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

Edward Haeusler
Pontifícia Universidade Católica do Rio de Janeiro
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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References found in this work BETA

On the Relationship Between Plane and Solid Geometry.Andrew Arana & Paolo Mancosu - 2012 - Review of Symbolic Logic 5 (2):294-353.
Reals by Abstraction.Bob Hale - 2000 - Philosophia Mathematica 8 (2):100--123.
Tarski's System of Geometry.Alfred Tarski & Steven Givant - 1999 - Bulletin of Symbolic Logic 5 (2):175-214.

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Citations of this work BETA

Euclid’s Common Notions and the Theory of Equivalence.Vincenzo De Risi - 2021 - Foundations of Science 26 (2):301-324.
David Hilbert and the Foundations of the Theory of Plane Area.Eduardo N. Giovannini - 2021 - Archive for History of Exact Sciences 75 (6):649-698.

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