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Kant on Complete Determination and Infinite Judgement

In the Transcendental Ideal Kant discusses the principle of complete determination: for every object and every predicate A, the object is either determinately A or not-A. He claims this principle is synthetic, but it appears to follow from the principle of excluded middle, which is analytic. He also makes a puzzling claim in support of its syntheticity: that it represents individual objects as deriving their possibility from the whole of possibility. This raises a puzzle about why Kant regarded it as synthetic, and what his explanatory claim means. I argue that the principle of complete determination does not follow from the principle of excluded middle because the externally negated or ‘negative’ judgement ‘Not (S is P)’ does not entail the internally negated or ‘infinite’ judgement ‘S is not-P.’ Kant's puzzling explanatory claim means that empirical objects are determined by the content of the totality of experience. This entails that empirical objects are completely determinate if and only if the totality of experience has a completely determinate content. I argue that it is not a priori whether experience has such a completely determinate content and thus not analytic that objects obey the principle of complete determination.