Abstraction, Axiomatization and Rigor: Pasch and Hilbert

  • Michael DetlefsenEmail author
Part of the Outstanding Contributions to Logic book series (OCTR, volume 9)


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.


Rigor Proof Pasch Hilbert Lambert Freudenthal premisory surreption Abstraction from meaning Semantic abstraction Abstraction condition Axiomatic method Axiomatizaton Formalization 

AMS Categories

00A30; 03A05 


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Authors and Affiliations

  1. 1.University of Notre DameNotre DameUSA

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