Another way of characterizing philosophy -- and possibly distinguishing it from science -- is that philosophers are just as concerned with the way the world could be as with the way it is.  One interesting feature of such a comparison is that (at least I understand things) it puts philosophy on a close footing with mathematics, or at least the kind of descriptive mathematics that makes its appearance in, for instance, theoretical physics -- or at least this is an open question, whether if mathematics is integral to our models of the way this world operates, mathematics can also provide descriptions of the way other, very different worlds operate.  Supposing this is plausible, the question remains: If philosophy is distinguished from science in that it is concerned with possibility in addition (not: instead of) actuality, in what ways does it differ from mathematics?

It is possible to re-conceive of the situation in this way: science is concerned with the totality of true mathematical statements about the world in which we live (and, of course, the practical manipulation of these true statements in that world); mathematics, on the other hand, encompasses the whole universe of true statements, whether they are about this world or not.  Philosophy, then, is left asking the following two sorts of questions: (1) What does it mean for P to be true, and (2) What does it mean that P could be true?  These two questions appear, at first glance, to have very little to do with each other, but in fact, they are deeply connected.  It is, after all, only by considering how things are not that we can come by a clearer understanding of how things in fact are.  Thus our answer to (2) cannot be separated out from our answer to (1).  Furthermore, visions of an entirely empirical philosophy, purged of hypotheticals and thought-experiments, are deeply mistaken: philosophy cannot proceed on the basis of the empirical (though it can, of course, and does endeavor to explain it, to whatever extent science can or does not) -- philosophy is inextricably bound up with the question, What would it be like if...?

At the close of this sketch, nonetheless, I would like to offer a potential objection.  'What,' someone will ask, 'Is the meaning of these hypotheticals?  And how does the philosopher come by them, if they are not an extension of his empirical knowledge?'  There are two ways out: the first involves a much closer look at and delineation of how we form concepts, and the second counters the strict empiricist on his own turf, objecting that if we could not even conceive of things except on the basis of what we experience, if our concepts were purely analytic and in no way synthetic, then we could not even make any progress in science itself, let alone philosophy, and so we ask him in turn how he accounts for scientific errors (mistaken hypotheses) if not as conceptions about the way the world might be, but is not.  

When science casts off a theory, it is up to philosophy to take the theory up and examine it, so to speak, in the light of reason.  Why?  First for the reasons we have indicated -- because learning about what isn't the case gives us a better understanding of the truth, but next and more importantly because science rarely if ever seems to totally abandon one concept in favor of another (though this is a claim which we must, of course, substantiate, and which I admit that I am not capable of substantiating at present); rather, the new theory grows out of the same soil as the old -- and because science is biased towards the accumulation and explanation of facts, one never gets a chance to tear up anything by the roots and see whether what would claim the title of an advance is not still mixed up with what has been abandoned.

What place, then, does one claim for philosophy?  Certainly we have no wish to return to the speculative efforts of the 19th (or even the 18th!) century -- certainly empiricism has earned its titles.  All I ask from it, in return, is that it acknowledge that the speculative resources that make science possible also make possible those critical efforts of philosophy, which simply seek to dig up established fact and plant it in foreign territory -- to observe whether and how it fares, to track essential or periphery mutations.  In this way philosophy conducts experiments of its own, and there need never be any question of whether the one is any less -- or more -- revealing than the other.