more from Gottlob Frege

Single Idea 18142

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem]

Full Idea

Frege inferred from the Julius Caesar problem that even though Hume's Principle sufficed as a single axiom for deducing the arithmetic of the finite cardinal numbers, still it does not explain our ordinary understanding of those numbers.

Gist of Idea

One-one correlations imply normal arithmetic, but don't explain our concept of a number

Source

Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]), quoted by David Bostock - Philosophy of Mathematics 9.A.2

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.267


Related Idea

Idea 18144 Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock]