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On Karttunen’s “The Syntax and Semantics of Questions”

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A Reader's Guide to Classic Papers in Formal Semantics

Part of the book series: Studies in Linguistics and Philosophy ((SLAP,volume 100))

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Abstract

Karttunen’s article on the syntax and semantics of questions is a milestone in the truth-conditional compositional semantics of interrogatives and of verbs that embed them. It is the first comprehensive study of the mapping between the syntax and the interpretation of the three different types of questions (polar, constituent and alternative questions) and presents the first semantic analysis of question-embedding verbs (QEVs henceforth) that assumes the same intensions for matrix and embedded interrogatives. This analysis continues to vastly inspire the ongoing research on the properties of questions and QEVs. This chapter illustrates Karttunen’s theory focusing on those formal details that have been the most influential in subsequent literature. In doing so, however, I will take the liberty to suggest a less than literal rendition of these details, in an attempt to make the discussion more accessible to today’s reader. The main departure that I make here from Karttunen’s 1977 is in the formal framework. Whereas Karttunen adopts Montague’s PTQ, here I will expose his ideas in Heim and Kratzer‘s type driven semantics.

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Notes

  1. 1.

    The difference between a semantically congruent answer and a mere response to a question is crucial in this view and it will become clearer in the coming sections.

  2. 2.

    Hamblin (1958) suggests that the denotation of a question is the set of its possible complete answers, whereas the more formally explicit theory in Hamblin (1973) derives as their denotations the sets of their possible “instantial” answers, a notion that is defined later in this chapter. Karttunen (1977) follows Hamblin (1973) in this respect.

  3. 3.

    For this rendition of Karttunen’s semantics I am immensely indebted to Irene Heim’s lectures and lecture notes on the semantics of interrogatives.

  4. 4.

    Unlike Hamblin, whose wh-phrases are interpreted in their base position, Karttunen adopts the syntactic hypothesis that all wh-phrases occupy a position above C at LF. Given this, (10b) results from the covert movement of the object wh-phrase. In (10c), the first trace is left by the overtly moved who and the second trace corresponds to the covert movement of whom. All traces are interpreted via the assignment function g, to be bound higher in the structure. This generates in both cases a constituent denoting an open sentence.

  5. 5.

    The proto-question in (13) also fails to represent the ‘original’ Karttunen denotation, because it fails to contain the true answer in all the worlds in which Mary doesn’t smile.

  6. 6.

    Following Heim and Kratzer (1998)’s analysis of binding, I assume an LF where the index of each moved DP is a separate head immediately inserted under the DP’s landing site and that constituents headed by indices denote predicate abstracts.

  7. 7.

    This mismatch can be avoided under the undesirable additional stipulation that wh-words are

    lexically ambiguous.

  8. 8.

    Abbreviating <st,t> as τq reveals the similarities and differences between the two types of determiners:

    • ⟦some⟧g,w = λP<e,t>. λQ<e,t>. ∃x [P(x) =1 ∧ Q(x) =1]

    • ⟦which⟧g,w = λP<e,t>. λQ<e,τq >. {p: ∃x [P(x) =1 ∧ Q(x)(p) =1]}

  9. 9.

    This is so because both the LFs below lead to type mismatches and are therefore un-interpretable.

    1. (i)

      [CP someone [1 [C′? [IP Mary saw t1]]]]

    2. (ii)

      [IP′ who [1 [IP Mary saw t1]]]

    Notice that Karttunen also needs to stipulate that the movement of wh-phrases above C is compulsory for mere syntactic reasons, in order to block (ii).

  10. 10.

    Due to the restriction to true answers, Karttunen’s denotation of the proto-question (i.e. Q(w)) might be empty. Given this, semantics of whether needs to be more complex:

    • ⟦whether⟧w =λQ<s,<st,t>>. {p: p ∈ Q(w) or [Q(w) = ∅ → p = {w: Q(w) = ∅}]}

    If Mary smiled in w, Q(w) = {that Mary smiled} = ⟦whether Mary smiled⟧w. If Mary didn’t smile in w, Q(w) = ∅ and ⟦whether Mary smiled⟧w = {p: p = {w: Q(w) = ∅}} = {p: p = {w: w ∉ that Mary smiled} = {That Mary didn’t smile}.

  11. 11.

    In polar questions, the presupposition that at least and at most one answer is true is trivially satisfied, since their answers are mutually exclusive and jointly exhaustive.

  12. 12.

    Karttunen’s theory is built on the assumption that questions denote the same sets of propositions whether they are embedded under a QEV or are uttered in isolation. In fact, Karttunen claims that the root questions too are occurrences of embedded questions under silent performative verbs. This kind of ‘performative hypothesis’ is problematic and it is also un-necessary within current semantic theorizing, where free and embedded occurrences of questions can be analyzed as sharing the same LF structure and therefore the same meaning. I will return to this point in my conclusions.

  13. 13.

    Recall that for any world w:

    • ans1(QH)(w) = ∩{p: p ∈ w ∧ p ∈ QH(w)} = {w: ∀p[p ∈ Kartt(QH)(w) → w∈ p}

  14. 14.

    This is so because in each one of these worlds {w: ∀p[p ∈ Kartt(QH)(w) → w ∈ p} is W, which is a tautology.

  15. 15.

    Here is a formal proof of this claim:

    For every world w,

    1. (i)

      ⟦student⟧w ⊆ ⟦person⟧w

    2. (ii)

      {p: ∃x [⟦student⟧w(x) =1 ∧ p = that x came to the party]}

      ⊆ {p: ∃x [⟦person⟧w(x)=1 ∧ p = that x came to the party]}

    3. (iii)

      ⟦which students were at the party⟧w ⊆ ⟦who was at the party⟧w

    4. (iv)

      Kartt(λw′.⟦which student was at the party⟧w ′)(w) ⊆ Kartt(λw′. ⟦who was at the party⟧w ′)(w)

    5. (v)

      ∩Kartt(λw′. ⟦who was at the party⟧w ′)(w))(w) ⊆

      ∩(Kartt(λw′. ⟦which students were at the party⟧w ′)(w))(w)

  16. 16.

    Heim (1994) observes that Karttunen’s analysis actually makes the correct prediction in the special case where some people were at the party but none of them are students. In this special case, due to the second condition in Karttunen’s semantics of know Q, Mary should know that of none of those who were at the party were students for (33) to be true. This amount of knowledge does not follow from (34).

  17. 17.

    In a theory like Groenendijk and Stokhof’s where questions are inherently strongly exhaustive, ans1 cannot be retrieved.

  18. 18.

    George (2013) argues that the above facts about surprise are not sufficient to prove the existence of a weakly exhaustive semantics of questions, suggesting instead that Heim’s weakly exhaustive judgments with surprise can be derived from a notion of ‘mention some’ answers; see George (2011) for additional discussion. The topic remains a matter of debate.

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Authors and Affiliations

  1. Department of Linguistics, Boğaziçi University, Bebek, Istanbul, Turkey

    Elena Guerzoni

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Correspondence to Elena Guerzoni .

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  1. Department of Translation and Language Sciences, Universitat Pompeu Fabra, Barcelona, Spain

    Louise McNally

  2. Department of Philosophy, Yale University, New Haven, CT, USA

    Zoltán Gendler Szabó

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Guerzoni, E. (2022). On Karttunen’s “The Syntax and Semantics of Questions”. In: McNally, L., Szabó, Z.G. (eds) A Reader's Guide to Classic Papers in Formal Semantics. Studies in Linguistics and Philosophy, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-030-85308-2_12

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