Single Idea 9953

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

Full Idea

Frege needs more than just saying that numbers are second-level concepts under which first-level concepts fall, because they can fall under many second-level concepts, such as that of existence.

Gist of Idea

Numbers are more than just 'second-level concepts', since existence is also one

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.25


A Reaction

This marks the end of the first stage of Frege's theory, which leads him on to objects and Hume's Principle. After you have written 'level' a few times, you begin to wonder whether thought and world really are carved up in such a neat way.