Robert 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.

I investigate the consequences of Nietzsche's perspectivism for notions of truth and objectivity, and show how the metaphor of visual perspective motivates an epistemology that avoids self-referential difficulties. Perspectivism's claim that every view is only one view, applied to itself, is often supposed to preclude the perspectivist's ability to offer reasons for her epistemology. Nietzsche's arguments for perspectivism depend on “internal reasons”, which have force not only in their own perspective, but also within the standards of alternative perspectives. Internal reasons allow a perspectivist argument against dogmatism without presupposing aperspectival criteria for theory choice. Nietzsche also offers “internal” conceptions of truth and objectivity which reduce them to a matter of meeting our epistemic standards. This view has pluralistic implications, which conflict with common sense, but it is nevertheless consistent and plausible. Nietzsche's position is similar to Putnam's recent internalism, and this is due to their common Kantian heritage.