As announced in class, homework #8 is just running through a couple of sentences using the system we went over in class (that is, with the modifications to the syntax, to the F function, with full specification of the evaluations at M,w,t,g. You can either use the definition of past tense on the bottom of page 6, below the tree in (16), or use the one we talk about next time with modals (at the end of the handout).
Here are the problems:
Part One. Work out the truth conditions of the following three sentences, step by step. First draw the structure that would be assigned to it by the syntactic rules, and then evaluate each node in the tree (from the bottom up) so that you can state the truth conditions of the sentence as a whole. NOTE: How you do sentence #2 depends partly on doing Part Two of this homework. Recommended order: Do sentence #1 and maybe sentence #3, then Part Two, then do sentence #2.
1) John likes Mary
2) John did not like Mary
3) John was hungry
For all of these, assume that JOHN and MARY are individuals in the universe of individuals, and that Fw,t(hungry) is a set of individuals who are hungry in world w at time t, and that Fw,t(like) is a set of ordered pairs of the form <liker, likee> expressing the liking relation between pairs of individuals.
Edit: I’ve reworded the question to be about the end result, not about order, see the subsequent blog entry for the explanation. Chances are it won’t make a difference to how you think about it, but with the edit, this problem is more accurate.
Part Two. Sentence #2 above has both negation and tense in it. Each of these require a “raising rule” for interpretation (Neg Raising and Tense Raising, respectively). Nothing we have right now says which one should wind up higher: do we raise Neg to a position above the position we raise Tense to, or do we raise Tense to a position above the position we raise Neg to? Nothing we have right now says which one should happen first: do we raise Neg and then raise Tense, or do we raise Tense and then raise Neg? It turns out that there is a restriction—only one order is possible. What is it?
(Hint: To figure out the answer to this, we need to consider what the meaning would be predicted to be for sentence #2 if tense raised higher than negation first and then negation raised second , as compared to what the meaning would be predicted to be if negation raised higher than tense first and then tense raised second. Informally, it will ultimately lead to the difference between the “there is a time in the past such that it is not the case that…” and “it is not the case that there is a time in the past such that…” These meanings are different. Which one can sentence #2 mean?
Although this does require judging an English sentence, I do not believe that the judgement should be difficult even if you are not a native speaker of English. If you work out what each of the two predicted meanings require the world to look like in order to be true, you’ll find that it’s pretty obviously one and not the other. However, it’s also (native speaker or not native speaker) a bit more difficult with a state like like. Think about it with a punctual verb like find, and you’ll probably see the answer quickly. We want to make sure that John did not find Mary is not always true (that is, it’s not enough that there just be some moment in the past that wasn’t a finding of Mary, even if there’s a different moment in the past that was a finding of Mary.).