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Single Idea 10224

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism]

Full Idea

The even numbers and the natural numbers greater than 4 both exemplify the natural-number structure. In the former, 6 plays the 3 role, and in the latter 8 plays the 3 role.

Gist of Idea

The even numbers have the natural-number structure, with 6 playing the role of 3


Stewart Shapiro (Philosophy of Mathematics [1997], 3.5)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.100

A Reaction

This begins to sound a bit odd. If you count the even numbers, 6 is the third one. I could count pebbles using only evens, but then presumably '6' would just mean '3'; it wouldn't be the actual number 6 acting in a different role, like Laurence Olivier.