Friday, February 01, 2008

The Ultimate Question: Kripke or Lewis?

Perhaps the most interesting question in metaphysics, to my mind, is whether identity facts are among the base facts; whether worlds or their constituent objects are prior; whether de dicto or de re modality is fundamental. (I take these to be different angles on the same core question.) We can illustrate the issue by way of my old example of duplicates Bob1 and Bob2 in the perfectly symmetrical universe. Although this possible world contains two of everything, presumably things could have been different. In particular, there might have been no duplication. But now we ask: how many ways are there for a world to be exactly like the mirror world, minus the duplication?

(A) The Kripkean Answer: Many. At the very least, you might have just Bob1's half of the universe, or just Bob2's half of the universe. So that's two possibilities. We might even mix and match, conceiving of a possibility containing precisely Bob2's world except that Bob1 exists in Bob2's place. To generalize: if there are n independent objects in each half of the symmetrical universe, then there will be 2^n ways to populate a possible world containing just one of each object. (Essentialists may deny that all the objects are independent in this way, though: perhaps Bob1 could not have been born to Bob2's mother. Such details needn't concern us here, though.)

(B) The Lewisian Answer: There is really just one possibility here. There is no difference between the various possibilities mentioned in the Kripkean answer. They are all describing one and the same way for a world to be. What we have imagined is a world which contains but a single Bob counterpart (and similarly for each other object in the mirror world). Whether he is really Bob1 or Bob2 is an empty question. In the strictest sense of identity, he is plainly neither. But as a counterpart, he can play a truthmaking role for counterfactual claims made about either. (E.g. "Bob1 might have existed without Bob2," and vice versa.)

I lean heavily in the Lewisian direction, since the idea that there could be any number of qualitatively identical worlds which nonetheless differ in the identities of their constituents strikes me as completely nutty. (There's nothing there to ground such a difference -- nothing in Bob's metaphysical makeup that could fix whether he is Bob1 or Bob2. Well, unless you care to introduce a 'haecceity' for just this purpose, but haecceities seem mysterious and insufficiently motivated posits.)

"That's nuts" does not, however, seem to convince the Kripkeans of my acquaintance. Can anyone suggest a better way to make progress on this issue? (Or some good papers to read? I'm not at all familiar with the literature.) I think Jack is with me on the specific case of time-points, at least, so maybe I just need a few more compelling examples to form a base from which to generalize...? More seriously, though, it seems like such a central issue that it cannot be settled on its own. Rather, we must do the hard work of exploring the implications for whole systems of Kripkean and Lewisian metaphysics, to see which approach ultimately bears fruit. What do you think?


  1. One thing that puzzles me about the way you have the example set up: shouldn't the Bobs be mirror-images of each other? What kind of symmetry do you have in mind? Perhaps something along a fifth dimension that does nothing but supply the possibility of the doubling?

  2. Yeah, the example is a bit loose, but I'm assuming it's possible to tweak the set-up so that there are no such qualitative differences. (Perhaps distance in time might suit this purpose better than space: think eternal recurrence, and then ask whether a one-off world contains the first Bob or the second or...)

  3. Hi Richard,

    I'm having some trouble following the question. Do you mean the 'mirror' worlds to be separate universes in some multiverse? It would seem like you need something as large as a universe to mirror a universe. But to keep it one world (at least for Lewis) you can let them be (even remotely) spatio-temporally accessible from one another. There are also worries here about whether your inhabitants are not just dupicates, but indiscernibles, since their extrinsic properties seem identical as well (are they in qualitatively identical quasi-universes?). I'm not sure that's possible without these things being (perhaps contingently) identical. But suppose the situation you set up is possible, and let that world be w. Now let w' be a world that contains all and only counterparts of one of those quasi-universes. Is that a different world for Lewis? It sure seems like it. But you seem motivated to deny this. So I think I'm not quite following the question you're asking.

  4. Hi Mike, thanks for the comment. To clarify: I agree that w' and w are two distinct worlds. (They are even qualitatively distinct since w contains twice as many objects as w'.) My question is whether it is possible to have multiple distinct possible worlds that are all qualitatively identical (indiscernible). I take it the Lewisian will deny this, whereas the Kripkean will allow that there are indiscernible worlds that differ in the identities of the objects contained therein: e.g. w' contains Bob1, whereas a similar world w'' might contain Bob2 in his place. Does that help?

    (I assume that there can be indiscernible objects within a world. But I guess that isn't essential to the present point.)

  5. Hi Richard,

    My question is whether it is possible to have multiple distinct possible worlds that are all qualitatively identical (indiscernible). I take it the Lewisian will deny this

    I think Lewis is of two minds about it (at least in '86). Well, they (the worlds) can be qualitatively indiscernible without being indiscernible, but let's say the question is indiscernilbility. I htink it would be right to say that he leans toward the negative, as you suggest. I'm less sure about the possibility of indiscernible objects in the same world; but it sounds a little unLewisian (recall that he came slowly to the view that there could be two counterparts in the same world). Let the indiscernible object(s) be some proton or lepton, l1 and l2. I'd imagine that they'd have to be situated in something like the way goliath and lumple are, unless we are assuming that there are indiscernible universes.
    But all of that is detail. How do you see this as related to the question of whether modality de re is more basic (or not) than modality de dicto? That's a question whose implications are far-reaching.

  6. Okay, put aside 'indiscernible' -- I don't know what that means if not 'qualitatively identical', but anyway it's this latter concept I care about.

    Now, I may be playing a little loose with the historical Lewis here, but my broadly 'Lewisian' position is that de dicto modality (as captured by purely qualitative - semantically neutral - world-descriptions) is fundamental, and we can construct de re modality via some kind of counterpart theory. Whole worlds are the starting point, and they can be fully captured by a purely qualitative description; they don't come with further identity facts or haecceities built in.

    On the Kripkean approach, by contrast, we start with objects (with particular identities), and stipulatively build worlds out of them. So, given two duplicates Bob1 and Bob2 in world w, the Kripkean can construct a possible world w' that contains only Bob1 (that very person!), or another possible world w'' that contains only Bob2 (that very person). This treats de re modality as fundamental, and we end up with more possible worlds than can be captured just by qualitative descriptions, since w' and w'' are qualitative identical (since their respective constituents, Bob1 and Bob2, are). For the Kripkean, a purely qualitative world-description would not suffice to tell us whether the world contained Bob1 or Bob2, and hence whether it is w' or w'' that we're looking at.

    In sum, the question whether we allow for duplicate worlds (on the basis of de re modal ascriptions for duplicate objects) tracks:

    (1) whether we take identity facts to be part of the fundamental base facts of a world (so that the qualitative facts alone do not entail all the facts).

    (2) whether particular objects (with particular identities) are prior to whole worlds.

    (3) whether de re modality is fundamental.

    p.s. I'm pretty tired, so if the above is unclear, let me know and I'll see if I can do better tomorrow.

  7. Hi Richard,

    I'm thinking that if Bob1 and Bob2 in same moment T1 pronounce "Wish I didn't exist", they both mean, and wish for something different. Bob1 wishes for Bob1 not to exist, and Bob2 wishes Bob2 not to exist.

    If at time T2, the symmetry is broken and Bob2 disappears, Bob1 wouldn't think that his wish is granted.

    I guess one could argue that the breaking of symmetry is propagated backwards in time, so that one can say that there was difference between Bob1 and Bob2, namely Bob1 was the one that WILL disappear at T2, and Bob1 the one that won't disappear.

    Anyway, very interesting question!

  8. Here you express your skepticism that two genuine possibilities (possible worlds) could differ only in terms of which haecceities are instantiated.

    I wonder if you think that two genuine possibilities could differ only in terms of which quiddities are instantiated. See Lewis' “Ramseyan Humility."

  9. The only way you can truly say there's two Bobs is if their universes are part of a meta-universe from which to count them.

    If so, they're not identical, because they'll have different spatial properties relative to the meta-universe. (I imagine Bob2 is behind and to the left of Bob1...although of course neither Bob1 nor Bob2 have the necessary perspective to be able to know this.)

    If you drop the metaverse, then there's no perspective which can actually perceive two Bobs, and indeed all their properties are identical. In this case, for all truths, it doesn't matter whether there's one Bob or an infinite number of Bobs, as these truths will just apply identically to all Bobs and all possible observers of Bobs. In this case, why not just bow to the degeneracy and say there's one Bob?


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