CAS LX 502CAS LX 502SemanticsSemantics

11b. Questions11b. Questions

Seeking truthSeeking truth Much of what we’ve done this semester Much of what we’ve done this semester has to do with characterizing (our has to do with characterizing (our knowledge of) the conditions under which knowledge of) the conditions under which sentences are true.sentences are true.

Every fish likes LorenEvery fish likes Loren True when being a fish implies liking True when being a fish implies liking Loren, false otherwise.Loren, false otherwise.

xxUU [ [ x x F F((fishfish) ) < <x, Fx, F((LorenLoren)>)> F F((likeslikes)])] (Note: this is the version we’ll end up with after (Note: this is the version we’ll end up with after Thanksgiving break, it differs in a couple of ways Thanksgiving break, it differs in a couple of ways from how we did this earlier in the semester—but from how we did this earlier in the semester—but that’s not important right now.)that’s not important right now.)

What is the meaning of What is the meaning of a question?a question?

There are things other than There are things other than declarative sentences, however. For declarative sentences, however. For example, there are questions. What is example, there are questions. What is the meaning of a question?the meaning of a question?

Who does Loren like?Who does Loren like?

A question is neither true nor false, A question is neither true nor false, but it does but it does communicatecommunicate something. How something. How can we describe our interpretation of can we describe our interpretation of a question like this?a question like this?

AnswerhoodAnswerhood

Who broke the toaster?Who broke the toaster? Homer (broke the toaster).Homer (broke the toaster). #It always rains on the 4th of #It always rains on the 4th of July.July.

What did Pat paint?What did Pat paint? (Pat painted) a sunny landscape.(Pat painted) a sunny landscape. #Homer (broke the toaster).#Homer (broke the toaster).

Answers and informationAnswers and information Who broke the toaster?Who broke the toaster? HomerHomer / / Homer didHomer did / / Homer broke the Homer broke the toastertoaster..

All three answers are conveying the same All three answers are conveying the same information: information: Homer broke the toasterHomer broke the toaster.. A question is a request for information, and A question is a request for information, and the minimal unit of “information” is a the minimal unit of “information” is a proposition (something that can be true or proposition (something that can be true or false).false).

So, So, HomerHomer here should really be viewed as here should really be viewed as just a shorthand form of just a shorthand form of Homer broke the Homer broke the toastertoaster..

AnswerhoodAnswerhood

Questions seem to specify the Questions seem to specify the kind of proposition that would kind of proposition that would successfully serve as an answer.successfully serve as an answer.

So: A proposition is defined in So: A proposition is defined in terms of the situations in which terms of the situations in which it is true (it is true (truth conditionstruth conditions). A ). A question is defined in terms of question is defined in terms of the propositions with which it is the propositions with which it is answered (answered (answerhood conditionsanswerhood conditions).).

Sets of possible Sets of possible answersanswers

That is, we can formally view a That is, we can formally view a question as a question as a set of possible answersset of possible answers or as a or as a predicate of propositionspredicate of propositions..

{Homer broke the toaster, Bart broke {Homer broke the toaster, Bart broke the toaster, Lisa broke the toaster, the toaster, Lisa broke the toaster, …}…} pp [ [ pp {Homer broke the toaster, …} ]{Homer broke the toaster, …} ] pp [ [ xxUU [ [ pp = = xx broke the toaster ] ] broke the toaster ] ]

Pragmatic Pragmatic considerationsconsiderations

Homer broke the toasterHomer broke the toaster is of type <t>—is of type <t>—it can be true or false.it can be true or false.

Upon hearing Upon hearing Homer broke the toasterHomer broke the toaster, , we can (in principle) evaluate its we can (in principle) evaluate its truth or falsity, or add it to our truth or falsity, or add it to our background knowledge, etc.background knowledge, etc.

Upon hearing Upon hearing Who broke the toaster?Who broke the toaster?, we , we have a specification of a type of have a specification of a type of proposition (those like proposition (those like x broke the x broke the toastertoaster), and we can interpret this as ), and we can interpret this as a request to provide the true one(s). a request to provide the true one(s). (type <t,t>)(type <t,t>)

Embedded propositionsEmbedded propositions We can embed sentences inside other We can embed sentences inside other sentences:sentences: Lisa thinks that Homer broke the toaster.Lisa thinks that Homer broke the toaster.

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

Embedded questionsEmbedded questions

Questions too can be embedded in other Questions too can be embedded in other sentences.sentences. Lisa wonders who broke the toaster.Lisa wonders who broke the toaster.

This isn’t a question. It’s a statement, a This isn’t a question. It’s a statement, a proposition, it’s either true or it’s false. proposition, it’s either true or it’s false. But whether it is true or false depends on But whether it is true or false depends on the meaning of the question the meaning of the question Who broke the Who broke the toaster?toaster?..

It means something like ‘Lisa wants to know It means something like ‘Lisa wants to know the answer to the question the answer to the question Who broke the Who broke the toaster?toaster?’ or ‘Lisa wants to know which of the ’ or ‘Lisa wants to know which of the propositions defined by propositions defined by Who broke the Who broke the toaster?toaster? is true’. is true’.

Wonder vs. knowWonder vs. know There are (at least) two kinds of There are (at least) two kinds of verbs that can embed questions. verbs that can embed questions. WonderWonder is one kind, but is one kind, but knowknow is is another:another: Lisa knows who broke the toaster.Lisa knows who broke the toaster.

Unlike Unlike wonderwonder, , knowknow can also embed can also embed propositions:propositions: *Lisa wonders that Homer broke the *Lisa wonders that Homer broke the toaster.toaster.

Lisa knows that Homer broke the toaster.Lisa knows that Homer broke the toaster.

Knowing Knowing pp

What does it mean to know something What does it mean to know something anyway?anyway? Lisa knows that Homer broke the toaster.Lisa knows that Homer broke the toaster.

It seems that this says that Lisa knows It seems that this says that Lisa knows that the conditions under which that the conditions under which Homer Homer broke the toasterbroke the toaster are true in fact hold. are true in fact hold.

Incidentally, Incidentally, knowknow also presupposes the also presupposes the truth of its complement as well:truth of its complement as well:

#Lisa knows that the moon is made of green #Lisa knows that the moon is made of green cheese.cheese.

Knowing Knowing QQ So what does it mean to know a question?So what does it mean to know a question?

Lisa knows who broke the toaster.Lisa knows who broke the toaster. The most obvious conclusion to leap to, The most obvious conclusion to leap to, that Lisa knows the answerhood that Lisa knows the answerhood conditions of the question, does not conditions of the question, does not seem right.seem right.

It’s not that Lisa knows what would It’s not that Lisa knows what would serve as an answer to serve as an answer to Who broke the Who broke the toaster?toaster?—rather, it’s that she knows —rather, it’s that she knows what the answer actually what the answer actually isis..

What you know is essentially What you know is essentially informationinformation, a proposition. That’s , a proposition. That’s pretty much what pretty much what know know means.means.

Coercing Coercing pp We can view We can view know Qknow Q as involving a form of as involving a form of “coercion” of the same kind as we have “coercion” of the same kind as we have seen with mass and count nouns.seen with mass and count nouns. Cooper ordered two coffees.Cooper ordered two coffees. Cooper ordered two (natural units of) coffee.Cooper ordered two (natural units of) coffee.

You can only count count nouns, so you You can only count count nouns, so you have to “package” the mass nouns have to “package” the mass nouns (covertly) first. You can only know (covertly) first. You can only know propositions, so you have to convert the propositions, so you have to convert the question to a proposition—its answer.question to a proposition—its answer. Andy knows who ordered coffee.Andy knows who ordered coffee. Andy knows (the answer to) Andy knows (the answer to) Who ordered coffee?Who ordered coffee?

The answer to The answer to QQ What is What is the answerthe answer to a question? to a question? A question specifies A question specifies possiblepossible answers, answers, but not the actual answer. The question but not the actual answer. The question provides only the options. provides only the options. {Cooper {Cooper ordered coffee, Andy ordered coffee, ordered coffee, Andy ordered coffee, Bob ordered coffee, …}Bob ordered coffee, …}

The actual answer depends on what’s The actual answer depends on what’s truetrue..

So, perhaps:So, perhaps: Ben knows (the true propositions from among Ben knows (the true propositions from among those specified by) those specified by) Who ordered coffee?Who ordered coffee?

Ben knows (that) Cooper ordered coffee.Ben knows (that) Cooper ordered coffee.

ExhaustivityExhaustivity Pat knows who left.Pat knows who left.Tracy left.Tracy left.

Pat knows that Tracy left.Pat knows that Tracy left.

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

So, Pat knows that Tracy left.So, Pat knows that Tracy left.

ExhaustivityExhaustivity Pat knows who left. Pat knows that Pat knows who left. Pat knows that Tracy left.Tracy left.Chris did not leave.Chris did not leave.

Does Pat know that Chris didn’t leave?Does Pat know that Chris didn’t leave?Well, maybe. Maybe not. No conclusion.Well, maybe. Maybe not. No conclusion.

Pat knows who left.Pat knows who left.Chris did not leave.Chris did not leave.

Does Pat know that Chris didn’t leave?Does Pat know that Chris didn’t leave? Pat knows the true propositions from Pat knows the true propositions from among those specified by among those specified by Who left?Who left?

Nobody left?Nobody left? Suppose nobody actually left.Suppose nobody actually left. Pat knows who left.Pat knows who left. Pat knows the true propositions from Pat knows the true propositions from among those specified by among those specified by Who left?Who left?..

Nobody left.Nobody left. There are no true propositions from There are no true propositions from among those specified by among those specified by Who left?Who left?..

So, have we said anything about what So, have we said anything about what Pat knows?Pat knows?

Intuitively, yes. But we predict no.Intuitively, yes. But we predict no.

Karttunen’s first Karttunen’s first approximationapproximation

Karttunen (1977) upon observing Karttunen (1977) upon observing this, suggested that in case this, suggested that in case there are no true propositions there are no true propositions among those picked out by the among those picked out by the question, question, know Qknow Q means means know know that Q has no true answersthat Q has no true answers..

That is, to know that the set That is, to know that the set of true propositions from among of true propositions from among those specified by those specified by QQ is empty. is empty.

(Strong) exhaustivity(Strong) exhaustivity Pat knows who left.Pat knows who left.Chris did not leave.Chris did not leave.

Pat knows that Chris did not leave.Pat knows that Chris did not leave.

We didn’t quite predict the intuition We didn’t quite predict the intuition herehere—if —if Pat knows who leftPat knows who left is just ‘Pat is just ‘Pat knows the true propositions from among knows the true propositions from among those specified by those specified by Who left?Who left?’ we don’t ’ we don’t predict anything about whether Pat predict anything about whether Pat knows Chris didn’t leave, since knows Chris didn’t leave, since Chris Chris leftleft was not among the true was not among the true propositions.propositions.

(Strong) exhaustivity(Strong) exhaustivity Based on this, it has been proposed Based on this, it has been proposed that what is going on here is notthat what is going on here is not Pat knows the true propositions from Pat knows the true propositions from among those specified by among those specified by Who left?Who left?

But the subtly different:But the subtly different: Pat knows Pat knows thatthat the true propositions from the true propositions from among those specified by among those specified by Who left?Who left? are are {{Tracy leftTracy left}.}.

If Pat knows that {If Pat knows that {Tracy leftTracy left} is the } is the whole set of true propositions from among whole set of true propositions from among the set {the set {Tracy leftTracy left, , Chris leftChris left, …}, then , …}, then Pat can conclude that Pat can conclude that Chris left Chris left isn’t isn’t true.true.

SurpriseSurprise

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

#Pat knew who left, but not who didn’t #Pat knew who left, but not who didn’t leave.leave.

Know vs. surpriseKnow vs. surprise

To finish up here, it seems that To finish up here, it seems that knowknow and and be surprised atbe surprised at differ in their differ in their meaning slightly when they embed a meaning slightly when they embed a question.question.

Where Where AAQQ are the true propositions from are the true propositions from among those specified by the question among those specified by the question QQ…… To know Q To know Q is to know is to know that that the true the true propositions from among those specified by propositions from among those specified by QQ are are AAQQ..

To be surprised at QTo be surprised at Q is to find the is to find the propositions in propositions in AAQQ somehow dissonant with somehow dissonant with other beliefs or conclusions.other beliefs or conclusions.

De dictoDe dicto vs. vs. de re de re againagain

There’s another potentially problematic There’s another potentially problematic aspect of Karttunen’s original view aspect of Karttunen’s original view (that to know who left is to know the (that to know who left is to know the true propositions in Atrue propositions in AQQ).).

It centers around the question of It centers around the question of whether if you know which secret agents whether if you know which secret agents left, you can tell secret agents from left, you can tell secret agents from ordinary civilians.ordinary civilians.

Can you know which secret agents left Can you know which secret agents left without knowing who is a secret agent?without knowing who is a secret agent?

If so, this is a version of the If so, this is a version of the de re de re interpretation.interpretation.

Karttunen predicts Karttunen predicts de de rere

AAQQ is the set of true propositions of is the set of true propositions of the form the form x leftx left where x is a secret where x is a secret agent who left.agent who left.

{Tom left, Zoe left}{Tom left, Zoe left} You can certainly know Tom left, even You can certainly know Tom left, even if you know nothing more about Tom than if you know nothing more about Tom than that that TomTom refers to him. refers to him. Ellie’s party. Tom & Zoe are at the party, Ellie’s party. Tom & Zoe are at the party, and are secret agents. Harry wants to know and are secret agents. Harry wants to know which secret agents left—he can ask Ellie, which secret agents left—he can ask Ellie, because Ellie knows which secret agents because Ellie knows which secret agents left, despite not knowing who the secret left, despite not knowing who the secret agents are.agents are.

The The de dicto de dicto readingreading A much easier reading of A much easier reading of I know which I know which secret agents leftsecret agents left, however, can be , however, can be false, even if I know who left—false, even if I know who left—specifically, if I don’t know who the specifically, if I don’t know who the secret agents are.secret agents are.

This, however, comes out from the This, however, comes out from the stronger interpretation of stronger interpretation of knowknow. If I . If I know that the true answers to know that the true answers to Which Which secret agents left?secret agents left? Are {Zoe left, Tom Are {Zoe left, Tom left}, then I know also that Zoe and left}, then I know also that Zoe and Tom are secret agents.Tom are secret agents. Also, I would know that anyone else either Also, I would know that anyone else either didn’t leave or isn’t a secret agent.didn’t leave or isn’t a secret agent.

Questions with Questions with quantifiersquantifiers

Which drink did everyone order?Which drink did everyone order? Individual: Individual: Everyone ordered coffee.Everyone ordered coffee. Pair-list: Pair-list: Pat ordered coffee, Tracy Pat ordered coffee, Tracy ordered rum, and Chris ordered tea.ordered rum, and Chris ordered tea.

Functional: Functional: Everyone ordered their Everyone ordered their favorite drink.favorite drink.

Everyone ordered something.Everyone ordered something. Namely, coffee.Namely, coffee. Mostly coffee or tea.Mostly coffee or tea.

Questions with Questions with quantifiersquantifiers

Which patron ordered everything?Which patron ordered everything? Individual:Individual: Tracy.Tracy. Pair-list:Pair-list: #Tracy ordered the fish, Pat #Tracy ordered the fish, Pat ordered the beef, Chris ordered the chicken.ordered the beef, Chris ordered the chicken.

Functional:Functional: #Its most enthusiastic proponent. #Its most enthusiastic proponent.

Every boyEvery boyii passed his passed hisii exam. exam. *His*Hisii exam stumped every boy exam stumped every boyii.. *Its*Itsii most enthusiastic proponent most enthusiastic proponent ordered everythingordered everythingii..

Questions with Questions with quantifiersquantifiers

Which drink did at few patrons order?Which drink did at few patrons order? Individual:Individual: coffee.coffee. Pair-list:Pair-list: #Tracy ordered coffee, Pat ordered #Tracy ordered coffee, Pat ordered tea.tea.

Functional:Functional: Their least favorite. Their least favorite.

For few patrons For few patrons xx, which drink did , which drink did xx order?order?

For every patron For every patron xx, which drink did , which drink did xx order?order?

Questions with Questions with quantifiersquantifiers

Individual answers are always possible.Individual answers are always possible. Functional answers seem to be possible only Functional answers seem to be possible only when bound pronouns are allowed in the when bound pronouns are allowed in the answer.answer. Every fatherEvery fatherii scolded his scolded hisii child. child. Who did every father scold?Who did every father scold? *His*Hisii mother scolded every boy mother scolded every boyii.. Who scolded every boy?Who scolded every boy?

List answers seem to be possible when the List answers seem to be possible when the quantifiers allow construction of a unique quantifiers allow construction of a unique set of simple questions to answer.set of simple questions to answer. Who did everyone scold?Who did everyone scold? Who did at most 3 people scold?Who did at most 3 people scold? Who did nobody scold?Who did nobody scold?

Librarians and limits Librarians and limits on QRon QR

Some librarian or other found every book.Some librarian or other found every book. One librarian, or one per book.One librarian, or one per book. [[SS some librarian found [ some librarian found [NPNP every book] ] every book] ] [[NPNP every book] every book]ii [ [SS some librarian found some librarian found ttii ]. ].

Some librarian knows that Pat found every Some librarian knows that Pat found every book.book. One librarian, but not one per book.One librarian, but not one per book.

In order to get the “one per book” interpretation, we In order to get the “one per book” interpretation, we would need to use QR to bring would need to use QR to bring every bookevery book up higher in up higher in the structure than the structure than some librarian or othersome librarian or other. This . This suggests that QR can only move a quantifier as high suggests that QR can only move a quantifier as high as the smallest S in which it is found.as the smallest S in which it is found. [[SS Some librarianSome librarian knows knows [[SS that Pat found that Pat found every every bookbook]]]]

[[NPNP every book] every book]ii [[SS some lib. knows some lib. knows [[SS that Pat found that Pat found ttii]]]]..

More about librariansMore about librarians

Some librarian or other found out which book Some librarian or other found out which book every student needed.every student needed. One librarian One librarian or one librarian per bookor one librarian per book.. Some librarian found out, for each student x, the Some librarian found out, for each student x, the book that x needed.book that x needed.

For each student x, there is a (possibly different) For each student x, there is a (possibly different) librarian that found out the book that x needed.librarian that found out the book that x needed.

That shouldn’t be possible:That shouldn’t be possible: [[SS some librariansome librarian found out found out

[[SS which book which book every student every student neededneeded]]]]..

Still more about Still more about librarianslibrarians

And it isn’t really…And it isn’t really… Some librarianSome librarianii or other found out which or other found out which book every boy stole from herbook every boy stole from herii.. One librarian, not one per boy.One librarian, not one per boy. #For every boy x, there is some librarian or #For every boy x, there is some librarian or other that found out the book that x stole from other that found out the book that x stole from her.her.

Why?Why? [[SS some librariansome librarianii found out found out

[[SS which book which book every boyevery boy stole from her stole from herii ]]]]

QR of questions?QR of questions?

Consider the pair-list kind of question Consider the pair-list kind of question What did everyone buy?What did everyone buy? interpreted as a interpreted as a series of questions series of questions What did Pat buy?What did Pat buy? What did Tracy buy?What did Tracy buy? … … defined by the defined by the smallest set that can count as smallest set that can count as everyoneeveryone.. Some librarian or other found outSome librarian or other found out

[which book every student needed].[which book every student needed].

For every question For every question QQ in the series in the series defined by Which book did every student defined by Which book did every student need?, some librarian or other found out need?, some librarian or other found out the answer to the answer to QQ..

QR of questions?QR of questions? Some librarian or other found out [which book every Some librarian or other found out [which book every student needed].student needed]. [[SS some librariansome librarian found out found out [[SS which book every student which book every student needed]needed] ]]

Some librarian or other found out every answer.Some librarian or other found out every answer. [[SS which book every student needed] which book every student needed]ii [ [SS some librarian some librarian found out found out ttii]]

It’s as if the entire embedded question acts as a It’s as if the entire embedded question acts as a quantifier. quantifier. That That isn’t moving out of its S.isn’t moving out of its S.

Idea: Idea: when a question is interpreted as a series of when a question is interpreted as a series of questions (the “pair-list” interpretation), it can questions (the “pair-list” interpretation), it can be considered a quantifier be considered a quantifier itselfitself..

Librarians continued…Librarians continued…

Some librarianSome librarianii or other found out which or other found out which book every boy stole from herbook every boy stole from herii.. For every question For every question QQ in the series defined by in the series defined by Which book did every boy steal from herWhich book did every boy steal from herii??, some , some librarianlibrarianii or other found out the answer to or other found out the answer to QQ..

[Which book did every boy steal from her][Which book did every boy steal from her]ii

some librariansome librarianii found out found out ttii.. The idea is that if the question is raised The idea is that if the question is raised up to a position above up to a position above some librariansome librarian in in the tree, the tree, some librariansome librarian no longer has no longer has scope/control over the pronoun scope/control over the pronoun herher, and so , and so the choice of (possibly different) the choice of (possibly different) librarians cannot determine the referent librarians cannot determine the referent of of herher..

Last point on Last point on librarians and QRlibrarians and QR

Some librarian or other thinks I found Some librarian or other thinks I found out which book every boy needed.out which book every boy needed. One librarian, not one-per-boy.One librarian, not one-per-boy.

[[SS Some librarian Some librarian or other thinks or other thinks [[SS I I found outfound out

[[SS which book which book every boyevery boy needed needed]] ]] ]]..

[[SS Some librarian Some librarian or other thinks or other thinks [[SS I I found outfound out

[[SS which book every boy needed] which book every boy needed] ]] ]]..