Ideas from 'Letter to Frege 29.12.1899' by David Hilbert [1899], by Theme Structure

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3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
If axioms and their implications have no contradictions, they pass my criterion of truth and existence
                        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.
                        From: David Hilbert (Letter to Frege 29.12.1899 [1899]), quoted by R Kaplan / E Kaplan - The Art of the Infinite 2 'Mind'
                        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.