Sunday, March 26, 2006

Absolute Possibility, or: On What There Isn't

Robert Stalnaker writes, "the only way to describe the world is to distinguish a way it is from other ways that it might have been." (Ways a World Might Be, p.67)

There seems something to this idea, that any substantive claim involves ruling out alternative possibilities (in some sense). But this is a very different notion of possibility from that which I've recently been highlighting. While my old sense concerned the genuine opportunity to have been actualized - what I called "real possibility" - this new sense is broader than that. Indeed, it's the broadest notion of possibility that we can appeal to. Let's call it "absolute possibility", since it encompasses every other form of possibility that there is. Rather than asking about just (say) the physically possible worlds, or my "really" possible worlds, here we ask about possible worlds of any type whatsoever.

The question then arises: how broad is this absolute possibility? Stalnaker wants to identify it with metaphysical possibility as standardly understood. He holds that propositions - the content of thoughts and sentences - are sets of (metaphysically) possible worlds. But this seems overly restrictive, and trivializes necessary truths. This view entails that the claims "there are infinitely many prime numbers", and "P or not-P" have the same content: the set of all possible worlds, i.e. the exclusion of none. Worse, because they exclude nothing, they say nothing. While this might be plausible for "P or not-P", it surely isn't plausible of "there are infinitely many prime numbers".

Of course, the obvious suggestion is that the latter claim rules out the possibility that there are only finitely many prime numbers. But Stalnaker wants to deny that that's even a possibility at all. If it isn't, then it seems there isn't anything there to rule out! But I think this sort of example shows that we need a broader and more fine-grained notion of possibility, which allows us to speak of (and subsequently exclude) scenarios which, strictly speaking, aren't metaphysically possible at all. After all, such strict impossibilities may at least be epistemically possible in the sense that we don't (initially) know them to be false. So it seems that there is something there for us to rule out. Substantive claims are clearly being made.

Stalnaker's alternative proposal is that we merely misunderstand what the sentences express; we fail to realize that those words express the necessary proposition. But that strikes me as an awfully inadequate response. It just isn't plausible that all necessary truths are saying the same thing (namely: nothing)!

Worse, his view prevents us from making any substantive claims about the totality of possible worlds (henceforth, the "multiverse" or MV). It surely seems like we can make such substantive claims. Suppose we disagree about whether unicorns are possible. Then we disagree about what the totality of possible worlds contains: I think there is a unicorn in there somewhere, and you don't. But to describe the MV like this is, according to Stalnaker, "to distinguish a way it is from other ways that it might have been." But on standard views - and certainly Stalnaker's - there are no "other ways" the MV could have been. Contingency is a feature of individual worlds; the multiverse as a whole is what it is necessarily. There couldn't have been a different set of possibilities. So, Stalnaker concludes (p.52), we can't really make any substantive claims about the MV.

That seems a really bizarre and indefensible claim. Stalnaker defends it on the grounds that his theory of content entails this conclusion. But surely that just shows his theory of content is wrong! Either that or I'm just confused, because I don't see how one could deny that it's a substantive question whether there is a unicorn-containing possible world. (At least on a Lewisian picture of modal realism. And David Lewis apparently shares Stalnaker's views on content, so I'm not sure how he defends that.)

So what is the appropriate response? It seems that we either have to broaden our notion of absolute possibility, or else give up our initial idea that descriptive content depends upon the exclusion of alternative possibilities.

The former option might seem preferable. But it threatens to leave us with a trivial notion of "absolute possibility" which includes, well, everything. And not just everything there is, but also everything there isn't, and couldn't possibly be. It's downright Meinongian. Indeed, this entire problem seems closely related to "the old Platonic riddle of nonbeing". As Quine wrote:
I cannot admit that there are some things which McX countenances and I do not, for in admitting that there are such things I should be contradicting my own rejection of them.

Likewise, we cannot allow that there are alternative possibilities besides those we recognize as possible, for admitting such possibilities contradicts our rejection of them! But as Quine taught us, we can coherently deny the existence of Xs by allowing the property of being X, and affirming that no thing exemplifies this property. So perhaps we can say that no thing has the property of being absolutely impossible. This allows us to coherently deny that there are absolute impossibilities.

But isn't this a substantive claim? In particular, doesn't it allow us to rule out the possibility that something has that property, or that there are absolute impossibilities? That would suggest that it's absolutely possible for there to be absolute impossibilities. Well, yes, but we've already granted that everything is absolutely possible, so this shouldn't be surprising. However, this has become such an empty and trivial notion that it isn't clear what good it does us.

It would probably be neater just to deny the initial claim, that substantive claims require the exclusion of possibilities. Perhaps it can be progress of sorts even to rule out claims that are impossible in every meaningful (or useful?) sense of the term. Or perhaps it's the very focus on exclusion that's leading us astray. I'm not sure what to think.

On p.66, Stalnaker makes the interesting point that there are two very different ways of looking at impossible claims. One option is to take the proposed scenario or "world" as given, and ask whether this world has the additional special property of being possible. We then have an abundance of worlds, split between those that are possible and those that aren't. But Stalnaker instead suggests that the question to ask is whether the expression succeeds in representing any kind of world at all. On his view, all worlds are (ipso facto) possible worlds, so talk of "impossible worlds" makes no sense. If it's impossible, then it's no world at all.

There seems something right about that. There are no absolutely impossible worlds, by definition. Absolute possibility is defined to encompass all the worlds that there are. But we might want to allow some worlds that are standardly held to be metaphysically impossible. I'm not sure about that yet.

So here are my current thoughts: we need some concept of absolute possibility, though for now I remain neutral on whether it's coextensive with the standard view of metaphysical possibility. On top of this, a subclass of worlds might possess the special property of "being really possible", in my sense. Even if some sort of strict metaphysical determinism is true, so that things couldn't really have turned out any differently from how they have (i.e. the actual world is the only one possessing my special property), we will still need those broader notions of possibility.

To avoid confusion or ambiguity, it might help to call them "ways the world isn't", rather than "ways the world might have been". We may hold that these 'ways' actually exist, as abstract entities of some kind, regardless of whether they ever had a hope of being instantiated by a concrete world of our kind.

We can speak of such 'ways' (or 'worlds') without any accompanying modal commitment, i.e. to the real possibility of their being instantiated. As such, it may be misleading to call them "possible worlds". Nothing is really being claimed about possibility (as I understand it) at all. We can avoid all the confusion displayed above if we take careful note of this. We can speak of all the ways the world isn't, without trying to force a distinction between "possible ways" and "impossible ways" (or disputes about whether the latter is a coherent notion). Clearly, if something is neither the way the world is, nor a way the world isn't, then it isn't any kind of worldly 'way' at all. So clarity is achieved in this respect.

We might then restate Stalnaker's thesis as follows: the only way to describe the world is to distinguish a way it is from other ways that it isn't. That seems plausible enough, though it perhaps risks falling into triviality. Is it possible to give a substantive account of the totality of different "ways"? As discussed at length above, we cannot distinguish the class of all ways from any alternative ways it could have been. (Anything not in the class of all 'ways' is, ipso facto, no 'way' at all.)

Or perhaps that's too quick. We might have meta-'ways' included in the original class. For example, perhaps one "way the world isn't" (mis)represents itself as being the only 'way' on offer. This representation could be included in our set of all ways, and we make substantive progress in understanding the totality when we manage to rule out this particular 'way' as being a misrepresentation.

I was beginning to despair of this post, but that might almost make sense. I'm too tired to tell for sure though. Will have to re-read this another day. Congrats to anyone else who actually managed to slog through all this. Apparently there's this thing some writers do called "editing", which helps cut down on messiness and incoherence. But for now, I think I just need to get some of these ideas down; the tidying can come later. (Suggestions welcome, of course.)


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