Kant''s claim that the justification of transcendental philosophy is a priori is puzzling because it should be consistent with (1) his general restriction on the justification of knowledge, that intuitions must play a role in the justification of all nondegenerate knowledge, with (2) the implausibility of a priori intuitions being the only ones on which transcendental philosophy is founded, and with (3) his professed view that transcendental philosophy is not analytic. I argue that this puzzle can be solved, that according (...) to Kant transcendental philosophy is justified a priori in the sense that the only empirical information required for its justification can be derived from any possible human experience. Transcendental justification does not rely on any more particular or special observations or experiments. Philip Kitcher''s general account of apriority in Kant captures this aspect of a priori knowledge. Nevertheless, I argue that Kitcher''s account goes wrong in the link it specifies between apriority and certainty. (shrink)

The effort to fit simple logical truths–like `if it's either red or green and it's not red, then it must be green'–into Kant's account of knowledge turns up a position more subtle and intriguing than might be expected at first glance.

I argue for the Wittgensteinian thesis that mathematical statements are expressions of norms, rather than descriptions of the world. An expression of a norm is a statement like a promise or a New Year's resolution, which says that someone is committed or entitled to a certain line of action. A expression of a norm is not a mere description of a regularity of human behavior, nor is it merely a descriptive statement which happens to entail a norms. The view can (...) be thought of as a sort of logicism for the logical expressivist---a person who believes that the purpose of logical language is to make explicit commitments and entitlements that are implicit in ordinary practice. The thesis that mathematical statements are expression of norms is a kind of logicism, not because it says that mathematics can be reduced to logic, but because it says that mathematical statements play the same role as logical statements. ;I contrast my position with two sets of views, an empiricist view, which says that mathematical knowledge is acquired and justified through experience, and a cluster of nativist and apriorist views, which say that mathematical knowledge is either hardwired into the human brain, or justified a priori, or both. To develop the empiricist view, I look at the work of Kitcher and Mill, arguing that although their ideas can withstand the criticisms brought against empiricism by Frege and others, they cannot reply to a version of the critique brought by Wittgenstein in the Remarks on the Foundations of Mathematics. To develop the nativist and apriorist views, I look at the work of contemporary developmental psychologists, like Gelman and Gallistel and Karen Wynn, as well as the work of philosophers who advocate the existence of a mathematical intuition, such as Kant, Husserl, and Parsons. After clarifying the definitions of "innate" and "a priori," I argue that the mechanisms proposed by the nativists cannot bring knowledge, and the existence of the mechanisms proposed by the apriorists is not supported by the arguments they give. (shrink)