Tag Archives: thought experiment

How we might have viewed the continuum hypothesis as a fundamental axiom necessary for mathematics, Oxford Phil Maths seminar, May 2025

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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 attitude toward the continuum hypothesis could 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 view the continuum hypothesis as a fundamental axiom of set theory, necessary for mathematics and indeed indispensable for calculus.

I shall be speaking on my paper: How the continuum hypothesis could have been a fundamental axiom

How the continuum hypothesis could have been a fundamental axiom

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Joel David Hamkins, “How the continuum hypothesis could have been a fundamental axiom,” Journal for the Philosophy of Mathematics (2024), arxiv:2407.02463.

Abstract. I describe a simple historical thought experiment showing how we might have come to view the continuum hypothesis as a fundamental axiom, one necessary for mathematics, indispensable even for calculus.

The JPM will launch in September 2024. Meanwhile, the preprint pdf is available at arxiv.org/pdf/2407.02463.

See also this talk I gave on the topic at the University of Oslo:

Slides-CH-could-have-been-fundamental-Hamkins-Oslo-June-2024-1Download

How the continuum hypothesis could have been a fundamental axiom, UC Irvine Logic & Philosoph of Science Colloquium, March 2024

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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 to describe how we might easily have come to view the continuum hypothesis as a fundamental axiom, one necessary for mathematics, indispensable even for calculus.

Slides-CH-could-have-been-fundamental-Hamkins-Irvine-March-2024Download

The paper is now available at How the continuum hypothesis could have been a fundamental axiom.