Poincaré's conventionalism in geometry results from presupposing, as though this was a mere analytic judgment, that the sources of knowledge are only two—logic and experience—exclusive of each other and exhausting all the possibilities. That presupposition also led Einstein, via a misunderstanding of Hilbert's axiomatic approach, to the idea that the axioms of geometry are empirical in character. Our knowledge of the non-logical principles of mathematics in general and of geometry in particular is synthetic a priori, but has epistemological attributes that are lacking in philosophy. That explains why all attempts at using the mathematical method to attain philosophical truth are doomed to failure.