more from Michèle Friend

Single Idea 8702

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

Full Idea

Structuralists give a historical account of why the 'same' number occupies different structures. Numbers are equivalent rather than identical. 8 is the immediate predecessor of 9 in the whole numbers, but in the rationals 9 has no predecessor.

Clarification

For 'rational' numbers see Idea 8668

Gist of Idea

In structuralism the number 8 is not quite the same in different structures, only equivalent

Source

Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4)

Book Reference

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.93


A Reaction

I don't become a different person if I move from a detached house to a terraced house. This suggests that 8 can't be entirely defined by its relations, and yet it is hard to see what its intrinsic nature could be, apart from the units which compose it.