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Domain restriction: the problem of the variable location revisited

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Abstract

Two theories of implicit domain restriction have gained considerable prominence over the last two decades. According to von Fintel (Restrictions on quantifier domaines, Ph.D. thesis, University of Massachusetts at Amherst, 1994), quantifiers come with covert restrictors and, as a result of this, induce domain restriction; according to Stanley [in Gerhard and Peter (eds) Logical form and language, Clarendon Press, Oxford, 2002; Stanley and Szabó (Mind Lang 15(2–3):2192–2161, 2000)], by contrast, nouns, as opposed to quantifiers, come with covert restrictors. In this article, I do three things. First, I assess the arguments that have been given for and against these two accounts and show that none of them is conclusive. Second, I advance a novel empirical argument based on the observed pragmatic behaviour of bare nouns, an argument that falsifies Stanley’s theory while providing clear evidence in support of von Fintel’s (1994). Finally, I discuss the relevance of the bare noun data in the context of another important debate—namely, whether domain restriction is a local mechanism only, or whether it can also be achieved by global means.

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Notes

  1. To allow for binding, C is often assumed to have a more complex structure: the standard move is to say that C is composed of a functional variable f (of type 〈e,〈e,t〉〉) and an argumental variable x (of type e); see von Fintel (1994) and Stanley and Szabó, (2000).

  2. g(C) is a one-place predicate meaning, that is, the characteristic function of a set of entities. For ease of exposition, and unless it is necessary to do otherwise, I shall identify one-place predicates with sets of entities, rather than with the characteristic functions thereof.

  3. See also Westerståhl (1984) and Martí (2003).

  4. ‘We currently have a number of good arguments supporting conflicting conclusions about where in the structure domain restriction variables are introduced. Unless we can debunk one set of these arguments, the outlook for this type of approach is not very promising.’ (Schwarz, 2009, pp. 108–109)

  5. In order to derive Reading A via co-reference, S&S would need to make non-trivial semantic assumptions, e.g., claiming that nouns are of type e—see Lasersohn (2021) for a recent proposal—and/or positing some type-shifting mechanism. But, if such a route were to be taken, it is not clear to me that the resulting account could be called ‘natural’ (I guess that would depend on what the benchmark for naturalness is, as well as on the precise details of the account).

  6. An anonymous reviewer points out that S&S’s argument would make more sense if it was interpreted against the backdrop of Elbourne’s (2001, 2005) description-theoretic approach to e-type anaphora. This is only partly true. On Elbourne’s approach, pronouns are definite articles followed by an NP which is deleted under identity with a preceding NP: for example, in (4), if NRT were to be assumed, the LF of they would be the peopleC, and the NP would be deleted under identity with peopleC in the first sentence. Notice, however, that NRT has no clear advantage over QRT on this approach, at least not in connection with the derivation of Reading A; indeed, if QRT were to be assumed, the LF of they would be theC people and the NP would be deleted under identity with people in the first sentence.

  7. Following Nouwen (2020), by ‘e-type pronoun’ I mean a pronoun that (i) has a linguistic antecedent, (ii) is not bound by its antecedent in the sense that the pronoun occurs in the syntactic scope of its antecedent and its reference co-varies with the antecedent, and (iii) doesn’t refer to the same referent its antecedent refers to.

  8. Neale’s (1990, p. 266) rule (P5b). A quantifier ‘[Dx:Fx]’ is non-maximal iff there is some G for which ‘[Dx:Fx](Gx)’ is true but ‘[every x: Fx](Gx)’ is false. Hence, most is non-maximal.

  9. See, for instance, Heim (1999), Farkas and Kiss (2000), or Sharvit and Stateva (2002).

  10. According to (8), every gradable adjective meaning R is downward monotonic, in the sense that the following holds of R: ∀x,d,d′[[R(d)(x) = 1 ∧ d > d′] → R(d′)(x) = 1]. Hence, on this account, John is four feet tall entails John is three feet tall.

  11. This move, of course, raises a number of technical issues, which Heim (1999) is aware of (for example, she considers the possibility that the semantics of gradable adjectives and modified nominal expressions may be related by a type-shifting rule). These issues, however, go beyond the scope of this article.

  12. Heim (1999, p. 3) writes: ‘Following von Fintel (1994), we may localize the context-dependency of quantifiers like every in an extra argument, a phonetically unrealized predicate variable that appears next to the determiner at LF and receives a value from the context of utterance. Adapted to the case at hand, this suggests that -est likewise takes an additional argument.’

  13. In (9), I am providing the curried version of Heim’s entry.

  14. I follow the notational convention from Heim and Kratzer (1998), where λx : ψ . α is written for the function that maps x to α if ψ, and otherwise incurs a presupposition failure.

  15. For ease of explanation, I am here assuming that nice isn’t a gradable adjective (though, of course, it is).

  16. Any attempt to argue that, in (12)a, there is an unpronounced noun at LF will face a non-trivial issue: indeed, such an account appears to predict that (i)a can have the reading in (i)b (and it clearly cannot).

    (i)

    Context: Talking about three brothers…

     

    a. # The tall is nice.

    b. The tall (brother) is nice.

  17. Example (15)a is reported in Kratzer (2004); however, it makes the same point as Breheny’s (2003) example (21)b.

  18. For any world w, ⟦[fake [American philosopher]]⟧w,g = {x : x is either a fake American and real philosopher in w or an American and fake philosopher in w or a fake American and a fake philosopher in w}. Evidence that this the correct denotation of fake American philosopher comes from the fact that one can truly say ‘she is a fake American philosopher’ if/when she refers to (a) a real philosopher who pretends to from the US, (b) a US citizen who pretends to be a philosopher, or (c) a person who pretends to be from the US and also pretends to be a philosopher.

  19. Given the context stipulated, (17)a could be ‘made sense of’: that is, it could plausibly be repaired into something like (17)b. However, the fact that (17)a strikes one as an odd sentence indicates that doctor is not restricted to company doctor: if it was, then no oddness would be perceived, because (17)a would have (17)b as a reading, and (17)b isn’t odd in the stipulated context—cf. (15)a, for example, which reads naturally as ‘every [American [fake philosopher]] is from Idaho’.

  20. Breheny (2003), it should be noted, also discusses two examples—given as (ii) and (iii) below—that are claimed to involve multiple bound dependencies. On the basis of these examples, he argues that domain restriction below an intensional adjective is possible.

    (ii)

    Context: Though art dealers are entirely scrupulous, many famous artists have become paranoid due to the long-term effects of absinthe; in particular, they each imagine that the otherwise scrupulous dealers are out to ruin the market value of just their paintings.

     

    a. Every paranoid artist thinks no dealer will stop at selling every forged painting.

    b. Everyx paranoid artist thinks noy dealer will stop at selling everyz [[forged [painting by x]] coming into y’s possession].

    (iii)

    a. Every government makes allowance for the fact that no type of watermarking will prevent the circulation of every counterfeit note.

    b. Everyx government makes allowance for the fact that noy type of watermarking will prevent the circulation of everyz[counterfeit [note of currency of x marked by y]].

    The claim is that (ii)a and (iii)a have (ii)b and (iii)b as readings, respectively. I absolutely fail to get these readings and would need to see experimental evidence to be persuaded that such readings exist. (ii)a, to me, even in the context stipulated, means something like ‘everyx paranoid artist thinks noy dealer will stop at selling everyz [[forged painting] coming into y’s possession]’; indeed, (ii)a seems false in a world in which every paranoid artist thinks that the relevant dealers would willingly sell every fake copy of their works while refusing to sell fake copies of other artists’ works (if (ii)a had (ii)b as a reading, then (ii)a would be true in such a world). Likewise, (iii)a, as far as I can tell, reads as ‘everyx government makes allowance for the fact that noy type of watermarking will prevent the circulation of everyz [[counterfeit note] present in government x’s territory]’; indeed, (iii)a seems false if, say, the Polish government, while making allowance for the fact that watermarking on Złoty banknotes will fail to prevent the circulation of counterfeit Złotys, makes no allowance for the fact that watermarking on Euro banknotes will fail to prevent the circulation of counterfeit Euros within Poland (if (iii)a had the reading in (iii)b, then it would not be possible, on the basis of this information, to establish whether (iii)a is true or false).

  21. Consider, for example, the following passage from Stanley (2002, p. 372): ‘According to NRT, the intuitive restriction on quantificational determiners such as “every”, “some”, and “most” is not due, as may seem obvious, to a restriction on the quantificational expressions themselves, but rather to a restriction on the nominal complements of these determiners.’

  22. That is, to provide an answer to such a QUD, it’s enough to restrict one’s attention to those people who are American citizens: for example, Spanish, Swedish, or French citizens, insofar as they are not also American citizens, can be safely ignored.

  23. A technical note: to model the meaning of a ‘fake’-containing DP, an intensional semantics is needed: indeed, ‘fake’ is an intensional adjective: it takes the intension of its complement as argument (the type of ‘fake’ is 〈〈s,〈e,t〉〉,〈e,t〉〉). In the intensional semantics laid out in von Fintel and Heim (2011), the composition of the NRT LF would proceed as follows. ⟦philosopherC⟧w,g would be interpreted by intersecting ⟦philosopher⟧w,g (the extension of ‘philosopher’ in w) with ⟦C⟧w,g (the extension of C under g in w). Then, ⟦philosopherC⟧w,g would be composed with ⟦fake⟧w,g via Intensional Functional Application (i.e. If α is a branching node and {β, γ} the set of its daughters, then, for any world w and assignment g: if ⟦β⟧w,g is a function whose domain contains λw.⟦γ⟧w,g, then ⟦α⟧w,g = ⟦β⟧w,g(λw.⟦γ⟧w,g)). Hence, ⟦fake philosopherC⟧w,g = ⟦fake⟧w,g(λw.⟦philosopherC⟧w,g).

  24. The issue of whether bare nouns in generic uses support domain restriction remains unsettled. Examples have been reported showing that generic DPs cannot be domain-restricted (e.g. Krifka, 1987; Teichman, 2015), but there are also cases of (what looks like) generic DPs where domain restriction appears to be at work (e.g. Condoravdi, 1994). There is an additional problem: judgments about whether generic DPs can be domain-restricted are confounded by several factors, such as the well-known exception tolerance property of generics as well as the fact that these DPs appear to resist explicit restrictions to a time or place (Carlson 1977, 1982).

  25. I am only aware of some examples (not minimal pairs) reported in Arregui (2008), which suggest that indefinites without an overt determiner may fail to take restricted domains in the scope of negation. The minimal pairs presented here reveal that determinerless indefinites do not support domain restriction, irrespective of whether negation is present.

  26. The issue of how the existential force of (22)b, (23)b and (24)b should be derived is a highly contentious one—see Carlson (1999) for a survey of different approaches. If D is taken to be occupied by a silent existential determiner then, in the light of the data reported here, that determiner would have to be stipulated not to introduce a domain variable. There are, however, a host of proposals that derive the existential reading of bare nouns without positing something like a silent some; for instance, existential closure (e.g. Diesing, 1992), type-shifting (e.g. Chierchia, 1998), quantification over stages (Carlson, 1977), or default interpretation of an empty D (Longobardi, 1994).

  27. By ‘lurks behind the scenes’, I just mean that the probability of (28)a1’s unrestricted reading being the reading intended by the speaker is very low—given pragmatic considerations—but, quite possibly, not 0. One can in fact increase the pragmatic pressure against the unrestricted reading and, by so doing, improve the quality of the judgment. Consider (iv) below, for example. Here, (iv)a1’s unrestricted reading is irrelevant, just like (28)a1’s, but, in addition, is (contextually) tautological; hence, in (iv)a1, the probability of the unrestricted reading being the intended reading is bound to be even lower than in (28)a1. Unsurprisingly, (iv)a1-b and (iv)a2-b exhibit no contrast whatsoever (in terms of acceptability).

    (iv)

    Context: Every apple from the churchyard’s apple tree has been eaten. Pastor Hannah allows John to eat one or two apples a day, but he isn’t allowed to eat them all at once. John’s sister tells Pastor Hannah that John broke the rules and, in a fit of hunger, ate every single apple from the churchyard’s apple tree. John contests this accusation by exclaiming:

     

    John:

    a1. I didn’t eat every apple!

    John’s sister:

    b. That’s not true John! You did eat every apple from the churchyard’s apple tree.

     

    John:

    a2. I didn’t eat every apple from the churchyard’s apple tree!

    John’s sister:

    b. That’s not true John! You did eat every apple from the churchyard’s apple tree.

     

    John:

    a3. I didn’t eat every apple (in the world)!

    John’s sister:

    b. # That’s not true John! You did eat every apple from the churchyard’s apple tree.

  28. More formally, p is a partial answer to Q (where p is a proposition and Q a partition of C, the Context Set) iff p ∩ C ≠ ∅ and, furthermore, there is an X ⊂ Q such that p ∩ C ⊆ ⋃X (such that p contextually entails ⋃X) (cf. Groenendijk and Stokhof, 1990).

  29. Without going into much detail, it is not hard to see where these implicatures are coming from. Take (31), for example; when officer cadet Smith utters I see red lights, he knows that his utterance will have the effect of (massively) increasing the probability mass of the QUD’s YES-cell; if Smith didn’t believe that, in fact, the red lights that he sees are being flashed from unit 202, then, by uttering I see red lights, he would be misleading his audience (i.e. though I see red lights would be true, it would have the effect of making Smith’s audience believe something that he does not himself believe). On the assumption that speakers are cooperative (in the broadly Gricean sense) and, among other things, do not mislead their audiences, it must be the case that Smith believes (or at least thinks more likely than not) that the red lights that he sees are being flashed from unit 202.

  30. I thank an anonymous SuB24 reviewer for this example.

  31. See Williams (2015, ch. 5) for a recent discussion on verbs and implicit arguments.

  32. This approach is also known as the implicit strategy (Neale 1990) and the model theoretic approach (Stanley and Szabó, 2000).

  33. As von Fintel (1994, p. 29, ftn. 15) remarks, this is an approach with a venerable pedigree, which includes luminaries such as John Wallis, August de Morgan, and George Boole.

  34. It is worth noting that, on the global approach, restrictions, although they are not locally intertwined with the recursive semantics, are nonetheless predicted to affect truth-conditional content. Thus, examples such as (26) or (34)a cannot be regarded as involving global domain restriction.

  35. Adapted from Cooper (1996).

  36. Soames’s (1986) classic example (i.e. everyone is asleep and being monitored by a research assistant) makes essentially the same point as (39); see also Lewis (1973) and McCawley (1979).

  37. The proposals in Kratzer (2007) and Schwarz (2009, 2012) are couched in the framework of situation semantics (Barwise and Perry, 1983); in this framework, global restrictions come about due to the fact that, to paraphrase Kratzer (2007), ‘assertions are about particular actual situations, and that those situations can be smaller or bigger parts of the actual world’. For the point that I’m making here, it does not matter whether global restrictions are cashed out in terms of relativisation to a (contextually restricted) universe of discourse or in terms of relativisation to a (contextually provided) situation: either approach predicts that (40)b should have a reading that, as a matter of fact, doesn’t have.

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Acknowledgements

I am deeply indebted to Benjamin Spector and Manuel Križ, whose comments improved this article at all stages of its production. For generous feedback and suggestions, I am very grateful to Daniel Rothschild, Philippe Schlenker, Jennifer Saul, Angelika Kratzer, Jeremy Kuhn, Matthew Mandelkern, and the article’s anonymous reviewers. For helpful discussions, I thank Adam Przepiórkowski, Rosanna Keefe, Paul Egré, Salvador Mascarenhas, Milica Denić, Diego Tajer, Andrés Soria Ruiz, Dan Hoek, Émile Enguehard, and Amir Anvari. I have given talks based on this material at the IJN/LINGUAE seminar (2 May 2019, Paris), the New Work in Philosophy of Language seminar organised by Matthew Mandelkern (8 May 2019, Oxford), and SPE11 (20-22 September 2019, Warsaw). I am grateful to the participants at those events, especially to Manfred Krifka, Stephanie Solt, and Elena Herburger at SPE11 for comments and suggestions. All remaining errors are my own. The research leading to these results received funding from the European Research Council, ERC Grant Agreement N° 788077– Orisem (PI: Schlenker) and from ANR-19-CE28-0004 (ProbaSem). Research was conducted at the Département d’Etudes Cognitives, École Normale Supérieure - PSL Research University. The Département d’Etudes Cognitives is supported by grants ANR-17-EURE-0017 FrontCog and ANR-10-IDEX-0001-02 PSL.

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    Diego Feinmann

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Feinmann, D. Domain restriction: the problem of the variable location revisited. Linguist and Philos 45, 1197–1226 (2022). https://doi.org/10.1007/s10988-021-09328-9

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