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Infinitary Hat Puzzles and the Aftermath
What color is your hat? The hat puzzle genre of logic puzzle grows from easy finite cases to absurd spectacular settings with infinitely many people in…
Jul 30
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Joel David Hamkins
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Zeno's paradox
Jan 7, 2023
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Joel David Hamkins
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Zeno's paradox
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The Book of Numbers
Jan 2, 2023
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Joel David Hamkins
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The Book of Numbers
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Potential versus actual infinity
Apr 14, 2023
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Joel David Hamkins
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Potential versus actual infinity
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Structuralism
Apr 4
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Joel David Hamkins
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Structuralism
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The Book of Infinity
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Infinitary Hat Puzzles and the Aftermath
What color is your hat? The hat puzzle genre of logic puzzle grows from easy finite cases to absurd spectacular settings with infinitely many people in…
Jul 30
•
Joel David Hamkins
6
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Infinitary Hat Puzzles and the Aftermath
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The Axiom of Choice
Can we choose an element from each set in a family of nonempty sets? Does every set have a well order? Is the axiom of choice arrogant overreach or does…
Jul 21
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Joel David Hamkins
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The Axiom of Choice
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Infinite Liars (from the archives)
Regrettably, this essay consists entirely of lies—every sentence in it, including this one, is false.
Apr 15
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Joel David Hamkins
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Infinite Liars (from the archives)
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A Panorama of Logic
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Quantifier elimination — Presburger arithmetic
The elementary theory of addition in the natural numbers admits a certain logical triviality—every assertion is equivalent to a simple combination of…
Jul 6
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Quantifier elimination — Presburger arithmetic
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Quantifier elimination — theory of successor
Every assertion about the structure ⟨ℕ,S,0⟩ of the natural-number successor is trivial, being equivalent to a quantifier-free assertion in this…
Jun 29
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Quantifier elimination — theory of successor
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Quantifier elimination — dense linear orders
In certain special theories, every assertion is equivalent to a trivial combination of atomic facts. Proving this for a given theory typically both…
Jun 15
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Joel David Hamkins
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Quantifier elimination — dense linear orders
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Proof and the Art
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Philosophy of Mathematics
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The mathematics and philosophy of the infinite
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Learning Labyrinths
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JDH Links
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JDH at MIT Press
My Books
Lectures on the Philosophy of Mathematics, MIT Press 2021
Proof and the Art of Mathematics, MIT Press 2020
Proof and the Art of Mathematics: Examples and Extensions, MIT Press, 2021
A Mathematician's Year in Japan, Kindle KDP, 2015
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