Wolfgang Schwarz

Reducing Things to Non-Existent Things

The difference between linguistic ersatzism, where possible worlds are replaced by sets of sentences, and modal fictionalism, where the pluriverse of all worlds is replaced by a large set of sentences describing all worlds at once, appears to be small. Nevertheless, I (still) think the analytic power of fictionalism is greatly diminished compared to that of linguistic ersatzism.

One of the great advantages of possibilia is that they provide a unified framework to reduce lots of kinds of things: properties can be identified with sets of possibilia, propositions with sets of worlds, meanings with functions from worlds to extensions, events with functions from worlds to regions, and so on. But suppose possibilia don't really exist, but exist only according to some fiction. Then properties can't be sets of possibilia. By the usual rule of interpreting statements about fictional entities, it will at most be true that according to the fiction, properties are sets of possibilia. But that doesn't help us if we're looking for a unified ontology. We'd like to know what properties really are, not what they are according to some fiction. If as fictionalists we think that properties really are sets of possibilia, then we have to conclude that properties don't really exist, just as the (other-worldly) possibilia don't really exist.

That's bad. For one, the initially plausible rejection of possible worlds has now turned into an incredible rejection of just about everything, including properties, propositions, meanings, events, sets, and maybe even hands and tables, which on some accounts are trans-word-fusions of counterparts. Secondly, the fictional reinterpretation now covers not only statements about worlds, but statements about almost everything. Almost whenever we say that such-and-such is the case -- that patience is a virtue, that the meeting has begun, etc. -- the fictionalist will say that we really only mean that according to a certain fiction, patience is a virtue, etc. But that is crazy. (In my view, it is already quite incredible that when we speak about possibilities we really only speak about what is the case according to a certain fiction. This seems obviously false to me, just as it is obviously false that when we speak about numbers we really only speak about what follows from certain axioms.)

So a fictionalist should better reject the reduction of properties etc. to possibilia. Since fictionalists arguably have to use modality either to describe their fiction or to explain what it means that something is the case "according to" it, not many applications of possibilia are left for the fictionalist to enjoy. He can still say things like "there is a world where swans are blue", but these aren't the really useful things one can do with worlds.

In "The Ersatz Pluriverse", Ted Sider makes two proposals for how to interpret statements about possibilia. The first is common fictionalism: reinterpret S as "it follows from the pluriverse fiction that S". The second is more interesting. It says that S is true iff it is true in all realistic Kripke models, where Kripke models are set theoretic constructions whose ultimate constituents don't matter, and a realistic model is one that respects all modal facts.

The second proposal looks more like structuralism than fictionalism, and probably escapes the problem of fictionalism. The structuralist can say that possible worlds really, literally exist; they are certain constituents of realistic Kripke models. But any realistic model is as good as any other, just as any omega sequence will do as 'the' sequence of natural numbers. Sets of possible worlds also exist, though the nature of their elements is very indeterminate, and therefore it is also indeterminate exactly which set a certain set of worlds is. (It is similarly indeterminate exactly which set is the set of mountains; here, too, I think Cantor was wrong to conclude that there is no set of mountains.)

Thus on Sider's second proposal, properties can be identified with sets of possibilia, and it doesn't follow that properties don't really exist. It only follows that nothing much can be said about the nature of their members, the possibilia. But that might be acceptable. After all, different philosophers have defended very different views about the nature of possibilia (that they are ordinary, concrete objects, or set theoretical constructions of ordinary objects, or open sentences, or abstract properties, or abstract sui general entities), so their real nature is hardly a Moorean fact.