Review of Symbolic Logic:1-28 (forthcoming)

Authors
Eduardo Giovannini
University of Vienna
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 classical Foundations of Geometry. Furthermore, our abstract treatment of this central proposition provides interesting insights for the development of a well-behaved theory of compatible magnitudes.
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DOI 10.1017/s1755020319000339
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Euclid’s Common Notions and the Theory of Equivalence.Vincenzo De Risi - 2021 - Foundations of Science 26 (2):301-324.

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