Kripke on the Structure of Possible Worlds

Yesterday I attended Saul Kripke’s talk at the Graduate Center (there are quite a few interesting talk coming up…also looking good are the cogsci talks). The title of the talk was “The Structure of Possible Worlds: a Preface to a statement” and was subtitled, “Prolegomena to a talk on possible worlds, some considerations” so maybe I didn’t really attend a talk. Much of the talk, um preface to a prolegomena to a talk, consisted of Kripke going over the history of his thinking on modality, punctuated with his usual wit and humor. My two favorite moments were (a) the one where, after talking for an hour (the scheduled length of the talk), he stops and says “I may have to go over because I haven’t come to the main point yet” and (b) the one where, while discussing modal realism, he says “what does God have to do to make a really existing merely possible world actual; give it a kiss?” Ah, that Kripke should have his own reality show…I bet it’d be really popular!

As to the content of the talk, or whatever, he seemed to be indicating that (he may have) changed his mind about how he conceives of possible worlds. Here is how he put it in the handout,

I used to think that a sufficient account of my view of what a possible world is might be given by something like a Russellian structured proposition describing it. Now i think that one cannot give an account of what a possible world is in and of itself, but only as part of the structure of all possible worlds, or at least that modal logic cannot rule this out. (Even if there is not a unique structure of all possible worlds, structures where the problem I have just described arise cannot be ruled out philosophically.)

A structured Russellian proposition is an abstract entity that has as its constituents the actual objects in the proposition. So, to modify the classic example, the proposition that Jennifer Aniston loves Brad Pitt has Jennifer Aniston (the actual person), Brad Pitt (the actual person), and the relation of loving as constituents and these constituents are ordered by the loving relation such that Jennifer loves Brad (which is a different ordering from Brad loving Jennifer). This is just a more refined way of putting the basic point of Naming and Necessity. When we ask if Al Gore could have won the election we are asking a question about the actual Al Gore. We are not talking about some distinct object which merely resembles Al Gore (or which merely has many of the same descriptions true of it). There is therefore no issue of how we re-identify Al Gore in various possible worlds; it is the actual Al Gore.

So why does he now think that we can’t do this? (Of course, he hasn’t really come to this conclusion officially. What he said was that it might be true and he sort of leaned towards thinking that it is true). The basic reasoning he employed relies on his argument that there can be objects which are indistinguishable in every way which are none the less distinct. There is no criterion of identity that distinguishes these objects; as Kripke put it “the only difference between them is that there is a difference.” His favorite example is the square root of -1, known as i. i is equal to whatever number equals -1 when multiplied by itself. This number is not on the real number line and so is known as an imaginary number. The problem comes when we realize that i and -i are distinct numbers and that everything that is true of the one is also true of the other. i and -i are distinct yet have no clear criterion of identity.

The problem that Kripke sees is that something like this might be true for possible worlds. To see this he talks about what he calls ‘grounded’ objects. So, let’s imagine a world where there is an person, let’s call him George, who does not exist in the actual world. Let’s say that George is the son of two people who actually exist but do not actually have kids. In the actual world the sperm and egg that come together to form George never meet, but they do in some possible world. So George is grounded in the actual gametes that he could be the product of. But there is also the possibility of ungrounded objects. So consider Georgette. Georgette is a women who does not exist in the actual world but does at some possible world, yet unlike George, Georgette is not the related to any past, present, or future actual person. The sperm and egg which come together to form Georgette at no time exist in the actual world; they are the products of an alternate history which does not overlap with the actual world (in this respect). Georgette is ungrounded.

So if there can be ungrounded entities then we can see that the following situation is possible. Imagine that there are two possible worlds each which has an extra hydrogen atom which is not related to anything that actually exists. These two extra hydrogen atoms are thus ungrounded. We can furthermore imagine that these two hydrogen atoms are indistinguishable from each other. Now if this is the case then the two possible worlds we are imagining are indistinguishable yet distinct. There is nothing that we could say about the possible world in and of itself that could distinguish between these two worlds. The only way that we could distinguish them is by noting their relative positions to each other in the overall space of possible worlds. Thus Kripke concludes that we cannot talk about individual possible worlds except in relation to the entire structure of modality, or to be more modest, he concludes that there is no a priori consideration that would rule this kind of automorphism out.

An interesting argument, and there is a lot more to say about it but I will come back to that later.

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8 thoughts on “Kripke on the Structure of Possible Worlds

  1. Pardon me if I’m missing something obvious — I haven’t worked on philosophy since the 70s — but what justifies saying that the two possible worlds, which each have an extra hydrogen atom, are distinct?

    I gather that the worlds of George and Georgette are distinct because they have different histories.

    But positing that there are two possible worlds (each with an extra hydrogen atom) and then immediately denying any difference between them (by saying that the two atoms are exactly alike and in the same locations) seems like giving with one hand and taking away with the other.

  2. Hi Larry, welcome back! 🙂

    As far as I can tell this is supposed to merely be an analogue of the i/-i situation. If there can be distinct objects that do not have distinct criteria of identity like i and -i then why can’t a hydrogen atom be like that? It certainly seems conceivable in that there is no obvious contradiction involved. So the two worlds do differ, but they only differ by in fact being different from each other. So we are not denying any difference between these two worlds we are merely denying any difference which would distinguish them from each other.

  3. Thank you for the welcome back. (Suddenly I have way more to read than I did before.)

    Maybe that’s the right way to understand the hydrogen example, as an analogue, so I guess my problem is with the idea that there could be such analogous things as hydrogen atoms that are somehow different but indistinguishable.

    I’ve been away from mathematics even longer than philosophy, so I first doubted whether -i and i are actually indistinguishable. I would have thought, for example, that -i + (-i) = -2i, and -i + i = 0, so the two values can be distinguished by how they relate to other numbers. Maybe that’s beside the point, even if it’s true, but I get the impression from some cursory reading that you can replace one value with the other in equations without any difference, strange as that seems.

    Did Kripke offer any non-mathematical examples, non-favorite cases in which we would agree that two non-abstract entities are different but indistinguishable in any way? Something from quantum mechanics perhaps?

    • You are right about it, but that is the point. There is no way to distinguish them except by appeal to their overall relations to all the other numbers. That is, there is nothing that one can say about i, all by itself, that would distinguish it from -i. Their distinctness only becomes visible when one looks at the overall structure of relations they have to the real numbers. The analogue is supposed to be two possible worlds that have no differences between them but are none the less distinct in the space of possible worlds.

      Kripke’s other favorite examples are Euclidean spaces that are completely homogeneous, and points on the surface of a uniform sphere. The quantum stuff could be appealed to but I think he thinks these are good enough.

  4. Hi,
    To the point above, considering that we can not distinguish i from -i unless we put it in some kind of relation and see the result:
    On the possible worlds argument, does Kripke (or anyone) claim that the possible worlds are different but indistinguishable in the sense that we can not observe the outputs of their relation from our spatiotemporally isolated world? But if this is so, how do we justify the existence of possible worlds or parallel universes in the first place? It seems to me that the M-theory is a great attempt in doing so, but I’m a bit confused as you see. I’d appreciate any clarification on this issue of possible worlds and many worlds interpretation. Sorry if it’s all a mess.

  5. By the way, what I mean by many worlds interpretation (also known as parallel universes) is the scientific one, which is an interpretation of quantum mechanics that asserts the objective reality of the wavefunction, but denies the reality of wavefunction collapse.
    Currently I’m working on a paper on possibilism and actualism, and I’m trying to back up the possibilism argument with this many worlds interpretation of quantum mechanics. Hope this helps, Merve.

  6. Hi Merve, thanks for the comment!

    Kripke does not think that possible worlds exist in the same way that the actual world does, though he does think that they are abstract objects. So, his view is not a many worlds view and his semantics is perfectly at home in an actualist interpretation….

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