more from Alan Musgrave

### Single Idea 10058

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic]

Full Idea

The axiom of Peano which states that no two numbers have the same successor requires the Axiom of Infinity for its proof.

Gist of Idea

No two numbers having the same successor relies on the Axiom of Infinity

Source

Alan Musgrave (Logicism Revisited [1977], §4 n)

Book Reference

-: 'British Soc for the Philosophy of Science' [-], p.112

A Reaction

[He refers to Russell 1919:131-2] The Axiom of Infinity is controversial and non-logical.