On the Essence and Identity of Numbers

Citation data:

THEORIA. An International Journal for Theory, History and Foundations of Science, ISSN: 0495-4548, Vol: 30, Issue: 3, Page: 317-329

Publication Year:
2015
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Repository URL:
http://philsci-archive.pitt.edu/id/eprint/12154
DOI:
10.1387/theoria.14099
Author(s):
Mario Gómez-Torrente
Publisher(s):
UPV/EHU Press, Euskal Herriko Unibertsitatea / Universidad del País Vasco
Tags:
Arts and Humanities
article description
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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