Monday, April 02, 2007

Throwing what down the toilet?

Possible-worlds are highly appreciated. Possible-logical-spaces, however, are not. I have been wondering about this for a couple days now. I see why people may think it is useless. But uselessness is not a proof of impossibility; and, thus, of non-existence at all.

If possible worlds are nothing over and above the objects and that inhabit them, and the distribution or pattern they observe, then logical space seems to be nothing over and above the possible worlds, and the distribution they observe, that define it. But then, if a different distribution of inhabitants is enough to determine a different possible world, why can a different distribution of possible worlds not define a different logical space? There seem to be many different logical spaces. There are infinitely many, in fact.

If possible worlds are nothing but the most inclusive set of things that are causally connected with each other, then logical spaces are nothing but the most inclusive set of things that are logically connected with each other. And if we can rigidly refer to inhabitants of possible worlds, maybe we can do so with inhabitants of logical space.

If closeness and similarity are relations that hold between possible worlds, then they are properties of different inhabitants of a possible logical space. If the same worlds, which we can refer to across logical spaces (i.e., rigidly), can have different relations of closeness and similarity among them, then the same worlds are inhabitants of different logical spaces. Hence, the worlds Plunk and Plank may be close in Logical space Peter, but not so much in Rob.

But then, a counterfactual that holds in close and similar worlds within logical space Rob, might never the less not hold within Logical space Peter. And so, counterfactuals, laws, and what not, require us to fix into a logical space (or a set of them), and not only into possible worlds (or a set of them). So they will be true in so far as we decide to narrow down our minds.

Surely this must be nonsense. For different worlds cannot differ in relation with other worlds (e.g., be closer or farther, similar or different) without differing in the way they are. But if they differ in the way they are, they are really just a different possible world. One and the same world cannot occupy different positions in logical space.

Even more surely, this latter cannot be so. For if there need be only one logical space, then there can’t be any different ways a world can be. Possibilities are not possibilities of worlds, worlds are always necessarily so, there cannot be any different ways a world might be. Hence, there cannot be such thing as change.

So I do not know, what chunk is it that we should junk? Is it possible worlds, or possible spaces? Is it both?