the week of october 22

reviewing the big topics so far

We started the week by reviewing the topics that occupied us during the first half of the semester. On the technical side, we reviewed the basics about sets, functions, and relations and then familiarized ourselves with the syntax and semantics of a propositional calculus, a predicate calculus and a typed lambda-calculus. On the empirical side, we learned how to interpret simple verbal projections within a Davidsonian event semantics, looked at Schein's argument for severing external arguments from verbal roots, agonized over the tension between the so-called "paradoxes of material implication" and Gibbard's proof, and then spent a few weeks sorting out different approaches to exhaustive interpretations, including the phenomenon of so-called "scalar implicatures". I picked this variety of topics because I did not only want to give you the most important technical tools to do semantic analysis, I also wanted to show you right at the beginning how exciting semantic analysis can be. And finally, I wanted to give you the opportunity to practice how to gracefully grope in the dark, and get used to the idea that the very way a phenomenon is conceptualized may not necessarily be shared among different approaches trying to understand it: The perceived differences between weak and strengthened interpretations for "or" and numerals, for example, are pragmatically derived on some accounts, but correspond to subtle differences in logical forms on others. This was quite a lot to swallow for novices in this field. The pace will be slower during the second half of the semester, and the emphasis will now be on fitting pieces together and solidifying technical skills.

technical exercises around definite descriptions

We expanded the syntax and semantics of the formal language TL from chapter 13 of Partee et al. by adding two new logical constants, the iota operator and the existential quantifier ∃!. We will call the expanded language "ETL". The two new symbols were not assigned types, but were introduced syncategorematically. The iota operator ι combines with a variable and an expression of type t to produce an expression of type e. ∃! combines with a variable and an expression of type t to form an expression of type t. After practicing a few formalizations with the new symbols, we had to face the most important issue raised by our semantics of the iota operator: during the computation of the denotation of a sentence it can happen that a part of it is not assigned a denotation. What does that mean for the sentence as a whole? Are our intuitions about the sentences to be formalized sharp enough to tell us what to to do in those cases? The question has been debated extensively and passionately in the literature on presuppositions. We started to probe into our intuitions about quantified sentences containing definite descriptions like "every boy petted the cat that licked him" or "no boy petted the cat that licked him". What predictions should our analysis make for such sentences on scenarios where some boys were not licked by any cat or were licked by more than one cat? Noah Constant explored ways of sharpening intuitions about such scenarios and presented his thoughts on Friday. Here is his squib on definedness and quantifier domains, and here is this week's updated handout "Technical preparation for definite descriptions".