Turnabout is Fair Play: A New Humean Response in the Old Debate with Kant

Kant claims that Hume failed to see that mathematics provides us with synthetic a priori knowledge; had he done so, Kant argues, Hume would have to admit the possibility of such knowledge in causal judgments as well. Instead, Kant insists that Hume treats mathematics as analytic, and so missed the key insights of the Critical philosophy. I argue that it is rather Kant who is mistaken: Hume, in fact, endorses a position very similar to the view that mathematics is synthetic and a priori, and arrives at an account of mathematical necessity that stands as a plausible alternative to Kant's. More importantly, recognizing this Humean account of mathematics exposes a potentially grave vulnerability in Kant's system that Hume might exploit: while mathematics can be seen as synthetic a priori knowledge, Hume can argue that this gives us good reason to think that causal judgments cannot meet this standard of necessity.