Does the fact that Kant defined synthetic a priori statements to be about conditions of possible experience require him to claim that all conclusions about conditions of possible experience are synthetic a priori? If so, how does he rule out the possibility of analytic statements being about conditions of possible experience? Thanks.
Kant associated synthetic apriori statements (e.g. "every change has a cause") with conditions of possible experience, because this is the only explanation that he found, of what makes these synthetic statements true and apriori. The situation is different with analytic statements, e.g. "this body is extended in space". For analytic statements, we have a ready explanation of what makes them true and apriori: an analytic statement expresses a connection of meanings. As Kant put it, in an analytic statement the predicate is contained in the subject. This makes the analytic statement apriori true, and nothing more is required. So since we already know what makes analytic statements true and apriori, there is no motive to associate them with the conditions of possible experience, or with any other extrinsic truth makers.
(P.s. Kant did not define synthetic a priori statements to be about conditions of possible experience. That conditions of possible experience are synthetic a priori, according to Kant, is proved by an argument. It is not true by definition.)
The 'Transcendental Analytic' is the 'analysis' of all a priori knowledge, analytic and synthetic, though focusing on the question "How are synthetical judgements a priori possible?". As Kant puts it: "Transcendental analytic is the dissection of the whole of our a priori knowledge into the elements of the pure cognition of the understanding." (Preface to Transcendental Analytic, Book I) Ipso facto the Analytic is itself analytic.
Analytic a priori statements, specifically, unlike synthetic ones, only apply to possible experience indirectly, since they are theoretically true regardless of experience. Ex. "It would be absurd to think of grounding an analytical judgement on experience, because in forming such a judgement I need not go out of the sphere of my conceptions." (Introduction, IV. Of the Difference between Analytical and Synthetical Judgements)
Ref: Critique of Pure Reason, trans. J.M.D. Meiklejohn (Everyman's Library 1959)