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Single Idea 18133

[from 'Philosophy of Mathematics' by David Bostock, in 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism ]

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]