more from James Robert Brown

Single Idea 9643

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory]

Full Idea

Maybe all of mathematics can be represented in set theory, but we should not think that mathematics is set theory. Functions can be represented as order pairs, but perhaps that is not what functions really are.

Gist of Idea

Set theory may represent all of mathematics, without actually being mathematics


James Robert Brown (Philosophy of Mathematics [1999], Ch. 7)

Book Reference

Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.102

A Reaction

This seems to me to be the correct view of the situation. If 2 is represented as {φ,{φ}}, why is that asymmetrical? The first digit seems to be the senior and original partner, but how could the digits of 2 differ from one another?