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Splitting situations

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Abstract

Szabó (Philos Rev 120(2):247–283, 2011) and Santorio (Philos Stud 164(1):41–59, 2013) have revived the case for Fodor’s (The linguistic description of opaque contexts, Ph.D. thesis, Massachusetts Institute of Technology, 1970) specific yet opaque readings of determiner phrases in intensional constructions. Szabó claims that the existence of such readings gives reason to abandon standard theories of movement. Santorio claims that such readings imply that a quantification analysis of indefinites is false. I’m not so sure. To make my case, I supply a situation semantics for these readings that both respects standard theories of movement and a quantificational analysis of indefinites.

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Notes

  1. Bad scope joke: Every five minutes a child is saved from drowning. Swim lessons would help the poor thing.

  2. I put aside existentials because I take Francez (2018) to convincingly show that split readings of existentials (what Francez calls summative readings) have idiosyncratic features and so require an idiosyncratic treatment.

  3. A situation “pronoun” is simply a variable over situations in the object language.

  4. For more encompassing overviews of situation semantics with situation pronouns, see Schwarz (2012), Elbourne (2013).

  5. Quine (1956) is often cited as the first to formalize this “traditional” theory of the relationship between scope and opacity.

  6. This example is inspired by one found in von Fintel and Heim (2011).

  7. What’s narrow is the scope of the determiner phrase with respect to the intensional expression. What’s transparent is the interpretation of the noun phrase restrictor.

  8. Tradition has other problems. May (1977) observed that finite clauses seem to be scope islands and so quantificational noun phrases cannot move outside of these clauses. Thus, tradition has troubles getting the de re reading of (8). Also, see Elbourne (2013) for situation theoretic discussion of problems for tradition first brought to light by Bäuerle (1983).

  9. I follow the convention of not relativizing denotations to variable assignments and contexts unless it matters for the purposes at hand.

  10. I assume in what follows that for any topic situation s and any resource situation \(s_r\), there is a situation \(s'\) such that \(s\leqslant s'\) and \(s_r \leqslant s'\). This assumption basically amounts to the claim that a topic situation and a resource situation are always part of the same world.

  11. See Kratzer (2016) for an overview of the distinction between topic and resource situations and their relation to domain restriction.

  12. I take this rule from Schwarz (2012), who takes it from Büring (2004).

  13. It should, however, be noted that Schwager (2009) argues that not all narrow-transparent readings can be accounted for by appealing to a situation/world pronoun in the syntax of determiner phrases. Since my interest is primarily in split readings rather narrow-transparent readings and, so far as I can see, Schwager’s arguments do not extend to split readings, I will put this issue aside.

  14. This is how I have been using the expressions all along.

  15. For clarity, let me recast the above points in terms context assigning a value to the situation pronoun ‘s\(_3\)’ in (4a\(^{split }\)) rather than in terms of the features of the given resource situation. In these terms, context assigns a value to ‘s\(_3\)’ , and in doing so, restricts the domain of quantification. Some contexts, like ones where (4a) is followed with (4b), will restrict the domain so that (21) requires that there be a specific runner that Mirah believes will win for the split reading to be true (à la Schwarzschild, 2002). Others may not.

  16. See the Appendix for a little more on guises and the two-pronoun view.

  17. One detail should be mentioned since otherwise it might be hard to see how the truth conditions are derived. Szabó introduces a new composition rule to overcome what would otherwise be type mismatches when a trace combines with the NP that stays behind: e.g., [t\(_1\) [runner from ND s\(_3\)]]. Here is the rule:

    figure ag

  18. I take for granted that the two main accounts of covert domain restriction (via syntax) are the domain variable view and the situation pronoun view (assumed in this paper). Just as the situation pronoun view has the determiner view and the predicate view, the domain variable approach has the determiner view, where the domain variable is a sister of the determiner (von Fintel, 1994), and the predicate view, where the domain variable is a sister of the nominal restrictor (Stanley and Gendler Szabó, 2000; Stanley, 2002). So, one might wonder whether a hybrid of the situation pronoun predicate view and domain variable determiner view can get around the above problem. For example, perhaps an LF along the following lines would suffice if the domain variable c was assigned a value that restricted the extension of thing in the appropriate way.

    (i):

    [[every c] thing]\(\lambda _1\)[Victor believes \(\varSigma _3\)[that [t\(_1\) [runner from North Dakota s\(_3\)]] will finish]]

    Perhaps this could work. But I’m not interested in such a view. It’s just a variant of the two-pronoun view and why bother with such a variant within a situation pronoun framework? Schwarz (2011) puts the point nicely:

    • Situation semantics is motivated by its capacity for accounting for various phenomena in natural language that are independent of domain restriction...we have no choice but to worry about what situations expressions are interpreted in, and once we do so, we better make sure that our theory is compatible with empirical facts about domain restriction. While it is inevitable for the partiality of situations to give rise to domain restriction effects, however, it is not certain from the outset that all such effects are due to situations. But working in a situation semantics, the general research strategy should be to explore exactly what domain restriction effects we can capture with the independently motivated mechanisms of our semantic theory before introducing any additional machinery. (pp. 18–19)

  19. The lexical entry would have to be different than it is in (10).

  20. I’m putting aside the possibility of type-shifting.

  21. So, there are no runners from North Dakota in the race and Jude believes that there were more runners than the pictures showed.

  22. Once again, I am making some simplifying assumptions; one of which is that ‘x doubts that p’ is to be interpreted along the lines of ‘x believes \(\lnot p\)’.

  23. Thanks to Christopher Tancredi for pressing me on the problems of impossibility and offering this example to clearly illustrate the problem.

  24. This example is from Keshet (2010).

  25. I thank an anonymous reviewer for bringing these issues to light.

  26. See Charlow and Sharvit (2014, p. 7). But to briefly illustrate why such a view is a standard view, let’s modify our earlier example of the narrow-transparent reading of Willa believes a friend of Maeva’s will win. Change the scenario so that when Willa looks over the contestants she instead says “Every one of those three over there will finish” and I, knowing that the three are the only friends of Maeva’s in the race, turn in your direction and say “Willa believes that every friend of Maeva’s will finish.” In such a case, there seems to be no difference between de re and narrow-transparent readings of what I said. And this is what the determiner view, for example, predicts. Either reading is true of a topic situation s iff every situation \(s'\) compatible with what Willa’s believes in s is such that every friend of Maeva’s in \(s_r\) finishes in \(s'\).

  27. The relevant split reading is the one that has the resource situation containing the contestants in the race.

  28. I thank an anonymous reviewer for bringing these issues to light.

  29. My earlier speculation that we treat the optical illusion as generating some kind of thing doesn’t seem to help explain the lack of a true de re reading of (32a) in such scenarios. Suppose the optical illusion generates some kind of thing. That thing is not a boy. So I see no hope for explaining the lack of a true de re reading on the grounds that the optical illusion generates a thing x such that x is a boy and Jude thinks that x walked.

  30. I thank Paul Elbourne for bringing this apparent problem to light.

  31. I should note that the two-pronoun view doesn’t need this general principle to explain what is wrong with contradictory sentences like “A philosopher who isn’t great is great” or “A pen that isn’t red is red.” In such sentences, both the topic situation and resource situation need to be “present” situations and if any “present” situation s is one where x isn’t F in s, then there is no “present” situation \(s'\) where x is F in \(s'\).

  32. Thanks to Christopher Tancredi for calling attention to the argument that follows.

  33. Importantly, he believes that no runner from ND will finish should be given a split reading here.

  34. Thanks to Christopher Tancredi for pressing me on the issue of negated belief ascriptions and suggesting quantification over topic situations as a plausible solution to the problem.

  35. Charlow and Sharvit (2014) suggest that believe can induce universal quantification over guises, especially in downward entailing environments. For the proposal at hand, the universal quantification would be over topic situations and the upshot would be that Betty’s utterance of “Victor believes that no runner from ND will finish” is true, on its split reading, iff every topic situation s (among the salient topic situations) is such that for every situation \(s'\) compatible with what Victor believes in s, no x in \(s_r\) is a runner from ND in \(s'\) who will finish in \(s'\). Given these truth conditions, Betty said something false. But I have the intuition that Betty said something true. So, I stick with existential approach in this example.

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Acknowledgements

Thanks to Paul Elbourne, Christopher Tancredi, and anonymous reviewers for comments that greatly improved this paper. Special thanks to Zoltán Szabó for getting it all started.

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  1. Department of Philosophy, Franklin and Marshall College, Lancaster, PA, 17601, USA

    Nicky Kroll

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Appendix

Appendix

Earlier in the paper, I expressed ambivalence about whether the two-pronoun view needs to be supplemented with guises or counterparts to account for split readings. But maybe I shouldn’t be so iffy. To see why, let’s modify the original Victor scenario so that he believes the pictures showed six different runners.Footnote 32 With this modification, there appears to be a problem for the two-pronoun view without guises. Recall that without guises, the split reading of (1) is assigned the following structure and denotation.

figure au

But in this modified scenario, there is no x such that Victor believes x is both from ND and will finish. Thus, it appears that the two-pronoun view predicts that the split reading of (1) is false in this scenario. This is problematic because it seems like the split reading of (1) remains true in such a scenario. Or so the worry goes.

The first thing to say is that it’s not entirely felicitous to utter (1), intending the split reading, when it is relevant to the topic situation that Victor believes that the pictures showed six different runners.

Suppose the “six different runners” belief were relevant to the topic situation. Then if Alf were to show Betty the pictures Victor picked out after uttering (1), Betty could easily say: “I don’t think so. He believes each picture picks out a different person and so actually he believes no runner from ND will finish.”Footnote 33 So, there’s reason to resist the split reading of (1) when it’s on topic that Victor believes that the pictures showed six different runners.

The issue seems to be that Victor has a few ways of thinking about each of a, c, and e. Under one way, they are each xs such that Victor thinks x will finish. Under another, they are each xs such that Victor thinks x is from ND. Under yet another, they are each xs such that Victor thinks x is from ND and so won’t finish as x is distinct from any runner in the “will finish” pile.

Guises provide one way of capturing Victor’s different ways of thinking about a, c, and e. Topic situations provide another.

Let \(s_1\) be a topic situation such that the beliefs relevant for determining what is compatible with what Victor believes in \(s_1\) are Victor’s de re beliefs about a, c, and e that each are xs such that Victor thinks x will finish and each are xs such that Victor thinks x is from ND. \(s_1\) might be “part of” a scenario in which Victor believes the pictures showed six different runners. But that belief plays no role in determining the situations compatible with what Victor believes in \(s_1\). It isn’t relevant. Let \(s_2\) be a topic situation where that belief is relevant. In \(s_2\), Victor’s de re beliefs about a, c, and e that each are xs such that x is from ND and so won’t finish as x is distinct from any runner in the “will finish” pile are the beliefs relevant for determining what is compatible with at Victor believes in \(s_2\).

With \(s_1\) and \(s_2\) in hand, the two-pronoun view without guises can account for the back-and-forth between Alf and Betty as a change in topic situation. When Alf utters (1), the topic situation is \(s_1\) and so the “six different runners” belief isn’t relevant to Alf’s assertion. When Betty responds, the topic situation changes to \(s_2\) and the “six different runners” belief is now relevant. This accounts for the intuition that Alf said something true and accounts for why it seems like Betty says something true too. In short, at least some of the work done by guises can be mimicked by having only certain de re beliefs of a subject play a role in determining what is compatible with what the subject believes in the topic situation.

But, one might worry, if a topic situation need not include all of the beliefs of a subject in the situation, then something needs to said about negated belief ascriptions. Go back to \(s_1\). The “six different runners” belief isn’t relevant. So, it seems to follow that (34) is true (de dicto) with respect to \(s_1\).

figure av

But it also seems that it would be infelicitous for Alf to assert (34) despite context offering \(s_1\) as a salient topic situation.

One thing to say in response is that to ignore something is not to treat it as non-existent. Yes, (34) is true in \(s_1\) because Alf is ignoring Victor’s belief that the pictures show distinct people. But Alf shouldn’t assert (34) because that would treat the belief as non-existent. Here’s a somewhat parallel case. I can know full well that a towel has some moisture but still truly say “The towel is dry.” I can properly ignore the moisture, given my communicative intentions. But I can’t follow “The towel is dry” with “There is no moisture in the towel.” That would be to treat what I am ignoring as not existing.

One might want a more explicit statement and justification of the pragmatic principle “To ignore is not to deny.” I have neither. So, let’s try another approach.

In Charlow and Sharvit (2014), belief ascriptions involve quantification over guises. Since we are using topic situations to mimic guises, perhaps we can avoid the problem posed by (34) by appealing to quantification over topic situations. Perhaps context makes salient a set of topic situations and the semantics for belief ascriptions involves existential generalization over the salient topic situations. If so, we could yield the following denotation for (34).Footnote 34

figure aw

If so, then (34) would be false even in a context with \(s_1\) as a salient topic situation. We would then have a straightforward explanation of why Alf shouldn’t utter (34).

Note that this makes the apparent disagreement between Alf and Betty no disagreement at all. There is a salient topic situation, \(s_1\), which makes Alf’s utterance of (1) true (on its split reading). There is also a salient topic situation, \(s_2\), which makes Betty’s utterance of “Victor believes no runner from ND will finish” true (on its split reading). So, within the same context, both are speaking truly.Footnote 35

I’m not sure if this is the right result. However, it does show how quantification over topic situations can mimic quantification over guises, at least with respect to split readings.

But now a number of questions arise about the how context makes salient a set of topic situations and how to best understand quantification over topic situations. Such questions, though, take us too far off topic. So, to the extent the issues raised in this appendix can be solved by supplementing the two-pronoun view with an already worked out guise semantics along the lines of Charlow and Sharvit (2014), I’m more than happy to do so.

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Kroll, N. Splitting situations. Linguist and Philos 46, 1051–1074 (2023). https://doi.org/10.1007/s10988-023-09380-7

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