week of september 10

what happened on monday

Lecture 3: More on verb meanings. We started out by thinking about traditional and Fregean denotations for transitive verbs like "supersede", and then tried to come up with a Fregean denotation for the ditransitive verb "introduce". We saw that Fregean denotations do not only determine a verb's arguments, they also determine a hierarchical structure for those arguments. The denotation of the transitive verb "supersede", for example, is the function f that maps any individual a to the function g (=f(a)) that maps any individual b to TRUE just in case b supersedes a. This means that the unique argument of f is always interpreted as the thing that is superseded, rather than the thing that supersedes. Put syntactically, we are saying that in a simple transitive sentence like "Rule 1 supersedes Rule 2", the direct object is an argument of the verb, but the subject is an argument of the VP. There is an asymmetry between the two arguments of a transitive verb. With Fregean denotations, this asymmetry is hard-wired into the denotations of verbs. On this conception of verb denotations, there is no separate representation of 'argument structure', there is no such thing as a 'theta grid' or what have you.

After praising the virtues of the verb denotations we looked at, I tried to submit them to a harsh critique. I tried to construct cases that seemed to create compositionality problems. The first case had to do with tense. We looked at a simple sentence with past tense: "Emma procrastinated". We recognized three meaningful pieces in this sentence: "Emma", the root of "procrastinate" and the past tense suffix "-ed". The challenge was to come up with a compositional semantics for sentences of this kind. An interesting proposal came from the audience. What if our domain of individuals did not just contain temporally complete individuals, but also temporal stages of individuals, including past stages of me, you, or Emma, for example? The root of "procrastinate" might then denote the (characteristic function of the) set of all procrastinating stages of individuals. The contribution of "-ed" could be to map (the characteristic function of) a set A of stages of individuals to (the characteristic function of) a particular subset of A: the set of all past stages of individuals in A. The whole sentence could then be said to be true just in case the set of all past procrastinating stages of individuals contains a stage of Emma. I had to acknowledge that this proposal had the potential to meet my compositionality challenge, even though the details would have to be worked out. My first attempt to discredit the verb denotations I had introduced earlier was not entirely successful, then. I constructed a second compositionality challenge with the help of adverbial modifiers. We looked at sentences like "Bea worked slowly" and "Norah wrote on the blackboard". The PP "on the blackboard" and the adverb "slowly" seem to make compositional contributions to the truth-conditions of the sentences they occur in. Can you see a way to derive those truth-conditions compositionally from the pieces "Bea", "Norah", "slowly", "on the blackboard", "worked", and "wrote" (let's not worry about the past tense this time)?

wednesday and beyond

Lecture 4: Warm-up exercises in event semantics. Cases of adverbial modification like "Norah wrote on the blackboard" finally convinced us that verbs should describe events in some way or other. "Norah writes on the blackboard" can describe situations where Norah's writing takes place on the blackboard. "Norah talked fast" describes situations where Norah's talking was fast, and so on. Events are entities who are not as clearly individuated as individuals like chairs and desks, however, and this is why it took some time for researchers to warm-up to them. To the present day, it is sometimes considered a virtue to propose semantic analyses that manage to avoid events, even at a considerable theoretical cost. On the other hand, evidence has accumulated that events are an important category of human cognition, and event-based semantic analyses have been highly successful in many areas, including argument association, aktionsarten, aspect, nominalization, and pluralization. I recommended Casati's book on shadows since it makes a very convincinging case that there are many highly respected objects in our ontology that have properties that upset our commonsensical beliefs.

To get used to working with an event-based semantics, we tried to come up with a compositional semantics for the simple sentence "it rained". What are the meaningful parts of this sentence? And what are their denotations? We were fairly confident about the denotation of the root of "rain". Now that we have events in our ontology, the root of "rain" should be a predicate of events, and its denotation should then be (the characteristic function of the) set of all raining events. Since any part of a raining event is itself a raining event, the set of all raining events is what is often called "homogeneous", that is, it is closed under the part relation. A set A is closed under the part relation iff the following condition holds: whenever a is in A and b is part of a, then b is in A as well. Homogeneity is a property that a number of adverbial modifiers (e.g. durational adverbials) are sensitive to. We have, for example: "It rained for two hours", "Emma jogged for two hours", "Ewan worked for two hours", but not "Caesar died for two hours", "we reached the shore for two hours", "we finished the paper for two hours", etc. Once we have a denotation for the root of "rain", it should not be too hard to figure out what kind of contribution the past tense morpheme "-ed" might make. It might denote an operation that maps (the characteristic function of) the set of raining events to (the characteristic function of) a certain subset, the set of past raining events. Once we get serious about tenses, we will have to say more about the exact denotation of the English past tense, but for the time being, we are mainly interested in the general principles of meaning composition, and the idea that tenses operate over (characteristic functions of) sets of events seems a promising one.

We now have a first working hypothesis about the denotation of "rained": it denotes(the characteristic function of) a set of events. It is a predicate, then, and, crucially, not the kind of thing that can be true or false. The whole sentence "it rained", on the other hand, is the kind of thing that can be true or false, and we are therefore still missing a piece. Might "it" be meaningful? I don't know. If "it" means something, it might be a pronoun that denotes a contextually salient event. In that case, the whole sentence "it rained" could be said to be true just in case the event denoted by "it" is a raining event. The exact details remain to be worked out, but even in its raw form, the proposal makes predictions that you might be able to evaluate. Can you think of arguments for or against the proposal? Just in case, here is an alternative proposal. Maybe "it" is a true expletive and has no denotation at all. In that case, there might be another piece in the sentence that takes us from a set of past raining events to a truth value. Maybe "-ed" has an additional job and also introduces existential quantification over events, as one of you suggested. The suffix "-ed" would then denote an operator that maps (the characteristic function of) a set of events to TRUE just in case the set contains a past event. Applied to the (characteristic function of) the set of all raining events, the operator would yield TRUE just in case there is a past raining event. What do you think of that proposal? Maybe it would be more plausible to assign the job of introducing existential quantification over events to another part of the sentence, maybe an unpronounced piece of inflection? Or could there be default existential quantification over events that is introduced in case there is no overt quantification over events as in "it rained fifty times"?

friday

I handed out a few pages of prose (lecture 5) for you to read at home. They contain summaries of some of the major points on event semantics that came up so far, e.g. isolating the denotations of verb roots, and Davidson's classical argument for event arguments. There are also a few examples of Davidsonian verb denotations in a Fregean semantics. The class time itself was mostly taken up by looking at two puzzles that I reproduced below. We spent quite some time on the first puzzle: counting problems with homogeneous predicates. I just started getting into the second puzzle at the end of the class. I was, in fact, struggling with the question of how to present the puzzle in a clear way. I will return to some of the issues involved next week. Needless to say, the puzzles are for you to think about and maybe solve - one day.

The puzzle of homogeneity: We developed a mini-semantics for verbs where - at least on one of the proposals we considered - the inflected verb "rained" denotes the set of all past raining events. We noted that if every part of a past raining event is also a past raining event, the set of all past raining events is homogeneous: it is closed under the part relation. This denotation causes trouble if we consider sentences with event quantifiers like "it rained at least a hundred times". We cannot say, for example, that that sentence is true just in case the set of all past raining events contains at least 100 members. Suppose it rained just once in the actual world, yesterday from 2:00 PM to 4:00 PM. That's an extended raining event with lots of parts that are also raining events - certainly more than a hundred. Should we modify the denotation of "rained", then, and only admit raining events that we can count, maximal spatio-temporally connected raining events, for example? That would make the denotation of "rained" non-homogeneous, and that might be an unwelcome consequence in view of durational adverbials like "for two hours", which - as we saw above - need to operate over expressions that denote homogeneous sets. Can you find a way out of this dilemma?

Where does existential quantification over events come in? We saw earlier that in order to account for the intuition that a sentence like "it rained" can be true or false, we can't let that sentence simply denote a set of events. There must be something in the sentence that takes us to a truth-value. Existential quantification over events was one possibility we considered, but we weren't sure how exactly it should be introduced. Default existential quantification over events was maybe the most promising option among those we came up with since we also have sentences with overt existential quantification over events like "it rained once", "it rained a hundred times", etc. But we still would have to find a place for default event quantification to come in when it comes in. Negative sentences might give us a clue. Take the sentence "it did not rain", for example. This sentence says that there is no past event of raining. It does not say that there is an event that is not a past raining event, which would be a fairly trivial thing to say. This means that negation should be above the place that introduces default existential quantification over events. But what about sentences with overt event quantifiers like "He didn't show up for work more than five times". Isn't that sentence ambiguous? Isn't there a reading that says that there were five instances of his not showing up for work? Five no-shows? What is a no-show event? It can't simply be an event that is not an event of showing up. Just about any event is such an event. And there is another puzzle: why is there an ambiguity with overt event quantification, but not with default event quantification, which necessarily takes scope under negation?