Seduction and the sorites

Consider a red-yellow sorites sequence. Famously, “There is a red patch right next to a non-red patch” looks awful. But deny it (assert its negation) and you have the major premise of the sorites paradox. Plenty of theorists want to say that the “sharp boundary” sentence turns out to be true. They then face the burden of saying why it’s unacceptable. Call that the burden of explaining the seductiveness of the sorites paradox.

There is a fair amount of discussion of this kind of thing, and I have my own favourites. But in reading the literature, I keep coming across one particular line. It is to explain, on the basis of your favoured theory of vagueness, why we should think that each instance of the existential is false. So, theorists explain why we’d be confident that this isn’t a red patch next to a non-red patch, and that isn’t a red patch next to a non-red patch. And so on throughout the series.

However, there’s something suspicious about that strategy. Consider the situation that generates the preface “paradox”. Of each sentence I write in my book, I’m highly confident that it’s true. But on the basis of general considerations, I’m highly confident that there’s some sentence somewhere in it that’s false.

Suppose we accept that, of each pair in the sorites series, we have grounds for thinking that the red/non-red boundary is not located there. Still, we have excellent general grounds (e.g. a short logical proof, from obvious premises using apparently uncontroversial principles) for the truth of the existential claim that the boundary is located somewhere. So far, it looks like we should be something like the preface situation. We should be comfortable with the existential claim that there is a cut-off somewhere (/there is an error somewhere in the book) while disbelieving each instance, that the cut-off is here (/the error occurs in this sentence).

But, of coures, the situation with the sorites is strikingly not like this. Despite the apparently compelling general grounds we can give for the truth of the existential, most of us find it really hard to believe.

The trouble is this: the simple fact that each instance of an existential appears false does not in general lead us to believe that the existential itself is false (the preface situation illustrates this). So there must be something special about the sorites case that makes the move seem compelling in this case. And I can’t see that the authors that I’ve been reading explain what that is.

(A variation on this theme occurs in Graff Fara’s “Shifting sands”. Roughly, she gives a contextualist(-ish) story about why each instance asserting that the cut-off is not here will be true. She then says that it is “no wonder” will count universal generalization (the major premise of the sorites) as true.

But again, it’s hard to see what general pattern of inferring this falls into (remembering that it has to be one so compelling that it survives confrontation with a short proof of the truth of the existential). After all, as I look around my room, the following are successively true: “my chair is currently visible” “my table is currently visible”, “my cabinet is currently visible” etc. I feel no temptation to generalize to “all of the medium sized objects in my room are currently visible”. I have reasons to think this general statement false, and that totally swamps my tendancy to generalize from the various instances. So again, the real question here is to explain why something similar doesn’t happen in the sorites. And I don’t see that question being addressed.)

17 responses to “Seduction and the sorites

  1. Hi Robbie,

    Bizarrely, something very similar came up yesterday in discussion after Jonas Ackerman’s talk at the vagueness seminar. It was generally agreed that you are right – the question is not being addressed. A couple of other things that came up: it’s not phenomenologically plausible that our route to the major premise is via the instances. More plausible is that we consider a (single) arbitrary case. Myself, I’m not sure even that is right – maybe we get the major premise directly by reflecting on features of the properties (redness and yellowness) as opposed to thinking about either instances or an arbitrary case.

  2. FWIW, I like the “confusion hypothesis” style solutions (suggested by St Andrews’s own Patrick Greenough, Brian Weatherson, Fine, Edgington and Keefe et al). The idea is that we are systematically inclined to certain scope errors involving “definitely, e.g. hearing “(Ex)Fx” as commiting one to “(Ex)Def(Fx)”. If so, one would predict that one would here the cut-off principle as expressing the proposition that there are no definite cut-offs. And that’s true! And of course, this story doesn’t rely at all on some fallacy in reasoning from instances to generalization.

  3. what i meant to say is that uttering the cut-off sentences is heard as commiting one to the existence of definite cut-offs, and that is *false*. Sorry for the negation that slipped in!

  4. Hi Carrie,

    I’m inclined to agree with you that the instance-based story isn’t phenomenologically plausible, if that means considering each case in turn then generalizing. I’m not sure what “considering a single arbitrary case” consists in; sounds like we’d need a worked out theory to assess whether the Graff Fara contextualist would be able to go to work on it.

    I see the appeal of holding that reflection on nature of properties (or perhaps conceptual reflection) is what grounds the intuitive verdict. I guess that may favour something like Eklund’s line on the seductiveness issue (roughly that tolerance is part of the competence-conditions for “red”).

    You might think of the confusion hypothesis as fitting into this last strategy. The idea would be that the major premise is enforced *given* we assume that “red” express the property of being definitely red; and “not red” expresses the property of being definitely not red. But, of course, the assumption is wrong. “red” expresses being red; and “not red” expresses being not red. Hence the difference between the intuitive verdicts and the actual truth value of the major premise.

  5. Robbie,

    I don’t think your last remarks are the most plausible way of putting the point. Isn’t it better to say that we assume that ‘red’ expresses being red, and ‘not red’ expresses being not red – surely we aren’t really all that likely to get those claims wrong! – but that we mistakenly believe that being red = being definitely red, and being not red = being definitely not red?

  6. Hi Andy,

    If I believe e expresses P, and that P=Q; I’m apt to believe e expresses Q… so Maybe the thought is that I shouldn’t deny that we believe that ‘red’ expresses red. But once we distinguish this from the metalinguistic belief that “‘red’ expresses red’ says something true, I’m no longer sure that we should credit ourselves with that belief.

    There may be problems with this ‘compositional’ way of trying to get to the confusion hypothesis… I wouldn’t want to be not committed to this particular way of formulating it. But I’m not sure I see the problem yet.


  7. hey Robbie,

    Actually, it’s often a bit more complicated than that, isn’t it? Even if I know that water=H20, I typically won’t move from knowing that “_is water” expresses being water to the knowledge that it expresses H20, because I’ll often have that kind of semantic knowledge encoded in a way that is sensitive to considerations of cognitive significance?

    In any case, the idea was precisely that the semantic claim that e expresses Q wasn’t really the assumption at the heart of the confusion – even if things are as you say, it comes out that we only accept that claim because it’s a valid consequence of another, more fundamental mistaken assumption P=Q, together with the true (tacit) belief that e expresses P. I don’t see any motivation for thinking that we only endorse the metalinguistic claim that ‘e expresses P’ expresses a truth, nor for holding off from crediting ourselves with the corresponding material-mode belief – if belief is the right word for that kind of tacit representation of semantic facts.

    This wasn’t supposed to be a problem for you in the sense of an objection btw. It was supposed to be a helpful suggestion about the formulation of your claim, and the real source of the confusion.

  8. Hi Andy,

    OK, I see things clearer now. Sorry for the clumsyness. I guess I’m not used to thinking of `expresses’ hyperintensionally (too much possible world semantics for you). In fact, I’m tempted to stop using a piece of semantic vocabulary whenever people start saying it is hyperintensional, and reach back into the goodbag of words for `meaning’ for one that we can agree doesn’t carry those overtones.

    But let’s drop the issue, coz I think you’re right that the real issue between us is over what role, if any, is played by a belief that `red’ expresses red. I was supposing that we do not believe this at all. Your view was that we do believe this (and that if we do believe that `red’ expresses det red, that’s only due to the joint upshot of that belief and another, false belief). I appreciate that both these may be ways to get the confusion hyp working. But I think mine’s a goer too.

    Let’s think of some other cases of mistaken linguistic beliefs. E.g. (an example Richard Heck uses a lot) let’s suppose that I think that `livid’ means flushed. Is the right way to describe this that I truly believe that `livid’ means livid, and then mistakenly believe that being livid is being flushed? I don’t find that a natural way to describe the situation at all.

    Nothing in my situation that you might typically look at to determine what I believe relates my use of the word `livid’ to lividness at all. When you look at all that kind of stuff, what you find is e.g. that I classify flushed people as `livid’. And that’s the sort of thing that makes it natural to ascribe to me the belief that `livid’ expresses flushedness.

    There is some other relevant behaviour: e.g. I’m inclined to say things like “livid’ means livid’. But in the first instance that kind of linguistic behaviour suggests we attribute the metalinguistic belief that that sentence is true. It’d take further argument to say that on this kind of basis we should attribute the belief that `livid’ means livid.

    I don’t think that things change significantly if we move to a view whereby the relevant `semantic beliefs’ are tacit representations rather than ordinary beliefs. Of course, maybe the sentence inscribed in the semantic box connects a representation of the nat-language word `red’ to the mentalese term for red. But what are the grounds for thinking this is so?

    Maybe something that favours your way of going about this over mine is exactly the parallel to the `livid’ case. There we exactly have misunderstanding of words, since the semantic belief involved is false. But maybe it is uncomfortable to tie the confusion hypothesis to the claim that *systematically* we misunderstand all the vague words we use! Better to say that we understand them correctly, but other false beliefs get in the way (e.g. that red=det red). Well maybe, but misunderstanding is not an all-or-nothing thing, and I guess I’m happy enough to say that we systematically misunderstand all vague words *a little bit* (i.e. that we believe they express a property that’s pretty near to the property that they actually express).

    BTW, Sorry if the previous reply was a little curt! I was typing it in from a handheld pc, which makes you apt to be a little shorter than otherwise…

  9. In the livid case, I typically apply ‘livid’ to flushed things, right? So ‘livid’ comes to mean flushed, given facts about use and naturalness. So why doesn’t ‘red’ come to mean Det red? After all, I typically apply it to Det red things, and Det red seems about as natural as red? How come ‘red’ still expresses being red, rather than Det red, on your view?

  10. Also, aren’t you moving from a first-person ‘disquotational’ attribution of meaning, as when you as a normal English speaker talk about what ‘red’ means in English, to re-interpretive third-person attribution, as when you consider somebody who misunderstands the English word ‘livid’, given the background of a well-established pattern of use by the rest of his linguistic community? Is it plausible that the whole of our community could be making a false assumption about what our word ‘red’ means, in a way which is seemingly avoidable via simple disquotation?

  11. On the first point, facts about how we use ‘red’ aren’t the only data about usage to consider. We also classify things as ‘not red’. And a semantic hypothesis that does well in explaining the facts about usage of `that’s red’ might not do so well in explaining facts about usage of `not red’. In the `livid’ case, it’s fact about historical/societal usage that mean that `livid’ still means pale, not flushed (arguably). In the ‘red’ case, on this view, it’s holistic constraints on interpretatability.

    Notice that it’s important to the view here that, though our confused subject believes that ‘red’ expresses det red, she doesn’t think that `red’ expresses not det red. Rather, she thinks it expresses det not red. That’s one thing that makes me uncomfortable with this way of developing the confusion hypothesis.

    I don’t get why I’m *moving* from one conception of meaning or meaning-attribution to another. I thought that we were talking throughout of *semantic facts*: i.e. what words means (in English, say, or maybe in my idiolect). Of course, lots of people can take a view on that: people speaking French, people speaking Welsh, you, me and the postman. So I’m certainly happy from the start with the `third person’ perspective (I don’t see why it should be called *re*interpretative.) I know there are conceptions of meaning which build in a (metaphysical) asymmetry between first and third-personal takes on meaning; Quine, later Field etc. But that’s pretty controversial take on the subject, and not one I was thinking of.

    I see that disquotation is (at least in classical settings) a way of guaranteeing you’re stating the true facts about meaning. So we could say something like `livid’ means livid and have some guarantee we’re speaking truly. But under the assumption that you have a false conception of what the word means (e.g. you think that it applies to flushed things) you are going to think that by saying that `livid’ means livid you’re expressing the proposition that `livid’ means flushed. So even if we don’t actually believe that `livid’ means livid (i.e. that `livid’ expresses the property of being pale), it’s entirely predicatable that we’d use that phrase, since we’d take it to express what we do believe, viz. that `livid’ means flushed. So I’m not seeing how bringing in the sort of homophonic resources that are available in the first-personal case are going to give us traction on the debate.

    all best

  12. hey man,

    like i said to you tonight, i think we must be thinking of some relevant issue in quite different ways. let’s fix a time to talk it through.


  13. Hi Robbie,

    I know this is going to sound simple-minded…

    In the preface case I have a good explanation of why the claim X ‘there is a mistake in my book somewhere’ is true: I’m not very smart and make loads of mistakes (and now I give a bunch of examples of my mistakes, although not from the book). Not only do I have a good argument that X is true, I can see HOW it is made true.

    In the sorities case I don’t have a good explanation of why the claim Y ‘there is precise point when it’s no longer a heap’ is true. I do have a good argument for Y, but I don’t see HOW it could be true.

    In fact, I have considerations that lead me to think that Y must be false: considerations about how meaning-determining facts are insufficient to set sharp satisfaction conditions for ‘is a heap’ etc.

    In contrast, although I may have some considerations that suggest that X is false (namely, my arguments for each claim in my book), these considerations that suggest that X is false aren’t nearly as impressive as those I have that suggest that Y is false.

    In both cases I have an excellent argument for the claim in question, X or Y. In the sorities case I have an excellent argument for ~Y; but in the preface I don’t have an excellent argument for ~X.

    Does any of that sound right?

  14. Hi Brian;

    There’s definitely something appealing about those thoughts. I suppose what I was resisting was the thought that by explaining why each individual claim seemed true, we’d thereby have explained why the universalisation seemed true. The parallel to the preface case was supposed to throw that into question.

    I’m not sure that you were intending the defend an entirely instances-based explanation of the seductiveness of the sorites. But in any case you mention something that does seem a useful thought for the defender of that line: the idea that our attitude towards the sorites conditionals is stronger than that towards the sentences in the book: in the latter case, we’re just confident that they’re true; but in the former case, we seem incapable of thinking what it would be for them to be false. If we could justify that stronger attitude towards the instances from our theory of vagueness, perhaps the generalization step might be defended.

    The other thought that’s in play in your comments is that there’s some non-instance based argument for the truth of the sorites conditional, and thus against the result of the sorites argument: e.g. general principles about meaning-determination. If I understand you right, then this kind of thing on its own, independent of the story about the instances seeming true, seem enough to motivate the major premise. So this wouldn’t vindicate the instances-based approach to explaining why the sorites is seductive.

    On the merits of the appeal to thoughts about meaning-determination itself: it does strike me as a pretty sophisticated thing to be appealing to when explaining why the folk find the sorites appealing. It also seems a little problematic in application to sophisticates: Presumably Williamson and Graff feel the intuitive pull of the sorites, even after giving up any principle about meaning-determination that’d impose no sharp boundaries. And supervaluationists still feel the appeal, even thought they have to think that the principle that forms the major premise of the sorites doesn’t express the thought that there are no sharp boundaries at all: that this has to be expressed by e.g. ~(Ex)D(Fx&~Fx’).


  15. Hi Robbie,

    Like you, I don’t think I was defending an instance-based explanation of the sorities. My explanation goes like this:

    a. Although I have an excellent philosophical argument (a sorites one) for the truth of claim Y ‘there is a number N such that a person with N hairs is bald but a person with N + 1 hairs isn’t bald’,
    b. I haven’t the slightest idea HOW claim Y could be true, and
    c. I have an excellent argument (the “insufficient meaning-determining facts” argument) against Y.

    You bring up the good point that in some sense part (c) of my explanation is too sophisticated or maybe complicated. Here are my initial thoughts about that.

    Here’s a standard sorites series:

    1. A person with 1 hair isn’t bald.
    2. A person with 2 hairs isn’t bald.
    3. A person with 3 hairs isn’t bald.

    We can’t imagine how it could be that for some n, (n) is true while (n + 1) is something other than true (it doesn’t even matter if (n + 1) is false or something else like indeterminate; how could one hair make ANY difference in alethic status?). Now Fred comes along and asks why we don’t want to draw a sharp cutoff in that sorites series. I’m guessing that we’ll INITIALLY say something very general like ‘Well, a mere hair can’t make the difference between being bald and not being bald’. But then Fred presses further: why is THAT true? I suspect that we’ll soon be driven to making semantic claims about ‘bald’. We will say things like ‘The word ‘bald’ is vague’ or, more informatively, ‘We don’t use ‘bald’ with exactness’ or, with even more informativeness, ‘No one ever defined ‘bald’ with enough precision’. And that’s what I’m trying to get at with the “insufficient meaning-determining facts” idea: whatever it is that fixed the meaning of ‘bald’ didn’t do it so that (n) would be true and (n + 1) not true.

    I think that the reason epistemicists find their own theory deeply counterintuitive is that they realize (a) that they are saying that my utterance of ‘He is bald’ has acquired a meaning such that it’s true if the guy has n hairs but not true if he has n + 1 hairs, and (b) that it’s deeply counterintuitive that my utterance has acquired such a discriminating meaning. I suspect that if they could become perfectly content with the idea that my utterance was so discriminating, then they’d be perfectly content with assigning a sharp cutoff to the sorites series above.

    Does any of that sound right?

  16. I do think, when people have sorites intuitions, you can drive people back to talking about semantics. In fact, that’s what we do in classrooms when trying to get people to be interested in the metasemantic issues that are in play in the vagueness literature! The issue, is, I guess, about direction of explanation: are the stuff we’re driven back to really the things that explain our object-language intuitions.

    I’m still worried about the conceptual sophistication point: suppose that kids aged n can be brought to feel the force of a sorites argument; are we going to supppose that they’ll also have (perhaps implicit?) conceptual resources to understand “vagueness”, “precise definition”, “exactness”. Not clear to me: but looks testable!

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