Frege's Changing Conception of Number

Theoria 78 (2):146-167 (2012)
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
Keywords number  extensions  objects  Frege  functions  concepts  logicism
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    Gottlob Frege (1953/1968). The Foundations of Arithmetic. Evanston, Ill.,Northwestern University Press.

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