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?