more from John P. Burgess

Single Idea 10184

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

Full Idea

On the structuralist interpretation, theorems of analysis concerning the real numbers R are about all complete ordered fields. So R, which appears to be the name of a specific structure, is taken to be a variable ranging over structures.

Gist of Idea

Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure

Source

John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], 1)


A Reaction

Since I am beginning to think that nearly all linguistic expressions should be understood as variables, I find this very appealing, even if Burgess hates it. Terms slide and drift, and are vague, between variable and determinate reference.