Practice final and key posted

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I have now posted the practice final and the key to the practice final.

The practice final is just what I handed out in class, but with the “Error! Reference not found.” typo fixed.

This is not a shining example of a great test, the time just ran out as I was preparing it, and I wanted to give you something. It’s actually a bit short, and the questions are not always unambiguous. Plus, I actually asked the same question twice. The real final will be like the practice final, except it will be debugged first: it will be clearer and maybe just a little bit longer.

Practice final: 4C

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Something went amiss with Question 4, part C. This question asks you to transform the structure given in the problem by using the Quantifier Raising rule. It doesn’t say you need to do Tense raising (and the Tense raising rule is not provided), so the structure you wind up still won’t quite be interpretable (contrary to the suggestion in the problem statement).

HW8: John didn’t like Mary, but he does now.

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The reason I suggested that for Part 2 of Homework 8 you consider a sentence like John did not find Mary instead of the actual sentence (John did not like Mary) is that the intuitions are quite a bit clearer, and make the point a bit more forcefully.

This point was made even more clearly in a question I just got over email: It’s perfectly sensible to say something like John didn’t like Mary, but he does now. If you think about this a bit, it would seem to run somewhat counter to the conclusion you get for John didn’t find Mary, and might suggest that both of the options (tense over negation, and negation over tense) are possible. That is, for find we want the sentence to mean something along the lines of John never found Mary (all the way up to now). But it seems like we might not want to force John did not like Mary to necessarily mean John never liked Mary (all the way up to now).

I still claim that only one of the options is possible, but we do need to say something about why you can say John didn’t like Mary, but he does now. This was part of what I planned to talk about tomorrow, but the basic idea is that past tense isn’t really talking about all time prior to now, but seems to be rather about a certain interval of time determined by the context. This was the force of the example I didn’t turn off the stove (spoken by somebody who is driving away for the weekend). This doesn’t mean “I have never turned off the stove in my life”, but rather it means that during the relevant past time interval (the time during the preparations for leaving), there were no turnings off of the stove.

So, for John didn’t like Mary, what I think that means is that during the whole (past part) of some relevant time interval, there was no time in that interval when John liked Mary. If the entire interval is completely before now, however, that’s not incompatible with the possibility that John likes Mary now.

The bottom line is that what I’m asking you do to in Part 2 of Homework 8 is, I believe, still true and valid, but the fact that I asked you do it with a sentence involving the state-verb like (rather than the punctual find) made it quite a bit easier to imagine the contextually relevant interval as being one that does not overlap with the utterance time, and therefore makes the judgment quite a bit harder. In principle, the same thing is true of John did not find Mary as well. If John and Mary are playing hide and seek, you can talk about the outcome of the second of three games played in the past by saying John did not find Mary, even if John found Mary in the first and third games. What that means is that during the entire interval of time occupied by the second game, there were no findings of Mary by John.

Anyway, this is kind of an extra complication, which we’ll discuss in more detail in class tomorrow when we finally address modals.

What’s with all the double brackets?

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In this most recent foray into formal semantics, I started doing something on the handout that I had not been doing before, which is using these “fat brackets.” “What are they?”, you may be asking yourself.

Basically, in places where I “ought to” have written fat brackets, in the earlier handouts in the semester I’d simply written regular brackets because it was just easier to typeset.

The fat brackets represent the semantic evaluation function—when you put fat brackets around something, you are referring to the “semantic value” of that thing within the brackets.

Of course, since I started using fat brackets on the handout, and there’s no easy way to type them on the blog, I’ve started using “[[” to represent the fat left bracket and “]]” to represent the fat right bracket.

So, for example, the semantic value of the word hungry would be written something like this:

[[ hungry ]]M,g,w,t = λx [ x ∈ Fw,t(hungry) ]

(This makes use of the lexical interpretation rule that says that if F provides a set of individuals, then the form of the semantic value is λx [ x ∈ the set of individuals F provides ]. See the handout.)

In case you were worried about all of these seemingly superfluous brackets, this is the explanation of why they’re there.

HW8: Present tense?

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Yes, once again I feel I really should have made the key right away. Lots of good questions coming in over email. Here’s the response to another one.

There is no explicit definition of the interpretation of Present tense on the handout. This is mainly because Past tense seemed more exciting, so I always used that as an example.

This is what it looked like:

[[ PAST S ]]M,g,w,t = ∃t′[t′ < t ∧ [[S]]M,g,w,t′ ]

(Where “t′ < t” is suppose to mean that t′ is before t.) That is: “There’s a time t′ before now, such that S is true at t′.”

There is a sort of obvious thing you can do to create the present tense version of this, which is just to change “<” to “=”. However, if you do this, you wind up saying something kind of overly complicated:

[[ PRES S ]]M,g,w,t = ∃t′[t′ = t ∧ [[S]]M,g,w,t′ ]

That is: “There’s a time t′, which is now, such that S is true at t′.”

But that’s really pretty much just the same thing as saying “S is true now.” So, really, the simplest version of this (and still just as accurate, and still requiring that Tense raises) would be simply to assume that the rule for present tense is:

[[ PRES S ]]M,g,w,t = [[S]]M,g,w,t

That is, PRES doesn’t really contribute anything to the meaning. You can use either of the interpretation rules for [PRES S] I gave above, but the second one is of course the simpler of the two.

HW8: A small logic error in my statement of Part 2

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I was just rethinking the homework Part 2, and I realized that there is a small error in the way I described the problem. Here’s the real issue:

In the structure you wind up with for Part 2 (that is, for the sentence #2), one of the following conditions seems to hold: either 1) tense is higher than negation or 2) negation is higher than tense.

I stated that as an ordering restriction (which one you have to raise first), but actually now that I look at the rules, it isn’t really about order. It really is about the outcome. It turns out that order doesn’t really matter, because it is possible while following the rules to raise one to the top of the structure, and then raise the second to a position that is actually below the first one you raised. I had been implicitly assuming that raising tense or negation or quantifiers must necessarily “extend” the structure (by adding the raised element to the very top of the tree), but the rules do not actually encode this requirement.

If you were making the same implicit assumption as I was, then fine, everything is good. But if you noticed that it was possible to “tuck in” a raised quantifier/negation/tense like this, then I just wanted to say explicitly here that the real question isn’t about order, but rather which of tense and negation needs to wind up higher in the structure after all of the transformations are done.

Going into that in just a bit more detail: Here are the rules for Neg raising and Tense raising:

[S X [ Neg Y ] ] → [S Neg [S X Y ] ]
[S X [ Tense Y ] ] → [S Tense [S X Y ] ]

Doing either one of them produces a “new S”. That is, you have your original S, minus the thing you raised, and then you have a new S that contains the thing you raised and the original S.

                 S
    S           / \\
   /_\\  -->  Neg   S
  X  /\\           /_\\
   Neg Y         X   Y

The rule doesn’t strictly speaking really require that the S in the lefthand tree be the topmost one in the whole structure, though. So, if you subsequently applied Tense raising, you could target the lower of the two Ses in the righthand tree. And then you’d have Neg higher than Tense, even though you moved Neg first. (If you instead target the higher S when applying Tense raising, then Tense would end up above Neg.)

The bottom line really is just that even the order in which you do the transformations (Neg raising and Tense raising) doesn’t determine which one will be higher in the end, so you have to interpret the question as being not about the order, but rather about the end result. Or, you could make the assumption I originally made when formulating the problem, and suppose that the S on the lefthand side of the Tense raising and Neg raising rules is the topmost one.

HW8: Making sure that John did not find Mary is not always true

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At the end of the statement about homework 8, I said that we want to make sure that John did not find Mary is not always true. To clarify what I mean here: In our task of formalizing our intuitions about meaning, we don’t want our semantic system to predict that John did not find Mary is true in this situation:

<----past----------now--->
   John finds
   Mary

It seems very clear from our intuitions about what this sentence would mean that if anything, that situation illustrated above is the best example of one in which John did not find Mary is false. But if we’re not careful, our semantics will predict that it would be true (on one reading of the sentence). That would be a bad prediction.

Edit: I changed the wording below a bit to reflect the change in the subsequent blog post.

If we allow Tense Raising and Neg Raising to occur in either order, or targeting either S in the structure, we predict that the sentence would have a reading that is true in the above situation. That is, one order (of Neg and Tense in the final structure) results in truth conditions that the illustration above would satisfy. What we need to do is stipulate that the final structure has to be one where Neg is above Tense, or stipulate that the final structure has to be one where Tense is above Neg one of the two rules (Tense Raising, Neg Raising) has to apply last—the question (in Part Two) is really asking which one has to wind up lower apply last. (And to sort of explain the problem that arises if the rules are applied in the wrong order—that is, why the situation above would turn out to meet the truth conditions.)

The property that the situation above has that’s relevant is that, although there is a moment in the past where John finds Mary, there are also plenty of moments in the past where John doesn’t find Mary. We have to make sure that the existence of such non-finding moments doesn’t render the sentence true. So, we have to stipulate a fixed order in the final structure between Neg and Tense to avoid that between Neg Raising and Tense Raising to avoid that.

HW8: Details, due Tuesday Dec 5

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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.).