Thursday, December 06, 2012

Analytic/Synthetic II

Thinking about some issues raised by Pseudonoma's comments on my previous Kant-and-mereotopology post, one question that keeps coming up is what connection would the account of synthetic judgments require? Kant says (A7):

Either the predicate B belongs to the subject A as something that is (covertly) contained in this concept A; or B lies entirely outside the concept A, though to be sure it stands in connection with it.

The second clause is synthetic or ampliative judgment. The relevant connection can't be internal definitional relevance, i.e., it can't be the connection of an internal part for the definition, because that would mark an analythic judgment. So it has to be in some way extrinsic to the definition as such. At the same time it's unclear whether, when considering definitions, anything can be relevant to anything else without overlapping it at some level of generality. So something in between seems relevant, and that would suggest something like an overlap. But we seem to have two different kinds of synthetic judgments: those like "The house is red" and those like "The shortest distance between two points is a straight line". The latter seems more obviously to have an overlap than the former. I'm more and more taken with the idea that the difference is that, as far as Kant goes, the former has to do with possible experience, whereas the latter has to do with the possibility of experience. Thus house and red overlap in the sense that they share general features (sensible, for instance) that mean it is possible that they can come together in experience, whereas straight line and shortest distance between two points as Kant understands them overlap in the sense that their sharing something is required for experience (of any sort that we would recognize) at all. But that's a rough characterization that would need more development, and I haven't a clue how it would further relate to Kant's broader question of how we can know synthetic a priori truths.