more from David Hilbert

Single Idea 18112

[catalogued under 6. Mathematics / C. Sources of Mathematics / 8. Finitism]

Full Idea

We can conceive mathematics to be a stock of two kinds of formulas: first, those to which the meaningful communications of finitary statements correspond; and secondly, other formulas which signify nothing and which are ideal structures of our theory.

Gist of Idea

Mathematics divides in two: meaningful finitary statements, and empty idealised statements


David Hilbert (On the Infinite [1925], p.196), quoted by David Bostock - Philosophy of Mathematics 6.1

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.174