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Order theory—an introduction
We begin to develop the elementary theory of orders, looking into order relations, strict orders, preorders, maximal versus greatest elements…
Dec 2
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Joel David Hamkins
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Order theory—an introduction
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November 2023
Number theory
An excerpt from Proof and the Art of Mathematics — the fundamental theorem of arithmetic
Nov 23
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Joel David Hamkins
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Number theory
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Functions
All kinds of functions—injective, surjective, bijective, one-to-one, onto, partial, total
Nov 18
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Joel David Hamkins
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Functions
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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…
Nov 10
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Joel David Hamkins
5
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Closures of a relation
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Equivalence relations
Fruitfully generalizing one of the most important and philosophically central relations that there is, the relation of identity.
Nov 3
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Joel David Hamkins
6
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Equivalence relations
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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…
Oct 27
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Joel David Hamkins
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The Liar (a logic song)
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Relational logic—an introduction
Moving beyond propositional logic to the logic of relations
Oct 22
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Joel David Hamkins
7
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Relational logic—an introduction
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Interpreting arithmetic
What is the philosophical significance, if any, of the fact that we can often find interpretations of arithmetic in other mathematical realms?
Oct 14
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Joel David Hamkins
10
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Interpreting arithmetic
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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…
Oct 7
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Joel David Hamkins
14
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Skolem's paradox
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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…
Sep 30
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Joel David Hamkins
6
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Boolean-algebra logic
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Plenitudinous Primes
A mathematical music video proving the infinitude of primes
Sep 23
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Joel David Hamkins
6
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Plenitudinous Primes
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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…
Sep 15
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Joel David Hamkins
4
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Logic as algebra, supertruth, superfalsity, paraconsistent logic
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