Full Idea
The predicative approach cannot accept either the usual definition of identity or the usual definition of the natural numbers, for both of these definitions are impredicative.
Gist of Idea
The usual definitions of identity and of natural numbers are impredicative
Source
David Bostock (Philosophy of Mathematics [2009], 8.3)
Book Reference
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.246
A Reaction
[Bostock 237-8 gives details]
Related Idea
Idea 14423 '0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell]