Bart Geurts

In the semantics of natural language, quantification may have received more attention than any other subject, and one of the main topics in psychological studies on deductive reasoning is syllogistic inference, which is just a restricted form of reasoning with quantifiers. But thus far the semantical and psychological enterprises have remained disconnected. This paper aims to show how our understanding of syllogistic reasoning may benefit from semantical research on quantification. I present a very simple logic that pivots on the monotonicity properties of quantified statements - properties that are known to be crucial not only to quantification but to a much wider range of semantical phenomena. This logic is shown to account for the experimental evidence available in the literature as well as for the data from a new experiment with cardinal quantifiers ("at least n" and "at most n"), which cannot be explained by any other theory of syllogistic reasoning

In this paper I present experimental data showing that the interpretation of donkey sentences is influenced by certain aspects of world knowledge that seem to elude introspective observation, which I try to explain by reference to a scale ranging from prototypical individuals (like children) to quite marginal ones (such as railway lines). This ontological cline interacts with the semantics of donkey sentences: as suggested already by the anecdotal data on which much of the literature is based, the effect of world knowledge is by and large restricted to donkey sentences with non-intersective determiners. I outline a psychological model which incorporates both ontological and logical factors, and suggest that there may be something wrong with the standard assumption that a statement's receiving a truth value requires that it have a definite reading.

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