Saturday, June 12, 2004

Lewis and im/possible worlds nominalism

I've just been reading about David Lewis' modal realism (in Loux's introductory textbook "Metaphysics"). It's interesting stuff.

The core idea is that if we take possible worlds as basic ontological entities, then we can use them to give a reductive account of many other things such as propositions, properties, and modal concepts. The disadvantage is that to define possible worlds in a basic way (i.e. without appeal to those other things listed, since we want to derive them from possible worlds) requires us to suppose that all possible worlds are just the same sorts of things as the actual world. We have to take them as existing in just the same way our world exists. And that's pretty hard to swallow.

But if we can bring ourselves to believe it, then it seems we have a very neat ontology, where the only ultimate sorts of entities are concrete particulars in these possible worlds, and sets thereof. Properties can be thought of as "functions from possible worlds to sets of objects". That is, the property of 'redness' (for example) is just a set-theoretic structure which assigns to each possible world, the set of concrete particulars which are red in that world. (In a way, it's just an elaborated version of austere nominalism, which defines the property F-ness as simply that set of all F objects.)

Propositions are trickier. They are to be analysed as being a certain set of possible worlds. Saying which set is not so easy. Loux mentions the intuitive answer - "the set of worlds where the proposition is true" - but of course that's circular. Loux suggests that we can remove the circularity though, because a world where P is true is just a world of a certain kind; a "P-ish world". Thus, the proposition 'all swans are white' is taken to really mean 'the set of all [all swans are white]-ish possible worlds'.

I don't like it. Apparently, it's the "all possible worlds are just as real as our world" bit which turns off most people. But I don't mind that so much. Rather, I just really don't like the account of propositions. It doesn't seem to describe propositions at all, but instead something else entirely. Saying that propositions are sets of possible worlds strikes me as the wrong way around. I'd rather take propositions as the basic ontological entity, and define possible worlds as (maximally comprehensive) sets of propositions. Much nicer. Well, more intuitive at least.

But I do quite like the account of properties. One obvious problem with set-based accounts is that properties which are exemplified by all the same objects would refer to the same set, and so, according to this account, would mean the same thing. For example, austere nominalism considers "being a featherless biped" and "being human" to be the same property, which is obviously an unacceptable result. Possible worlds nominalism improves this, since obviously the sets will differ in other possible worlds (where, say, chickens have no feathers). But there will still be some properties which are co-exemplified (i.e. exemplified by the same set of objects) in all possible worlds - Loux gives the example of being triangular and being trilateral (all objects with three angles also have three sides, and vice versa).

Now, inspired by Allan of FBC, I wonder if we could solve this problem by admitting impossible worlds into our ontology? As always, I don't know much about this stuff, but it does seem like an interesting idea. There is, after all, an impossible world where a 3-sided figure has 4 angles. So if we expand our account of properties so that it also involves sets of objects from impossible worlds, then we will get the desired result - namely, that triangularity and trilaterality refer to distinct properties.

There'd probably be all sorts of nasty side-effects as well, but I'm too tired to think about that right now. Fun stuff, impossible worlds.


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