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Single Idea 16864

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

Full Idea

If the law [of induction] can be proved, it will be included amongst the theorems of mathematics; if it cannot, it will be included amongst the axioms.

Gist of Idea

If principles are provable, they are theorems; if not, they are axioms

Source

Gottlob Frege (Logic in Mathematics [1914], p.203)

Book Ref

Frege,Gottlob: 'Posthumous Writings', ed/tr. Hermes/Long/White etc [Blackwell 1979], p.203


A Reaction

This links Frege with the traditional Euclidean view of axioms. The question, then, is how do we know them, given that we can't prove them.