An Argument for Counterpart Theory

[I have no idea if the following is at all novel or plausible.  Any feedback would be sweet!]

Here’s a puzzle.  David Lewis (1986) has argued for the following thesis:

L. Self-identity is not constituted, even in part, by having certain qualities.

Kit Fine (1994) argued for the following thesis:

F. An essential property of an object is any property that, in part, constitutes what it is to be that object.

Combining these two theses would seem to imply the following somewhat troubling thesis:

T. Objects do not have any qualities essentially.

I say that this thesis is troubling because, after all, it would seem to be part of, say, my essence that I have the quality of being human.[1] But how can it be both that I have no essential qualities and that being human is part of my essence? Let’s assume for the moment that we don’t want to reject either Lewis’s thesis or Fine’s thesis (I for one have been convinced by both authors). How then might we get out of trouble?

We might start by denying the claim that being human is part of my essence. We might try saying that although I am necessarily human, Fine (1994) has convinced us that not all necessarily had properties are essential properties,[2] and so it does not follow that I am essentially human. However, the claim that I am not essentially human just seems to me patently false: even if I accept Fine’s understanding of an essential property (which I do) as part of what it is for an object to be that object, it still seems to me that being human is part of my essence—that is, it seems to me that being human is part of what it is to be me.

The other way to avoid trouble is to deny the inference from (L) and (F) to (T). Is this plausible? At first it seems not. After all, the following seem to be straightforward translations of (L), (F), and (T)

L*. Given an object A and some x such that x = A, there is no quality Q such that x’s having Q constitutes, even in part, the fact that x = A.

F*. Given an object A and some x such that x = A, an essential property of A is any property P such that the fact that x has P constitutes, in part, the fact that x = A.

T*. Given an object A, there is no quality Q such that Q is an essential property of A.

And the inference from (L*) and (F*) to (T*) is clearly valid.

So what are we to do? Here’s one response I’d like to suggest: resist the interpretation of (F) as (F*) and instead hold that (F) should be understood as

FC. Given an object A and x such that x is the counterpart of A, an essential property of A is any property P such that the fact that x has P constitutes, in part, the fact that x is the counterpart of A.

Of course, it’s plausible to interpret (F) as (FC) only if our discourse is to be generally understood as about counterparts rather than interworld identicals. So in this way we have something of an argument for counterpart theory: it allows us to explain why three seemingly plausible theses are consistent, when otherwise they would be inconsistent.


[1] If you don’t think the property of being human is purely qualitative, substitute your own favorite essential quality of me.

[2] Fine’s favorite example: Socrates is necessarily a member of the singleton set {Socrates}, but Socrates it is not part of Socrates’ essence—that is, what it is to be Socrates—that Socrates is a member of {Socrates}.

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13 Responses to An Argument for Counterpart Theory

  1. David Gawthorne says:

    T is not troubling if one rejects the essential/non-essential property distinction and consider all properties to be possessed necessarily.

    If one takes a strict view of Leibniz’s Law then any difference of properties implies a difference of entity. One then relies on perdurantism about identity through change and counterpart theory to replace transworld identity. I think this is what Lewis would have in mind and why the synthesis of his views with an essentialist comes out strange.

  2. Dustin says:

    Hi David, thanks for the comment! Could you explain a bit more? What do you have in mind by “reject the essential/non-essential property distinction”? From the context, it seems like you mean “hold that all properties are essential”. But if that’s what you mean, I fail to see how T isn’t then *extremely* troubling.

    Perhaps you could just tell me exactly where you get off the boat. Do reject (L), (F), the claim that (T) is inconsistent with my being essentially human, or the claim that I am essentially human? If none of those, do you reject my explanation of why (L) and (F) don’t actually imply (T)? If so, do you have your own explanation?

  3. Shen-yi Liao says:

    Hey Dustin,

    This topic is cool! I forgot what Lewis says in Plurality, but I remember that in “Counterparts Persons” he revises his initial theory and distinguishes between the standard counterpart relation and counterpart relations generally that may vary by context. Which one are you thinking of in the formulation of (Fc)?

    It seems that the main distinction you want to make is that identity is distinct from “what it is to be”; the first is to be cashed out by the identity relation and the second is to be cashed out by the counterpart relation. Is that correct?

  4. Dustin says:

    Thanks for the comment, Sam!

    “It seems that the main distinction you want to make is that identity is distinct from “what it is to be”; the first is to be cashed out by the identity relation and the second is to be cashed out by the counterpart relation. Is that correct?”

    Exactly!

    “in “Counterparts Persons” he revises his initial theory and distinguishes between the standard counterpart relation and counterpart relations generally that may vary by context. Which one are you thinking of in the formulation of (Fc)?”

    Great question! I guess the answer depends on whether we think that “what it is to be” can vary by context. Hmm… perhaps the easy answer would be to say that it varies by context, but I’m tempted to go hardcore and say that it doesn’t. (I’m still trying to earn by badass credentials, you know?!) Let me think about it some more. Any thoughts of your own?

  5. davidgawthorne says:

    Perhaps I misunderstood L. Nevermind.

  6. a says:

    dustin-

    this seems totally sweet. i guess i’d be tempted to reject (L) outright, but i haven’t read lewis’ argument for this (or i have and i’ve forgotten it). do i correctly infer from sam’s comment that i should look in ‘plurality’?

    how’s australia? hope you’re having an amazing time!

  7. nate charlow says:

    I’m missing how this is an argument for counterpart theory. It looks to me like an argument for one of the following:

    1. There are no essential properties in the sense of F*. Well duh!

    2 (=(FC). The counterpart relation is constituted by essential properties.

    I can accept either (1) nor (2) without thinking that transworld identity is a matter of a counterpart relation holding between individuals (I take it this is what you mean by “counterpart theory”. If not, then what do you mean?). Maybe there is a useful relation R(,) that’s constituted by essential properties of one of the relata, but it’s an extra step to identify R with transworld identity.

    You’re probably going to point me to this sentence: “Of course, it’s plausible to interpret (F) as (FC) only if our discourse is to be generally understood as about counterparts rather than interworld identicals.” Honestly, I don’t know what you’re talking about here.

  8. nate charlow says:

    I should unpack that.

    If you’re not equivocating on “essential property”, there is no reason to think that the argument from L* and F* to T* is not sound. So, I agree, Fine shouldn’t be read as saying that the properties that constitute what it is to be x are what constitute the fact that x=x.

    So maybe the properties that constitute what it is to be x are what constitute the fact that R(x,y) (where R=the counterpart relation) for all y such that R(x,y). But why are the properties that constitute what it is to be x (necessarily? in a world?) to be identified with the properties that ground transworld identity? I’m missing the argument here.

    Another worry, not voiced above: you seem to be presupposing that R and = are the only candidates for understanding the relation that essential properties constitute. Whether or not this is plausible depends on what you understand “counterpart theory” to mean. If you think counterpart relations hold on account of purely qualitative resemblance relations between individuals, then there are many other candidates that could fill the space. Why think that essential properties play any constitution role for facts about qualitative resemblance relations?

  9. Dustin says:

    Nate, thanks for the comments and sorry it’s taken me so long to reply!

    I think the central misconception (due to my not being clearer) of your comment is that what I mean by “counterpart theory” is that “transworld identity is a matter of a counterpart relation holding between individuals”. That is certainly not what I (or anyone, as far as I know) has taken “counterpart theory” to mean. Lewis, to take the most obvious example, accepts counterpart theory but rejects the claim that individuals (as we typically understand term “individuals”) are ever transworld identical. Actually, given Lewis’s acceptance of (L), it would be *absurd* for him to accept counterpart theory under your definition–namely, as the thesis that transworld identity is a matter of a counterpart relation holding between individuals–since transworld identity is, after all, identity and counterparthood is, after all, constituted by qualitative similarity.

    What Lewis (and I) mean by counterpart theory is roughly this: subjunctive conditionals and modals such as

    1. If John were in Canberra, he’d be cold.
    2. John might have been cold.

    are made true by facts about John’s counterparts at other possible worlds, not facts about John at other possible worlds.

    As far as your “another worry” goes, no I’m not assuming that. I’m just saying: here are two plausible candidate relations. This one doesn’t seem to work. This other one does. Cool, so maybe it’s that one.

  10. Dustin says:

    So I’ve had some clearer thoughts about how exactly this is an argument for counterpart theory (as defined in my last comment).

    Fine rightly rejects the entailment from “A is necessarily P” to “A is essentially P”. However, he rightly admits the entailment from “A is essentially P” to “A is necessarily P”. How to explain why this later entailment holds?

    Note that if “A is essentially P” meant “part of what constitutes the fact that A = A is the fact that A is P”, this would explain why “A is essentially P” entails “A is necessarily P”, since necessarily A = A. But we already ruled-out, via Lewis’s thesis, that reading of “A is essentially P”. So is there another explanation?

    Suppose, as I’m claiming, that “A is essentially P” means “Given any x such that x is the counterpart of A, part of what constitutes the fact that x is the counterpart of A is the fact that x is P”. Now GIVEN counterpart theory–in particular the claim that

    1. A is necessarily P

    is true just in case every counterpart of A is P–it follows that “A is essentially P” entails “A is necessarily P”.

    So there’s the argument for counterpart theory: counterpart theory together with the counterpart analysis of “essentially P” explains why “A is essentially P” entails “A is necessarily P”. That’s not to say that there couldn’t be another explanation. Just that it’s *an explanation* and perhaps the *best on offer*. So what we really have here is an (inference to the best explanation) argument for a combination of two theses: counterpart theory AND the counterpart analysis of essence.

  11. nate charlow says:

    Ok, I see what’s going on a bit better now. Thanks.

    I shouldn’t have said “transworld identity”. I was using this (misleadingly, it seems) as shorthand for the idea that, in giving a semantics for modal talk and modal logic, something playing the theoretical role (the “transworld identity” role) of defining a set of accessible individuals for the purposes of quantification — either numerical identity or ersatz identity constituted by the counterpart relation — must be appealed to.

    Two analogues of my original questions still hold:

    1. Why are the properties that constitute what it is to be x to be identified with the properties that ground ersatz transworld identity? Why think that all essential properties (including, if there are such things, essentially relational essential properties?) have something to do with qualitative facts? Or are you offering a revisionist proposal for understanding what it is for something to be something else’s counterpart? Maybe this is pressing a bit too hard, but I’m interested to know what your thinking is here.

    2. Grant that the properties that constitute what it is to be x ground, in part, ersatz transworld identity. Is this an argument for using ersatz transworld identity in our model for modal logic and discourse? Two reasons for worry:

    2a. Why couldn’t there be a counterpart x of A that isn’t P (where P is a property constituting what it is to be A)? Your argument in your last comment just assumes that all facts about which individuals are counterparts of A have to be constituted in part by those individuals having P, given that essential properties constitute facts about counterpart relations. But two distinct and unrelated facts F1 and F2 can on different occasions both constitute the fact that F3. The fact that I’m in pain is presently constituted in part by my C-fibers firing. The fact that I’m in pain is (after the Singularity) constituted in part by a silicon chip being electrically stimulated. Maybe your assumption is plausible, but, given a framework in which NEC=∀, it doesn’t seem to be explaining why essence entails necessity, so much as taking it for granted.

    Given that we can make Fine and Lewis’ positions consistent while embracing a weaker interpretation of Fine’s claim, why should we opt for the stronger one? Maybe because it’s strictly consistent with thinking that a counterpart of A might lack P, and that’s ridiculous. But accepting that neutralizes the supposed explanatory power of the counterpart-theoretic semantics for necessity.

    2b. Given 2a, why is this an argument for counterpart theory? I can accept that the counterpart relation is constituted by essential properties without thinking that the counterpart relation is what should play the transworld identity role in the model.

  12. Dustin says:

    Thanks for the excellent follow-up questions, Nate! I’m not sure what to make of all the (rhetorical?) questions in (1), so let me just ignore them for the time being on the grounds that they are at this point “pressing too hard”. Also, I’m also not sure what to make of (2b), since what I mean by “counterpart relation” is simply “that relation which plays the transworld identity role in the model” (if by the latter you mean “that relation used in the interpretation of sentences such as ‘John might have been in Canberra’, etc”).

    But as for (2a), yes, I think this is a very important worry. You’re right that presumably for some counterparts x and y of A, there will be some properties that partly constitute the fact that x is the counterpart of A that do not partly constitute the fact that y is the counterpart of A. But I’m thinking that an essential property P of A is a property such that for ANY counterpart x of A, the fact that x is the counterpart of A is partly constituted by the fact that x is P. I admit that (F^C) was not written this way… soz. So let me just state it once here for clarity:

    FC. P is an essential property of A iff for ANY x such that x is a counterpart of A, P constitutes, in part, the fact that x is a counterpart of A.

    You may worry that there are no such properties. But take me and any of my counterparts. For any of those counterparts, isn’t it true that their being human is, in part, what makes them counterparts of me? (It’s tempting to say something like: isn’t it true that if they WEREN’T human, they wouldn’t be my counterparts–but I think you can see why I don’t want to go down that road.) Take any rock in another possible world. Isn’t one of the reasons why no such rock is a counterpart of me the fact that no such rock is human?

    Here’s maybe a little more precise way to work things out. Take an actual object A, a world w, and an individual x in w such that x is the counterpart of A. Lewis says that the fact that x is the counterpart of A at w is constituted by (I) x’s being the most (saliently) similar thing in w to A and (II) x’s being SUFFICIENTLY (saliently) similar to A. Perhaps my suggestion then is this: to be sufficiently (saliently) similar, an object must have certain properties. The having of these properties will then be what constitutes, in part, the fact that any counterpart x of A is the counterpart of A. [Note that I’m not wedded to this way of working out (FC), but maybe this could work].

    Anyway, thanks again for the great questions. I think it will be very fruitful to work out their answers in more detail. But if I’m right about that, then isn’t the fruitfulness of my view something of an argument for it? Yeah, I think so.

  13. Dustin says:

    Oh, RE: your point (2b), I think I see now what what you mean. I think you probably take “counterpart relation” to simply mean something like the relation defined by (I) and (II) above. Then you take it as a substantive claim that the counterpart relation is that relation that play the transworld identity relation in the model. OK, I was taking things the other way around: “counterpart relation” for me simply means “that relation which plays the transworld identity role (but isn’t transworld identity) in the model” and taking (I) and (II) to be substantive claims about that relation. But yeah, I haven’t been very clear about this, so thanks.

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