Ryan Anderson

I defend Kant’s definition of analyticity in terms of concept “containment”, which has engendered widespread scepticism. Kant deployed a clear, technical notion of containment based on ideas standard within traditional logic, notably genus/species hierarchies formed via logical division. Kant’s analytic/synthetic distinction thereby undermines the logico-metaphysical system of Christian Wolff, showing that the Wolffian paradigm lacks the expressive power even to represent essential knowledge, including elementary mathematics, and so cannot provide an adequate system of philosophy. The results clarify the extent to which analyticity sensu Kant can illuminate the problem of a priori knowledge generally.

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

Kant famously rejected an empiricist account of causal claims, because it cannot account for the necessity and universality of causal laws. He then concludes that causal claims must have an a priori basis:1the concept of cause cannot arise in this [empiricist] way at all, but must either be grounded in the understanding completely a priori or else be entirely surrendered as a mere fantasy of the brain. For this concept always requires that something A be of such a kind that something else B follows from it necessarily and in accordance with an absolutely universal rule. Appearances may well offer cases from which a rule is possible in accordance with which something usually happens, but never a rule in accordance with which the succession is necessary; thus to the synthesis of cause and effect there belongs a dignity that can never be expressed empirically, namely that the effect does not merely come along with the cause, but is posited through it and follows from it. [A 91/B 123-4]So much is clearly Kant’s view, and as long as we remain with the vague formulation that causal generalizations have some a priori ground or other, commentators agree.