This will be a talk for the new Mathematical Philosophy Seminar here at the University of Notre Dame. Monday, September 21, 2026, 4pm, in Malloy Hall.
Title: How the continuum hypothesis could have been a fundamental axiom, one necessary for mathematics
Speaker: Joel David Hamkins, O’Hara Professor of Logic, Notre Dame
Abstract. I shall describe a simple historical thought experiment showing how our attitude toward the continuum hypothesis might easily have been very different than it is. If our mathematical history had been just a little different, I claim, if certain mathematical discoveries had been made in a slightly different order, then we would naturally have come to view the continuum hypothesis as a fundamental axiom of set theory, necessary for mathematics, indispensable even for the core ideas of calculus.
The talk is based on this paper:
- Joel David Hamkins, “How the continuum hypothesis could have been a fundamental axiom,” Journal for the Philosophy of Mathematics (2024), DOI:10.36253/jpm-2936, arxiv:2407.02463.