more from Gottlob Frege

Single Idea 16870

[catalogued under 5. Theory of Logic / K. Features of Logics / 1. Axiomatisation]

Full Idea

The axioms are theorems, but truths for which no proof can be given in our system, and no proof is needed. It follows from this that there are no false axioms, and we cannot accept a thought as an axiom if we are in doubt about its truth.

Gist of Idea

Axioms are truths which cannot be doubted, and for which no proof is needed


Gottlob Frege (Logic in Mathematics [1914], p.205)

Book Reference

Frege,Gottlob: 'Posthumous Writings', ed/tr. Hermes/Long/White etc [Blackwell 1979], p.205

A Reaction

He struggles to be as objective as possible, but has to concede that whether we can 'doubt' the axiom is one of the criteria.

Related Idea

Idea 16867 Logic not only proves things, but also reveals logical relations between them [Frege]