On Numerical Sameness / Identity / “Absolute” Identity

I’ve been reading some stuff about identity and relative identity lately, in the process of writing something on relative identity versions of trinitarianism. This post is to share some good finds.

In his excellent entry “Relative Identity veteran logican and philosopher of language Harry Deutsch says about the best that can be said for relative identity theories – that maybe, arguably, they solve or help to solve various metaphysical problems. See his sections 2 and 4 for these. His section 5 is a penetrating analysis of Geach’s very hard to follow arguments.

Deutsch’s point of view is very different from that held by most philosophers. For this, see chapter 1 of Colin McGinn’s Logical Properties. (NDPR review.) This is more or less  the “orthodox” view that most philosophers hold, atheist or theist, trinitarian or not. I largely agree with it, except for its Platonic aspect. I uphold the logic of identity as McGinn understands it, but do not want to commit to the existence of abstracta like relations. I think the truthmaker of a sentence like “Dubya just is George Bush” is going to be a concrete object, the ex-president himself. In this, I’m in the minority; most philosophers find abstracta indispensible.

Another place one can start is Harold Noonan‘s excellent “Identity” entry. He’s an excellent philosopher, and the piece has many virtues; in particular, see his section 2 on Leibniz’s Law vs. substitutivity principles.

The best thing I’ve ever read on identity and relative identity is John Hawthorne’s chapter “Identity” in The Oxford Handbook of Metaphysics. A version is available to scribd users here.

  • This piece is very rich, and defies easy summary.
  • A basic point is that “identity” in a basic, unanalyzable concept, and so we ought not worry about circular definition. Geach’s failure to recognize this is a core problem with his whole project. (p. 122)
  • Hawthorne’s section 3.1 brings out the many problems facing Geach’s project. His conclusion: “In sum: it is no mere artefact of philosophical fashion that Geach’s relative identity approach has few adherents.” (p. 123) You’ll have to read the piece to see why.
  • Another basic, crucial point, I would paraphrase as follows. (p. 100) We all understand “something is cold and fizzy”. The shows that we have a concept of identity; if that sentence is true, the cold thing just is the fizzy thing. Contrast with the sentence: “something is cold, and something is fizzy.” That we have this concept of identity, of course, doesn’t imply that we understand identity-logic, or have any theoretical opinions on the subject at all.
  • Hawthorne’s main point is that “Puzzles that are articulated using the word ‘identity’ are not puzzles about the identity relation itself.” (p. 99) When I think about the many metaphysical treatments I’ve read recently of the puzzles Deutsch discusses, I think this is an emerging consensus. There are always other moves to be made, and all sorts of weird metaphysical doctrines to be brought into play. But the emerging consensus is that identity is to be held constant; the concept of identity is common coin in these disputes, just as is, say, the assumptions that modus ponens is valid, or that no contradiction is true.
  • By the examples he gives, it is plain that Hawthorne is well aware that evaluating Trinity and Incarnation theories necessitate careful thinking about identity, but he doesn’t ever entry the fray. (But he almost does – see p. 120 fn. 38.)

Be forewarned; there are pervasive confusions about numerical sameness among Christian theologians nowadays, in particular about personal identity (the relation being the same self as). This is largely due, I think, to uncritical reliance on poorly done philosophy. This is not due to any intrinsic difference between the fields or any commitment intrinsic to Christianity, as there are and have been theologians who are thoroughly clear-headed about identity. The solution is to digest well done philosophy, so as to be able to make clear distinctions and to reason surefootedly; that’s the reason for this post. Don’t give in to the temptation to foolishly heap scorn on “absolute” identity or on Leibniz’s Law, as if they were mere speculations, and things to which you yourself are not committed.

About Dale

Dale Tuggy is a Professor of Philosophy at SUNY Fredonia, where he teaches courses in analytic theology, philosophy of religion, religious studies, and the history of philosophy.

6 Responses to On Numerical Sameness / Identity / “Absolute” Identity

  1. Hmm, literally yesterday, I submitted a note to Philosophia Christi on weak relative identity in general partnerships and the Trinity. The submission is between NY and CA while I post. I’ll refrain from commenting until after I hear from the reviewers, except to say that I made major revisions on my PhilPaper article. :)

  2. Joseph Jedwab says:

    Very good Dale. Just a few points.

    1. I agree Geach is not easy. And we can say the same about many of the folk writing on the topic around his time: David Wiggins (Sameness and Substance) and Michael Dummett (Frege: Philosophy of Language).

    2. I found Noonan very helpful. He was a graduate student of Geach, who mentions him favourably to Quine in correspondence. I especially like Noonan’s contribution “Relative Identity” in A Companion to the Philosophy of Language, ed. by Hale and Wright (Blackwell). He usefully separates a number of different theses and isolates the sortal relativity of identity thesis, which says it can be that a and b are the same F but different Gs.

    3. I also think Hawthorne’s piece is an excellent critique of Geach’s approach to relative identity. It’s been a while for me, but I was a bit surprised at some of the points you made. First, there is the point with the concept of identity being basic. I don’t remember this being a big part of Geach’s case. More important were the examples of the sortal relativity of identity. And also important is this puzzle. We can say that the concept of same F comes from the concept of same and F. Or we can say the concept of same and F comes from the concept of same F. A benefit of the second and cost for the first way is that we can explain how we have sortal concepts of being an F from the concept of same F: x is an F iff x is the same F as x. But on the first way, how do we explain how we make a distinction between sortal and adjectival concepts? I can put together same and dog to get same dog. Why can’t I put together same and red to get same red, not in the sense of the same shade of colour but in the sense of the same red thing? You can say the distinction between sortal and adjectival concepts is also basic. But now you have two kinds of primitive: identity and sortal concepts. Whereas the second way only has one kind of primitive: same F relation concepts. Secondly, there is the point with “something is cold and fizzy”. This is a point that Geach himself makes in his Replies in Peter Geach: Philosophical Encounters, ed. by Lewis (Kluwer). He would say this shows we have the concept of same or same F, but of course he would reject the claim that this shows there is such a thing as classical or absolute identity.

    4. The application of Geach’s approach to relative identity to the Trinity or Incarnation doesn’t work well as I recall. This was done by James Cain along time ago. And I think there are insuperable problems there. Far better, in my view, is the approach and application we find in van Inwagen.

    5. Also Rea’s strategy seems to me importantly different. It holds on to classical identity. Van Inwagen in his first papers remains neutral over whether to abandon classical identity. His most recent paper seems to reject classical identity. But it’s unclear that there is a change of mind here or that this just makes for simpler exposition to a less philosophically trained audience. Rea’s strategy is to invoke sameness without identity as a solution to the problem of material constitution. This solution is supposed to have many of the benefits of the standard solution (the coincidence solution) without the cost of saying that there are *two* material objects that share the same matter in the same place at once. What really clinches it for him is that sameness without identity not only solves the problem of material constitution but structurally similar problems for the doctrines of the Trinity and Incarnation.

    6. Don’t forget that van Inwagen gives us a recipe for constructing a relation that in every normal situation behaves as classical identity does. And so we could explain why we think something like classical identity holds in all situations, when in fact something like it breaks down in Trinitarian or Christological situations.

    So the upshot is this. If you take the path of relative identity, don’t go the Geach/Cain way, take the van Inwagen/Rea way.

  3. Dale says:

    Joseph, thank for you this excellent comment! Man, there’s material for at least 3 posts here.

    Some replies:

    1. Fair enough.
    2. Since this is a sort of bibliographic post, I’ve taken the liberty of bolding and linking your mention of the Noonan piece. I’ve now read it, and yes, it is excellent. Again, much clearer than Geach.
    3. About identity being basic: what I said was too compressed – sorry. Here’s the passage from Hawthorne I had in mind:

    …one presumes Geach will offer an argument to the effect that the concept of absolute identity is incoherent. But what we really find instead is an argument to the effect that there is no straightforward mechanism for defining absolute identity that is provided by the resources of logic (without an identity predicate) alone, nor even by a second-order logic that provides the means for quantifying over a (restricted) domain of properties. But since the concept of identity is plausibly a basic one, it is not clear how to move from these remarks about definition to a conclusion that asserts the incoherence of the concept of absolute identity.” (p. 122)

    About the examples – surmen, water, Tib and Tibbles, passengers, etc. – I never was tempted to think they showed anything about identity. I thought they were just puzzles in metaphysics, and it struck me that the most popular solutions always leave the notion of absolute identity intact. It also struck me a odd, given what else Geach wants to say, that expounding some of these examples requires the concept of =. e.g. the idea that there are thousands of distinct (not =) things on the mat each of which is a cat.

    About this business of explaining how we explain how we have sortal concepts: I never have understood Geach’s obsession with “criteria of identity,” or quite how such are supposed to be supplied by certain concepts. I think this is just because I don’t believe in criteria of identity (either diachronic or at a time). In this connection, I found the preceding essay in that same book helpful, “Objects and criteria of identity” by E. J. Lowe (ch. 24, pp. 613-33) (although he fully believes in the importance of such) as well as Trenton Merricks’s “There Are No Criteria of Identity Over Time,” Nous 32:1, 106-24. It seems that some make too much of the thought experiment where I tell you to “count all the things in this room.” This is allegedly impossible in principle. (Lowe, p. 615) Nonsense. God could do it; he knows what simples are there, and what the true principles of mereology are. That we can’t do it only shows that it is not obvious to us what the correct metaphysics of substance is.

    4. Joseph, do you mean there’s some specifically theological problem with Cain’s application? Myself, I think I only see problems with RI theory itself. Another applier of Geach to the Trinity was A.P. Martinich, in two beautifully clear pieces: “Identity and Trinity,” The Journal of Religion (1978), 169-81 and “God, Emperor and Relative Identity,” Franciscan Studies 39 (1979), 180-91.

    5. Yes, absolutely. I don’t see Rea as doing at all the same thing as Geach. Rea is doing metaphysics, and as he points out gives a grounding to the controversial claim that sometimes, x and y can be the same F but different Gs. I’m pretty sure PVI believes in =. And he’s confirmed in correspondence to me that his strategy is apologetic. He’s not claiming this is what the Trinity doctrine means, but only IF read that way, THEN it’s self-consistent. AND, here’s the important point: we can’t be sure that it isn’t to be understood that we. SO, we can’t be sure that it’s self-contradictory. About Rea, I agree that his project is a thing of beauty, philosophy done well. But in fact I don’t grant that the solution works for either case. I have a big hairy paper submitted on this; I’ll post when it gets accepted.

    6. Thank you. I need to look at that again. PVI’s piece too is a thing of beauty, and the sort of piece where very, very few people in the world can perform. I need to make sure I appreciate the significance of that point; I’m not sure what to make of it. I mean, if we all know truths of the form x=y, then why exactly should we care that things might appear just as they are to us, and yet there be no such thing as =.

    Please do push back more on any of this, esp. the last. You’re of course welcome to make it a post.

  4. Joseph Jedwab says:

    Thanks Dale. Let me address the Cain point. This is all written up in my doctoral dissertation. So let me share the results and skip the argument’s details. Folk can press me for the details if they want them.

    Cain’s application is distinctively Geachian. It makes use of the distinction between restricted and unrestricted quantification and names of and for Fs. There are difficulties with his proposal about how reduplicatives work. But it turns out that the application raises three main problems.

    1. The account implies that God is not a person. Suppose God is a person. Then he must be the same person as each divine Person, only one divine Person, or no divine Person. If each, then the divine Persons are the same divine Person as each other, which is wrong. If only one, then this is unorthodox or ad hoc, which is bad. If none, there are at least four divine divine Persons, which is also bad. And note that this problem does not arise for van Inwagen or Rea.

    2. Cain says different things are true of the Son and Jesus. He wants at least to make room for the claim that the Son is impassible but Jesus is passible. Now everything true of both the Son and Jesus is true of Christ. But what is true of only the Son is true of Christ only as a divine Person. And what is true only Jesus is true of Christ only as a human. But then though as a divine Person, Christ is impassible and as a human, Christ is passible, Christ is neither passible nor impassible simpliciter, which is impossible.

    3. Cain proposes that ‘the Son’ is a name for a divine Person, ‘Jesus’ is a name for a human, and ‘Christ’ is a name for a divine Person and a human. By an indiscernibility principle that Cain establishes using only Geachian assumptions, it follows that the Son, Christ are indiscernible and Christ and Jesus are indiscernible, and so the Son and Jesus are indiscernible.

    Again, these last two problems don’t arise for van Inwagen or Rea. As far as I can see, they arise only because Cain is using Geachian apparatus.

    A P Martinich and John Zeis’s work on relative identity and the Trinity are alright as far as they go but they don’t go very far. Their work isn’t nearly as comprehensive as what van Inwagen or Rea offer. I also remember Richard Cartwright had a decent objection to Martinich. But the details escape me at the moment.

  5. David Chua says:

    Hi Joseph,

    Just some questions on the points you raised in your last post:

    (1) I see how this would be a problem for Cain, but I don’t see the big difference between Cain’s and van Inwagen’s approach. My understanding of why Van Inwagen doesn’t encounter the problem in question is that he uses the sortal of ‘being’, coupled with a so-called principle of the uniformity of the divine nature, with the upshot that predications are permissible of God *as if* God were a person/single agent. I don’t see how this approach isn’t available to Cain (‘God’ and ‘being’ seem to me interchangeable). Or am I misunderstanding the point? Why should I suppose God should be a person and not a God/being?

    (2) What stops Cain from biting the bullet and saying, Christ is in a sense both passible and impassible simpliciter, which is not so much a contradiction but an ill-formed formulation of the two reduplicatives in question? (I don’t see what stops Cain from modifying his RI syntax to make this the case). What I want to think is, Cain’s analysis seems no worse off than – say – van Inwagen’s.

    (3) Again, could Cain just get out of this problem via RI syntax? I.e., Son and Jesus are indiscernible qua person, but not qua human nature (or whatever).

    Thanks (both to you and Dale) for shedding great light on this debate. (reading Hawthorne’s article was awesome). Right now I think agree with what Dale said earlier – ignoring the problems with RI itself, it seems like a consistent enough solution.

  6. Harry Deutsch said that he will site my THE JOURNAL JURISPRUDENCE 21 article “Natural Unity and Paradoxes of Legal Persons” in his next SEP major revision of “Relative Identity” in, but I have no idea when that will be.

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