De zolt’s postulate: An abstract approach

Review of Symbolic Logic 15 (1):197-224 (2022)
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Abstract

A theory of magnitudes involves criteria for their equivalence, comparison and addition. In this article we examine these aspects from an abstract viewpoint, by focusing on the so-called De Zolt’s postulate in the theory of equivalence of plane polygons. We formulate an abstract version of this postulate and derive it from some selected principles for magnitudes. We also formulate and derive an abstract version of Euclid’s Common Notion 5, and analyze its logical relation to the former proposition. These results prove to be relevant for the clarification of some key conceptual aspects of Hilbert’s proof of De Zolt’s postulate, in his classicalFoundations of Geometry. Furthermore, our abstract treatment of this central proposition provides interesting insights for the development of a well-behaved theory ofcompatiblemagnitudes.

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Author Profiles

Edward Haeusler
Pontifícia Universidade Católica do Rio de Janeiro