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What we talk about when we talk about numbers

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What we talk about when we talk about numbers. / Pettigrew, Richard.

In: Annals of Pure and Applied Logic, Vol. 169, No. 12, 12.2018, p. 1437-1456.

Research output: Contribution to journalArticle

Harvard

Pettigrew, R 2018, 'What we talk about when we talk about numbers', Annals of Pure and Applied Logic, vol. 169, no. 12, pp. 1437-1456. https://doi.org/10.1016/j.apal.2018.08.009

APA

Vancouver

Pettigrew R. What we talk about when we talk about numbers. Annals of Pure and Applied Logic. 2018 Dec;169(12):1437-1456. https://doi.org/10.1016/j.apal.2018.08.009

Author

Pettigrew, Richard. / What we talk about when we talk about numbers. In: Annals of Pure and Applied Logic. 2018 ; Vol. 169, No. 12. pp. 1437-1456.

Bibtex

@article{304f7f74688c482b99c65f684f244399,
title = "What we talk about when we talk about numbers",
abstract = "In this paper, I describe and motivate a new species of mathematical structuralism, which I call Instrumental Nominalism about Set-Theoretic Structuralism. As the name suggests, this approach takes standard Set-Theoretic Structuralism of the sort championed by Bourbaki, and removes its ontological commitments by taking an instrumental nominalist approach to that ontology of the sort described by Joseph Melia and Gideon Rosen. I argue that this avoids all of the problems that plague other versions of structuralism.",
keywords = "Foundations of mathematics, Mathematical structuralism, Nominalism, Philosophy of mathematics, Set-theoretic foundations",
author = "Richard Pettigrew",
year = "2018",
month = "12",
doi = "10.1016/j.apal.2018.08.009",
language = "English",
volume = "169",
pages = "1437--1456",
journal = "Annals of Pure and Applied Logic",
issn = "0168-0072",
publisher = "Elsevier Masson SAS",
number = "12",

}

RIS - suitable for import to EndNote

TY - JOUR

T1 - What we talk about when we talk about numbers

AU - Pettigrew, Richard

PY - 2018/12

Y1 - 2018/12

N2 - In this paper, I describe and motivate a new species of mathematical structuralism, which I call Instrumental Nominalism about Set-Theoretic Structuralism. As the name suggests, this approach takes standard Set-Theoretic Structuralism of the sort championed by Bourbaki, and removes its ontological commitments by taking an instrumental nominalist approach to that ontology of the sort described by Joseph Melia and Gideon Rosen. I argue that this avoids all of the problems that plague other versions of structuralism.

AB - In this paper, I describe and motivate a new species of mathematical structuralism, which I call Instrumental Nominalism about Set-Theoretic Structuralism. As the name suggests, this approach takes standard Set-Theoretic Structuralism of the sort championed by Bourbaki, and removes its ontological commitments by taking an instrumental nominalist approach to that ontology of the sort described by Joseph Melia and Gideon Rosen. I argue that this avoids all of the problems that plague other versions of structuralism.

KW - Foundations of mathematics

KW - Mathematical structuralism

KW - Nominalism

KW - Philosophy of mathematics

KW - Set-theoretic foundations

UR - http://www.scopus.com/inward/record.url?scp=85051138078&partnerID=8YFLogxK

U2 - 10.1016/j.apal.2018.08.009

DO - 10.1016/j.apal.2018.08.009

M3 - Article

VL - 169

SP - 1437

EP - 1456

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

SN - 0168-0072

IS - 12

ER -