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Enough clauses, (non)finiteness, and modality

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Abstract

Infinitives are known to encode covert modality in certain environments including infinitival relatives and questions. Beyond these environments, however, the precise distribution and interpretation of infinitival modality remains poorly understood. In that light, this paper investigates infinitive-embedding enough/too sentences like Pat is tall enough to be the thief or Lee is too old to drive. These sentences have a modal semantics whose compositional source is contested: on one approach, the infinitive encodes the modality, and on another approach, the enough/too morpheme itself is modal. To adjudicate this debate, I consider heretofore largely overlooked finite-clause-embedding enough sentences like Pat is tall enough that she might/must be the thief or Lee was fast enough that she won the race. They provide, I argue, novel support for the view that the modality is in the embedded clause (whether nonfinite or finite) and not in enough/too. I then compare the covert modality of nonfinite enough clauses to the covert modality of infinitival relatives, questions, and complements to attitude predicates and content nouns. I generalize that covert modality in nonfinite clauses never encodes epistemic necessity, and I tentatively hypothesize that this constraint reflects the marked status of nonfiniteness in the finite/nonfinite opposition.

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Notes

  1. See also Zhang (2018) for an approach that does not fit into this dichotomy so neatly. For Zhang, those enough/too sentences that enable implicative readings (i.e., readings in which the propositional content of the infinitive is entailed to be true) are biclausal and instantiate a cause-consequence relationship but are otherwise not necessarily modal at all, whereas those enough/too sentences that do not enable implicative readings are monoclausal and the infinitive contains a modal element, à la Meier (2003). Implicativity in enough/too sentences is revisited in Sect. 4.4 below.

  2. Some speakers I’ve consulted report finding the sentences in (6), in which enough embeds a finite necessity modal, to be somewhat odd. Possibly this is because they require extra contextual support to receive a sensible interpretation. For example, (6a) says, roughly, that Pat’s height meets a threshold that compels the conclusion that she is the thief. (Below we consider formalizations of these truth conditions.) Absent any context, this is unlikely to be true, because presumably there are many other individuals that are at least as tall as Pat. But suppose we’re in a context where we’ve narrowed down the potential thieves to just three individuals. Then, we reason that among these three individuals, only Pat is tall enough to have carried out the theft. (Perhaps, the stolen item was taken from a high shelf that only Pat could reach.) In that context, (6a) is true and appropriate.

  3. An anonymous reviewer points out that Meier’s (2000) dissertation, written in German, considers finite-clause-embedding genug ‘enough’ and zu ‘too’ sentences in German. See also fn. 15 below.

  4. As far as I can tell, so can be inserted between enough and that in all the sentences in (5)-(7) without affecting the acceptability or the truth conditions of those sentences. In what follows, I set aside these so-augmented variants, saving a full investigation of their properties for another occasion.

  5. It should also be noted that enough/too infinitives can have overt subjects, in which case the nonfinite complementizer for is obligatory, and the matrix subject typically binds a gap or overt pronoun somewhere in the embedded clause. An example is given in (9). It is also possible for a nonfinite enough/too clause to have both a (non-obligatorily controlled) PRO subject and a gap, as in (10).

    1. (i)

      This soup1 is cool enough [for me to eat \(\{\underline{\phantom{\quad}}_{1}/\text{it}_{1}\}\)].

    1. (ii)

      This table1 is light enough [PRO to lift \(\underline{\phantom{\quad}}_{1}\)].

    These fine points of variation in nonfinite enough/too clauses are orthogonal to the argumentation in this paper.

  6. Atomic semantic types used in this paper are: e (individuals), t (truth values), d (degrees), and s (possible worlds).

  7. An anonymous reviewer points out that these two approaches do not exhaust the hypothesis space. For example, it could be that the modality is not syntactically encoded at all but instead has a pragmatic source. The focus of this paper, however, is on the choice between the two predominant approaches in the literature. Furthermore, the modal clause approach—which I ultimately argue for—receives convergent support from the fact that covert infinitival modality is already well established in other environments, including infinitival relatives and questions.

  8. These informal paraphrases are a bit different when a negative polar adjective like short is involved. One of Meier’s (2003) aims is to develop an approach to enough/too sentences that works equally well for both positive polar adjectives like tall and old and negative polar adjectives like short and young. For the sake of concision, I set negative polar adjectives aside in this paper.

  9. A more sophisticated approach would have modals introduce not just one but two accessibility relations, one for the modal base and the other for the ordering source. (See Meier 2003, fn. 12.) Here, I follow Meier in working without ordering sources, though these could be added without affecting any of this paper’s crucial points.

  10. Unlike Meier (2003), I use generalized quantifier notation (see, e.g., Altshuler et al. 2019 and references therein) throughout this paper, following the format [Qu: ϕ](ψ), where Q is a quantifier, u is a variable, ϕ is the restriction, and ψ is the scope.

  11. max and min are functions from degree abstractions to the unique maximal or minimal degrees satisfying them, respectively. They can be characterized formally as in (15).

    1. (i)

      For any degree abstraction D:

      1. a.

        max(D) = ιd[D(d) ∧ ¬∃d′[D(d′) ∧ d′ > d]]

      2. b.

        min(D) = ιd[D(d) ∧ ¬∃d′[D(d′) ∧ d′ < d]]

  12. Here I focus specifically on von Stechow et al.’s (2004) version of the modal enough approach. Other versions include those found in Hacquard (2005) and Schwarzschild (2008). For arguments against Hacquard’s version and in favor of von Stechow et al.’s, see Nadathur (2019). For more on Schwarzschild’s (very different) version of the modal enough approach, see Sect. 3.2.2 below.

  13. von Stechow et al. assume that the accessibility relation and the infinitive combine in the syntax and are fed in as one argument of enough/too, whereas I treat the accessibility relation and the infinitive as two separate arguments of enough/too. This difference is inconsequential to this paper’s aims.

  14. In (42), the modal forms might’ve and could are employed not to allow for counterfactuality as in (38) above, but rather simply to maintain consistent past tense throughout.

  15. In earlier work, Meier (2000) (writing in German and about German data) also comes to the conclusion reached here that finiteness correlates with necessity and non-finiteness with possibility. I thank an anonymous reviewer for drawing my attention to this fact.

  16. Actually, Schwarzschild (2008) does not provide formal truth conditions for enough sentences, but rather only for too sentences. For Schwarzschild, Pat is too tall to be the thief has truth conditions along the lines of “There is some height such that because Pat is at least that height, it is not the case that Pat might be the thief.” Removing the bolded negation yields sensible Schwarzschild-style truth conditions for enough sentences, and so that is what I do in (56). It should also be noted that Schwarzschild’s approach employs existential quantification over what he calls ‘thresholds’ rather than over degrees. The choice between degrees and thresholds is orthogonal to the concerns of this paper.

  17. I say would because Schwarzschild does not actually give a compositional semantics for enough sentences (see fn. 16 above). But in his approach to too sentences, the possibility modality is encoded into too rather than too’s clausal complement.

  18. Cf. also Zhang (2018), who uses the concept of cause-consequence to account for actuality inferences in enough/too sentences. Zhang’s account, however, differs from the one entertained here in several ways. One difference is that for Zhang, the cause-consequence relations is a by-product of having a biclausal structure, whereas on the present account, it is encoded by the because operator which is built into the denotation of enough. Another salient difference is that for Zhang, only some enough/too sentences (those that have a biclausal structure) have a cause-consequence interpretation and thereby give rise to actuality inferences. On the present account, by contrast, all such sentences have a cause-consequence interpretation, although in some cases the consequence has a modal semantics, unlike the kinds of actuality inferences typically discussed in the literature.

  19. There is also a sense in which the second strategy is, as it stands, incomplete, because it relies on a meta-language operator because that is not formally defined. A reduction of because to more familiar theoretical terms, perhaps using possible worlds, might enable a more careful investigation of what is at stake in the choice between the two hypotheses.

  20. We briefly revisit this assumption in Sect. 3.4 below.

  21. von Stechow et al. (2004) might point to anankastic conditionals as independent evidence, because they develop an approach to such conditionals “with the buletic/deontic modal in the if-clause made semantically vacuous on the LF” (p. 1). See, however, Condoravdi and Lauer (2016), who argue against such an approach to anankastic conditionals and develop an alternative viable approach that avoids semantically vacuous modals.

  22. The denotation for so in (96) follows Meier’s (2003, p. 97) proposal that so and enough have identical denotations. One way in which this is oversimplified is that so gives rise to an entailment to the positive form of a gradable adjective, whereas enough does not, as brought out by the minimal pair in (95)-(96).

    1. (i)

      Kim is short, but at least she’s tall enough that she can reach this shelf.

    1. (ii)

      Kim is short, ??but at least she’s so tall that she can reach this shelf.

    For the purpose of the discussion at hand, however, we can set this difference aside.

  23. A more sophisticated approach might try to capitalize on the counterfactuality of too complements, and pursue the line that finite clauses are ruled out in counterfactual environments. However, even finite clauses with overtly counterfactual morphosyntax, like in (97), are ruled out in too complements, as seen in (98).

    1. (i)

      If [Pat were the thief], she would be shorter.

    1. (ii)

      *Pat is too tall [that she were the thief].

    In this connection, it is noteworthy that, unlike English, German zu ‘too’ allows finite complements, but those complements have to have irrealis marking (Meier 2000).

  24. This property of enough/too sentences may also be reflected cross-linguistically in one of the conclusions of Fortuin’s (2013) survey of excess and sufficiency constructions in 59 languages. According to Fortuin, “the concepts of excess and sufficiency are inherently associated with the concept of goal-directedness” (p. 31, emphasis added). See also Nelson (1980) for a similar conclusion, to the effect that enough and too sentences (whether truncated or not) always have a modal interpretation, and see Humberstone and Cappelen (2006) for critical discussion.

  25. Hackl and Nissenbaum (2012) also acknowledge that under very limited conditions, it is possible for nonfinite relative clauses to lack a modal semantics altogether. According to Bhatt (2006), this happens only with subject-gap infinitives and only when there is a superlative, an ordinal, or only present, as in (104).

    1. (i)

      the tallest/first/only student to arrive

      ≈ the tallest/first/only student who arrived

    I set these aside in what follows.

  26. Bhatt (1999, 2006) notes that under certain conditions, circumstantial readings seem to be possible, such as in the most salient interpretation of (108) above. Bhatt (2006, pp. 129-132) ultimately argues, however, that such examples should be assimilated to the deontic cases.

  27. It’s worth noting that there is an obvious parallel between this approach to the finite/nonfinite opposition and current theories of the indicative/subjunctive mood opposition that associate indicative mood with commitment (see Silk 2018, Portner and Rubinstein 2020 for two variants of this approach) or veridicality (see Giannakidou and Mari 2021 for a recent overview). A comprehensive picture will probably need to consider both infinitives and finite subjunctive clauses as two kinds of departures from the default setting associated with finite indicative clauses. But I will have to leave this to future work.

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Acknowledgements

For helpful comments on earlier drafts of this work, I would like to thank Prerna Nadathur, Linmin Zhang, two anonymous reviewers, and the NALS editorial team. Of course, all remaining errors are my own.

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    Thomas Grano

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Grano, T. Enough clauses, (non)finiteness, and modality. Nat Lang Semantics 30, 115–153 (2022). https://doi.org/10.1007/s11050-022-09190-w

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