It adds up after all: Kant's philosophy of arithmetic in light of the traditional logic

Abstract
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
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Ian Proops (2005). Kant's Conception of Analytic Judgment. Philosophy and Phenomenological Research 70 (3):588–612.
Lanier R. Anderson (2005). Neo-Kantianism and the Roots of Anti-Psychologism. British Journal for the History of Philosophy 13 (2):287 – 323.
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