more from David Hilbert

Single Idea 15716

[catalogued under 3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth]

Full Idea

If the arbitrarily given axioms do not contradict each other with all their consequences, then they are true and the things defined by the axioms exist. For me this is the criterion of truth and existence.

Gist of Idea

If axioms and their implications have no contradictions, they pass my criterion of truth and existence


David Hilbert (Letter to Frege 29.12.1899 [1899]), quoted by R Kaplan / E Kaplan - The Art of the Infinite 2 'Mind'

Book Reference

Kaplan,R and Kaplan,E: 'The Art of the Infinite' [Penguin 2004], p.51

A Reaction

If an axiom says something equivalent to 'fairies exist, but they are totally undetectable', this would seem to avoid contradiction with anything, and hence be true. Hilbert's idea sounds crazy to me. He developed full Formalism later.