more from James Robert Brown

Single Idea 9612

[catalogued under 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism]

Full Idea

A simple argument makes it clear that all mathematical arguments are abstract: there are infinitely many numbers, but only a finite number of physical entities, so most mathematical objects are non-physical. The best assumption is that they all are.

Gist of Idea

There is an infinity of mathematical objects, so they can't be physical


James Robert Brown (Philosophy of Mathematics [1999], Ch. 2)

Book Reference

Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.12

A Reaction

This, it seems to me, is where constructivists score well (cf. Idea 9608). I don't have an infinity of bricks to build an infinity of houses, but I can imagine that the bricks just keep coming if I need them. Imagination is what is unbounded.

Related Idea

Idea 9608 There are no constructions for many highly desirable results in mathematics [Brown,JR]