Single Idea 10139

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers]

Full Idea

Frege identifies each conceptual abstract with the corresponding extension of concepts. But the extensions themselves are among the abstracts, so each extension is identical with the class of all concepts that have that extension, which is absurd.

Gist of Idea

Frege gives an incoherent account of extensions resulting from abstraction

Source

comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kit Fine - The Limits of Abstraction I.2

Book Reference

Fine,Kit: 'The Limits of Abstraction' [OUP 2008], p.29


A Reaction

Fine says this point is 'from the standpoint of a general theory of abstracts', which presumably was implied in Frege, but not actually spelled out.