Existential Bare Plurals and Quantifier Scope by Jake Nebel

The views and opinions expressed in this article are those of the author and do not necessarily reflect the views of Victory Briefs.

Jake Nebel is a PhD candidate in philosophy at New York University, executive director at Victory Briefs, and (starting fall 2019) assistant professor of philosophy at the University of Southern California.

Let’s start with some background. “Authoritarian regimes” is a bare plural: it’s a plural noun phrase without an explicit determiner (e.g., “five,” “some,” “all,” “the,” “most”). Bare plurals are typically used to express generic generalizations, as in “Ravens are black.” Unlike universally quantified statements, generics tolerate exceptions. For example, “Ravens are black” is true even though “All ravens are black” is false.

In addition to generic readings, bare plurals can also sometimes have existential readings, as if they were preceded by “some.” For example, “Ravens are outside” is true just in case there are some ravens—i.e., more than one—outside. Unlike existential statements, generic generalizations are not entailed by specific instances. For example, the generic “Ravens are white” is false even though some ravens are indeed white; white ravens are white not because they are ravens but because they have leucism.

For reasons I’ve given elsewhere, and which apply straightforwardly to this topic, I think “authoritarian regimes” is a generic bare plural, not an existential one. My reasons include (i) that it fails the upward-entailment test for existential bare plurals (the resolution doesn’t entail that the United States ought not provide military aid to governments, even though all authoritarian regimes are governments); (ii) that bare plurals denote kinds of things, not specific members of those kinds, and so get an existential reading only in very specific circumstances which don’t seem to obtain in this resolution; (iii) that generics are our default means of generalization, especially in moral contexts, so we should expect the resolution to be generic absent strong evidence to the contrary; and, most importantly, (iv) that we can simply tell that it’s generic by linguistic intuition, which is the primary source of data for linguistic theorizing.

The generic interpretation implies that many affirmative advocacies—those that specify particular authoritarian regimes to which the United States ought not provide military aid, leaving open the possibility of providing aid to all other authoritarian regimes—do not affirm the resolution, because generic generalizations are not entailed by specific instances.1 To affirm the resolution, regime-specific affirmatives require an existential interpretation of “authoritarian regimes,” which is incorrect. In this article, however, I want to suppose for the sake of argument that the existential interpretation is correct, and argue that regime-specific affirmatives—even those that specify more than one regime—still violate the existential interpretation. In the course of laying out the argument, we’ll learn about an idea of crucial importance to both philosophy and linguistics—the concept of quantifier scope—and, rather than finish my dissertation, I’d like to introduce debaters to that idea.

To introduce the concept of scope, consider the sentence,

  1. Every student read some book.

This sentence is ambiguous between two interpretations. On one interpretation, (1) says that there is some book b such that, for every student s, s read b. On this interpretation, the universal quantifier “every” is within the scope of the existential quantifier “some”; the existential quantifier has wider scope than the universal quantifier. This wide-scope interpretation of “some book” requires every student to have read the same book. On another interpretation, (1) says that, for every student s, there is some book b such that s read b. On this interpretation, the existential quantifier is within the scope of the universal quantifier; the existential quantifier has narrower scope than the universal quantifier. This narrow-scope interpretation of “some book” allows each student to have read a different book.

Let’s apply this distinction to the existential interpretation of “authoritarian regimes.” The question is: what is the scope of the allegedly existential “authoritarian regimes” with respect to “ought not”? If it takes narrow scope, the resolution would mean roughly the same thing as,

  1. It ought not be the case that there are authoritarian regimes to which the United States provides military aid.

On this reading, the affirmative has to argue that there ought to be no authoritarian regimes to which the U.S. provides aid. Not only does the narrow-scope reading not allow the affirmative to specify a particular set of authoritarian regimes; it requires the affirmative to advocate something with respect to all authoritarian regimes. This is even stronger than the generic reading! This happens, in short, because the negation of an existentially quantified statement (it’s not the case that some x is F) is the universal generalization of a negation (every x is not F—i.e., no x is F). Regime-specific affirmatives therefore violate the narrow-scope reading.

By contrast, on a wide-scope reading, the resolution would mean roughly the same thing as,

  1. There are authoritarian regimes such that it ought not be the case that the United States provides military aid to those regimes.

This convoluted claim is not exactly an attractive interpretation of the resolution. For one thing, there already are authoritarian regimes to which the United States doesn’t provide military aid, so the resolution surprisingly recommends a state of affairs that already obtains. But, more importantly, (3) is just obvious and uncontroversial. Who seriously denies that there are some authoritarian regimes to which the United States shouldn’t provide military aid? It is prima facie extremely unlikely that the intended or actual meaning of a debate resolution would be an obvious and uncontroversial proposition that recommends the status quo.

Unlikely, yet not impossible, you might say. But there’s a much bigger problem for the wide-scope existential reading: existential bare plurals just can’t take wide scope. It is independently and cross-linguistically established that existential bare plurals can only receive narrow scope readings; they do not give rise to scope ambiguities. Consider, for example,

  1. Every student read philosophy books.
  2. Sam did not read philosophy books.

In these sentences, the bare plural “philosophy books” is existential, not generic. We might therefore expect that, like “some book” in (1), it could take either narrow or wide scope with respect to the universal quantifier in (4) and the negation operator in (5). But it can’t. It can only take narrow scope. (4) says that, for every student, there are philosophy books that the student read (narrow scope), not that there are philosophy books such that every student read those books (wide scope); there is no reading of (4) that requires every student to have read the same books. And (5) says that it’s not the case that there are philosophy books that Sam read (narrow scope), not merely that there are philosophy books that Sam didn’t read (wide scope); there is no reading of (5) on which it’s true even if Sam has read all but two philosophy books ever written.

Here is one way to observe this constraint in the context of the resolution. Consider the sentence,

  1. The United States ought to provide military aid to authoritarian regimes and the United States ought not provide military aid to authoritarian regimes.

This sentence expresses a contradiction (or, at least, a hard moral dilemma in which the United States can’t help but do what it shouldn’t). But if “authoritarian regimes” is an existential bare plural that can take wide scope, then (6) should have a reading on which it means that some authoritarian regimes are such that the United States ought to give them military aid and that some (i.e., possibly different) authoritarian regimes are such that the United States ought not give them military aid—which is perfectly consistent, not contradictory. It has no such reading. This shows that, even if existential bare plurals could take wide scope in principle, and even if “authoritarian regimes” is an existential bare plural, it could not take wide scope in the context of the resolution.

We can now put the argument together. Affirmatives that restrict their advocacy to particular regimes require a wide-scope existential interpretation of “authoritarian regimes,” as in (3). But, even if such an interpretation were attractive, existential bare plurals can only receive narrow scope. On a narrow-scope existential reading, as in (2), the resolution would say that it shouldn’t be the case that there are authoritarian regimes to which the United States provides military aid—in other words, that the United States should provide military aid to no authoritarian regimes. This interpretation is even stronger than the generic interpretation, and is violated by affirmatives that restrict their advocacy to particular regimes. So regime-specific affirmatives do not even meet the existential interpretation of “authoritarian regimes.”

To affirm the resolution, proponents of regime-specific affirmatives must show (i) that the bare plural “authoritarian regimes,” as it occurs in the resolution, has an existential reading, (ii) that existential bare plurals can take wide scope, and (iii) that a wide-scope existential reading of this resolution is at all attractive, despite rendering the resolution obvious and uncontroversial. None of these claims seems to me very plausible, and I think it’s safe to conclude that not all of them are true.

But even if they are—even if “authoritarian regimes” can and should take a wide-scope existential reading—I suspect that what many proponents of regime-specific affirmatives really want is for single-regime affirmatives, which advocate that the United States not provide military aid to some one authoritarian regime, to affirm the resolution. Even on a wide-scope existential reading, though, single-regime advocacies do not affirm the resolution because existential bare plurals are still plurals: they require more than one witnessing instance. No matter how wonderful it would be to debate such affirmatives, allowing them is no advantage of the wide-scope existential reading. The resolution simply has no reading on which single-regime advocacies affirm the resolution. You can’t always get what you want.

  1. There’s a Leslie card that is sometimes read as an “I meet” against this violation, and sometimes as a counterinterpretation. This evidence is badly mistagged and misrepresented. The evidence makes the true observation that definite singulars—i.e., singular noun phrases using the definite article “the”—can be used to state generic generalizations (e.g., “The typewriter is obsolete,” or “The woolly mammoth went extinct in the early Holocene era”). This fact is somehow warped to conclude, absurdly, that generics can be affirmed by specifying particular instances. That’s quite a blatant non-sequitur, and indeed Leslie is explicit that generics are generalizations about kinds, not claims about particular members of those kinds.

    To be charitable, I can only speculate that those who don’t take themselves to be misrepresenting the Leslie card are either confused about what definite singulars are or are fallaciously reasoning as follows: (i) as Leslie observes, definite singulars can be used to express generics; so (ii) generics expressed using bare plurals can also be expressed using definite singulars; and (iii) sentences containing definite singulars are entailed by any witnessing instance; so (iv) generics expressed using bare plurals are entailed by any witnessing instance; therefore (v) if the resolution is a bare plural generic, it can be entailed by any witnessing instance. Of course, (i) is true, but (ii) doesn’t follow from (i) and is false: the resolution is a counterexample (try rephrasing it with “the authoritarian regime” without changing its meaning), and more generally Leslie has discussed several interesting differences between bare plural generics and their definite singular counterparts. More importantly, though, (iii) is false—in fact, inconsistent with (ii)—because generic definites are most certainly not entailed by the existence of a single instance; that’s part of what it is for them to be generic. Not even ordinary (nongeneric) definites are entailed by just any witnessing instance, because the definite article presupposes uniqueness: “the F is G” presupposes that there is just one contextually salient F, so on a nongeneric reading there couldn’t be more than one F for the affirmative to choose from. Finally, the falsity of (iv) should be obvious to anyone who has read Leslie’s article or any other introduction to generics that comments on the distinction between generics and existentially quantified statements. But the argument is self-defeating anyway, for if (iv) were true, the inference to (v) would be invalid: (iv) is a generic that would, if true, imply only that some generic (i.e., not necessarily the resolution) can be entailed by a single instance.

    Another widely misused card from Leslie observes that there’s no obvious connection between genericity and frequency, since some generics seem true even though only a small minority of their instances obtain (e.g., “Mosquitos carry malaria”). Some claim that these these “striking property” generics are false overgeneralizations, but suppose we share Leslie’s view on this issue (as I’m inclined to do). What would need to be shown for this to support the counterinterpretation or “I meet” is that (i) the resolution is (or is relevantly like) a striking property generic and that (ii) any striking property generic can be affirmed by a single instance. I know of no reason to believe (i), and (ii) is clearly false; in fact, Leslie insists that genericity is distinct from all of the standard quantifiers, including those—e.g., “at least one”—that can be affirmed by a single instance.

    If you continue to think that these (or any other) cards support an “I meet” or counterinterpretation, please say so in the comments section below and I’ll try to work through them with you.


  • Jonas
    • Jake Nebel

      Jonas, do you think that single-regime affirmatives would be topical even if the resolution were explicitly (2)—”It ought not be the case that there are authoritarian regimes to which the United States provides military aid”?

      • Jonas

        I think that complicates things. Because the question is no longer whether an agent should take a course of action about a regime. The 2nd issue is that “the case” is something you have added which observes one state of affairs. The 3rd is the awkward phrasing, it’s not a question of what the US should do, it’s a question of whether or not those regimes should even exist. I think a reading of the topic in which it’s consistent with a true understanding of topicality would be the authoritarian regimes to which the US provides military aid are the caselist and the Affirmative can still affirm an instance of that resolution. I think it necessitates a little more work on the behalf of the reader, but I don’t think it’s impossible. I also think even if anything above is suspect, that worrding of the resolution is in no way the same as the current one. Obviously if “the case” means the existence of NO AID to ANY authoritarian regimes, it would mean that there is only one aff. I think it’s also the word “are” which seems to imply existence that has complicated this renewed interpretation.

        • Jake Nebel

          Let me try a simpler case. Suppose the resolution were explicitly, “The United States ought to provide military aid to no/zero authoritarian regimes.” Or even “The United States ought to provide military aid to none of the following regimes: [list of all authoritarian regimes].” Is your view that, even on those resolutions, single-regime affirmatives would be topical?

        • Jonas

          I don’t. Like on the “any” constitutionally protected free speech topic. If it were no auth. Regimes then single regimes would not be T.

        • Jake Nebel

          Oh, okay. But my point in the article is that, on an existential interpretation of “authoritarian regimes,” the actual resolution means pretty much the same thing as the “no/zero” formulation.

  • Jacob Nails

    On a very tangential note, I noticed you still seem to prefer interpreting ‘ought’ as describing desirable states of affairs, e.g. in “It ought not be the case that there are authoritarian regimes to which the United States provides military aid.”

    What would you then say is wrong with an affirmative that merely defends the claim that authoritarian regimes ought not exist? That would seem to entail the truth of the resolution as you’ve worded it in the quote above (and equally so, I think, on the generic reading).

    • Jake Nebel

      Thanks Jacob—that’s complicated. A few things.

      Although I take “ought” to always express a propositional operator (“it ought to be the case that p”), I don’t think this forces a desirability reading in all cases. For example, on the view that’s probably closest to linguistic orthodoxy, “ought” and other modals like “can” and “must” always express propositional operators but are sensitive to at least two contextual parameters: first, a set of accessible worlds (the “modal base”) and, second, a way of ordering those worlds (the “ordering source”) with respect to proximity to some ideal. On this semantics, “It ought to be the case that p” is true relative to a modal base and ordering source just in case, most of the p-worlds in the modal base are ranked higher than the not-p worlds, or most of the top-ranked worlds are p-worlds, or something like that (a few different possibilities here in the literature).

      I take it that, on the most natural reading of the resolution, the ordering source is the set of the U.S.’s obligations. So, very roughly, the resolution is true just in case, in most of the accessible worlds in which the U.S. does not provide military aid to authoritarian regimes, the U.S. comes closer to satisfying its obligations than it does in the worlds where it does provide military aid to authoritarian regimes. That’s just a long way of saying that you can still get an obligation reading despite taking the resolution to have something like the logical form I’ve assigned it.

      What stops the affirmative from arguing that, in worlds in which authoritarian regimes don’t exist, the U.S. comes closer to satisfying its obligations than in worlds where they do exist? My view is that such worlds are just not in the resolution’s modal base. Context excludes them from consideration, just as it excludes from consideration worlds in which the U.S. doesn’t exist, or in which the U.S. is the only country that exists, or in which there are no militaries: the resolution, in some sense, takes their existence for granted.

      So, in short, even though “There are no authoritarian regimes” entails “There are no authoritarian regimes to which the U.S. provides military aid,” that doesn’t mean “There ought to be no authoritarian regimes” entails “There ought to be no authoritarian regimes to which the U.S. provides military aid,” because the latter “ought” but not the former holds fixed the existence of authoritarian regimes (at least, on the relevant reading).

      Two other things to note:

      There seems to be independent reason to deny that “It ought to be the case that p” necessarily implies “It ought to be the case that q” even if p entails q—I take that to be the moral of Professor Procrastinate-style cases.
      I’m not sure you’re right that the same issue arises for the generic interpretation, because generic bare plurals arguably don’t presuppose existence (e.g., “Trespassers will be prosecuted” doesn’t presuppose that there are or even will be trespassers). My sense is that the issues here are subtle; there’s a book by Yael Greenberg which talks a lot about the existence presuppositions of different kinds of generics.

      • Jacob Nails

        That all makes sense to me. It did bring to mind one more question. Suppose one side proves that there are in fact no authoritarian regimes. Would you take this to negate the existential reading?

        Intuitively, I’d think “It’s not the case that the US ought to provide military aid to Wakanda” is true, as Wakanda doesn’t exist, but “The US ought not provide military aid to Wakanda” is false. I’m not that familiar with the semantics of “ought,” but I’m guessing that it would go something like this: there is no obligation to bring about p rather than q unless both p and q are within the modal base. Maybe it hinges on the different possible interpretations you referenced, but I’d think this scenario negates (assuming ‘regimes’ weren’t read generically, of course, per note #2).

        And I did leave a comment of actual relevance to the topic at hand, I promise! Alas, it seems to have been caught up in the spam filter.

        • Jake Nebel

          Well, I would take the nonexistence of authoritarian regimes to negate the wide-scope existential reading, but I’m not sure about the narrow-scope reading. One thought about your Wakanda example is that one might take the existence of Wakanda to be a presupposition of the resolution and think that presupposition failure results not in falsity but in lack of truth value. (Sorry about the spam filter! Should be cleared now—along with a bunch of other comments that were apparently stuck in it for some reason.)

  • Ujjwal Krishnamurthi

    Jacob Nails approves–Saratoga

    • Jacob Nails

      Thanks, Ujjwal.

      I had students ask (paraphrasing) “Why is example #1 applicable? The resolution doesn’t have the word ‘every’, so it doesn’t create the same ambiguity. And why not compare ‘regimes’ to ‘United States’? After all, that’s the subject, like ‘every book’ was in the previous example.” This seemed like a reasonable question worth clarifying.

      It’s not that you can pick any two terms in the topic and compare their scope, and it’s not that you compare the scope of nouns in the subject to those in the predicate, which were the two readings that debaters I discussed this article with seemed to settle on.

      Quantified nouns can create scope ambiguities when alongside other operators. One example is having multiple quantifiers in the same sentence, as with ‘every’ and ‘some’ in “Every student read some book.” Another example is a quantifier plus negation, as with the resolutional example of ‘ought not’ and the existential reading of ‘regimes.’ There’s a few others, too, such as quantified nouns plus adverbs (consider the two meanings of “someone always initiates theory”) or conjunctions (“There are 5 aff and neg speeches” could lead a layperson to think LD has 10 speeches).

      The reason that the ambiguity in the topic is between ‘ought not’ and ‘regimes’ rather than some other noun phrase and ‘regimes’ is because it’s a slightly different case of ambiguity than the preceding example. It’s a question of whether the quantifier scopes over negation, rather than which of two quantifiers scopes over the other (not that this affects the applicability of the example; the same principles apply).

      Here’s a few examples for any other students also trying to understand how the point about scope ambiguities from the two-quantifiers example extends to negations:

      All students have not read the assigned book.
      I have not read thousands of books.

      The first sentence has a subject quantifier (‘all’) plus negation, and the latter has an object quantifier (‘thousands’) plus negation. Both have two possible readings depending on whether the quantifier scopes over negation. The first sentence could mean “No student read the book” or “At least one student did not read the book. The second sentence could mean “There are thousands of books that I have not read” or “I have read 999 or fewer books.” In each case, the first example I listed is the one where the quantifier has wider scope than the negation.

      This hopefully also clear up an additional terminological confusion that some debaters have had. I’ve heard students referring to the “wide scope reading of the resolution.” This doesn’t doesn’t make sense on its own as scope here isn’t a property of the sentence; it’s a property of the specific operator. When you see phrases in this article like “on a wide-scope reading,” you should interpret that as “on a wide-scope reading of the existentially quantified noun phrase (‘authoritarian regimes’)” or even more precisely as “on a reading in which the quantifier is wider in scope than the negation.” One could equally choose to refer to the sentences as ‘wide scope negation’ and ‘narrow scope negation’, and then ‘wide scope’ and ‘narrow scope’ would correspond to the opposite sentences from the ones labeled as such in this article, as the wide scope negation corresponds to the narrow scope quantifier, and vice versa.

      Having judged dozens of these T – Bare Plurals debates, I think I can safely predict that this article will be cited in plenty of debate rounds, including many in which it does not apply, so I’ll leave one last note to posterity: if you’re reading this article in Summer 2019 or later, the brunt of it probably isn’t relevant to whatever the current resolution is. The first 3.5 paragraphs or so may very well still be useful, as generic bare plurals crop up in LD resolutions all the time, but the last topic where the main thrust of this article would have been relevant was JanFeb ’10 (“Resolved: Economic sanctions ought not be used to achieve foreign policy objectives”). There have been some edge cases in topics since then, but all so contrived and hypothetical as to not be worth listing. Sorry, but you’ll have to update your “A2: Bare Plurals = Existentials” blocks again once this topic ends.

  • Joshua George

    Yes time for Nebel 19