Saturday, May 06, 2006

The Limits of Truth Conditions

It's sometimes suggested that to understand a term is to grasp its intension, or what possibilities it rules out, or - in short - its truth conditions. But necessary co-incidence does not an analysis make. As we've noted before, this runs into trouble when we start dealing in necessary truths. We wouldn't want to analyze "all bachelors are unmarried" as meaning the same thing as "seven is a prime number", for instance. We might get around this by employing structured propositions, since at least the components ("bachelor", "seven") have different intensions. But that's not really what I want to talk about here.

I'm more concerned about attempts to understand modality itself by way of truth-conditional analysis. For example, "P is a necessary truth iff P is true in all possible worlds." That's true enough, but is it really illuminating? Is that the definition of necessity, or merely our theoretical gloss? Is being true in all worlds really what a proposition's necessity consists in? (If anything, I would say the opposite. Taking our modal concepts as fundamental, perhaps the equivalence thesis is a partial definition of possible worlds.)

Kit Fine, in 'The Varieties of Necessity', uses the doctrine of logical fatalism to illustrate the analysis/truth-equivalence distinction. According to the fatalist, ours is the only possible world. Thus we have the claim (*): "for every proposition p, p is necessary iff it is true." And since the fatalist holds this claim to be true, they'll also think it is necessary. So chuck the word "Necessarily..." in front to obtain thesis (**). Fine continues:
But even the logical fatalist will not accept (**) as a correct definition of necessity, despite the presence of necessary coincidence and the absence of circularity, since it will be important for him to maintain that the necessity of a proposition does not consist in its being true. It so happens, if I may put it this way, that every true proposition is necessary; but the proposition's being true is not that in which its necessity consists.

We can make sense of the notion of substantive necessary co-incidence (even if Hume wouldn't like it, and even if we think it's ultimately mistaken). So to say that two things necessarily coincide cannot be the same as saying they're the same thing. So claims of necessary coincidence do not by themselves amount to analyses. Even if the claim of coincidence is correct, the analysis might well not be.

Speaking of Kit Fine, recall that my post on Fundamental Modal Spaces explained why nomological possibility cannot be fully captured by the standard definition of "consistency with the laws of nature". That may be extensionally adequate, providing us with co-incidental "truth conditions" of when something is or isn't nomologically possible. But there's more to the concept than that. This definition fails to capture its distinctive modal force.

My worry can be even more forcefully illustrated by David Lewis' "realist" analysis of modality. He claims that possible worlds are concrete spatio-temporal regions just like our universe, but completely separate and isolated from one another. But while it's certainly possible that there could exist a multitude of such regions, this doesn't strike me as having anything much to do with our modal concepts. Lewis' ontology seems perfectly coherent, and I have no great problem with positing the existence of every spatiotemporal region that could possibly be. I just don't think that these concrete worlds, if they exist, are the basis of modality. Rather than comprising the space of possible worlds, Lewis' concrete worlds would all just be part of one big actuality. As I explained over at the Missouri blog:
Let us suppose that it happens that there are multiple disconnected spatio-temporal regions. That’s the way things are. But things could have been different. Our region might have been the only one to exist. Or perhaps there could’ve been exactly 27 spatio-temporal regions. That seems like a coherent possibility. (Note: a possibility, not 27 of them.)

Those are a few alternatives. An alternative, or “possible world”, being a maximal compossibility. Thus [as explained here] merely stating the positive facts about our region does not suffice, because it leaves open a range of other compossibilities. But if you add a “that’s all” clause, i.e. claiming “no other spatiotemporal regions exist”, then we have a maximal compossibility, or “world”.

Clearly, Lewis’ “worlds” aren’t really alternative possibilities in this sense. They can co-exist, or co-obtain, in a way that maximal compossibilities (by definition) cannot.

In effect, I grant Lewis his ontology but deny his modal semantics. When I say "P is possible", I do not mean that "P is true in some concrete world". As explained above, that's just not what our modal concepts are about.

Lewis might point out that his analysis gives perfect results. If we redefine 'actually' to mean 'in this spatiotemporal region', 'possibly' to mean 'in some spatiotemporal region', and 'necessarily' to mean 'in all spatiotemporal regions', then -- in combination with Lewis' ontology -- this analysis might well give us the correct truth value for every first-order modal statement. His analysis would then be extensionally adequate. Its truth conditions won't lead us astray. But still, I want to say, that isn't good enough.

There's more to modality than being able to say which modal statements are true or false. We should also want to understand why this is so. And Lewis' theory gets the "why" all wrong. It may be extensionally adequate, but that would be a mere matter of coincidence. Modal truths may co-vary with Lewisian worlds, but they are not true in virtue of those worlds. The Lewisian analysis may track modal truths, but it fails to capture what those truths consist in.

If I recall correctly (I don't have his book on hand), Chihara made a similar point by comparing Lewis' theory to a "Divine Thoughts" modal realist theory. The ontological part of this theory claims that God entertains the thought of each possibility in his mind. The associated semantic thesis is that our term 'possible world' refers to these divine thoughts. Hence "P is necessary iff P is true in all divinely imagined worlds", etc. Even if this semantic thesis were extensionally adequate, it's still quite obviously mistaken. Our modal concepts simply aren't about divinely imagined worlds. Nor concrete ones. They're about possible ones, where this modal component is not reducible to any purely non-modal components of our ontology.

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