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Single Idea 7738

[from 'Grundlagen der Arithmetik (Foundations)' by Gottlob Frege, in 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers ]

Full Idea

Zero is the extension of 'is equinumerous with the concept "is not self-identical"' (which holds of no objects); ..one is defined as the extension of 'is equinumerous with the concept "is identical to zero"'.

Clarification

The 'extension' is the members of that set

Gist of Idea

Zero is defined using 'is not self-identical', and one by using the concept of zero

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Joan Weiner - Frege Ch.4

Book Reference

Weiner,Joan: 'Frege' [OUP 1999], p.66


A Reaction

It sounds like some sort of cheating to define zero in terms of objects, but one in terms of concepts.