I’ve recently finished a draft of the first chapter for my masters thesis, on the topic of mathematical structuralism. I argue that the philosophical discussion of mathematical structuralism has, by and large, misrepresented mathematical attitudes on the subject. This dialogue, beginning with Benacerraf’s classic What Numbers Could Not Be, has focused on the ontology of [...]

In a recent joint paper with Jeremy Avigad and John Mumma (forthcoming in the Review of Symbolic Logic, preprint available at the arXiv), we devise a formal system that is intended to faithfully capture the notion of Euclidean geometric proofs. Specifically, is meant to be a formal counterpart to Books I through [...]

For my first few blog posts here at unwanted capture, I’m going to talk about a subject that I will return to often: rethinking our mathematical foundations aesthetically. This time, I want to look at our definitions for the continuum; I think that a non-standard approach can give us a cleaner presentation which is closer [...]