more from David Hume

Single Idea 8649

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle]

Full Idea

When two numbers are so combin'd, as that the one has always a unit answering to every unit of the other, we pronounce them equal.

Gist of Idea

Two numbers are equal if all of their units correspond to one another


David Hume (Treatise of Human Nature [1739], 1.3.1)

Book Reference

Hume,David: 'A Treatise of Human Nature', ed/tr. Mossner,Ernest C. [Penguin 1969], p.119

A Reaction

This became known as Hume's Principle after Frege made use of it for logicism (Foundations 63). It reduces equality to something fairly simple and visual (one-to-one correspondence). But we also say that two logicians or musicians are 'equal' in ability.