Abstraction, axiomatization and rigor

Pasch and Hilbert

Michael Detlefsen

pp. 161-178

in: Geoffrey Hellman, Roy T. Cook (eds), Hilary Putnam on logic and mathematics, Berlin, Springer, 2018

Abstract

In the late nineteenth century, Pasch made a well known statement concerning the conditions of attaining rigor in geometrical proof. The criterion he offered called not only for the elimination of appeals to geometrical figures, but of appeals to meanings of geometrical terms more generally. Not long after Pasch, Hilbert (and others) proposed an alternative standard of rigor. My aim in this paper is to clarify the relationship between Pasch's and Hilbert's standards of rigor. There are, I believe, fundamental differences between them.

Cited authors

Hilbert David