Single Idea 8692

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

Full Idea

Wright proposed removing Frege's basic law V (which led to paradox), replacing it with Frege's 'number principle' (identity of numbers is one-to-one correspondence). The new system is formally consistent, and the Peano axioms can be derived from it.

Clarification

See Idea 5897 for a simplified summary of Peano

Gist of Idea

Frege has a good system if his 'number principle' replaces his basic law V

Source

report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Michèle Friend - Introducing the Philosophy of Mathematics 3.7

Book Reference

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.71


A Reaction

The 'number principle' is also called 'Hume's principle'. This idea of Wright's resurrected the project of logicism. The jury is ought again... Frege himself questioned whether the number principle was a part of logic, which would be bad for 'logicism'.

Related Idea

Idea 5897 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew]