Bart Geurts

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 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.

Gricean pragmatics has often been criticised for being implausible from a psychological point of view. This line of criticism is never backed up by empirical evidence, but more importantly, it ignores the fact that Grice never meant to advance a processing theory, in the first place. Taking our lead from Marr, we distinguish between two levels of explanation: at the W-level, we are concerned with what agents do and why; at the H-level, we ask how agents do whatever it is they do. Whereas pragmatics is pitched at the W-level, processing theories are at the H-level. This is not to say that pragmatics has no implications for psychology at all, but it is to say that its implications are less direct than is often supposed

The domain of a quantifier is determined by a variety of factors, which broadly speaking fall into two types. On the one hand, the context of utterance plays a role: if the focus of attention is on a particular collection of kangaroos, for example, then “Q kangaroos” is likely to range over the individuals in that set. On the other hand, the utterance itself will help to establish the quantificational domain, inter alia through presuppositions triggered within the sentence. In this paper, we concentrate our attention on constructions like the following, in which “the square to which... ” is the critical presupposition trigger: Q circles... Q of these circles... Q of these five circles...... have the same colour as the square to which they are connected. Many theories predict that all instances of these schemata will give rise to the presupposition that every circle is connected to a square. We present an analysis which predicts that these sentences should generally be accepted in a context in which not all the circles are connected to a square, with one exception only: if a quantified sentence is of type and Q is non-intersective, then the sentence should be more likely to be rejected. Furthermore, we predict that manipulating the context so as to make the connected circles more or less salient should have an effect on statements with non-intersective quantifiers only. These predictions were tested in a series of experiments