Pasch is usually credited with having presented the first axiomatization of a geometrical theory, but the Vorlesungen über neuere Geometrie (1882) contains many features which do not fit the Hilbertian paradigm. Thus Pasch, while axiomatizing his “elementary geometry,” claims that it is an empirically true theory. Scholars usually regard the discrepancies between Pasch and the post-Hilbertian standard method as mere inconsistencies of Pasch's theory. On the contrary, this article aims at reconstructing the coherence and originality of the Vorlesungen. We will first display the historical background of this work and then try to reconcile Pasch's logical axiomatic claim with his empiricist stance. More importantly, we will insist on the remarkable logical procedures worked out by Pasch in order to adapt his mathematical development to the strictures of his broad philosophical position.

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To cite this version:Sébastien Gandon. Toward a topic-specific logicism? Russell's theory of geometry in ABSTRACT: Russell's philosophy is rightly described as a programme of reduction of mathematics to logic. Now, the theory of geometry developed in 1903 does not fit this picture well, since it is deeply rooted in the purely synthetic projective approach, which conflicts with all the endeavours to reduce geometry to analytical geometry.The first goal of this paper is to present an overview of this conception. The second aim is more far-reaching.The fact that such a theory of geometry was sustained by Russell compels us to question the meaning of logicism:how it is possible to reconcile Russell's global reductionism standpoint with his local defense of the specifities of geometry?