more from David Hilbert

Single Idea 17697

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

Full Idea

The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment.

Gist of Idea

The existence of an arbitrarily large number refutes the idea that numbers come from experience


David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130)

Book Reference

'From Frege to Gödel 1879-1931', ed/tr. Heijenoort,Jean van [Harvard 1967], p.130

A Reaction

Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'.