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Single Idea 9909

[from 'What Numbers Could Not Be' by Paul Benacerraf, in 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism ]

Full Idea

Any object can play the role of 3; that is, any object can be the third element in some progression. What is peculiar to 3 is that it defines that role, not by being a paradigm, but by representing the relation of any third member of a progression.

Gist of Idea

The number 3 defines the role of being third in a progression

Source

Paul Benacerraf (What Numbers Could Not Be [1965], IIIC)

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.291


A Reaction

An interesting early attempt to spell out the structuralist idea. I'm thinking that the role is spelled out by the intersection of patterns which involve threes.