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Single Idea 8641

[from 'Grundlagen der Arithmetik (Foundations)' by Gottlob Frege, in 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units ]

Full Idea

What are we supposed to abstract from to get from the moon to the number 1? We do get certain concepts, such as satellite, but 1 is not to be met with. In the case of 0 we have no objects at all. ..The essence of number must work for 0 and 1.

Gist of Idea

You can abstract concepts from the moon, but the number one is not among them

Source

Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §44)

Book Reference

Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.57


A Reaction

Note that Frege seems to be conceding psychological abstraction for most other concepts. But why can't you abstract from your abstractions, to reach high-level abstractions? And why should numbers not emerge at those higher levels?