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On Skolem’s paradox and the transitive submodel theorem, Rust Belt Workshop in the Philosophy of Logic, Language, and Mathematics, February 2025 | Joel David Hamkins
This will be a talk for the Rust Belt Workshop in the Philosophy of Logic, Language, and Mathematics, held at Ohio State University in Columbus, Ohio, February 8-9, 2025, University Hall (230 N Ova…
Determinateness of truth does not come for free from determinateness of objects, Singapore, November 2024 | Joel David Hamkins
This will be a talk for the (In)determinacy in Mathematics conference at the National University of Singapore, 20-22 November 2024 Abstract. I shall discuss the question whether we may regard…
Infinite-time computable analogues of the universal algorithm, Generalized Computability Theory Workshop, Spain, August 2014 | Joel David Hamkins
This will be a talk at the Generalized Computability Theory workshop in Castro Urdiales, Spain, a beautiful setting on the sea near Bilbao, 19-23 August 2024. Abstract. I shall present infinite-tim…
How we might have viewed the continuum hypothesis as a fundamental axiom necessary for mathematics, Oxford Phil Maths seminar, May 2025 | Joel David Hamkins
This will be a talk for the Philosophy of Mathematics Seminar at the University of Oxford, 19 May 2025. Abstract. I shall describe a simple historical thought experiment showing how our a…
Mathematics, Philosophy of Set Theory and Infinity, Back to the Stone Age interview, May 2024 | Joel David Hamkins
I was interviewed by Francesco Cavina for the Back to the Stone Age series on May 17, 2024, with a sweeping discussion of the philosophy of set theory, infinity, the continuum hypothesis, beauty in…
Life Story of Mathematician & Philosopher of Infinity, interviewed by The Human Podcast, May 2024 | Joel David Hamkins
I was interviewed by The Human Podcast on 17 May 2024. Please enjoy our sweeping conversation about nature of infinity, the nature of abstract mathematical existence, the applicability of mathemati…
The continuum hypothesis could have been a fundamental axiom, CFORS Grad Conference, Oslo, June 2024 | Joel David Hamkins
I shall be giving a keynote lecture for the CFORS Grad Conference at the University of Oslo, 19-20 June 2024. Abstract. I shall describe a simple historical thought experiment showing how…
Forcing is simply the iterative conception undertaken with multivalued logic, ForcingFest, Oslo, June 2024 | Joel David Hamkins
I shall be speaking at the ForcingFest meeting at the University of Oslo, 21 June 2024. Abstract. I will explain how the forcing construction can be seen as a direct implementation of the iterative…
How the continuum hypothesis could have been a fundamental axiom, UC Irvine Logic & Philosoph of Science Colloquium, March 2024 | Joel David Hamkins
This will be a talk for the Logic and Philosophy of Science Colloquium at the University of California at Irvine, 15 March 2024. Abstract. With a simple historical thought experiment, I should like…
Pluralism in the foundations of mathematics, ASL invited address, joint APA/ASL meeting, New York, January 2024 | Joel David Hamkins
This will be an invited ASL address at the joint meeting of the ASL with the APA Eastern Division conference, held in New York 15-18 January 2024. My talk will be 16 January 2024 11:00 am. Abstract…
The surprising strength of second-order reflection in urelement set theory, Luminy, October 2023 | Joel David Hamkins
This will be a talk at the XVII International Luminy Workshop in Set Theory at the Centre International de Rencontres Mathématiques (CIRM) near Marseille, France, held 9-13 October 2023. Abstract. …
What is potentialist second-order logic? Konstanz Actualism and Potentialism Conference 2023 | Joel David Hamkins
This is a talk for the Actualism and Potentialism Conference at the University of Konstanz, 28-29 September 2023. Abstract. What is or should be the potentialist account of classes? It turns out th…
Philosophy of Mathematics and Truth, interview with Matthew Geleta on Paradigm Podcast | Joel David Hamkins
We had a sweeping discussion touching upon many issues in the philosophy of mathematics, including the nature of mathematical truth, mathematical abstraction, the nature of mathematical existence, …
An exploration of infinite games—infinite Wordle and the Mastermind numbers, Harvard, October 2023 | Joel David Hamkins
This will be a talk 18 October 2023 for the Colloquium of the Harvard Center for Mathematical Sciences and Applications (CMSA). Abstract: Let us explore the nature of strategic reasoning in infinit…
Pointwise definable and Leibnizian extensions of models of arithmetic and set theory, Madison Logic Seminar, April 2023 | Joel David Hamkins
Abstract. I shall present a new flexible method showing that every countable model of PA admits a pointwise definable-elementary end-extension. Also, any model of PA of size at most continuum admit…
Natural Instances of Illfoundedness and Nonlinearity in the Hierarchy of Consistency Strength, Oxford Phil Math Seminar, May 2023 | Joel David Hamkins
Abstract. There is an unexplained logical mystery in the foundations of mathematics, namely, our best and strongest mathematical theories seem to be linearly ordered and indeed well-ordered by cons…
Set-theoretic forcing as a computational process, Midwest Computability Seminar, Chicago, May 2023 | Joel David Hamkins
This is a talk for the MidWest Computability Seminar conference held May 2, 2023 at the University of Chicago. The talk will be available via Zoom at Abstract: I shall explore several senses in whi…
The Math Tea argument: must there be numbers we can neither describe nor define? Barcelona March 2023 | Joel David Hamkins
This will be a talk 15 March 2023 for the Mathematics Department of the University of Barcelona, organized jointly with the Set Theory Seminar. Abstract. According to the math tea argument, perhaps…
Infinite games—strategies, logic, theory, and computation, Northeastern, June 2023 | Joel David Hamkins
This will be an online Zoom talk for the Boston Computaton Club, a graduate seminar in computer science at Northeastern University, 16 June 12pm EST (note change in date/time). Contact the organize…