more from E Reck / M Price

Single Idea 10176

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism]

Full Idea

Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model.

Gist of Idea

Universalist Structuralism is based on generalised if-then claims, not one particular model

Source

E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], 5)


A Reaction

There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator.