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Frege's Critique of Formalism
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Arts, Department of Philosophy, Logic and Metaphysics.
2018 (English)In: NEW ESSAYS ON FREGE: BETWEEN SCIENCE AND LITERATURE / [ed] Bengtsson, G Saatela, S Pichler, A, SPRINGER INTERNATIONAL PUBLISHING AG , 2018, p. 75-86Conference paper, Published paper (Refereed)
Abstract [en]

This paper deals with Frege's early critique of formalism in the philosophy of mathematics. Frege opposes meaningful arithmetic, according to which arithmetical formulas express a sense and arithmetical rules are grounded in the reference of the signs, to formal arithmetic, exemplified in particular by J. Thomae, whose "formal standpoint", according to Frege, is that arithmetic should be understood as a manipulation of meaningless figures. However, Frege's discussion of Thomae's analogy between arithmetic and chess shows that Frege does not understand his main point, which is that we must distinguish conceptually between statements about chess figures, and the chess pieces they represent. Indeed, Thomae's fruitful use of this comparison undermines the ontological conception of arithmetic represented by Frege. The chess pieces do not go proxy for anything (as the number signs do in Frege's 'meaningful arithmetic'), but playing chess is not for that reason just manipulation of physical chess figures. This is also Wittgenstein's point when he criticizes Frege for not seeing the "justified side of formalism". Thomae's formalism can be clarified by using the distinction between sign and symbol. Symbols are never meaningless or empty forms or signs, since they have a role or function in a symbolism, which one may call their meaning. The discussion of the chess analogy shows that Frege fails to see this operative aspect of the symbolism. We can conclude that the "formal standpoint" that Frege criticizes is his fabrication, rather than anything we can attribute to Thomae.

Place, publisher, year, edition, pages
SPRINGER INTERNATIONAL PUBLISHING AG , 2018. p. 75-86
Series
Nordic Wittgenstein Studies, ISSN 2520-1514
Keywords [en]
Arithmetic, Formalism, Frege, Mathematical symbolism, Reference, Sense, Thomae, Wittgenstein
National Category
Philosophy
Identifiers
URN: urn:nbn:se:uu:diva-383555DOI: 10.1007/978-3-319-71186-7_5ISI: 000466511000005ISBN: 978-3-319-71186-7 (electronic)ISBN: 978-3-319-71185-0 (print)OAI: oai:DiVA.org:uu-383555DiVA, id: diva2:1316554
Conference
International Workshop on Frege between Poetry and Science, DEC, 2014, Univ Bergen, Dept Philosophy, Bergen, NORWAY
Available from: 2019-05-20 Created: 2019-05-20 Last updated: 2019-05-20Bibliographically approved

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Stenlund, Sören

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