Single Idea 17804

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics]

Full Idea

No axiomatic theory, formal or informal, of first or of higher order can logically play a foundational role in mathematics. ...It is obvious that you cannot use the axiomatic method to explain what the axiomatic method is.

Gist of Idea

Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms


John Mayberry (What Required for Foundation for Maths? [1994], p.415-2)

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.415