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Single Idea 9902

[from 'Grundlagen der Arithmetik (Foundations)' by Gottlob Frege, in 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers ]

Full Idea

Frege view (which has little to commend it) was that the number 3 is the extension of the concept 'equivalent with some 3-membered set'; that is, for Frege a number was an equivalence class - the class of all classes equivalent with a given class.

Gist of Idea

Frege's incorrect view is that a number is an equivalence class

Source

comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Paul Benacerraf - What Numbers Could Not Be II

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.281


A Reaction

Frege is a platonist, who takes numbers to be objects, so this equivalence class must be identical with an object. What exactly was Frege claiming? I mean, really exactly?