In this paper I argue that, contrary to what several prominent scholars of On Certainty have claimed, Wittgenstein did not maintain that simple mathematical propositions like "2 ~ 2 = 4"or "12 ~ 12 = 144,"much like G. E. Moore's truisms, could be examples of hinge propositions. In particular, given his overall conception of mathematics, it was impossible for him to single out these simpler mathematical propositions from the rest of mathematical statements, to reserve only to them a normative function. I then maintain that these mathematical examples were introduced merely as objects of comparison to bring out some peculiar features of the only hinges he countenanced in On Certainty, which were all outside the realm of mathematics. I then close by gesturing at how the distinction between mathematical hinges and non-hinges could be exemplified and by exploring its consequences with respect to (Wittgenstein's) philosophy of mathematics.

Are there mathematical hinges? / Coliva, A.. - In: INTERNATIONAL JOURNAL FOR THE STUDY OF SKEPTICISM. - ISSN 2210-5700. - 10:3-4(2020), pp. 346-366. [10.1163/22105700-BJA10013]

Are there mathematical hinges?

Coliva A.
2020

Abstract

In this paper I argue that, contrary to what several prominent scholars of On Certainty have claimed, Wittgenstein did not maintain that simple mathematical propositions like "2 ~ 2 = 4"or "12 ~ 12 = 144,"much like G. E. Moore's truisms, could be examples of hinge propositions. In particular, given his overall conception of mathematics, it was impossible for him to single out these simpler mathematical propositions from the rest of mathematical statements, to reserve only to them a normative function. I then maintain that these mathematical examples were introduced merely as objects of comparison to bring out some peculiar features of the only hinges he countenanced in On Certainty, which were all outside the realm of mathematics. I then close by gesturing at how the distinction between mathematical hinges and non-hinges could be exemplified and by exploring its consequences with respect to (Wittgenstein's) philosophy of mathematics.
2020
10
3-4
346
366
Are there mathematical hinges? / Coliva, A.. - In: INTERNATIONAL JOURNAL FOR THE STUDY OF SKEPTICISM. - ISSN 2210-5700. - 10:3-4(2020), pp. 346-366. [10.1163/22105700-BJA10013]
Coliva, A.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1253817
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 6
social impact