there is something that they compose but nothing that they are identical to. I can’t see how I am denying the identity of the relations if I deny that they ‘both’ obtain.”OK, so you’re maintaining the connection between identity and composition: the xs are identical to something(s) iff there is something(s) that they compose.But then I think what you’re committed to denying is the connection between existence and identity: the xs exist iff they are/it is self-identical.You think that some many exists without being identical to or composing any one. I think the relevant claim is: some many exists without being identical to or composing *anything(s)*. And I think that’s not possible, because of the existence-identity connection. That is, it’s not possible for the xs to exist, but there is nothing they compose and nothing they are identical to. Because those quantifiers in the ‘there is nothing…’ parts are not straightforwardly either singular or plural.Relatedly — you say that “there’s no obvious incoherence in claiming that some many is *not* identical to any one (after all, that’s what they vast majority of us think about *every* plurality!)” — right, because the vast majority of us have a hard time getting our heads around composition as identity! I mean, there *is* an obvious incoherence in claiming that some one is not identical to any one. The point is this: I think a good CAI-er has to engage in the kind of singular/plural slurring I’ve just been doing…. and I suspect it’s crucial here. You are resisting Trenton’s argument by refusing to slur, and I think that’s what makes it the case that you’re not quite taking CAI fully on board as a premise for the reductio. Then again, the dialectical stuff is tricky. Whose job is it to defend the CAI singular-plural-slurred versions of the existence/identity and identity/composition connections? I guess I’m thinking that if you take the latter as a premise for reductio, you have to take the former too. And I guess you’re thinking not. Herm. Philosophy is hard.

  11. Thanks Karen, that’s really helpful.The existence/identity condition definitely seems like where the action is. Now there’s a sense in which I think the principle is innocuous: because I certainly think that if you’ve got the Xs each of the Xs is identical to something, and I certainly think that if you’ve got the sum of the Xs, it’s identical to something. What I’m denying is the necessity of the claim that if you’ve got the Xs then you’ve got something that is identical to the Xs, and everything else is going to hinge on the denial of that necessity.It is hard. I can’t really argue for denying the necessity on the grounds that I can conceive of the negation, because I just can’t conceive *any* of these many-one identity claims to be true. All I can say is that insofar as I understand CAI, I can understand CAI with the weaker existence/identity claim as much as I can understand CAI with the stronger existence/identity claim.I’m happy to grant that the latter theory entails the necessity of universalism. I expect my opponents to accept that the former theory does not, and is compatible with the contingency of composition. I guess my claim then is that, given the possibility-first methodology, the weaker theory should be accepted before the stronger one unless we’re shown what exactly is wrong with it.

  12. Hi Ross,I want to make sure I understand the state of play. Let’s pick up theargument where we are assuming: (i) The x’s are identical to A in w; (ii) A exists in w; (iii) Necessarily, if the x’s are identical to A, then necessarily if A exists, then the x’s are identical to A.You note that (i) – (iii) yield (iv) the x’s are identical to A in @only if we are given that A exists in @. (There’s also Brouwerschereasoning in there.) And our assumption for reductio of the falsity ofmereological universalism + “composition is identity” motivatesrejecting the idea that A exists in @. So far so good. Now Bennettresponds: if the x’s are identical to A in w, then they have the samemodal existence profile, i.e.: (v) Necessarily, if the x’s are identical to A, then necessarily, the x’s exist iff A exists.Thus, if you accept (vi) the x’s exist in @then (v) plus reasoning analogous to the original argument will yieldthe existence of A in @, and Merricks’s argument will go through.Thus, I don’t think you can grant (as you seem to further down in youroriginal post) that the x’s exist. If I understand you correctly, theposition you hold post-Bennett is that there is an ambiguity in theclaim that the x’s exist. To wit, (vi) is ambiguous between: (vi)_a Each of the x’s exist and (vi)_b There is an individual that is the x’s. (Perhaps colloquially: “The x’s collectively exist”)Read (v) in accordance with (vi)_a, and it’s false. Read (v) inaccordance with (vi)_b and it’s true, but the reductio assumptionsrequire denying that the x’s (collectively) exist in @.If this is a correct reconstruction, I suspect that the claim forMerricks’s opponenent to deny on either horn of your dilemma is thatthe x’s (collectively) exist in @.And I definitely don’t think any questions are begged unless youregard your reflections as doing anything more than showing thatMerricks’s argument does not establish the intended conclusion: thereis a prima facie coherent position according to which MereologicalUniversalism is false and composition is identity.Incidentally, I would point you to some work in progress by Paul Hovdathat discusses the relevant ambiguity thesis and the import of theclaim that composition is identity. I think the paper mostinteresting to you would be “How Composition Could be Identity”. Ifyou email him, I’m sure he would send you a copy.- Louis deRosset

  13. Hi Louis,yep – that’s how I understand the state of play too. (Although I don’t think I’ve changed anything I believed post my discussion with Karen – but I do think I’ve become more clear on what it was I previously believed!)Thanks for the pointer to the WIP.Ross

  14. Hi Ross,BTW, I think, so long as the key move in resisting the argument is todeny that the x’s (collectively) exist in @, your response can beimproved so as not to rely on the idea that a contingent existent isnot self-identical in a world in which it does not exist. This claimis controversial in some quarter worth taking seriously. (I haveDavid Kaplan in mind.)For even if the x’s (collectively) are identical to A in @, they, likeA, don’t exist in @. The inference in the Barcan/Kripke argument from (vii) the x’s (collectively) are identical to A in @to (viii) the x’s compose in @requires exactly the existence premise at issue, viz. (vi)_b. (I’mreading “the x’s compose in @” as “there is an individual A such thatthe x’s (collectively) compose A.”)Yours,Louis

  15. Fun topic! I wanted to elaborate on something Karen said, that “a good CAI-er has to engage in…singular/plural slurring.” I think that’s right, and I think in doing so, the CAI-er has a response to your claim that that “it only makes sense to ascribe a property like being self-identical to a plurality of things if there is some one thing that the plurality is identical to.” I actually agree with this claim on it’s surface. But that’s because the predicate “is self-identical” is forcing a singular reading of the subject term. Rephrased neutrally, and in a way that is not loading the case against the composition as identity theorist, your claim is easily rejected by the CAI-er.To see this, notice that we can take the predicate “is self-identical” as used in (1), where ‘x’ here is neutral and can be read as either a singular or plural subject term:(1) x is self-identical.And replace it, without loss of meaning, with the synonymous predicate “is identical to itself” as used in (2):(2) x is identical to itself. But notice that this replacement sentence makes more explicit the presumed singularity of the subject term. Try, if you like, to force a plural subject term for ‘x’. You get something ungrammatical like (3): (3) x, y, and z is identical to itself. Notice that (3) is ungrammatical even if x = y = z. (At least it seems to me. I find the sentence “Superman, Clark Kent, and Cal El is identical to itself” totally ungrammatical.) This shouldn’t be too surprising, however, since the “is” and “itself” are both words that assume a singular subject. So what we need is a predicate that will allow a plural subject term, since disallowing this will already be assuming that CI is false. One easy way to do this is to take the predicate “is identical to itself” and turn it into the plural counterpart: “are identical to themselves.” Then we can have grammatical sentences like:(4) x, y, and z are identical to themselves. If we like, we can introduce a jerry-rigged plural counterpart predicate of ‘is self-identical’—something like ‘are selves-identical.’ Then, we can make a singular/plural-neutral predicate by producing an (admittedly ugly and cumbersome) hybrid predicate such as ‘is/are self-/selves-identical’, for whenever it is underdetermined whether we are dealing with many or one. So we get sentences such as (5), again, assuming that ‘x’ can be either a singular or plural term.:(5) x is/are self-/selves-identical.We can now see that your claim that “it only makes sense to ascribe a property like being self-identical to a plurality of things if there is some one thing that the plurality is identical to” is true only because the predicate you are employing—“being self-identical”—is a singular predicate, which requires a singular subject term to preserve grammaticality. But insofar as we are worried about the deep metaphysical underpinnings about claims about identity, and not mere grammaticality, we can then use our jerry-rigged singular/plural neutral predicate as used in (5). This sentence—albeit ugly—saves us from begging the question against CI, and also allows us to see how a CAI-er can resist your claim. For notice that if we replace “being self-identical” with our new neutral predicate, in your original claim, we get (6), which, I take it, is not true:(6) “it only makes sense to ascribe a property like is/are self-/selves-identical to a plurality of things if there is some one thing that the plurality is identical to.” -Meg

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