more from David Hilbert

Single Idea 12459

[catalogued under 6. Mathematics / C. Sources of Mathematics / 7. Formalism]

Full Idea

The subject matter of mathematics is the concrete symbols themselves whose structure is immediately clear and recognisable.

Gist of Idea

The subject matter of mathematics is immediate and clear concrete symbols


David Hilbert (On the Infinite [1925], p.192)

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.192

A Reaction

I don't think many people will agree with Hilbert here. Does he mean token-symbols or type-symbols? You can do maths in your head, or with different symbols. If type-symbols, you have to explain what a type is.