Single Idea 5399

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

Full Idea

If induction was the source of our mathematical knowledge, we should proceed differently. In fact, a certain number of instances make us think of two abstractly, and we then see the general principle, and further instances become unnecessary.

Gist of Idea

Maths is not known by induction, because further instances are not needed to support it

Source

Bertrand Russell (Problems of Philosophy [1912], Ch. 7)

Book Reference

Russell,Bertrand: 'The Problems of Philosophy' [OUP 1995], p.43


A Reaction

In practice, of course, we stop checking whether the sun has come up yet again this morning. Russell's point is better expressed as: if contradictory evidence were observed, we would believe the arithmetic and doubt the experience.