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On the Essence and Identity of Numbers

Gómez-Torrente, Mario (2015) On the Essence and Identity of Numbers. THEORIA. An International Journal for Theory, History and Foundations of Science, 30 (3). pp. 317-329. ISSN 2171-679X

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Abstract

Taking as premises some reasonable principles about the essences of natural numbers, pluralities and sets, the paper offers two types of argument for the conclusions that the natural numbers could not be the Zermelo numbers, the von Neumann numbers, the “Kripke numbers”, or the positions in the ω-structure, among other things. These conclusions are thus Benacerrafian in form, but it is emphasized that the two kinds of argument offered in the paper are anti-Benacerrafian in substance, as they are perfectly compatible and in fact congenial with some views on which the numbers could be things of certain other kinds.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Gómez-Torrente, Mariomariogt@unam.mx
Additional Information: ISSN: 0495-4548 (print)
Keywords: arithmetic; ontology; Benacerraf
Subjects: Specific Sciences > Mathematics
General Issues > Realism/Anti-realism
Depositing User: Unnamed user with email theoria@ehu.es
Date Deposited: 08 Jun 2016 19:27
Last Modified: 08 Jun 2016 19:27
Item ID: 12154
Journal or Publication Title: THEORIA. An International Journal for Theory, History and Foundations of Science
Publisher: Euskal Herriko Unibertsitatea / Universidad del País Vasco
Official URL: http://www.ehu.eus/ojs/index.php/THEORIA/article/v...
DOI or Unique Handle: https://doi.org/10.1387/theoria.14099
Subjects: Specific Sciences > Mathematics
General Issues > Realism/Anti-realism
Date: September 2015
Page Range: pp. 317-329
Volume: 30
Number: 3
ISSN: 2171-679X
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/12154

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