“The problem (of infinity) is inherently attractive and the questions that are so simple to ask yet the analysis of them is so subtle,” he said. “My favorite situation occurs when a question in philosophy gives rise to a kind of mathematical analysis, whose resolution then raises additional philosophical questions or refinements of the philosophical issues in a kind of feedback cycle.”
One debate currently raging in the mathematical philosophy field is the philosophy of set theory and asking, “Is there only one mathematical reality or is there a kind of indefiniteness to mathematical questions?”
Hamkins, previously a professor of logic at Oxford University, is working on a book project, The Book of Infinity.
His prior work includes the books Proof and the Art of Mathematics and Lectures on the Philosophy of Mathematics, and journal articles on the set-theoretic multiverse, the modal logic of forcing, the dream solution of the continuum hypothesis, and transfinite game values in infinite chess.
At Notre Dame, he’s happy to explore set theory, potentialism, and modal model theory with students and faculty.
“There's such a strong logic group in both philosophy and in mathematics,” he said. “And the students are just fantastic to work with. I really hope to show them the beauty in the subject that I see.”