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Definite descriptions
Definite descriptions, such as "the badly juggling clown," succeed when the intended individual is indeed characterized by the property. But how does…
May 18
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Joel David Hamkins
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Definite descriptions
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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
10
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What are the real numbers, really?
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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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April 2024
Nondefinability and higher definability
Nondefinability, definable sets and relations, and implicit definability
Apr 28
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Joel David Hamkins
3
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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
4
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Pointwise definability versus Leibnizian discernibility
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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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Famous quotations in first-order predicate logic
Can you translate these famous sayings?
Apr 10
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Joel David Hamkins
9
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Famous quotations in first-order predicate logic
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Structuralism
For mathematical insight, according to the structuralist imperative, investigate mathematical structure and consider mathematical concepts only as…
Apr 4
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Joel David Hamkins
13
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Structuralism
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March 2024
Isomorphisms and elementary equivalence
Isomorphic structures exhibit identical truths—they have the same theory. But conversely, not all structures with the same theory are isomorphic.
Mar 30
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Joel David Hamkins
6
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Isomorphisms and elementary equivalence
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Substructures and chains of models
Truth propogates through an elementary chain of models to the limit.
Mar 25
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Joel David Hamkins
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Substructures and chains of models
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Theory theory
Let us explore the theory of theories, the theory of models, the theory of models of theories, and the theory of theories of models.
Mar 19
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Joel David Hamkins
8
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Theory theory
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More applications of induction
An excerpt from Proof and the Art of Mathematics
Mar 13
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Joel David Hamkins
2
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More applications of induction
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