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
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) 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]