aboutlogic #13 | Joel David Hamkins – Set Theory, Pluralism & the Multiverse View
6/3/20261 hr 25 min
aboutlogic #13 | In this episode of aboutlogic, we’re joined by Joel David Hamkins, professor at the University of Notre Dame and a leading figure in set theory, mathematical logic, and the philosophy of mathematics. Joel shares his insights into the multiverse view of set theory, a perspective that challenges the traditional "universe view" by embracing a pluralistic approach to mathematical truth. We explore how this view connects to constructivism, potentialism, and the foundations of mathematics, and discuss its implications for understanding concepts like the Continuum Hypothesis (CH) and the nature of mathematical reality. Joel also reflects on the historical contingency of mathematical axioms, the role of categoricity in mathematics, and how different philosophical perspectives, such as Platonism, formalism, and fictionalism, shape the way mathematicians approach their work. Whether you're a mathematician, philosopher, or simply curious about the foundations of logic, this conversation offers a deep dive into the diverse and evolving landscape of mathematical thought.
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First 90 secondsJoel David Hamkins· Guest0:00
The multiverse view or pluralism is more often called set-theoretic pluralism is the view that, that there isn't just one true set-theoretic reality, but rather a, a kind of, uh, plurality of different set-theoretic concepts, each giving rise to their own kind of set-theoretic truth. The way it's often described, set-theoretic pluralism, it's not about the theory and our descriptions of the theory. Rather, it's a kind of reality base. There are different concepts of set that give rise to their own independent set-theoretic world, so to speak.
Speaker 1· Host0:33
[upbeat music] Hey, folks. Sorry for this little break. Our first season was, uh, supported by the Akademie der Wissenschaften in Hamburg, but since this support ran out, we are now looking to crowdfund our little endeavor here. So if you want to chip in and feel particularly generous, feel free to go to buymeacoffee.com/aboutlogic and contribute whatever you would like to. Thanks for your support, and now back to the episode.
Torsten· Host1:01
Hello. Yeah. Welcome to About Logic, and we're very pleased to have Joel Hamkins here, who is professor at the University of Notre Dame, which is not in France, uh, but in- [laughs] ... close to Chicago, I understand. And, um, yeah, uh, very nice, uh, pleased to have you here. And you previously were at the University of Oxford. Is this correct? Yeah. Okay.
Joel David Hamkins· Guest1:25
That's right. Yes, I was in Oxford. And before that, I was for many years in New York, in