more from James Robert Brown

Single Idea 9628

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique]

Full Idea

Set theory is at the very heart of mathematics; it may even be all there is to mathematics. The notion of set, however, seems quite contrary to the spirit of structuralism.

Gist of Idea

Sets seem basic to mathematics, but they don't suit structuralism


James Robert Brown (Philosophy of Mathematics [1999], Ch. 4)

Book Reference

Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.61

A Reaction

So much the worse for sets, I say. You can, for example, define ordinality in terms of sets, but that is no good if ordinality is basic to the nature of numbers, rather than a later addition.