A uniform semantics for embedded interrogatives: an answer, not necessarily the answer

Abstract

Our paper addresses the following question: Is there a general characterization, for all predicates P that take both declarative and interrogative complements (responsive predicates in the sense of Lahiri’s 2002 typology, see Lahiri, Questions and Answers in Embedded Contexts, OUP, 2002), of the meaning of the P-interrogative clause construction in terms of the meaning of the P-declarative clause construction? On our account, if P is a responsive predicate and Q a question embedded under P, then the meaning of ‘P + Q’ is, informally, “to be in the relation expressed by P to some potential complete answer to Q”. We show that this rule allows us to derive veridical and non-veridical readings of embedded questions, depending on whether the embedding verb is veridical or not, and provide novel empirical evidence supporting the generalization. We then enrich our basic proposal to account for the presuppositions induced by the embedding verbs, as well as for the generation of intermediate exhaustive readings of embedded questions (Klinedinst and Rothschild in Semant Pragmat 4:1–23, 2011).

Appendix: More on tautological basic answers

There are various ways in which our proposal might be modified regarding its treatment of the special case where the actual basic complete answer is the tautology. In this appendix, we discuss three possible modifications of our proposal.

1.1 A. Eliminating any reference to basic complete answers

Note that our proposal makes use of three distinct notions of answers: basic complete answers, Karttunen-complete answers, and strongly exhaustive answers, where Karttunen-complete answers and basic complete answers only differ regarding the special case where the basic complete answer is the tautology. Now, we can wonder what would follow if we eliminated completely any reference to basic complete answers, i.e. if we used Karttunen answers only, even in the presuppositional part of our meaning postulates. In such a case we could simply define $Q(w)$ differently, so that it would directly denote what is currently denoted by $Kart_{Q}(Q(w))$. In other words, pot(Q) would now be identified to the set of potential Karttunen-complete answers, rather than that of basic complete answers. But instead of introducing new definitions, let us rather keep our definitions, in terms of which we can state the resulting proposal as follows:

• (132) Meaning postulate for both the strongly exhaustive and the intermediate readings (modified version #1)

  $[\![\hbox {P}_{\mathrm{strong/intermediate}}]\!]^{\mathrm{w}} = {\uplambda }\hbox {Q}.{\uplambda }\hbox {x}{:}\,\exists \hbox {p} \in \hbox {pot(Q)}([\![\hbox {P}_{\mathrm{decl}}]\!]^{\mathrm{w}}(\hbox {Kart}_{\mathrm{Q}}(\hbox {p}))(\hbox {x})$ is defined & $[\![\hbox {P}_{\mathrm{decl}}]\!]^{\mathrm{w}}(\hbox {exh}_{\mathrm{Q}}(\hbox {p}))(\hbox {x})$ is defined).

  $\exists \hbox {p}\in \hbox {pot(Q)}([\![\hbox {P}_{\mathrm{decl}}]\!]^{\mathrm{w}}(\hbox {Kart}_{\mathrm{Q}}(\hbox {p}))(\hbox {x})$ is defined & $[\![\hbox {P}_{\mathrm{decl}}]\!]^{\mathrm{w}}(\hbox {exh}_{\mathrm{Q}}(\hbox {p}))(\hbox {x})$ is defined & $[\![\hbox {P}_{\mathrm{decl}}]\!]^{\mathrm{w}}(\mathbf{param}_{\mathbf{Q}}(\hbox {p}))(\hbox {x})=1$

  & there is no $\hbox {p}'\in \hbox {pot(Q)}$ such that

  • $\hbox {p}'\subset \hbox {p}$

  • 
  • 

  where param is a variable that takes as its value either exh or Kart.

Now, compared to our ‘official’ proposal, this does not change anything for predicates which are ‘presuppositionally’ monotone-increasing, such as know, forget, and surprise (X knows that S presupposes $S$, X forgets that S and It surprised X that S presuppose S and X knows/used to know S). In particular, we still predict that It surprised Mary who came, on the intermediate reading, is neither a presuppositional failure nor trivally false in case nobody came. That is, such a sentence will entail that if nobody came, Mary knows it and is surprised by that fact. The proposal however makes a difference for predicates which are presuppositionally non-monotone-increasing, such as discover (X discovers that S presupposes S and X did not believe S). Whereas on the ‘official’ proposal, as we discussed, John discovered who came is a presupposition failure if in fact nobody came, on this new proposal the sentence can be true if nobody came, provided John didn’t know at some point that nobody came and came to believe that nobody came. We tend to think that our ‘official’ proposal makes a better prediction, but, as pointed out by a reviewer, it might be problematic not to make parallel predictions for surprise and for discover. That is, one might think that if John discovered who came is a presupposition failure when nobody came, so should be It surprised John who came.

1.2 B. A presuppositional variant for the weakly exhaustive reading

Another possibility would be to introduce, only in the rule for the intermediate reading, a presupposition ensuring that the basic complete answer to which the agent is related via the relevant attitude is not the tautology. On such a view, the rule for the strongly exhaustive reading would remain the same as in our official proposal, but we could not state the rule for the intermediate reading in terms of just a change of ‘parameter’ in the assertive part of the rule. We would also distinguish both readings in terms of their presuppositional behavior. The rule for the intermediate reading would then be stated as follows:

• (133) Meaning postulate for the intermediate readings (modified version #2)

  $[\![\hbox {P}_{\mathrm{intermediate}}]\!]^{\mathrm{w}} = {\uplambda }\hbox {Q}.{\uplambda }\mathrm{x}{:}\,\exists \mathrm{p} \in \hbox {pot(Q)}$ (p is not the tautology and $[\![\hbox {P}_{\mathrm{decl}}]\!]^{\mathrm{w}}(\hbox {p})(\hbox {x})$ is defined & $[\![\hbox {P}_{\mathrm{decl}}]\!]^{\mathrm{w}}(\hbox {exh}_{\mathrm{Q}}(\hbox {p}))(\hbox {x})$ is defined).

  $\exists \hbox {p}\in \hbox {pot(Q)}$(p is not the tautology and $[\![\hbox {P}_{\mathrm{decl}}]\!]^{\mathrm{w}}(\hbox {p})(\hbox {x})$ is defined & $[\![\hbox {P}_{\mathrm{decl}}]\!]^{\mathrm{w}}(\hbox {exh}_{\mathrm{Q}}(\hbox {p}))(\hbox {x})$ is defined & $[\![~\hbox {P}_{\mathrm{decl}}]\!]^{\mathrm{w}}(\hbox {p})(\hbox {x})=1$ & there is no $\hbox {p}'\in \hbox {pot(Q)}$ such that

  • $\hbox {p}' \subset \hbox {p}$

  • 
  • 

If we adopt this proposal, both sentences John knows who came and It surprised John who came, on the intermediate reading, would presuppose that someone came. The fact that John knows who came is not judged to be a presuppositional failure, but is rather judged true, if nobody came and John knows that fact, would then be attributed to the availability of the strongly exhaustive reading (which would not trigger such a presupposition). It might also be expected that It surprised Mary who came would tend to be perceived as infelicitous if it is known that nobody came, given that the intermediate reading might be the preferred reading with surprise (in fact, Guerzoni and Sharvit 2007 argue that it is the only reading). Nothing would change for John discovered who came. It would still be predicted to be a presuppositional failure if nobody came, both on the intermediate and on the strongly exhaustive reading (cf. our discussion in Sect. 6).

1.3 C. A more radical move: eliminating any reference to Karttunen-complete answers

Recall the motivation for using Karttunen-complete answers rather than basic complete answers for the intermediate reading: we do not want to predict that John knows who came is true when nobody came and John has no belief whatsoever. But we may try to explain this intuition not in terms of the semantics of embedded questions, but in pragmatic terms. A potential motivation for using basic complete answers rather than Karttunen-complete answers has to to with verbs such as tell and predict on their non-veridical use, and with non-presuppositional question-embedding predicates such as be certain about. In a nutshell, we will show such a move allows us to predict an interesting generalization: on their non-factive, non-veridical uses, verbs like tell and predict only license a strongly exhaustive reading. And likewise a non-presuppositional predicate like be certain about is only compatible with the strongly exhaustive reading.

Let us first illustrate the generalization. For the sentence Mary is certain about which students came to be true, Mary must be certain about a certain strongly exhaustive answer. If she is only certain, say, that the students Sue and Al came and has no idea for others, the sentence is false. As for predict, a sentence such as (134) below entails that Mary made a complete prediction, in the sense that her prediction was interpreted as a claim about what the actual strongly exhaustive reading is [Of course Mary does not need to have explicitly predicted who would come and who would not come. She may have said ‘Mary and Peter will come’, which, as an answer to ‘Who will come’, is easily intepreted as implying that nobody besides Mary and Peter will come].

• (134) Peter predicted which of the four students would attend the party, but he proved wrong.

To see this, consider (134) uttered in the context described in (135) below:

• (135)

  • a. Scenario: Peter wondered who would attend a certain party among four students, John, Sue, Fred, and Mary. He predicted that John and Sue would go and made no prediction about the others – he actually said that he had no idea about Fred and Mary. In fact it turned out that neither John nor Sue attended the party.

  • b. Sentence: Peter predicted which of the four students would attend the party, but he proved wrong.

According to our informants, (135)b is false in such a scenario. We can contrast this scenario with another one where Peter made a complete, exhaustive prediction that turned out to be false.

• (136)

  • a. Scenario: Peter wondered who would attend a certain party among four students, John, Sue, Fred, and Mary. He predicted that John and Sue would go and that Fred and Mary would not. In fact the reverse turned out to be true: only Fred and Mary attended the party.

  • b. Sentence: Peter predicted which of the four students would attend the party, but he proved wrong

Even though the non-veridical use of predict is somewhat dispreferred for some speakers, there is a very clear contrast between (135) and (136), in that (136), unlike (135), can be judged true. This shows that the non-veridical use of predict, which may be less salient than its veridical use, is in any case only compatible with the strongly exhaustive reading.

It turns out that this state of affairs is easy to predict if we adopt the proposal in (137) instead of our official proposal, whereby the intermediate reading is defined with no reference to Karttunen-complete answers (note that this proposal is essentially what you get if you add to (113) the clauses that take care of the ‘no-false belief’ constraint).

• (137) Meaning postulate for the intermediate readings (modified version #3)

  $[\![\hbox {P}_{\mathrm{intermediate}}]\!]^{\mathrm{w}} = {\uplambda }\hbox {Q}.{\uplambda }\hbox {x}{:}\,\exists \hbox {p} \in \hbox {pot(Q)}([\![\hbox {P}_{\mathrm{decl}}]\!]^{\mathrm{w}}(\hbox {p})(\hbox {x})$ is defined & $[\![\hbox {P}_{\mathrm{decl}}]\!]^{\mathrm{w}}(\hbox {exh}_{\mathrm{Q}}(\hbox {p}))(\hbox {x})$ is defined).

  $\exists \hbox {p}\in \hbox {pot(Q)}([\![\hbox {P}_{\mathrm{decl}}]\!]^{\mathrm{w}}(\hbox {p})(\hbox {x})$ is defined & $[\![\hbox {P}_{\mathrm{decl}}]\!]^{\mathrm{w}}(\hbox {exh}_{\mathrm{Q}}(\hbox {p}))(\hbox {x})$ is defined & $[\![\hbox {P}_{\mathrm{decl}}]\!]^{\mathrm{w}}(\hbox {p})(\hbox {x})=1$

  & there is no $\hbox {p}'\subset \hbox {pot(Q)}$ such that

  • $\hbox {p}'\subset \hbox {p}$

  • &

  • &

On this proposal, we get the following prediction:

• (138)

  • Mary predicted which guests attended the party.

  • Presupposition: there is a potential basic complete answer p to ‘which guests attended the party?’ such that $[\![\hbox {predict}]\!]^{\mathrm{w}}(\hbox {p})(\hbox {Mary})$ and $[\![\hbox {predict}]\!]^{\mathrm{w}}(\hbox {exh}_{\mathrm{Q}}(\hbox {p}))(\hbox {Mary})$ are defined.

  • $\varvec{\rightarrow }$ This is always true (because non-factive predict has no presupposition)

  • Assertion: there is a potential basic complete answer p to ‘which guests attended the party?” such that Mary predicted p and Mary did not predict any stronger basic complete answer.

The presupposition is vacuous. As to the assertion, it is true as soon as Mary predicted that some potential basic complete answer is true. Take indeed the strongest potential basic complete answer that Mary predicted. Such a proposition satisfies the existential statement of the assertive part of the rule. So even if the strongest potential basic answer that Mary predicted is the tautology, the sentence comes out true. In fact, the sentence ends up equivalent to Mary predicted the tautology. Assuming that predict is monotone-increasing with respect to its complement, as soon as Mary predicted something, she predicted the tautology. So the sentence is true when Mary predicted the tautology and entails that Mary predicted the tautology, hence it simply expresses the proposition that Mary predicted the tautology. Likewise, if we use non-veridical, non-factive tell, Mary told Peter who came comes out true if and only if Mary told Peter the tautology. This, we surmise, is sufficient to explain why the weakly exhaustive reading is not detected for these non-presuppositional uses of tell and predict. On some quite standard assumptions X told Y the tautology and X predicted the tautology are themselves tautologies. Even if we do not subscribe to such a view, the interpretation that results from our rule is such that the content of the embedded clause plays no role at all in the truth conditions, which may be sufficient to rule out this reading on pragmatic grounds. Finally, with be certain about, on the weakly exhaustive reading, John is certain about who came would come out equivalent to John is certain that the tautology is true, which is plausibly itself tautological.

It is important to note here that with know, or any other presuppositional predicate, the rule for intermediate readings as stated in (137) does not give rise to such trivial readings, thanks to the presuppositional part of the rule, which becomes non-vacuous for these verbs and constrains the identity of the basic complete answer that can satisfy the existential statement.Mary knows which students came is predicted to be equivalent (on the intermediate reading) to ‘Either no student came and there is no student x such that Mary believes that x came, or Mary knows, for every student who came, that these students came, and does not falsely believe, of a student who didn’t come, that he came’. But if we adopt (137), we still need to explain why, on the intermediate reading, Mary knows which students came is not judged true when Mary does not have any idea about who came and in fact no students came (this is the problem of tautological basic answers).

We would like to suggest that this judgment might itself be explained in pragmatic terms. Note that when it is common knowledge that no student came, Mary knows which students came becomes equivalent to the claim there is no student such that Mary believes that this student came (but she may have no belief at all about students). So in such a context, the sentence does not assign any knowledge to Mary. Though we cannot pin down the precise underlying pragmatic principle that would make such a use of a know deviant, it seems to us that a pragmatic explanation for this specific case is plausible—for instance, because the use of know in Mary knows Q normally licenses the inference that Mary knows something about Q. This line of explanation actually predicts that we should be able to set up a context where the sentence is in fact judged true when Mary has no knowledge whatsoever. What we need is a context where the speaker does not have the belief that no student came, but does not exclude that possibility either. On top of that, the relevant scenario must be such that the attitude bearer (the subject of know) is presented as having no false positive beliefs about the question but also as having no true negative beliefs (so that we are sure that we probe the intermediate reading). Constructing such a context and then the appropriate scenario proves pretty hard, which is in itself suggestive, as it may explain the intuition that if Mary has no knowledge whatsoever Mary knows Q is false (in fact only quite implausible contexts and scenarios seem to meet all these conditions). Nevertheless, here is an attempt to set up such a context (thanks to Danny Fox for suggesting this specific scenario):

• (139)    Every Friday at 5 pm, the radio gives the names of the people who won the lottery. John’s father, who is old and has memory problems, listens to the radio all the time. If nobody wins, John’s father doesn’t notice that no list is read, so he does not know that nobody wins. If a list is read, he doesn’t know that it’s the complete list. But he does remember the list of the names for some time after 5 pm. On a certain day, John tells his wife at 5.05 pm: “I’ll call my father. He knows who won the lottery.”

If in fact on that day nobody won the lottery, was John’s sentence false? Our impression (and that of our informants) is that even upon learning that there was no winner and so John’s father knew nothing at all, one does not conclude that John was wrong. We conclude, very tentatively, that it might be possible to defend the proposal (137).