Tuesday, May 29, 2007

What is possible?

Presumably for something to be possible, e.g. epistemically possible (i.e. subjectively consistent with our other beliefs) or nomologically possible (i.e. objectively consistent with the laws of nature), it must be at least logically possible. So then, what is logical possibility? It cannot be mere consistency, for consistency is always with something. Perhaps it is self-consistency, i.e. the absence of self-contradiction, but what is that?
...... To begin with common sense, G E Moore thought that the idea that he was only dreaming, when he was actually lecturing, contradicted what he knew of himself, but was it then logically impossible that he was dreaming? After all, dreams might be very vivid, and even Putnam’s argument would not make it logically impossible for him to have just fallen asleep. And (on another topic that I’ve waffled about recently) the idea that I am nothing more than biochemical complexity, that seems to contradict what I know of myself, but I don’t imagine that I’d be allowed to call the theory of evolution logically impossible.
...... I’ve seen logical possibility associated with conceivability, e.g. a round square is inconceivable because it appears to be self-contradictory. But surely the laws that actually govern nature might be inconceivable by us (even in principle), and yet we would want them to be logically possible. And from mathematics, a typical real number is by itself too complex to be conceivable, but we think of it as conceivable because the real number line (which includes it) is conceivable, if not by you then by someone suitably authoritative. (And we allow that formal real numbers might be logically impossible, if inconsistencies lurk within the formalism.)
...... Suppose that there are aliens out there who know a lot more than we do about geometry. And suppose (if you can) that they tell us (one day) that there are square squares (in our geometries, with the usual meanings for those words) and round squares (in some others, similarly). Prima facie those conceivable aliens could, conceivably, be right about that (or so we could think, not unreasonably, if that happened, because after all, our experts have been wrong about elementary geometry, in the recent past, for all that it seemed to many of them that they could not possibly get such things wrong). But are round squares logically possible?
...... Anyway, does the discovery of a contradiction necessarily amount to the discovery of logical impossibility (and hence of non-existence)? I don’t think so because it might instead be that our predicates have been found to be less definite than we had thought (if their subject clearly exists). So even when that does not seem to be the case, how sure may we justifiably be that that was not possible? (I’m thinking here of the superficial similarity between a wave-particle, which is logically possible, and a round square, which is not.)
...... After all, Descartes’ demon (the rationalist’s friend) does not seem to be inconceivable or self-contradictory, and such a demon might possibly hypnotise us, so that not only do we make errors, when we reflect upon some of our predicates, we also believe ourselves to be incapable of such errors (much as we rationalists like to think we are, sometimes).
...... So, to return to common sense (i.e. to delete most of the above waffle, and post the rest), I’m left thinking that logical possibility must be, if anything, consistency within some given system of logic. Since we have many (inconsistent) logics, we would therefore have many (inconsistent) sorts of logical possibility. But presumably we want there to be one special one, that our system of possible worlds (with which we analyse our subjunctive conditionals), built upon our preferred system of logic, is attempting to model accurately; so I’m back to my original question (with no clear view of how to attempt to answer it), what is that?

No comments: