CAS LX b. Questions

Seeking truth Much of what we’ve done this semester has to do with characterizing (our knowledge of) the conditions under which sentences are true. Every fish likes Loren True when being a fish implies liking Loren, false otherwise.  x  U [ x  F(fish)   F(likes)]

What is the meaning of a question? There are things other than declarative sentences, however. For example, there are questions. What is the meaning of a question? Who does Loren like? A question is neither true nor false, but it does communicate something. How can we describe our interpretation of a question like this?

Answerhood Who broke the toaster? Homer (broke the toaster). #It always rains on the 4th of July. What did Pat paint? (Pat painted) a sunny landscape. #Homer (broke the toaster).

Answers and information Who broke the toaster? Homer / Homer did / Homer broke the toaster. All three answers are conveying the same information: Homer broke the toaster. A question is a request for information, and the minimal unit of “information” is a proposition (something that can be true or false). So, Homer here should really be viewed as just a shorthand form of Homer broke the toaster.

Answerhood Questions seem to specify the kind of proposition that would successfully serve as an answer. So: A proposition is defined in terms of the situations in which it is true (truth conditions). A question is defined in terms of the propositions with which it is answered (answerhood conditions).

Sets of possible answers That is, we can formally view a question as a set of possible answers or as a predicate of propositions. {Homer broke the toaster, Bart broke the toaster, Lisa broke the toaster, …} p [ p  {Homer broke the toaster, …} ] p [  x  U [ p = x broke the toaster ] ]

Pragmatic considerations Homer broke the toaster is of type —it can be true or false. Upon hearing Homer broke the toaster, we can (in principle) evaluate its truth or falsity, or add it to our background knowledge, etc. Upon hearing Who broke the toaster?, we have a specification of a type of proposition (those like x broke the toaster), and we can interpret this as a request to provide the true one(s). (type )

Embedded propositions We can embed sentences inside other sentences: Lisa thinks that Homer broke the toaster. Homer broke the toaster is either true or false, but that has no bearing on whether Lisa thinks that Homer broke the toaster is true or false—what matters is how Lisa believes the world to be, not how the world actually is. Still, it is relevant that Homer broke the toaster can be true or false; the truth conditions of Homer broke the toaster still play a role in the overall meaning.

Embedded questions Questions too can be embedded in other sentences. Lisa wonders who broke the toaster. This isn’t a question. It’s a statement, a proposition, it’s either true or it’s false. But whether it is true or false depends on the meaning of the question Who broke the toaster?. It means something like ‘Lisa wants to know the answer to the question Who broke the toaster?’ or ‘Lisa wants to know which of the propositions defined by Who broke the toaster? is true’.

Wonder vs. know There are (at least) two kinds of verbs that can embed questions. Wonder is one kind, but know is another: Lisa knows who broke the toaster. Unlike wonder, know can also embed propositions: *Lisa wonders that Homer broke the toaster. Lisa knows that Homer broke the toaster.

Knowing p What does it mean to know something anyway? Lisa knows that Homer broke the toaster. It seems that this says that Lisa knows that the conditions under which Homer broke the toaster are true in fact hold. Incidentally, know also presupposes the truth of its complement as well: #Lisa knows that the moon is made of green cheese.

Knowing Q So what does it mean to know a question? Lisa knows who broke the toaster. The most obvious conclusion to leap to, that Lisa knows the answerhood conditions of the question, does not seem right. It’s not that Lisa knows what would serve as an answer to Who broke the toaster?—rather, it’s that she knows what the answer actually is. What you know is essentially information, a proposition. That’s pretty much what know means.

Coercing p We can view know Q as involving a form of “coercion” of the same kind as we have seen with mass and count nouns. Marge ordered two coffees. Marge ordered two (natural units of) coffee. You can only count count nouns, so you have to “package” the mass nouns (covertly) first. You can only know propositions, so you have to convert the question to a proposition—its answer. Bart knows who ordered coffee. Bart knows (the answer to) Who ordered coffee?

The answer to Q What is the answer to a question? A question specifies possible answers, but not the actual answer. The question provides only the options. {Marge ordered coffee, Homer ordered coffee, Lisa ordered coffee, …} The actual answer depends on what’s true. So, perhaps: Bart knows (the true propositions from among those specified by) Who ordered coffee? Bart knows (that) Marge ordered coffee.

Exhaustivity Pat knows who left. Tracy left. Pat knows that Tracy left. This is good, we predict that. Pat knows the true propositions from among those specified by Who left? Tracy left is a true proposition among those specified by Who left? So, Pat knows that Tracy left.

Exhaustivity Pat knows that Tracy left. Chris did not leave. Does Pat know that Chris didn’t leave? Well, maybe. Maybe not. No conclusion. Pat knows who left. Chris did not leave. Does Pat know that Chris didn’t leave? Pat knows the true propositions from among those specified by Who left?

Nobody left? Suppose nobody actually left. Pat knows who left. Pat knows the true propositions from among those specified by Who left?. Nobody left. There are no true propositions from among those specified by Who left?. So, have we said anything about what Pat knows? Intuitively, yes. But we predict no.

Karttunen’s first approximation Karttunen (1977) upon observing this, suggested that in case there are no true propositions among those picked out by the question, know Q means know that Q has no true answers. That is, to know that the set of true propositions from among those specified by Q is empty.

(Strong) exhaustivity Pat knows who left. Chris did not leave. Pat knows that Chris did not leave. We didn’t quite predict the intuition here—if Pat knows who left is just ‘Pat knows the true propositions from among those specified by Who left?’ we don’t predict anything about whether Pat knows Chris didn’t leave, since Chris left was not among the true propositions.

(Strong) exhaustivity Based on this, it has been proposed that what is going on here is not Pat knows the true propositions from among those specified by Who left? But the subtly different: Pat knows that the true propositions from among those specified by Who left? are {Tracy left}. If Pat knows that {Tracy left} is the whole set of true propositions from among the set {Tracy left, Chris left, …}, then Pat can conclude that Chris left isn’t true.

Surprise Pat was surprised at who left. There is still some use for the original formulation, though—unlike know, surprise seems not to care about the false propositions. Pat was surprised at who left, but not at who didn’t leave. #Pat knew who left, but not who didn’t leave.

Know vs. surprise To finish up here, it seems that know and be surprised at differ in their meaning slightly when they embed a question. Where A Q are the true propositions from among those specified by the question Q… To know Q is to know that the true propositions from among those specified by Q are A Q. To be surprised at Q is to find the propositions in A Q somehow dissonant with other beliefs or conclusions.

Questions with quantifiers Which drink did everyone order? Individual: Everyone ordered coffee. Pair-list: Pat ordered coffee, Tracy ordered rum, and Chris ordered tea. Functional: Everyone ordered their favorite drink. Everyone ordered something. Namely, coffee. Mostly coffee or tea.

Questions with quantifiers Which patron ordered everything? Individual: Tracy. Pair-list: #Tracy ordered the fish, Pat ordered the beef, Chris ordered the chicken. Functional: #Its most enthusiastic proponent. Every boy i passed his i exam. *His i exam stumped every boy i. *Its i most enthusasitc proponent ordered everything i.

Questions with quantifiers Which drink did at few patrons order? Individual: coffee. Pair-list: #Tracy ordered coffee, Pat ordered tea. Functional: Their least favorite. For few patrons x, which drink did x order? For every patron x, which drink did x order?

Questions with quantifiers Individual answers are always possible. Functional answers seem to be possible only when bound pronouns are allowed in the answer. Every father i scolded his i child. Who did every father scold? His i mother scolded every boy i. Who scolded every boy? List answers seem to be possible when the quantifiers allow construction of a unique set of simple questions to answer. Who did everyone scold? Who did at most 3 people scold? Who did nobody scold?

Librarians and limits on QR Some librarian or other found every book. One librarian, or one per book. [ S some librarian found [ NP every book] ] [ NP every book] i [ S some librarian found t i ]. Some librarian knows that Pat found every book. One librarian, but not one per book. In order to get the “one per book” interpretation, we would need to use QR to bring every book up higher in the structure than some librarian or other. This suggests that QR can only move a quantifier as high as the smallest S in which it is found. [ S Some librarian knows [ S that Pat found every book]] [ NP every book] i [ S some lib. knows [ S that Pat found t i ]].

More about librarians Some librarian or other found out which book every student needed. One librarian or one librarian per book. Some librarian found out, for each student x, the book that x needed. For each student x, there is a (possibly different) librarian that found out the book that x needed. That shouldn’t be possible: [ S some librarian found out [ S which book every student needed]].

Still more about librarians And it isn’t really… Some librarian i or other found out which book every boy stole from her i. One librarian, not one per boy. #For every boy x, there is some librarian or other that found out the book that x stole from her. Why? [ S some librarian i found out [ S which book every boy stole from her i ]]

QR of questions? Consider the pair-list kind of question What did everyone buy? interpreted as a series of questions What did Pat buy? What did Tracy buy? … defined by the smallest set that can count as everyone. Some librarian or other found out [which book every student needed]. For every question Q in the series defined by Which book did every student need?, some librarian or other found out the answer to Q.

QR of questions? Some librarian or other found out [which book every student needed]. [ S some librarian found out [ S which book every student needed] ] Some librarian or other found out every answer. [ S which book every student needed] i [ S some librarian found out t i ] It’s as if the entire embedded question acts as a quantifier. That isn’t moving out of its S. Idea: when a question is interpreted as a series of questions (the “pair- list” interpretation), it can be considered a quantifier itself.

Librarians continued… Some librarian i or other found out which book every boy stole from her i. For every question Q in the series defined by Which book did every boy steal from her i ?, some librarian i or other found out the answer to Q. [Which book did every boy steal from her] i some librarian i found out t i. The idea is that if the question is raised up to a position above some librarian in the tree, some librarian no longer has scope/control over the pronoun her, and so the choice of (possibly different) librarians cannot determine the referent of her.

Last point on librarians and QR Some librarian or other thinks I found out which book every boy needed. One librarian, not one-per boy. [ S Some librarian or other thinks [ S I found out [ S which book every boy needed] ] ].

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