The indispensability argument and the nature of mathematical objects

  1. Plebani, Matteo
Journal:
Theoria: an international journal for theory, history and foundations of science

ISSN: 0495-4548

Year of publication: 2018

Volume: 33

Issue: 2

Pages: 249-263

Type: Article

DOI: 10.1387/THEORIA.17613 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

More publications in: Theoria: an international journal for theory, history and foundations of science

Abstract

Two conceptions of the nature of mathematical objects are contrasted: the conception of mathematical objects as preconceived objects (Yablo 2010), and heavy duty platonism (Knowles 2015). It is argued that some theses defended by friends of the indispensability argument are in harmony with heavy duty platonism and in tension with the conception of mathematical objects as preconceived objects.

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Funding information

* Many thanks to audiences in Santiago de Compostela, Munich and Pavia. This work has been fi-nanced by the Spanish Ministry of Economy and Competitiveness and FEDER through the projects FFI2013-41415-P (The explanatory function of abstract objects: their nature and cognoscibility), FFI2017-82534-P (Abstract Objects: For and Against. A Neo-Carnapian Way Out) and through a Juan de la Cierva-formación fellowship (IJCI-2014-19943).

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