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Single Idea 14423

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

Full Idea

That '0', 'number' and 'successor' cannot be defined by means of Peano's five axioms, but must be independently understood.

Gist of Idea

'0', 'number' and 'successor' cannot be defined by Peano's axioms

Source

Bertrand Russell (Introduction to Mathematical Philosophy [1919], I)

Book Ref

Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.9

Related Idea

Idea 18133 The usual definitions of identity and of natural numbers are impredicative [Bostock]