De Zolt’s Postulate: An Abstract Approach

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


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 (“If a polygon is divided into polygonal parts in any given way, then the union of all but one of these parts is not equivalent to the given polygon”). 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 (“The whole is greater than the part”), 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(1899). Furthermore, our abstract treatment of this central proposition provides interesting insights for the development of a well-behaved theory ofcompatiblemagnitudes.



    Upload a copy of this work     Papers currently archived: 83,878

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

On having bad contractions, or: no room for recovery.Neil Tennant - 1997 - Journal of Applied Non-Classical Logics 7 (1-2):241-266.
Formalizing Euclid’s first axiom.John Corcoran - 2014 - Bulletin of Symbolic Logic 20 (3):404-405.
American Postulate Theorists and Alfred Tarski.Michael Scanlan - 2003 - History and Philosophy of Logic 24 (4):307-325.
Abstract hierarchies and degrees.Ljubomir L. Ivanov - 1989 - Journal of Symbolic Logic 54 (1):16-25.
Geometry as an extension of the group theory.A. Prusińska & L. Szczerba - 2002 - Logic and Logical Philosophy 10:131.


Added to PP

9 (#978,273)

6 months
1 (#501,187)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Edward Haeusler
Pontifícia Universidade Católica do Rio de Janeiro