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Joel David Hamkins

mathematics and philosophy of the infinite

Joel David Hamkins

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Tag Archives: Cody Roux

The Church of Logic podcast, April 2025

Posted on April 21, 2025 by Joel David Hamkins
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I was interviewed by Cody Roux for The Church of Logic podcast—a fascinating sweeping conversation on issues in the philosophy of mathematics and set theory, including what I described as a fundamental dichotomy between two perspectives on the nature of mathematics and what it is all about. Cody and I have affinities with opposite sides of this dichotomy, which made for a fruitful exchange.

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Posted in Talks, Videos | Tagged Cody Roux, philosophy of logic, philosophy of mathematics, philosophy of set theory, podcast, The Church of Logic | Leave a reply

Infinitely More

On going first

Would you rather go first or second? In many games, there is a definite advantage one way or the other. How can we redress these imbalances, if we seek to make truly fair and balanced games?

Joel David Hamkins
15 HR AGO
3
How we might have viewed the continuum hypothesis as a fundamental axiom necessary for mathematics

By mounting a philosophical historical thought experiment, I argue that our attitude toward the continuum hypothesis could easily have been very different than it is.

Joel David Hamkins
May 22
5
12
Take my Philosophy and Logic of Games final exam!

Can you pass the exam for my games course?

Joel David Hamkins
May 14
10
10
Proof and the Art of Mathematics, MIT Press, 2020

Recent Comments

  • Thomas on Alan Turing, On computable numbers
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  • David Roberts on Skolem’s paradox and the countable transitive submodel theorem, Leeds Set Theory Seminar, May 2025

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RSS Mathoverflow activity

  • Comment by Joel David Hamkins on Is V[r0,…,rk,…] a proper extension
    If someone wants to push the idea through, please feel free to post an answer.
  • Comment by Joel David Hamkins on Is V[r0,…,rk,…] a proper extension
    Yes, in fact I was thinking about exactly that case. One needs to verify that the composition of those forcing notion is still improper. Is this clear?
  • Comment by Joel David Hamkins on Is V[r0,…,rk,…] a proper extension
    This would answer your question negatively, if we had an improper extension that was stationary preserving and generated by a real (with a Cohen real present). Perhaps we can just do some improper forcing stat-preserving forcing, followed by almost disjoint coding to get the extension generated by a real?
  • Comment by Joel David Hamkins on Is V[r0,…,rk,…] a proper extension
    If you have any Cohen real at all and W is generated by some real r, not necessary Cohen, then you can achieve the situation of your third bullet point, by splitting the Cohen real into countably many, and changing one bit in each so as to code the given real r into the sequence.
  • Answer by Joel David Hamkins for How might fundamental mathematics differ for entities with intuitive comprehension of the continuum?
    The answer to your question is the subject of descriptive set theory, which is all about trying to understand the hierarchy of logical complexity that arises in a context where the real numbers are given as basic objects. This is far beyond the arithmetic hierarchy, studying the projective hierarchy, and we analyze the complexity of […]
  • Comment by Joel David Hamkins on How does a global well order provide a selector?
    It is definable from
  • Comment by Joel David Hamkins on A form of reverse mathematics that works with hereditarily finite sets instead of numbers
    Ah, sorry, I don't have a reference. But I think of this as a trivial step of applying the bi-interpretation.
  • Comment by Joel David Hamkins on How might fundamental mathematics differ for entities with intuitive comprehension of the continuum?
    I was writing an answer to this question, all about descriptive set theory, but the question was closed.

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