It is well known that most is not first-order definable, and that the proof is in Barwise and Cooper’s 1981 paper. Actually, Barwise and Cooper present two theorems that bear on the issue. Their theorem C12 says that, for any pair of one-place predicates A and B, there is no sentence of classical predicate logic that is true iff ‘Most A are B’ is. (I assume that ‘Most A are B’ means that more than half of the A’s are B, but the only thing that matters is that most is proportional.) Barwise and Coop…
Read moreIt is well known that most is not first-order definable, and that the proof is in Barwise and Cooper’s 1981 paper. Actually, Barwise and Cooper present two theorems that bear on the issue. Their theorem C12 says that, for any pair of one-place predicates A and B, there is no sentence of classical predicate logic that is true iff ‘Most A are B’ is. (I assume that ‘Most A are B’ means that more than half of the A’s are B, but the only thing that matters is that most is proportional.) Barwise and Cooper’s C13 states that the foregoing result remains valid when classical logic is enriched with a unary quantifier Q so defined that Qx(Ax) is true iff more than half of the entities in the domain of quantification are A’s.
