more from E Reck / M Price

### Single Idea 10169

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism]

Full Idea

Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to.

Gist of Idea

Relativist Structuralism just stipulates one successful model as its arithmetic

Source

E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)

A Reaction

The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight?