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September 11th, 2009

Embedded Quantifier Domain Restriction

Blome-Tillmann (PDF) also aims to counter an objection Jason Stanley raises to Lewisian contextualism. The objection turns on part of the picture of how so-called ‘quantifier domain restriction’ works that Jason worked out with Zoltán Szabó. Often when we say All Fs are Gs, we really mean All C Fs are Gs, where C is a contextually specified property. So when I say Every student passed, that utterance might express the proposition that Every student in my class passed.

Now there’s a question about what happens when sentences like All Fs are Gs are embedded in various contexts. Quantifier embeddings tend to allow for certain kinds of ambiguity. For instance, when we have a sentence like If p were true, all Fs would be G, that could express either of the following two propositions. (We’re ignoring context sensitivity for now, but we’ll return to it in a second.)

We naturally interpret (1) the first way, and (2) the second way.

(1) If I had won the last Presidential election, everyone who voted for me would regret it by now.
(2) If Hilary Clinton had been the Democratic nominee, everyone who voted for Barack Obama would have voted for her.

Given this, you might expect that we could get a similar ambiguity with C. That is, when you have a quantifier that’s tacitly restricted by C, you might expect that you could interpret a sentence like If p were true, all Fs would be G in either of these two ways. (In each of these interpretations, I’ve left F ambiguous; so these are just partial disambiguations.)

Surprisingly, you can’t get the second of these readings. That’s something Jason and Zoltán argue for, and that Jason also argues for in Knowledge and Practical Interests. He also argues that to complete a contextualist explanation of sceptical intuitions, you need the second of these readings.

Blome-Tillmann accepts the second of these premises, i.e. that the contextualist needs both kinds of readings, but thinks the first premise is false, i.e. he thinks both readings are available. He thinks he has examples that show you can get the kind of reading Jason denies is possible. But I don’t think his examples show any such thing. Here are the examples he gives.

(5) If there were no philosophers, then the philosophers doing research in the field of applied ethics would be missed most painfully by the public.
(6) If there were no beer, everybody drinking beer on a regular basis would be much healthier.
(7) If I suddenly were the only person alive, I would miss the Frege scholars most.

These are all sentences of (more or less) the form If p were true, all Fs would be G, and they should all be interpreted a la our disambiguation above. That is, they should be interpreted as quantifying over actual _F_s, not things that would be F if p were true. But the existence of such sentences is completely irrelevant to the issue Jason is raising. The question isn’t whether there is an ambiguity in F, it is whether there is an ambiguity in C. And nothing Blome-Tillmann raises suggests Jason’s claim that there is no ambiguity in that position is wrong. So I don’t think his defence of the contextualist account of embedded knowledge ascriptions works.

I suspect the situation for the contextualist is actually a little worse than the above discussion suggests. I think (though I’m not sure I’ve got the dialectic right at this point) that the contextualist needs a reading of If p were true, all Fs would be G where it means:

The reason I think the contextualist needs that is that the contextualist, or at least the contextualist that Blome-Tillmann is defending analyses S knows that p as Every ~p possibility is ruled out by S’s evidence, and then insists that there is a contextual domain restriction on this, so it means something like Every ~p possibility (that I’m not properly ignoring) is ruled out by S’s evidence. They also want to accept that in a context where:

then (3) is still intutively false since we aren’t actually ignoring Cartesian doubts.

(3) If I were to look in the fridge and ignore Cartesian doubts, then I’d know there is beer in the fridge.

But the only way to get that to come out false, and false for the right reasons, is to fix on our actual quantifier domain restriction, but look at worlds that would be ruled out with the counterfactually available evidence. And I don’t see any reason to think that’s a possible disambiguation of embedded quantifiers.

Posted by Brian Weatherson in Uncategorized

8 Comments »

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8 Responses to “Embedded Quantifier Domain Restriction”

  1. Michael Kremer says:

    How about this?

    If Jim and his buddies had come to the party, all the beer would be gone by now.

    Let C be the property of being beer provided for the party (by the party givers, say).

    I think this can be read in the way Jason and Stanley deny is possible, that is:

    If Jim and his buddies had come to the party, all the beer (which was actually provided) would be gone by now.

    Maybe I can strengthen the case for this as follows:

    If Jim and his buddies had been at the party, all the beer would be gone by now. Therefore, we’d have had to send someone out to get more beer.

    (That’s supposed to make clear that the beer that would be gone is the beer actually provided, not the beer that would have been provided in case Jim and his buddies had showed up.)

  2. Michael Kremer says:

    I see a possible problem with the case given by myself above. The problem is that it might be held that C should be being beer initially provided for the party, and that this would be the same whether Jim and his buddies showed up or not.

    Here is another case. Consider the following two sentences (C here is the property of being a student enrolled in my class):

    (*) If I had fewer students, every student would do an in class presentation. (this does not admit of the disputed reading)

    (**) If I had more class sessions, everyone would do an in class presentation. (this seems to admit the disputed reading — but it might be replied that there is no difference between the two readings, because my having more class sessions would not affect the number of students).

    But I am not so sure about this. Perhaps if I had more class sessions, since this would be known in advance to the students signing up for the class, a different group of students would sign up. The point of (**) is that if I had more class sessions, I could assign a presentation to each of the students actually enrolled in the class.

  3. Michael Kremer says:

    Maybe (*) should be:

    If I had fewer students, everyone would do an in class presentation.

    Sorry for the multiple posts!

  4. Brian Weatherson says:

    Michael,

    I agree with the worry in post 2 about post 1. It isn’t clear just what the value of C is in the original case. It doesn’t seem completely ad hoc to say that it is, as you say, “available at the start of the party”, or “provided by party goers on arrival”. It would, after all, be odd to say this.

    • If Joe and his buddies had come to the party, all the beer would be gone, and we’d have to drink the beer Joe brought.

    Whereas this seems much better.

    • If Joe and his buddies had come to the party, all the beer would be gone, and we’d have to get more beer.

    The class cases do seem like better candidates. There it is very hard to find a plausible C other than “in this class” or “in my class”. Some of your examples look worrying for Jason. Here’s another variant that might also raise problems.

    (***) If this class had been cancelled, everyone would know less logic than they actually do.

    It seems very plausible there to say that the quantifier is restricted to people actually taking the class, not to people who would be taking the (cancelled!) class in a counterfactual world.

  5. jasoncs says:

    Brian,

    I liked Blome-Tillman’s paper, and the issue of embeddings is very important in evaluting contextualist proposals versus metaphysical proposals like IRI. However, no doubt due to my overly terse exposition, Blome-Tillman misunderstood my argument against Lewis’s version of contextualism in Section 3 of his paper. Brian, you are right that the existence of sentences like (5), (6), and (7) is irrelevant to my argument. But I’m not yet sure if it’s irrelevant for the reason you say. So let me explain it in my own terms.

    Blome-Tillman takes my argument to rest on the following implausible principle:

    (ST) Counterfactually embedded quantified noun phrases take their semantic values in the relevant counterfactual situation described
    in the antecedent of the counterfactual.

    Blome-Tillman’s (5), (6), and (7) are meant as counterexamples to this principle. But my argument does not in any way depend upon (ST).

    I’m going to submit this comment, and then continue…

  6. jasoncs says:

    First, a point about (ST). (ST) as stated is bizarre. No expression takes on a new semantic value when in the scope of a normal modal operator – unless it’s some kind of meta-linguistic operator. Before we can discuss these issues, we have to make the distinction between a property and the extension of that property, relative to a circumstance of evaluation. The issue is whether quantifier domains are properties that take on different extensions relative to different circumstances of evaluation, or rather extensions -equivalently, properties that have the same extension relative to every circumstance of evaluation.

    In the argument against Lewis, I rehearse some examples from the literature on quantifier domain restriction that establish that quantifier domains have to be properties that take on different extensions relative to different circumstances of evaluation. (These types of example are originally due to Scott Soames, in his arguments against situation semantics – since prima facie the situation semantic account of domain restriction entails that quantifier domains don’t vary across circumstances of evaluation).

  7. jasoncs says:

    I give two arguments that Lewis is committed to the view that his ‘rules of proper ignoring’ specify a property that, relative to different circumstances of evaluation, has different extensions (different sets of possibilities). The first is just an argument by analogy. Lewis models his kind of contextualism on quantifier domain restriction. Since quantifier domains are properties that have potentially different extensions relative to different circumstances of evaluation, Lewis’s epistemic domains also should be properties that have potentially different extensions relative to different circumstances of evaluation. I regard this argument as a weak, prima facie case.

    The second argument is that we have to take Lewis’s rules for proper ignoring as specifying a property that takes different extensions relative to different possible worlds.

    Lewis is trying to give us a recipe such that we can fill in the following:

    x is a possibility that is not properly ignored by the ascriber iff x has properties P, Q, and R.

    Suppose we take this as a character rule (in Kaplan’s sense) for ‘knows that p’, so that the content of a use of ‘knows that p’ is determined by the set of possibilities that, in the context of use, has properties P, Q, and R (Lewis’s various ‘rules’). The resulting view is subject to counterexample. Take the rule of actuality, which tells us that the actual world is never properly ignored. This is meant to ensure factivity. But if Lewis’s rules are character-rules, then the content of a use of (say) ‘knows that snow is white’ would require that snow is white in the actual world. But then it would be possible to know that snow is white, even though snow isn’t white. Surely, knowledge isn’t just factive – it’s necessarily factive. If Lewis’s rule of actuality were part of a character-rule that fixed the content of ‘know’ relative to a context of use, then we would have a counterexample to the necessary factivity of knowledge.

    Maybe this is more straightforward – to get the necessary factivity of knowledge, if x knows that p in a world w, p is true in w. The truth-value of p in the actual world is not what is at issue. So the rule of actuality doesn’t us to fix the content of a use of ‘know’ by throwing the actual world into what’s not properly ignored by the ascriber. It rather is part of the specification of the property of not properly ignoring. Someone knows a proposition at a world w if and only if their evidence rules out the worlds not properly ignored by the ascriber at w. The rule of actuality should have the consequence that w is not properly ignored by the ascriber at w (even if the ascriber is not in w!). The rule of belief tells us that no possibility believed to obtain by the subject is properly ignored by the ascriber. But in order to deal with modal embeddings, it must be that it is the possibilities the subject believes to obtain at the counterfactual circumstance that are not possibly ignored – or else someone could know that p, without believing that p (as long as their actual beliefs were taken into account).

    Then I move on to the rule of attention, and I say that it too should be treated in a parallel manner. Then at the very least Lewis’s theory allows for a reading of the following that is true:

    (H) Hannah doesn’t know that p. But if we had been ignoring certain possibilities, she would have known that p.

    But there is no true reading of (H). So any theory that entails that there is a true reading of (H) is problematic in the same way that IRI is problematic.

    So the issue is not the non-existence of certain readings, but rather the presence of certain readings that don’t seem to be there. That’s a worry for IRI, and it’s also a worry for Lewis’s version of contextualism. (ST) doesn’t really come in at all.

    For the record, I assume that there are readings of all quantified sentences in which (conversational context permitting) the quantifier domain is a property that has the same extension with respect to every world (which one could get by rigidfying), as well as readings in which the quantifier domain is a property that has different extensions with respect to different possible worlds. So I disagree with the presumed intended reading of (ST). But it’s not relevant to my argument anyway.

  8. dtlocke says:

    Hi Jason,

    You still around?

    I’ve always thought that Lewis would have done better to include truth and belief in the analysis of knowledge, and thus do without the rules of actuality and belief. Suppose I’m right about that. This gives us:

    (L+BT) S knows that P iff S believes that P, P is true, and S’s evidence eliminates all possibilities in which not-P.

    That eliminates the need for the rules of actuality and belief, and so neutralizes 2/3 of what you say above. Of course, it might raise other problems, but let’s set these aside for the moment, since it seems you have an objection that, if sound, applies to (L+TB) as well as it applies to Lewis’s original analysis.

    You write:

    Then I move on to the rule of attention, and I say that it too should be treated in a parallel manner. Then at the very least Lewis’s theory allows for a reading of the following that is true:

    (H) Hannah doesn’t know that p. But if we had been ignoring certain possibilities, she would have known that p.

    But there is no true reading of (H). So any theory that entails that there is a true reading of (H) is problematic in the same way that IRI is problematic.

    That sounds like a pretty good argument, if you’re right that ‘the rule of attention… should be treated in a parallel manner’. I see why you think the rules of actuality and belief should be treated as you say, but could you explain why the rule of attention should be treated that way?

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