How should one conceive of the method of mathematics, if one takes a naturalist stance? Mathematical knowledge is regarded as the paradigm of certain knowledge, since mathematics is based on the axiomatic method. Natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some naturalists try to naturalize mathematics relying on Darwinism. But several difficulties arise when one tries to naturalize in this way the traditional view of mathematics, according to which mathematical knowledge is certain and the method of mathematics is the axiomatic method. This paper suggests that, in order to naturalize mathematics through Darwinism, it is better to take the method of mathematics not to be the axiomatic method.

Mathematical knowledge and naturalism / Sterpetti, F. - In: PHILOSOPHIA. - ISSN 0048-3893. - 47:1(2019), pp. 225-247. [10.1007/s11406-018-9953-1]

Mathematical knowledge and naturalism

Sterpetti F
2019

Abstract

How should one conceive of the method of mathematics, if one takes a naturalist stance? Mathematical knowledge is regarded as the paradigm of certain knowledge, since mathematics is based on the axiomatic method. Natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some naturalists try to naturalize mathematics relying on Darwinism. But several difficulties arise when one tries to naturalize in this way the traditional view of mathematics, according to which mathematical knowledge is certain and the method of mathematics is the axiomatic method. This paper suggests that, in order to naturalize mathematics through Darwinism, it is better to take the method of mathematics not to be the axiomatic method.
2019
axiomatic method; Darwinism; mathematical knowledge; mathematical platonism; naturalism
01 Pubblicazione su rivista::01a Articolo in rivista
Mathematical knowledge and naturalism / Sterpetti, F. - In: PHILOSOPHIA. - ISSN 0048-3893. - 47:1(2019), pp. 225-247. [10.1007/s11406-018-9953-1]
File allegati a questo prodotto
File Dimensione Formato  
Sterpetti_Mathematical_2019.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 590.73 kB
Formato Adobe PDF
590.73 kB Adobe PDF   Contatta l'autore
Sterpetti_Mathematical-pre_2019.pdf

accesso aperto

Tipologia: Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 651.27 kB
Formato Adobe PDF
651.27 kB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1271943
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact