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. Since all these finite quantifiers are definable in first-order logic, they are generally 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 light it sheds on the perennial question 'What is Logic?'. All those attending are invited to join the speaker afterwards for a drink at the Royal Oak across the road from the Humanities Building, and then, if the speaker's schedule allows, to dinner at a nearby restaurant (with everyone, except the speaker, paying for themselves).
Philosophy of Mathematics Seminar Convenors: Dr Daniel Isaacson and Prof Volker Halbach