system
Given the following post, respond as if you're commenting on Reddit:
human
What is the utility of Kant's distinction between analytic/synthetic and a priori/a posteriori knowledge before expounding upon his premises of the categories of the mind in Critique of Pure Reason?

So I am a little confused about why he begins his metaphysics with this. I get that the categories of the mind are a priori (although the usage of a priori here is still perplexing - how can categories, conceptual filters belonging to the mind, be called a priori if they themselves are not actual knowledge, only objects of knowledge?) and that maybe clarifying the definition of that would be useful, but overall a little confused. Feel free to spew to me about the work in general if it seems I am misunderstanding something; the more the merrier.

Thank you so much!!!
gpt
The best way that I've seen this explained is that the distinctions are a way in which Kant *formalizes* an already existing problem: how to account for concepts like causality? Recall especially that Kant is responding, in part, to Hume - Hume's problem is that experience alone cannot provide us with a concept of causality (all you can experience are 'constant conjunctions'). So *empiricism* cannot furnish the ground for causality. However it's also clear that *logic* alone (rationalism), can't do the trick either: no logical connection between propositions can provides us with a ground for causality either (recall Kant's dismantling of the ontological argument: existence is not a predicate: you can't 'logic' your way into existence). 

So if causality cannot be accounted for either by means of 'sheer' empiricism nor 'sheer' rationalism, you need a kind of 'third way' to account for causality. For what is causality? It is an *extralogical* connection between things: a relation that is not 'merely' logical (causality can't be reduced to transitive relations between propositions), nor merely empirical. A connection stronger than 'constant conjunction', but not as strong as logical transitivity: neither *a posteriori* nor *analytically a priori*: it must belong instead to the order of the *synthetic a priori -* an 'alogical' connection. This is the sense in which these distinctions *name* existing problems in philosophy, as Kant understood them. This is why the whole of the CPR is oriented towards to question of 'how is the synthetic a priori possible?'. This is, as a were, a synonym for 'how is (knowledge of) causality possible?', among other things (to which Kant will answer: 'because transcendental subjectivity').

This is also why Kant sees himself as charting a path between both empricism and rationalism. If you keep Hume in mind while trying to understand these terms (and Leibniz to a certain extent), it helps alot.