more from William W. Tait

Single Idea 13416

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

Full Idea

The axiomatic conception of mathematics is the only viable one. ...But they are true because they are axioms, in contrast to the view advanced by Frege (to Hilbert) that to be a candidate for axiomhood a statement must be true.

Gist of Idea

Mathematics must be based on axioms, which are true because they are axioms, not vice versa

Source

report of William W. Tait (Intro to 'Provenance of Pure Reason' [2005], p.4) by Charles Parsons - Review of Tait 'Provenance of Pure Reason' 2

Book Reference

-: 'Philosophia Mathematica' [-], p.222


A Reaction

This looks like the classic twentieth century shift in the attitude to axioms. The Greek idea is that they must be self-evident truths, but the Tait-style view is that they are just the first steps in establishing a logical structure. I prefer the Greeks.