Tuesday, June 27, 2023

Possible Worlds, Ersatzism, Circularity

'Ersatzism' in modal metaphysics is a label we owe to David Lewis; in effect, he takes it to be the primary opposed position to his own position of modal realism. On modal realism, possible worlds are actually worlds just like ours, but slightly different. Lewis contrasted this with what he saw as the alternatives, which is the position that possible worlds are ersatz worlds. This has caught on; it's an embarrassment, I think, that this is so, and people who are opposed to modal realism should not have let Lewis seize the linguistic high ground in this way. In fact, on any reasonable view that gets labeled as ersatzism, possible worlds are not ersatz worlds, in either sense of 'ersatz'. They are not substitutes for worlds, and they are not fake worlds. Lewis's entire position is based on assuming that 'possible worlds' is a literal description; his argument is ultimately that the only way this can be the case is if the actual worlds exist, and that all the other alternatives on the table arise from people treating non-worlds as if they were worlds. The fundamental problem with this is that the only reason we call them 'possible worlds' is that Kripke happened to use this as a convenient figurative expression. Precisely because people kept taking the label literally, Kripke later regretted using this figure of speech. It's purely a historical accident that we call them 'possible worlds'.* Lewis was simply wrong to assume that possible worlds were worlds; it is something Lewis just takes to be obvious on the basis of a name that was given to them for a completely different reason. That he definitely was wrong can be seen by the fact -- which we already knew well before Lewis -- that a 'possible world' could actually be a moment in time or a location in space (to give just two examples) rather than a world.

In any case, one of Lewis's major arguments against what he calls 'ersatzism' is that it's circular. It cannot explain possibility because regardless of how you build your 'ersatz worlds', whether from sentences or propositions or fragments of the actual world, or whatever, you can only select the right one's by assuming possibility. For instance, if you take possible worlds to be maximally consistent sets of propositions, the only way to understand 'consistent' is in terms of what is possible, so your selection of the right sets of propositions will presuppose what counts as possible. Therefore ersatzism cannot explain possibilities. But this is another good example of a confusion that comes from thinking of possible worlds as necessarily worlds. For the most reasonable interpretation of possible world semantics is that the formalism is modeling possibilities; no one has to try to make it explain possibilities. We find in the actual world that things can be possibly this or that; we can model this formally with possible world semantics; the point of the latter is to give you a rigorous way of talking about possibilities, not giving you an account of how anything is possible at all. It's just not even a relevant consideration; one might as well complain that calculus in physics has to assume that things change. Of course it does. It's not an explanation of change; rather, you use the tools of calculus to construct some very useful things in understanding what does change.

What Lewis does happen to get right -- although he seems to have reached the point through many wrong turns and thus gets it in a garbled form -- is in identifying the only thing that could explain possibility: actuality, or actual being. Possibilities depend on what actually exists, and when we think through counterfactuals or the like, we do so based on actual things, and especially on actual causes. This will always be a fundamental principle, regardless of how exactly one might interpret the standard possible world semantics, because it's not about 'possible worlds' but about something much more fundamental than possible worlds, which we use possible world semantics to describe.


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* This is sufficient for a complete answer to an argument sometimes given to reduce the implausibility of possible worlds being existing worlds. Ted Parent's IEP article on Modal Metaphysics gives a good summary of it: 
Despite the prima facie implausibility, however, there is a type of indispensability argument which may speak in favor of the view. The idea is that talk of “possible worlds” is too useful to modal semantics to see it as a mere fa├žon de parler (way of speaking). In the hard sciences, moreover, if an unobservable entity is theoretically useful, that is often seen as a reason to think it exists. In like manner, says Lewis, the theoretical utility of possible worlds provides at least some reason to believe that these objects exist (in the only sense of ‘exist’ that there is).
What this establishes is that there is reason to think that possible world semantics is capturing something genuine about what it is used to describe. The fact that we call the logical objects posited by PWS 'possible worlds' is entirely incidental to everything that is useful about them. We could use them exactly the same way even if, instead of 'possible worlds', we used Carnap's 'state descriptions' or Kripke's later suggestion of 'counterfactual situations'. We could just call them 'complete possibilities' or 'possibility-slices of the actual world'. All of these are figures of speech, but so is 'possible worlds'. The Lewisian argument is just as if we called the mathematical object created by putting things in one-to-one correspondence a 'tally' and then insisted that because we can use mathematics to describe the world, the world must be made of actually existing physical tallies. The whole argument manages to make multiple category mistakes in one bizarre inferential leap that derives entirely from a contingent event in the history of how we came to name things.