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The indispensability argument and the nature of mathematical objects

Plebani, Matteo (2018) The indispensability argument and the nature of mathematical objects. THEORIA. An International Journal for Theory, History and Foundations of Science, 33 (2). pp. 249-263. ISSN 2171-679X

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Abstract

I will contrast two conceptions of the nature of mathematical objects: the conception of mathematical objects as preconceived objects (Yablo 2010), and heavy duty platonism (Knowles 2015). I will argue that friends of the indispensability argument are committed to some metaphysical theses and that one promising way to motivate such theses is to adopt heavy duty platonism. On the other hand, combining the indispensability argument with the conception of mathematical objects as preconceived objects yields an unstable position. The conclusion is that the metaphysical commitments of the indispensability argument should be carefully scrutinized.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Plebani, Matteoplebani.matteo@gmail.com
Additional Information: ISSN: 0495-4548 (print)
Keywords: indispensability argument; heavy duty platonism; metaphysical grounding
Subjects: Specific Sciences > Mathematics > Applicability
Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Ontology
Specific Sciences > Mathematics
Depositing User: Unnamed user with email theoria@ehu.es
Date Deposited: 20 Jun 2018 18:01
Last Modified: 20 Jun 2018 18:01
Item ID: 14795
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.17613
Subjects: Specific Sciences > Mathematics > Applicability
Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Ontology
Specific Sciences > Mathematics
Date: May 2018
Page Range: pp. 249-263
Volume: 33
Number: 2
ISSN: 2171-679X
URI: https://philsci-archive.pitt.edu/id/eprint/14795

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