CAS LX 502 Semantics

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CAS LX 502Semantics

• 11b. Questions

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Seeking truth

• Much of what weve 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) ? ltx, F(Loren)gt ? F(likes)
• (Note this is the version well end up with
  after Thanksgiving break, it differs in a couple
  of ways from how we did this earlier in the
  semesterbut thats not important right now.)

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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?

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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).

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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.

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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).

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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

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Pragmatic considerations

• Homer broke the toaster is of type lttgtit 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 ltt,tgt)

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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
  falsewhat 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.

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Embedded questions

• Questions too can be embedded in other sentences.
• Lisa wonders who broke the toaster.
• This isnt a question. Its a statement, a
  proposition, its either true or its 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.

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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.

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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.

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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.
• Its not that Lisa knows what would serve as an
  answer to Who broke the toaster?rather, its
  that she knows what the answer actually is.
• What you know is essentially information, a
  proposition. Thats pretty much what know means.

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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.
• Cooper ordered two coffees.
• Cooper 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 propositionits answer.
• Andy knows who ordered coffee.
• Andy knows (the answer to) Who ordered coffee?

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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. Cooper ordered coffee, Andy ordered
  coffee, Bob ordered coffee,
• The actual answer depends on whats true.
• So, perhaps
• Ben knows (the true propositions from among those
  specified by) Who ordered coffee?
• Ben knows (that) Cooper ordered coffee.

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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.

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Exhaustivity

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

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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.

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Karttunens 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.

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(Strong) exhaustivity

• Pat knows who left.Chris did not leave.
• Pat knows that Chris did not leave.
• We didnt quite predict the intuition hereif Pat
  knows who left is just Pat knows the true
  propositions from among those specified by Who
  left? we dont predict anything about whether
  Pat knows Chris didnt leave, since Chris left
  was not among the true propositions.

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(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 isnt true.

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Surprise

• Pat was surprised at who left.
• There is still some use for the original
  formulation, thoughunlike know, surprise seems
  not to care about the false propositions.
• Pat was surprised at who left, but not at who
  didnt leave.
• Pat knew who left, but not who didnt leave.

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

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De dicto vs. de re again

• Theres another potentially problematic aspect of
  Karttunens original view (that to know who left
  is to know the true propositions in AQ).
• It centers around the question of whether if you
  know which secret agents left, you can tell
  secret agents from ordinary civilians.
• Can you know which secret agents left without
  knowing who is a secret agent?
• If so, this is a version of the de re
  interpretation.

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Karttunen predicts de re

• AQ is the set of true propositions of the form x
  left where x is a secret agent who left.
• Tom left, Zoe left
• You can certainly know Tom left, even if you know
  nothing more about Tom than that Tom refers to
  him.
• Ellies party. Tom Zoe are at the party, and
  are secret agents. Harry wants to know which
  secret agents lefthe can ask Ellie, because
  Ellie knows which secret agents left, despite not
  knowing who the secret agents are.

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The de dicto reading

• A much easier reading of I know which secret
  agents left, however, can be false, even if I
  know who leftspecifically, if I dont know who
  the secret agents are.
• This, however, comes out from the stronger
  interpretation of know. If I know that the true
  answers to Which secret agents left? Are Zoe
  left, Tom left, then I know also that Zoe and
  Tom are secret agents.
• Also, I would know that anyone else either didnt
  leave or isnt a secret agent.

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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.

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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 boyi passed hisi exam.
• Hisi exam stumped every boyi.
• Itsi most enthusiastic proponent ordered
  everythingi.

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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?

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Questions with quantifiers

• Individual answers are always possible.
• Functional answers seem to be possible only when
  bound pronouns are allowed in the answer.
• Every fatheri scolded hisi child.
• Who did every father scold?
• Hisi mother scolded every boyi.
• 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?

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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 booki S some librarian found ti .
• 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 booki S some lib. knows S that Pat
  found ti.

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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 shouldnt be possible
• S some librarian found out S which book
  every student needed.

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Still more about librarians

• And it isnt really
• Some librariani or other found out which book
  every boy stole from heri.
• 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 librariani found out S which book
  every boy stole from heri

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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.

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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 neededi S some
  librarian found out ti
• Its as if the entire embedded question acts as a
  quantifier. That isnt 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.

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Librarians continued

• Some librariani or other found out which book
  every boy stole from heri.
• For every question Q in the series defined by
  Which book did every boy steal from heri?, some
  librariani or other found out the answer to Q.
• Which book did every boy steal from
  heri some librariani found out ti.
• 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.

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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 .
• S Some librarian or other thinks S I found
  out S which book every boy needed .

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