[Revised entry by Timothy Bays on February 5, 2025.
Changes to: Main text, notes.html]
Skolem’s Paradox involves a seeming conflict between two theorems from classical logic. The Lowenheim-Skolem theorem says that if a first-order theory has infinite models, then it has models whose domains are only countable. Cantor’s theorem says that some sets are uncountable. Skolem’s Paradox arises when we notice that the basic principles of Cantorian set theory – i.e., the very principles used to prove Cantor’s theorem on the existence of uncountable…
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