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 Reference
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]