PASCH’S PHILOSOPHY OF MATHEMATICS

Moritz Pasch (1843-1930) gave the first rigorous axiomatization of projective geometry in his Vorlesungen fiber neuere Geometrie (1882), in which he also clearly formulated the view that deductions must be independent from the meanings of the nonlogical terms involved. Pasch also presented in these lectures the main tenets of his philosophy of mathematics, which he continued to elaborate on throughout the rest of his life. This philosophy is quite unique in combining a deductivist methodology with a radically empiricist epistemology for mathematics. By taking into consideration publications from the entire span of Paschʹs career, the latter decades of which he devoted primarily to careful reflections on the nature of mathematics and of mathematical knowledge, Paschʹs highly original, but virtually unknown, philosophy of mathematics is presented.