Single Idea 17784

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers]

Full Idea

We eliminate the real numbers by giving an axiomatic definition of the species of complete ordered fields. These axioms are categorical (mutually isomorphic), and thus are mathematically indistinguishable.

Gist of Idea

Real numbers can be eliminated, by axiom systems for complete ordered fields


John Mayberry (What Required for Foundation for Maths? [1994], p.408-2)

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.408

A Reaction

Hence my clever mathematical friend says that it is a terrible misunderstanding to think that mathematics is about numbers. Mayberry says the reals are one ordered field, but mathematics now studies all ordered fields together.

Related Idea

Idea 14158 Quantity is not part of mathematics, where it is replaced by order [Russell]