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November 2023
Number theory
An excerpt from Proof and the Art of Mathematics — the fundamental theorem of arithmetic
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Joel David Hamkins
1
Functions
All kinds of functions—injective, surjective, bijective, one-to-one, onto, partial, total
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Joel David Hamkins
3
Closures of a relation
Let us continue our explorations in relational logic. We begin by showing the independence of the properties of reflexibity, symmetry, and transitivity…
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Joel David Hamkins
2
Equivalence relations
Fruitfully generalizing one of the most important and philosophically central relations that there is, the relation of identity.
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Joel David Hamkins
October 2023
The Liar (a logic song)
My new logic music video is out! A collaboration with the supremely talented Hannah Hoffman. The laughing Liar lights logic's law afire, laughing as the…
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Joel David Hamkins
Relational logic—an introduction
Moving beyond propositional logic to the logic of relations
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Joel David Hamkins
Interpreting arithmetic
What is the philosophical significance, if any, of the fact that we can often find interpretations of arithmetic in other mathematical realms?
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Joel David Hamkins
4
Skolem's paradox
Our best mathematical accounts of infinity exhibit a shocking lack of absoluteness—the very same set can be countable in one set-theoretic world…
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Joel David Hamkins
2
September 2023
Boolean-algebra logic
Consider the four-valued logic pictured here, which we denote by 𝟚2 because it will turn out to be an instance of the more general power-set logics 𝟚X…
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Joel David Hamkins
Plenitudinous Primes
A mathematical music video proving the infinitude of primes
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Joel David Hamkins
Logic as algebra, supertruth, superfalsity, paraconsistent logic
An abstract view of our various logics as algebraic systems of truth values equipped with logical operations. How do they embed in or project to one…
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Joel David Hamkins
© 2023 Joel David Hamkins
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