Frege's Changing Conception of Number

Theoria 78 (2):146-167 (2012)
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Abstract

I trace changes to Frege's understanding of numbers, arguing in particular that the view of arithmetic based in geometry developed at the end of his life (1924–1925) was not as radical a deviation from his views during the logicist period as some have suggested. Indeed, by looking at his earlier views regarding the connection between numbers and second-level concepts, his understanding of extensions of concepts, and the changes to his views, firstly, in between Grundlagen and Grundgesetze, and, later, after learning of Russell's paradox, this position is a natural position for him to have retreated to, when properly understood.

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Kevin Klement
University of Massachusetts, Amherst

Citations of this work

Formal Arithmetic Before Grundgesetze.Richard Kimberly Heck - 2019 - In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic. Oxford: Oxford University Press. pp. 497-537.
Saying Something about a Concept: Frege on Statements of Number.Mark Textor - 2021 - History and Philosophy of Logic 42 (1):60-71.
Quantification and Paradox.Edward Ferrier - 2018 - Dissertation, University of Massachusetts Amherst

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References found in this work

The foundations of arithmetic.Gottlob Frege - 1884/1950 - Evanston, Ill.,: Northwestern University Press.
Introduction to mathematical philosophy.Bertrand Russell - 1919 - New York: Dover Publications.
Posthumous Writings.Gottlob Frege (ed.) - 1979 - Blackwell.
Collected Papers on Mathematics, Logic, and Philosophy.Gottlob Frege - 1991 - Wiley-Blackwell. Edited by Brian McGuinness.
Introduction to Mathematical Philosophy.Bertrand Russell - 1919 - Revue Philosophique de la France Et de l'Etranger 89:465-466.

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