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What are the real numbers, really?
The real real numbers—what are they? Must we answer?
May 12
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Joel David Hamkins
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What are the real numbers, really?
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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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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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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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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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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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The surreal numbers
All the numbers great and small. The surreal numbers, generated in a recursive process of completion, unify the real numbers, the ordinals, and the…
Jan 6
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Joel David Hamkins
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The surreal numbers
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The sand reckoner
How many grains of sand would you need to fill the universe? Archimedes shows off his number prowess in the 3rd century BC. Let us hear his argument and…
Jun 15, 2023
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Joel David Hamkins
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The sand reckoner
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A Panorama of Logic
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Stipulative definitions
The logic of expanding a formal language by introducing defined terms and relations
May 5
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Joel David Hamkins
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Stipulative definitions
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Nondefinability and higher definability
Nondefinability, definable sets and relations, and implicit definability
Apr 28
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Joel David Hamkins
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Nondefinability and higher definability
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Pointwise definability versus Leibnizian discernibility
A model is pointwise definable when every individual has a property only it has. The model is Leibnizian if distinct individuals fulfill different…
Apr 22
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Joel David Hamkins
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Pointwise definability versus Leibnizian discernibility
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Proof and the Art
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Philosophy of Mathematics
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Infinitely More
The mathematics and philosophy of the infinite
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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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