Officially, for Kant, judgments are analytic iff the predicate is "contained in" the subject. I defend the containment definition against the common charge of obscurity, and argue that arithmetic cannot be analytic, in the resulting sense. My account deploys two traditional logical notions: logical division and concept hierarchies. Division separates a genus concept into exclusive, exhaustive species. Repeated divisions generate a hierarchy, in which lower species are derived from their genus, by adding differentia(e). Hierarchies afford a straightforward sense of containment: (...) genera are contained in the species formed from them. Kant's thesis then amounts to the claim that no concept hierarchy conforming to division rules can express truths like '7+5=12.' Kant is correct. Operation concepts ( ) bear two relations to number concepts: and are inputs, is output. To capture both relations, hierarchies must posit overlaps between concepts that violate the exclusion rule. Thus, such truths are synthetic. (shrink)

By way of a reply to Charles Parsons's paper in the Nagel Festschrift, Kant's notion of intuition (Anschauung) is examined. It is argued that for Kant the immediate relation which an intuition has to its object is a mere corollary to its singularity. It does not presuppose (as Parsons suggests) any presence of the object to the mind. This is shown, e.g., by the Prolegomena § 8, where the objects of intuitions a priori are denied by Kant to be so (...) present. They yield knowledge, not in virtue of their immediacy but in virtue of their ideality. (shrink)

According to rationalists, synthetic a priori propositions convey new knowledge, whereas analytic propositions are non-informative or vacuous conceptual truths. However, as we argue in this article, each a priori proposition is necessarily true because of its semantic constituents and the way they are combined, and hence can be transformed into its equivalent analytic form. So each synthetic a priori proposition conveys only non-informative conceptual truths like analytic propositions.