week of september 17

monday

We started the week with a short reflection on the puzzle of existential event quantification we had run into on Friday. How come default existential quantification of the Davidsonian event argument must take place within the scope of negation, as shown by the unambiguity of "John didn't show up for work", whereas overt event quantifiers can take scope over or under negation, as shown by "John didn't show up for work twice"? The puzzle was left in your lap for further investigation, and we moved on to a very different topic, the lambda notation.

We will eventually use a common standard notation for lambda expressions, but we can't do so before we have certain formal tools in place. In the meantime we'll use the informal lambda notation in the Heim & Kratzer book as a warm-up. It is good to reflect on what it takes to create a notation for functions that can be denotations of expressions of natural languages. I alerted you to a difficulty we faced with the informal lambda notation in our book. The difficulty comes up on page 35 and has to do with finding a suitable value description for the representation of functions of type <et>, for example. Take the denotation of the root of the verb "procrastinate". It is a function from the set of humans in our domain D to the set of truth-values {0,1}. Any human being is mapped to 1 if he/she procrastinates and to 0 otherwise. How are we going to represent this function as an expression of the form "lambda x: x is a member of D & x is human. ... x ..."? What we are looking for is a suitable value description that depends on the individual variable "x" and refers to a truth-value depending on the value of "x". In the book, we propose to use the value description "x procrastinates" in this case, but without explicit convention, it is not clear in which sense this expression refers to a truth-value depending on the value of "x". Heim and Kratzer therefore introduce the convention that a lambda expression like "lambda x: x is a member of D and x is human. x procrastinates" denotes the function that maps every individual that satisfies the domain condition to 1 if it satisfies the value description, and to 0 if it doesn't. Non-sentential value descriptions like that in "lambda x: x is a member of D and x is human. the birthday of x " are interpreted as they are in English: For any assignment of a value to "x", "the birthday of x" refers to the birthday of the value of "x". Ultimately, we want a completely general syntactic definition of what a possible lambda expression is and an equally general semantic definition telling us for each well-formed lambda expression what function it denotes. Chapter 13, section 2 of the Partee et al. book introduces you to the syntax and semantics of a typed lambda calculus that is widely used in natural language semantics.

Looking at the extensional semantic system that we are currently working with, we reminded ourselves that there, too, we made the admittedly unintuitive move to let sentences denote truth-values. As the discussion in 2.1.2 emphasizes, the system is nevertheless capable of deriving truth-conditions for sentences in the end. In the long run, the idea to let sentences denote truth-values will prove wrong, however, but we will have to wait until chapter 12 before we see that: a compositionality argument will force us to look for more finely differentiated sentence denotations.

During the last 15 minutes of the class you did group work. You practiced the informal lambda notation and tried to compute the denotation of a direct perception report like "Mary saw Ben cross the street." Please submit one collective group work report per group.

Wednesday

We talked about "direct" or "epistemically neutral perception reports like "Meryl saw Beryl feed the raccoon", which contrast with so-called "indirect" or "epistemically non-neutral" perception reports like "Meryl saw that Beryl fed the raccoon". If Meryl saw Beryl feed the raccoon, she must have seen the actual feeding event. If she saw that Beryl fed the raccoon it may have been sufficient for her to see the evidence of what Beryl did. Direct perception reports are famous for their "transparency" properties: If what Beryl fed the raccoon was poisoned food and Meryl saw that feeding, then it is true that Meryl saw Beryl poison the raccoon even though Meryl might not have realized that she witnessed a poisoning. "Meryl saw Beryl poison the raccoon, but she had no idea that the raccoon was being poisoned" is not a contradiction. In contrast, "Meryl saw that Beryl poisoned the raccoon, but she had no idea that the raccoon was being poisoned" is a contradiction. The two sentences differ in the kind of complement they embed, and in the best of all possible worlds we would want to derive the meaning difference between the two types of sentences from the syntactic differences between their complements. We are not quite there yet, however. With the tools we have, we can put together a decent analysis for direct perception reports, but we are not yet ready for indirect perception reports. Our extensional semantics has reached its limits. Here are two interesting articles on direct perception reports in the Journal of Philosophy: one by Jon Barwise (1981) and the other one by Jim Higginbotham (1983). Access is free from Campus or via the library.

Both groups working together on Monday presented a flawless analysis of direct perception reports. You saw that the bare infinitive embedded under the perception verb should denote (the characteristic function of) a set of events, and the definition of the denotation of the root of "see" should introduce existential quantification over events. For our example above we would end up with something like the following: "Meryl saw Beryl feed the raccoon" is true just in case there are events e and e' such that e is a past event of Meryl seeing e' and e' is an event of Beryl feeding the raccoon". If there is just one event of Meryl feeding the raccoon in our universe of discourse, and that event is in fact a poisoning event, then our analysis correctly predicts that if "Meryl saw feed the raccoon" is true, then "Meryl saw Beryl poison the raccoon" is, too. Our event-based analysis captures the transparency properties of this construction correctly, but as long as we can't account for indirect perception reports, our success with direct perception reports is nothing to brag about. Some of you wondered whether there should be tense in the embedded infinitive, but decided against this. This decision was right. There is nothing in the embedded clause that constrains the time of the feeding event with respect to the time where it was perceived. If Meryl is a witch, she may see events that occur in the future. Watching a video, a judge may see Beryl poison the raccoon weeks later. Another important observation you contributed was that the only analysis of direct perception reports that is currently available to us forces us to assume an ambiguity for the verb "see" that does not seem to be justified. The "see" we see in "Beryl saw Meryl" seems to be a regular transitive verb that semantically selects ("s-selects") an individual as its internal argument. On the other hand, for "Meryl saw Beryl poison the raccoon" our current assumptions force us to assume that the verb "see" s-selects a property of events as its internal argument. Wouldn't we want a unified analysis where "see" uniformly s-selects a 'thing' (that is, an individual proper or event)? Read Higginbotham's paper for a possible answer.

Friday

We discussed another puzzle about bare infinitives. If bare infinitives denote properties of events, how are we going to interpret the conjunction in "Adam saw Beth arrive and Cecilia leave"? Simple predicate conjunction of the kind you will encounter in Heim & Kratzer's Chapter 4 does not give us the correct result. "Beth arrive and Cecilia leave" would denote a property of events that is true of any event just in case it is both an arrival by Beth and a departure by Cecilia. But there are no such events. What should we do? Some suggested that there may be ellipsis. "Adam saw Beth arrive and Cecilia leave" may be an elliptical version of "Adam saw Beth arrive and Adam saw Cecilia leave". How does this proposal fare when the subject is a quantifier phrase? Look at: "Somebody saw Beth arrive and Cecilia leave". Can this sentence be paraphrased as "somebody saw Beth arrive and somebody saw Cecilia leave"? Similar cases: "Exactly five witnesses saw Beth arrive and Cecilia leave", or "don't drink and drive". "Don't drink and drive" does not tell us that we should not drink and should not drive. What does it tell us, though? Another proposal that was made in response to the predicate conjunction data we looked at was to recognize a different type of conjunction for event predicates. Maybe we could have a form of ("non-Boolean") conjunction that has the effect that "Beth arrive and Cecilia leave" denotes a property that is true of an event e just in case e is the sum of events e1 and e2 such that e1 is an arrival by Beth and e2 is an arrival by Cecilia. What is the sum of two events? What kind of operation is that sum operation? Check out the entry on mereology (by Achille Varzi) in the Stanford Encyclopedia of Philosophy. We now have two possible solutions for our puzzle on the table: a syntactic solution that posits ellipsis and a semantic solution that posits non-Boolean conjunction. Can you see yourself defend one of the two? How? We'll come back to the topic next week.

While speculating about a possible ellipsis solution for our conjunction dilemma, we stumbled over an interesting property of English conjunctions that does not seem to be shared by comparable constructions in German or Brazilian Portuguese. In English, I can say "Yesterday I visited my girl friend and brother" to convey that I visited my girl friend and my brother. Even controlling for gender, this is not possible in German: "Ich habe meinen Vater und Schwiegersohn besucht" ("I visited my father and son in law") does imply, I think, that I visited someone who was both my father and my son in law. This phenomenon is discussed by Caroline Heycock and Roberto Zamparalli in "Friends and Colleagues: Plurality, Coordination, and the Structure of DP" in Natural Language Semantics. Free Access from Campus or via the UMass library.

At the end of the class I mentioned that in late Egyptian and Coptic, there is a special verb form, the "conjunctive", whose function seems to be to conjoin predicates of events via non-Boolean conjunction. You can read more about this construction in Leo Depuydt's 1993 book Conjunction, Contiguity, Contingency: On Relationships between Events in the Egyptian and Coptic Verbal Systems. Oxford University Press. Non-Boolean conjunction of event predicates might also be involved in a certain kind of serial verb construction ("consequential serial verb constructions", CSVCs) that Mark Baker and Osamuyimen T. Stewart have discussed in a series of unpublished papers. As described in Baker & Stewart (2002), "Semantically, CSVCs describe composite events, which are made up of two distinct subevents that the agent performs in sequence as part of a single overall plan." Depuydt characterizes the function of the conjunctive in a similar way: "In what follows, it is argued that one of the functions of the Late Egyptian, Demotic, and Coptic conjunctive--also its original function--is to present two or more events jointly as single notions".