more from Kit Fine

Single Idea 10529

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

Full Idea

Neo-Fregeans have thought that Hume's Principle, and the like, might be definitive of number and therefore not subject to the usual epistemological worries over its truth.

Clarification

Hume's Principle defines 'equinumerous' by one-to-one mapping

Gist of Idea

If Hume's Principle can define numbers, we needn't worry about its truth

Source

Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310)

Book Reference

-: 'Philosophical Studies' [-], p.310


A Reaction

This seems to be the underlying dream of logicism - that arithmetic is actually brought into existence by definitions, rather than by truths derived from elsewhere. But we must be able to count physical objects, as well as just counting numbers.