PhilSci Archive

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

[img]
Preview
Text
14099-56027-1-PB.pdf - Published Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.

Download (206kB) | Preview

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.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

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: 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.pitt.edu/id/eprint/12154

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Altmetric.com

Actions (login required)

View Item View Item