High school mathematics education focuses on calculation. It’s all about getting the right answer to some problem, like finding the x such that x² + 3x = 18. This almost entirely excludes the notion of a mathematical proof, to the point that there are highly educated people who have never even heard of the concept.…

Do Peano’s axioms define the natural numbers? Would it be possible for any system of axioms to do so? Some musings after Mathieu Marion’s article ‘Wittgenstein on Surveyability of Proofs’. (I don’t think there’s anything original in here; it’s just me thinking through the topic.) What are the natural numbers? Of course, they’re 0, 1,…

For my Philosophy of Time course, my students and I read the second chapter of Ted Sider’s Four-Dimensionalism (2001). It’s called “Against Presentism” and serves very well as an introduction to attacks on that particular position. Perhaps I’ll blog about this chapter later on: as a defender of presentism, I certainly have some critical thoughts.…