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Single Idea 9977

[from 'The Principles of Mathematics' by Bertrand Russell, in 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique ]

Full Idea

It is impossible that the ordinals should be, as Dedekind suggests, nothing but the terms of such relations as constitute a progression. If they are anything at all, they must be intrinsically something.

Gist of Idea

Ordinals can't be defined just by progression; they have intrinsic qualities

Source

Bertrand Russell (The Principles of Mathematics [1903], §242)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.249


A Reaction

This is the obvious platonist response to the incipient doctrine of structuralism. We have a chicken-and-egg problem. Bricks need intrinsic properties to make a structure. A structure isomorphic to numbers is not thereby the numbers.