Single Idea 18148

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

Full Idea

Hume's Principle will not do as an implicit definition because it makes a positive claim about the size of the universe (which no mere definition can do), and because it does not by itself explain what the numbers are.

Gist of Idea

Hume's Principle is a definition with existential claims, and won't explain numbers

Source

David Bostock (Philosophy of Mathematics [2009], 9.A.2)

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.274


Related Idea

Idea 18145 Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock]