Vagueness survey paper III (epistemicism)

This is the third section of my first draft of a survey paper on vagueness, which I’m distributing in the hope of getting feedback, from the picky to the substantive!

In the first two sections, I introduced some puzzles, and said some general methodology things about accounting for vague language—in effect, some of the issues that come up in giving a theory in a vague metalanguage. The next three sections are the three sample accounts I look at. The first, flowing naturally on from “textbook semantic theories”, is the least revisionary: semantics in a classical setting.

Now, if I lots of time, I’d talk about Delia Graff Fara’s contextualism, the “sneaky classicism” of people like McGee and McLaughlin (and Dave Barnett, and Cian Dorr, and Elizabeth Barnes [joint with me in one place!]). But there’s only so much I can fit in, and Williamson’s epistemicism seems the natural representative theory here.

Then there’s the issue of how to present it. I’m always uncomfortable when people use “epistemicism” as synonym for just the straightforward reading of classical semantics—sharp cut-offs and so on (somebody suggested the name “sharpism” for that view–I can’t remember who though). The point about epistemicism—why people finding it interesting—is surely not that bit of it. It’s that it seems to predict where others retrodict; and it seems principled where others seem ad hoc. Williamson takes formulations of parts of the basic toolkit of epistemology—safety principles; and uses these to explain borderineness (and ultimately the higher-order structure of vagueness). That’s what’s so super-cool about it.

I’m a bit worried in the current version I’ve downplayed the sharpist element so much. After all, that’s where a lot of the discussion has gone on. In part, that betrays my frustration with the debate—there are some fun little arguments around the details, but on the big issue I don’t see that much progress has been made. It feels to me like we’ve got a bit of  a standoff. At minimum I’m going to have to add a bunch of references to this stuff, but I wonder what people think about the balance as it is here.

I have indulged a little bit in raising one of the features that always puzzles me about epistemicism: I see that Williamson has an elegant explanation about why we can’t ever identify a cut-off. But I just don’t see what the story is about why we find the existential itself so awful. The analogy to lottery cases seems helpful here. Anyway, on with the section:

Vagueness Survey Paper, Part III.


One way to try to explain the puzzles of vagueness look to resources outwith the philosophy of language. This is the direction pursued by epistemicists such as Timothy Williamson.

One distinctive feature of the epistemicist package is retaining classical logic and semantics. It’s a big advantage of this view that we can keep textbook semantic clauses described earlier, as well as seemingly obvious truths such as that “Harry is bald” is true iff Harry is bald (revisionary semantic theorists have great trouble saving this apparently platudinous claim). Another part of the package is a robust face-value reading of what’s involved in doing this. There really is a specific set that is the extension of “bald”—a particular cut-off in the sorites series for bald, and so on (some one of the horrible conjunctions given earlier is just true). Some other theorists say these things but try to sweeten the pill—to say that admitting all this is compatible with saying that in a strong sense there’s no fact of the matter where this cut-off is (see McGee McLaughlin; Barnett; Dorr; Barnes). Williamson takes the medicine straight: incredible as it might sound, our words really do carve the world in a sharp, non-fuzzy way.

The hard-nosed endorsement of classical logic and semantics at a face-value reading is just scene-setting: the real task is to explain the puzzles that vagueness poses. If the attempt to make sense of “no fact of the matter” rhetoric is given up, what else can we appeal to?

As the name suggests, Williamson and his ilk appeal to epistemology to defuse the puzzle. Let us consider borderlineness first. Start again from the idea that we are ignorant of whether Harry is bald, when he is a borderline case. The puzzle was to explain why this was so, and why the unknowability was of such a strong and ineliminable sort.

Williamson’s proposal makes use of a general constraint on knowledge: the idea that in order to know that p, it cannot be a matter of luck that one’s belief that p is true. Williamson articulates this as the following “safety principle”:

For “S knows that p” to be true (in such situation s), “p” must be true in any marginally different situation s* (where one forms the same beliefs using the same methods) in which “S believes p” is true.

The idea is that the situations s* represent “easy possibilities”: falsity at an easy possibility makes a true belief too lucky to count as knowledge.

This first element of Williamson’s view is independently motivated epistemology. The second element is that the extensions of vague predicates, though sharp, are unstable. They depend on exact details of the patterns of use of vague predicates, and small shifts in the latter can induce small shifts in the (sharp) boundaries of vague predicates.

Given these two, we can explain our ignorance in borderline cases. A borderline case of “bald”  is just one where the boundary of “bald” is close enough that a marginally different pattern of usage could induce a switch from (say) Harry being a member of the extension of “bald” to not being in that extension. If that’s the case, then even if one truly believed that Harry was bald, there will be an easy possibility where one forms the same beliefs for the same reasons, but that sentence is false. Applying the safety principle,  the belief can’t count as knowledge.

Given that the source of ignorance resides in the sharp but unstable boundaries of vague predicates, one can see why gathering information about hair-distributions won’t overcome the relevant obstacle to knowledge. This is why the ignorance in borderline cases seems ineliminable.

What about the sorites? Williamson, of course, will say that one of the premises if false—there is a sharp boundary, we simply can’t know what that is. It’s unclear whether this is enough to “solve” the sorites paradox however. As well as knowing what premise to reject, we’d like to know why we found the case paradoxical in the first place. Why do we find the idea of a sharp cut off so incredible (especially since there’s a very simple, valid argument from obvious premises to this effect available)? Williamson can give an account of why we’d never feel able to accept any one of the individual conjunctions (Man n is bald and man n+1 is not). But that doesn’t explain why we’re uneasy (to say the least) with the thought that some such conjunction is true—i.e. that there is a sharp cut-off. I’ll never know in advance which ticket will win a lottery; but I’m entirely comfortable with the thought that one will win. Why don’t we feel the same about the sorites?

2 responses to “Vagueness survey paper III (epistemicism)

  1. A few thoughts — and I’ll again try to take the perspective of a reader who might be relatively new to vagueness studies (yet with a decent, say, logic background):

    I see you’re going with epistemicism before talking in detail about superval. Might it make more sense to do it the other way round — maybe this would give more power to the point re: the benefits of preserving classical logic? Plus, it might provide a bit more historical perspective?

    One thing that would be neat to see in this survey paper (actually, I’d like to see it in more survey papers in general) is at least something brief about the current state of opinion among philosophers about the topic. It’s nice, I think, to be able to read a survey and know that, (say) superval is more well-known, or popular, or whatever, than, say, contextualism. I know it’s always hard to do that (too bad Gallup doesn’t poll philosophers), but for the big points it might be helpful.

    Another thing that struck me in this part was in the final paragraph: “It’s unclear whether this is enough to “solve” the sorites paradox however.” I immediately thought of Schiffer on ‘happy vs. unhappy face’ solutions. Perhaps more detailed talk (in Part One, maybe?) about what would really constitute a logic/language *solution* or explanation of the sorities (whether happy or unhappy face) might provide a nice framework for the entire paper.

  2. Re the ordering. I guess part of my thinking was that it’s interesting to see what you might have to buy in to to defend a non-revisionary theory, before considering this or that way of revising. In a sense, I’m betraying my view of the proper methodology here!

    But you’re right that what happens is I give a theory that reached canonical formulation in 1994 before giving a theory that’s been hanging around in the 1970’s. And the whole tone of the survey piece at the moment is very ahistorical. In a sense, that’s happened because I’m using a lot of the space to give quite detailed descriptions of the mechanics of three sample theories, rather than taking a more overall view of the state of the literature.

    One thing that will happen if I track historical order, is that I’ll lose a sort of intrinsic order of theories: from least to most revisionary. On the historical ordering I’d start with Fine, go to Williamson, and finish with Field. It’d work more nicely if I had done degree theory, since I could then do Machina (for example), then Fine, then Williamson (which is the order in Williamson’s book, for example). But then the discussion of vague metalanguages wouldn’t make much sense. It’s all a bit of a balancing act.

    I agree that something on current state of opinion among philosophers would be nice. I’m always a bit wary of such statements, because I’m not sure I know what the current distribution of opinion is, or how to find out (I can estimate among my friends, say, but that’s a pretty biased sample). I suspect one reason why you don’t find that sort of stuff in survey papers is that it’s going to be easy to annoy people by saying such things.

    Yes, the Schiffer stuff did come to mind here—and also some other stuff (from Wright and Greenough and Weatherson for example). I should try to find a way to work that in. Maybe you’re right that the first section is the place to do it. Space is always the issue!

    Thanks again for these comments—really useful.

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