Single Idea 10027

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers]

Full Idea

I take the view that (agreeing with Aristotle) mathematics only requires the notion of a potential infinity, ...and that mathematics is higher-order modal logic.

Gist of Idea

Mathematics is higher-order modal logic

Source

Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984])

Book Reference

-: 'Journal of Philosophy' [-], p.149


A Reaction

Modern 'modal' accounts of mathematics I take to be heirs of 'if-thenism', which seems to have been Russell's development of Frege's original logicism. I'm beginning to think it is right. But what is the subject-matter of arithmetic?