more from Gottlob Frege

Single Idea 16883

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers]

Full Idea

For Frege, no arithmetical statement is an axiom, because all are provable.

Gist of Idea

Arithmetical statements can't be axioms, because they are provable


report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Tyler Burge - Frege on Knowing the Foundations 1

Book Reference

Burge,Tyler: 'Truth, Thought, Reason (on Frege)' [OUP 2001], p.325

A Reaction

This is Frege's logicism, in which the true and unprovable axioms are all found in the logic, not in the arithmetic. Compare that view with the Dedekind/Peano axioms.