the week of march 31

verb meanings

This week's topic were verb meanings. We started out by separating verb roots and verbal inflections, and then worked with the traditional assumption that the denotations of intransitive verb roots are sets of individuals, and the denotations of transitive verb roots are sets of pairs of individuals. We stated the corresponding composition rules for simple sentences consisting of an intransitive verb root and a name, or a transitive verb root and two names. Our next step consisted in making a slight change in the verb root denotations we posited: we implemented the Fregean program of reducing all meaning composition to functional application. Our new Fregean denotations for intransitive verb roots were no longer sets of individuals, but the characteristic functions of such sets. If A is a subset of our universe of individuals U, then the characteristic function of A is that function from U to {True, False} that maps any member of U to True if it is a member of A, and to False otherwise. Things became more complicated when we looked at Fregean denotations for transitive verb roots. Those roots now had to denote functions that map individuals to functions from individuals to truth values. That is, we are now talking about verb denotations that are functions whose range are sets of functions. In the long run, the benefit of Fregean denotations is that we do no longer have to stipulate special rules for meaning composition: all meaning composition reduces to functional application. Here are the slides we looked at while working on the blackboard at the same time. The week ended with questions and answers about Fregean verb denotations. After clarifying some formal aspects of our current conception of verb denotations, we submitted those denotations to a first empirical evaluation. On the positive side, we observed that those denotations (a) determined a verb's arguments, (b) determined a hierarchical structure for a verb's arguments, and (c) determined the verb's contribution to the truth-conditions of whatever sentence it may be part of. On the negative side, we saw that certain adverbial modifiers place conditions on the events described by verbs. Our current conception of verb meanings has no place for events, however. Our next move will be to work towards verb denotations that account for the fact that (a) verbs describe events, (b) a verb's arguments pick out distinguished participants in those events, and (c) adverbial modifiers often place constraints on the events described by the VPs they modify. This revised view of verb denotations will allow us to connect up with Parsons' book. Here is the handout that we used as a guide for our discussions. Since you are now advanced enough to work out good answers to deep semantic questions collectively in class, the handout mostly gives you the questions and some of the data, but, in most cases, not the answers we arrived at together, nor the additional data that were brought up. I left enough space in the handout for you to create a complete protocol of what went on in class.

lab session

Florian and I discussed some highlights of the take-home exams. Florian's comments on your experimental designs are here. We then did a short group exercise on Fregean versus traditional denotations for transitive verbs. The materials for the group exercise are here. At the end of the class, we took a vote that decided that we will work with Fregean denotations for the rest of the semester.