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Joel David Hamkins

mathematics and philosophy of the infinite

Joel David Hamkins

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Tag Archives: podcast

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

Tactics versus strategies—the case of chess

Does chess admit of winning or drawing tactics? Which information exactly do we need to include as part of the board position?

Joel David Hamkins
Aug 17
8
6
The tactical variation of the fundamental theorem

We prove the tactical variation of the fundamental theorem of finite games—for finite games with sufficiently rich board positions, one of the players has a winning tactic or both have drawing tactics

Joel David Hamkins
Aug 10
6
2
Tactics versus strategies in the theory of games

How do tactics differ from strategies? Does the fundamental theorem of finite games hold for tactics? Must every finite game have a winning tactic for one player or drawing tactics for both?

Joel David Hamkins
Aug 3
12
6
Proof and the Art of Mathematics, MIT Press, 2020

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Recent Comments

  • Joseph Shipman on The elementary theory of surreal arithmetic is bi-interpretable with set theory, Kobe, Japan, September 2025
  • Joseph Shipman on The elementary theory of surreal arithmetic is bi-interpretable with set theory, Kobe, Japan, September 2025
  • Did Turing ever halt? HPS Colloquium, Notre Dame, October 2025 | Joel David Hamkins on Did Turing prove the undecidability of the halting problem?
  • Lecture series on the philosophy of mathematics | Joel David Hamkins on Lectures on the Philosophy of Mathematics
  • How the continuum hypothesis might have been a fundamental axiom, Lanzhou China, July 2025 | Joel David Hamkins on How the continuum hypothesis could have been a fundamental axiom

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RSS Mathoverflow activity

  • Comment by Joel David Hamkins on Is every directed graph the quotient of poset where boundary nodes are identified?
    Not always. Consider a diamond, where the max and min have two edges, or the one point order, where it has none.
  • Comment by Joel David Hamkins on Is every directed graph the quotient of poset where boundary nodes are identified?
    And when you refer to vertices in a partial order "with exactly one edge" are you referring instead to the minimal and maximal elements? Also, I normally think of posets as reflexive relations, but this would make all your digraphs have loops at every vertex. So I guess you want an irreflexive version of partial […]
  • Comment by Joel David Hamkins on Is every directed graph the quotient of poset where boundary nodes are identified?
    Could you clarify what you intend by the quotient of a partial order by an equivalence relation, when it is not a congruence? I guess you mean that every instance of the order relation suffices for an edge in the quotient?
  • Comment by Joel David Hamkins on Algorithms to count restricted injections
    Have you mixed up 𝑛 and 𝑚 in the beginning? You have 𝑓⁡(𝑎), where 𝑎 is from {1,…,𝑚}, but the domain of 𝑓 is said to be {1,…,𝑛}. If $n
  • Comment by Joel David Hamkins on Terminology: commonly used name for an 𝜔 machine?
    Of course ultimately the computational power has nothing to do with fitting the computation into finite time, but rather just the idea of making sense of a computation with infinitely many steps. So you may be interested in the Büchi automata (en.wikipedia.org/wiki/B%C3%BCchi_automaton), and beyond this, the infinite time Turing machines (jstor.org/stable/2586556), which extend the operation […]
  • Comment by Joel David Hamkins on Is this theory of bottomless hierarchy, consistent?
    Ah, sorry, you had the comma before → not after, namely, ∃𝑦 ∈𝐴 :𝜙, →.
  • Comment by Joel David Hamkins on Is this theory of bottomless hierarchy, consistent?
    I confess that I have long been a little confused by your manner of using colons and commas in formal expressions, since it is different from what I am used to in first-order logic or in type theory. For example, how am I to read the meaning of "∃𝑦 ∈𝐴 :𝜙 →,"? And how are we […]
  • Comment by Joel David Hamkins on Is every external downshifting elementary embedding 𝑗 with 𝑗⁡(𝑥) =𝑗⁡[𝑥], an automorphism?
    Ah, yes, of course. Thanks!

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