Which cardinality quantifiers are logical?

Talk held by Alexander Paseau (Wadham College, Oxford, UK) at the KGRC Friday seminar on 2018‑03‑16.


By a cardinality quantifier, I understand an expression of the form ‘There are at least $X$ ...’ for $X$ a cardinal. The finite cardinality quantifiers are thus all expressions of the form ‘There are at least $n$ ...’ where $n$ is finite (‘There's at least one...’, ‘There are at least two ...’ and so on). Since all these finite quantifiers are definable in first-order logic, they are universally taken to be logical. What about transfinite cardinality quantifiers, the first of which is ‘There are infinitely many’? Which of them is logical? I argue that they all are. The talk will explain the answer's significance and the new light it sheds on the perennial question ‘What is Logic?’.

Time and Place

Sandwiches at 12:00pm in the KGRC meeting room

Talk at a convenient time afterward in the KGRC lecture room

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Kurt Gödel Research Center for Mathematical Logic. Währinger Straße 25, 1090 Wien, Austria. Phone +43-1-4277-50501. Last updated: 2018-03-01, 14:21.