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.
CITATION STYLE
Nelson, L. (2016). Lecture XI. In Argumentation Library (Vol. 26, pp. 99–107). Springer Nature. https://doi.org/10.1007/978-3-319-20783-4_12
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