more from A.George / D.J.Velleman

### Single Idea 10133

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

Full Idea

The derivability of Peano's Postulates from Hume's Principle in second-order logic has been dubbed 'Frege's Theorem', (though Frege would not have been interested, because he didn't think Hume's Principle gave an adequate definition of numebrs).

Gist of Idea

Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle

Source

A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8 n1)

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.215

A Reaction

Frege said the numbers were the sets which were the extensions of the sets created by Hume's Principle.