December 13, 2006

Taking Epistemicism Seriously (Frances)

If one hasn’t worked hard on the topic of vagueness, it can be hard to take epistemicism seriously. You wonder: everyone SAYS that Tim Williamson is unbelievably smart, but since he believes in cutoffs doesn’t that mean there is something seriously wrong with him? I mean, really: how much good sense could he have if he believes that my remark to a visiting speaker ‘The auditorium is a short walk from here’ is true if it’s X inches away and false if it’s X + 1 inches away? Williamson just doesn’t know when to give up on predicate calculus!

Before I thought hard about vagueness I didn’t actually have that attitude but I had some attraction to it. Now that I’ve thought hard about vagueness I think epistemicism is one of the two most plausible theories of vagueness (the other being the semantic nihilism of Sider & Braun, which says that all vague sentences aren’t true).

Shortly before Halloween you are walking to Farmer Fred’s farm. Your children want to see the pumpkins that they will carve. You say to them, in an obviously apt and relevant circumstance, ‘There is a pumpkin by the tree’. Call the situation you were in S1; so ‘There is a pumpkin by the tree’ is true when evaluated with respect to S1. Now an atom or atomic particle inside the pumpkin moves out of the pumpkin. Call the resulting situation S2. Consider the claim you made earlier, in S1, with your use of ‘There is a pumpkin by the tree’: is that claim true when evaluated with respect to S2 instead of S1? Obviously, the answer is ‘yes’, assuming there are any pumpkins and trees at all. When we consider the ordinary, everyday meaning of ‘There is a pumpkin by the tree’, given that it was true and not false in S1 it must be true when evaluated with respect to S2 as well. Continue the process and you get a series like this (pumkin claim = the claim you made in S1 when you uttered 'There is a pumpkin by the tree'), where the first column has the situations and the second column has the alethic status of the pumpkin claim:

S1 ------------ true
S2 ----------- true
S3 ----------- true
Sn ----------- ??
Sbig – 2 ---- false
Sbig – 1 ---- false
Sbig --------- false

It sure seems as though the ‘true’ entries in the second column have to stop somewhere. Perhaps the entries in the second column of our table don’t go from ‘true’ to ‘false’. That is, maybe the claim made by your use in S1 of ‘There is a pumpkin by the tree’, when applied to situations Sn – 1 and Sn goes from true to indeterminate—or maybe to indeterminately indeterminate (or indeterminately indeterminately indeterminately … indeterminate). Or maybe to just plain meaningless. Or maybe to both true and false (so it keeps being true but just adds falsity for some strange reason). Or maybe its status with respect to Sn changes with the wind, or my hair color, or some more likely factor. Or maybe it has no satisfaction status whatsoever with respect to Sn (not even meaningless). Or, what might not be any different, there might be no fact of the matter as to the satisfaction status with respect to Sn (whatever that idea comes to). Or perhaps it becomes incoherent to even apply the pumpkin claim to Sn. Or maybe it isn’t true, it isn’t false, it isn’t neither true nor false, and it isn’t neither true, false, nor neither true nor false (got that?). Finally, maybe the truth about the pumpkin claim with respect to Sn is best captured by a Zen master’s reaction to ‘What is the sound of one hand clapping?’

The great strength of epistemicism is just this: IT DOESN'T MATTER which of these many options one takes. Be as clever or as simple as you like with your theory regarding the status of the pumpkin claim, it still seems inevitable that its truth-value is ridiculously dependent on the minuscule movement of a single electron (a nanometer, say). After all, we know that the pumpkin claim applied to Sn – 1 is just plain true and not false: surely, S1, S2, S3, S4, and another trillion or so situations involved perfectly good healthy pumpkins, if pumpkins exist at all (the sum total of a trillion of these changes wouldn’t even be visible to the naked eye and wouldn’t effect the functioning of the pumpkin), and ‘There is a pumpkin by the tree’, understood to have its perfectly ordinary meaning expressed in S1, was nothing other than just plain true with respect to those trillion or so situations. However, we also know that it’s not the case that the pumpkin claim applied to Sn is just plain true (because it’s meaningless, indeterminate, indeterminately indeterminate, alethically unstable, alethically overdetermined or inconsistent, lacks any satisfaction status, [insert Zen master’s response], etc). So, something happened as a result of that ridiculously tiny change from Sn – 1 to Sn; it marks some very sharp cutoff that did not happen in the change from Sn – 2 to Sn – 1. It makes no difference (for the existence of satisfaction cutoffs) as to what descriptions of the situation after the change are correct (if any). The point is that ‘There’s a pumpkin by the tree’, understood in the perfectly normal way, is true, meaningful, and not false when evaluated with respect to the first trillion or so situations, but at some point in the series of situations it stops having that exact status.

It’s no good to protest that the table given above can’t be completed, or that it’s indeterminate whether it can be completed, or that it’s indeterminate whether it’s indeterminate whether it can be completed, or…. The first trillion or so slots in the second column CAN be completed: they all have nothing other than ‘true’ in them. Now you tell me: starting from the top, what is the last row we can correctly complete with just ‘true’? The trillionth row? Then that’s our satisfaction cutoff, and I couldn’t care less what you want to say about the trillionth row, no matter how sophisticated it is. You might want to say, ‘We might as well stop at this point, although we could have stopped earlier’. But in the trillionth row you could NOT have stopped putting in ‘true’; that would have been just as much of a mistake as if you had stopped after the first row or the thousandth row.

You might think that I’m illicitly assuming that for any pair of consecutive rows the question ‘Do they have the same alethic status?’ has an answer. Sadly, no! Most everyone will agree that ‘true’ goes in the first row, and they’ll agree that ‘Do the first and second rows have the same alethic status?’ has an answer: ‘yes, they do have the same status’. And most everyone will agree that that ‘Do the second and third rows have the same alethic status?’ has an answer: ‘yes, they do have the same status’. It doesn’t take a genius to see where this is going. If one is like Michael Tye, for instance, one will agree with what I just said about the first three rows, but one will hold that ‘Do the nth and (n + 1)st rows have the same alethic status?’ sometimes has an answer but sometimes it doesn’t. Fine: when does it first not have an answer? We know it has answer for the first three rows. Does it first fail to have an answer for rows 10,000 and 10,001? Then that’s our sharp cutoff. That is, whereas the pumpkin claim was true and not false when evaluated with respect to S10,000, there is no answer to whether it’s true and not false when evaluated with respect to S10,001.

Eventually, we take seriously both epistemicism and nihilism!


Anonymous said...

I'm not sure what you mean by epistemicism here. I took it to be standard that epistemicism is committed to the thesis that both classical logic and semantics are appropriate for vague discourse. So on what I took to be the standard classification, Williamson and Sorensen are epistemicists, but Crispin Wright isn't since although he has adopted the view that vagueness is an epistemic phenomenon, and that borderline-case-hood is an epistemic status, he gives up on classical logic and semantics and the 'associated bivalent metaphysics'.

If we're not building that sort of classicism into the characterization of the position, it would be helpful to know how we are to understand epistemicism in the post.

Also, this problem seems somewhat related, but interesting different, to the forced-march Sorites (where we demand a complete set of verdicts about the cases in a Sorites series from a particular subject or group of subjects). The problem there is that the subject can't return a uniform set of verdicts throughout the series (because then she'll have judged the clear non-F cases in the series to be F). So she must "jump" at some point in the series; but then there is a pair of cases, n and n+1, s.t. she judged Fn but did not judge Fn+1 (which is not to say she judged ~Fn+1; maybe she hedged, or said there's no fact of the matter, or simply fell silent). On views according to which truth-value is sensitive to a single step along the Sorites series, and moreover sensitive at an unknowable point in the series, we have difficulties explaining how the forced-march subject could be justified in marking out this pair-wise distinction with her judgments (in F-ness between n and n+1), when she's completely incapable of tracking the point in the series where the shift in status occurs. So there's a danger any advantages epistemicism possesses when we're confronted with your problem are going to convert into disadvantages when we're interested in the forced-march. (There's obviously a lot of work needs to be done to tighten this into an objection to the epistemicism, but I hope the shape of the objection is clear enough).

Ps. Let me take the opportunity to thank you for the reference to your paper on closure. I've read it, but other things got in the way of me properly processing it yet.

Joe said...

Take a sorites series of situations S1 through S10 and suppose that in S1 it is true that x satisfies the vague predicate, say, is bald. then somewhere down the line, say at S4, a question arises about whether we can safely say that x is bald. You propose then that S4 be taken as the sharp cut-off. If we retain classical logic, then it follows that at S4 it is false that x is bald. Accordingly, at S5 it is false that x is bald.

However, we know that in S10 x is not bald. Suppose at S6 a question arises about whether we can safely say that x is not bald. So S6 is to be taken as the sharp cut-off. It follows that in S6 it is false that x is not-bald. That is, in S6 it is true that x is bald. Accordingly, in S5 it is true that x is bald.

In sum, in S5, it is both true and false that x is bald.

Bryan Frances said...

I should have specified what I meant by ‘epistemicism’! I realize now that it was a bad choice.

I meant something like this: there are sharp cutoffs in meaning. For example, in the auditorium case in which I say to the visiting speaker ‘The auditorium is a short walk from here’ there is a sharp cutoff in meaning if my utterance was true if we were X inches away but my utterance had some other alethic status (including “null” if you like) if we were X + 1 inches away. That’s ALL I meant by ‘epistemicism’. So, there is no endorsement of bivalence or classical logic. Also, there is no endorsement of any epistemological theses (e.g., regarding why we don’t know the location of the cutoffs).

Maybe ‘Sharpism’ would be a more descriptive (but really ugly) name for the view that there are these sharp cutoffs.

In effect, I’m saying (in an essay I’m working on) that just about everyone—supervaluationist, etc—is committed to the existence of Sharpism. In addition, the most counterintuitive thing about epistemicism—which says among other things that my auditorium utterance went from ‘true’ to ‘false’ as we go from X inches to X + 1 inches—is its endorsement of sharp cutoffs. But never mind that part of the argument. What I’m interested in is whether the pumpkin argument is a good argument for Sharpism: the pumpkin claim is true when evaluated with respect to Sn – 1 and has some other alethic status (including “null” or whatever) when evaluated with respect to Sn, where these two Ss are incredibly similar.


I wasn’t sure what your objection is. If we force Tom at gunpoint to fill out the table in my original post, he’ll be screwed, for sure. He has every reason to start by putting in ‘true’ and end with putting in ‘false’, and he’ll be forced to switch from ‘true’ to something else at some point. Pretend that he writes ‘true’ for S1000 and writes ‘indeterminate’ (or ‘false’; it doesn’t matter) for S1001. If there are sharp cutoffs, he has almost no chance of locating them correctly. He has some justification for the idea that there has to be a sudden switch, and he knows it doesn’t happen near the beginning or near the end, but he has no way of knowing where it occurs. How is this a problem for Sharpism?

The better objection to Sharpism is this: how could any collection of facts determine that my use of ‘The auditorium is a short walk from here’ expresses a meaning that is just plain true in Sn – 1 but not just plain true in Sn? The problem is seeing how any natural facts (or objects or states of affairs or whatnot), precise or not, could set the cutoffs. We just can’t see how a normal utterance could ACQUIRE such an incredibly discriminating meaning. Even if we gathered exceedingly detailed data on language use, linguistic dispositions, and the nature of the physical environment, how on earth would all that detail even matter to the fixation of sharp cutoffs?

Anonymous said...

"If we force Tom at gunpoint to fill out the table in my original post, he’ll be screwed, for sure."

I haven't yet been convinced of this. If it really were the case that no theory of vagueness would allow a subject to return a complete set of verdicts without tripping herself up in some manner, then presumably we should conclude that we've just set up the rules of the forced-march in such a way that they can't all be obeyed.

I've talked to several people who have drawn this conclusion, but at the moment it strikes me as premature. There are some incredibly sophisticated solutions to this problem - for example, Diana Raffman's contextualist response in 'Vagueness Without Paradox. (I here argued that Raffman's own presentation of this solution is problematic given her commitment to classical semantics and logic, but even if that's right, perhaps in another framework it would fare better).

So, to try to be clear, I don't think we can simply turn down the challenge on the grounds that there's no way to meet it. There seem to be promising lines of attack still open. If it should prove (as I've suggested, though not shown) that epistemicism - in the usual sense - renders the issues arising from the forced-march intractable, while some of its competitors tract them, that's surely to be chalked up as a cost of the position. Anyway, I'm not sure how relevant this is, given your more recent characterization of the view under discussion, so I should stop.

On the suggested objection to sharpism, I wonder if Roy Cook's work might allow the sharpist to dodge these questions. Roy's really responding to Sainsbury and Tye when they suggest that any theory of vagueness that represents the way a vague predicate classifies as a matter of it drawing set-theoretic boundaries must be mistaken, since its constitutive of vague expressions that they don't draw such sharp boundaries.

Roy's picture requires buying into a lot of his philosophy of logic, but it might allow one to defend sharpism while turning down these sorts of questions about how natural facts could determine sharp cutoffs in good conscience. I'm just thinking out loud just now, as is probably obvious, but in any case the abstract for Roy's interesting paper can be found here.

Anonymous said...

I like the term "sharpism"! Just my defective aesthetic sense, probably.. I'm going to start using it. (1) below just constitutes a plea to distinguish these things, (2) has something more substantive to say in response to the pumpkin example.

(1) I think it's vital that we distinguish sharpism from epistemicism. Epistemicism is in part an explanation of what vagueness is: that it is vague whether p if p is unknowable for certain special reasons. And that does explanatory work for him: e.g. in explaining the logic of "definitely", patterns of assertability etc. You might think that there are real problems with the epistemic side of this story (I do). You might think that the semantic analysis of what it is to be vague offered by degree theory or supervaluationism, or the pragmatic theory offered by contextualists are *better* at this job. If so, then even if we all have to be sharpists, there'll be the question of whether we should be epistemicist sharpists, or supervaluational sharpists, or whatever. The best sharpist explanation may well be a non-classicist sharpism.

The reason this is important is that sharpism, by itself, is no theory of vagueness. It doesn't tell us what it is for something to be vague; it doesn't tell us why the sorites seemed compelling. It doesn't even tell us how to block the sorites, since it's compatible with a load of different stories about how to block it (e.g. those emerging on degree theory vs. supervaluationism vs. classicism). Maybe you could build a theory of vagueness out of sharpism alone, but I'm not seeing how this is to be done at the moment.

(2) If you're a degree theorist, you might think that the aleithic status constantly changes through the pumpkin case (think of a degree theorist who thinks that no sentence has degree of truth 1: notice that that's not to say that they're untrue, unless we identify truth with true-to-degree-1, which'd be contentious). I don't think that this commits one to sharpism in anything like the form the epistemicist believes in.

Sharpism may upset people for one of two reasons: (a) because they're not up for changes alethic status (of e.g. "x is bald") being generated by tiny changes in the subvening properties (no of hairs x has); (b) because they're not up for big changes in alethic status being generated by tiny changes in those subvening properties. Let's call (a) "sharpism with jumps" and (b) "sharpism without jumps". (On this stuff, see Nick JJ Smith's nice piece in the AJP: Vagueness as Closeness).

Epistemicists are committed to sharpism with jumps. That's counterintuitive. Tweak something tiny, and something huge happens: we fall from truth to falsity. Degree theorists only look to be committed to sharpism without jumps. And I'm not sure that that's so counterintuitive. I make a tiny change in how many hairs I have, and the result is a tiny changes in the degree to which I satisfy "bald". Where's so surprising about that?

Bryan Frances said...

Hi Robbie,

In my work-in-progress I called sharpism ‘minimal epistemicism’. I take it that only epistemicism admits that there are sharp cutoffs, and that’s why I chose the name. But a separate name might be better.

I am not sure about the degrees of truth idea. With regard to the pumpkin argument:

Assume for the moment that the pumpkin claim is perfectly true, fully true, and 100% true (or however one wants to put it), with respect to at least the first trillion situations, S1 through ST, ‘T’ for ‘trillion’. (A trillion atoms or atomic particles is nothing for a living pumpkin, even a small one.) Since it’s not 100% (or fully or perfectly) true for all the situations, at some point it goes to something less than 100% true; perhaps it goes to 99.999% true. The sharp cutoffs haven’t gone away! We’re still stuck with sharpism, which I thought degrees of truth people would want to avoid.

However, let’s suppose that when we start to take away even the first electron (from the point at which the pumpkin is at its largest, say) the pumpkin claim goes from fully true to some tiny fraction less than fully true. So there is a decrease in satisfaction status with every subsequent situation.

But how could the satisfaction status of your linguistic noise ‘There is a pumpkin by the tree’ come to be so incredibly sensitive to microscopic changes inside the pumpkin? We still have linguistic miracles; sharpism hasn’t gone away. You seem to suggest that lots of tiny changes in alethic status are more plausible than one big change from ‘true’ to ‘false’. I’m not seeing how size matters. What I find incredible is the sharpist’s claim that your utterance of ‘There is a pumpkin by the tree’ could acquire an absurdly sensitive satisfaction condition, so the alethic status changes with an electron movement—and in that statement size or number of sharp cutoffs doesn’t matter. Even if we gathered exceedingly detailed data on language use, linguistic dispositions, and the nature of the physical environment, how on earth would all that detail have the result that your utterance went from one degree of truth to another with a nanometer movement of an electron inside the pumpkin?

Second, what counts as fully true? When in the pumpkin’s development does it become fully true that there is a pumpkin by the tree? Is it when it’s maximally big? Or is it never fully true? Moreover, and this is a slightly different point, what electron movements count as increasing the satisfaction status and which result in decreases? I can’t imagine defending any answers.

So, I guess I’m saying that the main objection to sharpism lies in the fact that we can’t imagine how our utterances and other remarks could acquire exceedingly sensitive satisfaction conditions. I read somewhere that Williamson somewhere says something like ‘Yes, but we don’t know how meaning gets fixed period, vague or precise, so don’t blame it on epistemicism’. Maybe if we had a decent idea of how meaning gets fixed we would find sharpism palatable. Yes, there are sharp cutoffs, but we can tame them with the appropriate theory of meaning.

Anonymous said...

Yeah, that's pretty much Williamson's response. It's in his 1992 paper 'Vagueness and Ignorance', reprinted in the Keefe and Smith reader.

Anonymous said...

Hi Brian,

I was thinking about a degree-theoretic sharpism. I guess one point to thinking about this case is to argue that there’s room for incredulous stares against Williamsonian epistemicism, even if you’re a sharpist. (Most degree theorists, I agree, don’t want to be sharpists. But I know at least a couple who are sharpists). The basic thought against sharpism-with-jumps, of the Williamsonian kind, is that it’s so damn arbitrary where the sharp cut-off comes. Why does the one and only shift in alethic status come there?

By contrast, I don’t find the idea of extreme sensitivity implausible (I might not like sharpist degree theories for other reasons, but extreme sensitivity isn’t a motivating factor). Just as a point of principle, consider the following extremely crude scenario: suppose there was a convention that the degree of truth of “x is tall” should track the height of x, so that “x is tall” is truer than “y is tall” iff x is of greater height than y. Though I don’t think that the degree theorist should endorse the thesis that there are such conventions (for the kind of reasons that Keefe outlines in her chapter on degree theories), and of course it’s far from a theory that would uniquely assign degrees of truth, I don’t find myself incredulously staring at the idea that practice could establish such a connection. But it does generate extreme sensitivity: if x is of greater height than y, even by a nanometer, the alethic status of “x is tall” and “y is tall” must differ. That’s enough for me to persuade myself that extreme sensitivity isn’t the main difficulty with a metasemantics for degree theories. (There are other good issues in the vicinity that you raise: such as, once we drop the idealizing assumption that all changes in the objects can be unambiguously classified as increases or decreases in height, how do we proceed? There’s a worry there, but it doesn’t seem to me to have anything particularly to do with extreme sensitivity, or, indeed, the sorites paradox).

Here’s a way of hearing all this as bluster: assume that “truth to degree 1” is truth simpliciter; and that all other degrees of truth are just so many ways of being untrue. Then it sounds like (1) the shift from true-to-degree-1 to any other degree of truth will be deeply significant (as significant as the epistemicists shift from truth to falsity, perhaps); (2) a degree theorist who tries to say that nothing (outside logic and maths, perhaps) is true-to-degree-1 will be revealed as a crypto-nihilist.

I think the degree theorist should do everything in their power to resist the identification of truth simpliciter with truth-to-degree-1 (of course, that's not to say that they *do* do this...). Perhaps they should say that truth is truth to a high enough degree, where it’s vague how high is high enough. Perhaps they should say, instead, that “truth simpliciter” should be eliminated in favour of the new, graded notions of truth. Either way, the burden should be put on the opponent to say why there’s anything particularly interesting or significant about truth-to-degree-1 (why, for example, do you think you can’t defend the view whereby “the pumpkin is large” is never true to degree 1?).

(There’s an intriguing connection here to Unger on flatness. It’s uncomfortable to say that something is flat, yet that there are things that are flatter. Likewise, it’s uncomfortable to say that something is true, yet there are things which are truer. But in both cases, I think we should resist the suggested implication: that only Euclidean planes or sentences that are true-to-degree-1, can be flat or true respectively).

Lastly, on the terminological issue. The reason I’m so opposed to using “epistemicism” for what we’ve been calling sharpism, is exactly that I can imagine lots of non-epistemicists being sharpists. As I’ve said, I know of a couple of sharpist-inclined degree theorists. There are also sharpist contextualists (Graff Fara) and supervaluationists (Heck). Prima facie, epistemicism is a theory of the nature of vagueness that competes with the semantic/pragmatic answers that such theorists offer. So it’d be surprising if they were to count as epistemicist. More plausibly, you might think that any sharpist has to be an epistemicist about higher-order vagueness (in particular, about the putative vagueness of “true to degree 1” or “supertrue” or “true in dthat context”). But there’s other options here: they could simply deny that such “higher order” predicates are vague at all. Anyway, whatever they say about the higher-order issues, it seems at best misleading to call them epistemicists simpliciter.

Bryan Frances said...

Hi Robbie,

First, thanks for continuing the discussion. It’s very helpful to me.

Second, I’ve been inclined to comment on several of your blog entries but I never feel as though I adequately understand what you’re saying. You, Ross, Andy, and all those other St. Andrewsish people use too many big words for an American hick like me (just ask Joe about what a hick I am, riding in my pickup truck with my dog and shotgun in the back). I know Andy didn’t go to St. Andrews but it always seemed like he did! (For those of you who don’t know what I’m talking about: I used to be at Leeds, Robbie replaced me there, and Leeds has Ross Cameron, Joe Melia, and Andy McGonigal.)

Third, I’m happier with ‘sharpism’ (my new phrase) than with ‘minimal epistemicism’ (my old phrase), for the reasons you give. And it doesn’t seem that ugly after awhile.

Fourth, as I write this I’m attracted to the idea that if we have to swallow sharpism, then whether there is just one cutoff (from ‘true’ to ‘false’) or zillions of cutoffs (as posited by degree-theoretic sharpism), is just a detail IF we’re focusing on the sorites. Sure, the number of cutoffs is very important for the theory of truth, but if what keeps you up at night is the sorites (this is true for me), then the thing you’ll focus your attention on after seeing the excellence of the argument for sharpism will be ‘How in God’s name do meaning-determining facts suffice to generate cutoffs?’ instead of anything like ‘How many cutoffs are there?’

Fifth, here’s why as I write this I’m attracted to that idea. We start with a wonderfully paradigmatic pumpkin in situation S1 (see my original post for review), and subsequent situations are generated by nanometer movements of constituent electrons. ‘There is a pumpkin by the tree’ is fully, completely, perfectly true for S1. Now you’re suggesting that it might decrease in alethic status for every subsequent situation. Thus, through some miracle the meaning-determining factors in S1 that set the semantics of the S1 use of ‘There is a pumpkin by the tree’ conspired to give it a semantics such that a nanometer movement of an electron more-or-less out of the pumpkin made that linguistic use less true. That just seems insane, right? Now aren’t you just peeing in your pants wondering how on earth the utterance of ‘There is a pumpkin by the tree’ managed to acquire a meaning so unbelievably discriminating? I am!

Sixth, I agree that degree-theoretic sharpism is more plausible for ‘tall’ than for ‘pumpkin’, but that’s because it’s reasonable that ‘tall’ “comes from” the scalar ‘taller’ while it’s not reasonable (right?) to hold the analogous view for ‘pumpkin’.

Seventh, I also agree that the problem with sharpism isn’t merely extreme sensitivity in meanings for vague terms. Instead, I’m guessing that it’s something like extreme sensitivity in meanings for vague terms when there is to all appearances nothing in our linguistic practice & dispositions to generate the sensitivity.

Eighth, here is an idea as to how utterances could acquire such sensitive meanings. (I got the idea from discussions with Andy!) There are these magical rules of interpretation that assign meanings to our linguistic moves. Andy called them (or something like them) ‘Mr. Context’. In carrying out their work, they employ a device I call the ‘random cutoff generator’. They use it in order to assign meanings. They are benevolent linguistic legislators. Unfortunately, I can’t see how to convert that germ of an idea into anything decent.

Anonymous said...

I think everyone should agree that there are at least two potential reasons to find sharpist views incredible: (a) extreme sensitivity of alethic status to miniscule changes in features of the situation description; (b) (seemingly) extreme arbitriness in the placement of a change of alethic status. What degree-theoretic multiplication of cut-offs gives you, arguably, is a way of getting rid of arbitriness: if there are changes everywhere, it’s no longer arbitrary that there are changes here. That seems a significant advance qua being a believable solution to the sorites, totally independent of any purely semantic/theory of truth significance that multiplying truth-values may have.

Of course, you can resist this by thinking that all the incredulity in the vicinity should be directed towards (a) rather than (b). But I don’t buy that at all. (Personally, it's (b) I find most shocking in epistemicism. Insofar as I find degree theory hard to swallow, it’s because it seems arbitrary how a sentence gets this exact degree of truth. That’s a quite different issue from the (allegedly) problematic feature that the degrees of truth of a sentence change from one case to another, which differ only in extremely small ways.)

In at least some cases (“tall” and other nicely behaved adjectives) extreme sensitivity doesn’t seem to me to be incredible. To your question “how in God’s name do meaning-determining facts suffice to generate cutoffs?”, a perfectly reasonable answer seems to be: they link the alethic status of “x is tall” to the height of x; and x’s height changes across the cut-off.

But I now see why you focused on the pumpkin case: it is much less obvious how to give a story that makes intelligible how extreme sensitivity arises with such nouns. I’m interested in the methodology here. What’s the objection supposed to be? That there’s some aspect of the pumpkin case that makes it in principle hard to see how extreme sensitivity could arise? Or that we can’t see in full detail in this case how extreme sensitivity arises?

On the latter point, I guess I just think it’s over-ambitious to demand a fully detailed answer to the pumpkin case. Someone once told me “hard cases make bad law”: I’d prefer to work with the simple, lab-room examples of very simple adjectives and nouns. If I can get an understanding of how extreme sensitivity arises in those cases, I’ll put down my inability to give a plausible explanation of how it arises in the pumpkin case, not to some problem-in-principle with extreme sensitivity, but to my lack of a full understanding of pumpkin-hood and its relation to pumpkin-making properties.

If the challenge is of the former kind, the first question to ask is: what’s supposed to be the aspect of the situation which is supposed to cause in principle difficulties? I’d think that the burden is now on you to say what that feature is. It’s not just that “pumpkin” is a noun. One can well imagine arguing that “boy” just means “young male human”, and so inherits all the extreme sensitivity of the well-behaved adjective “young”. (It is it really so mad to think that at least some of the (putative) incredible sensitivity of “pumpkin” could come from it meaning something like “mature fruit(?) of the pumpkin-plant”?)

Bryan Frances said...


I’m still having a hard time seeing how degree-theoretic sharpism (DTS) deals with (b), the extreme arbitrariness of cutoffs.

Here’s why. In S1 we have a paradigmatic pumpkin; in S2 we do as well, as the only difference is the presence of one electron. According to DTS ‘There is a pumpkin by the tree’ has changed in alethic status when evaluated with respect to S1 and S2. Suppose it is less true for S2 compared to S1. This difference in alethic status strikes me as arbitrary: why should ‘There is a pumpkin by the tree’ go down in alethic status because an electron has moved out of it? Why shouldn’t it go up in status? Or just stay the same? Surely, the pumpkin could change physically and not have that physical change be marked with a change in alethic status; there aren’t alethic changes literally everywhere. And when I think about how the pumpkin looks as the electron leaves ever so gradually, it seems arbitrary to me that THAT movement right there is the one that caused ‘There is a pumpkin by the tree’ to change its alethic status given that the previous movement of that electron didn’t cause any change in alethic status.

Let me try to put the point this way: it seems arbitrary to me WHICH electron movements result in alethic changes, and it seems arbitrary to me the VALUE of the alethic change associated with various movements (arbitrary in size and arbitrary in being positive or negative). I take it that the arbitrariness of epistemicism is akin to the first kind of arbitrariness: it seems arbitrary which electron movement resulted in the alethic status going from ‘true’ to ‘false’.

And what about ‘There is something pumpkinish or pumpkin-like by the tree’? Are we going to say that there are degrees of being pumpkinish?

Now for ‘tall’. I see how one could initially think the ‘tall’ case will end up okay for DTS, since we can envision how ‘tall’ gets a meaning so that if John is taller in T1 than he is in T2, then ‘John is tall’ is truer when evaluated with respect to T1 than with respect to T2—even when the difference in height is a nanometer. But the details of the case seem to raise the same issues as for the pumpkin—but not as a result of ‘tall’ but as a result of ‘John’s height’. The difference in T1 and T2 is that an electron left the surface of John’s head. What electron leavings result in decreases in height and which don’t? I think we get the same arbitrariness as in the pumpkin case.

I also think it’s a mistake to focus too much on the “easy” cases. It might turn out, ironically, that coming up with a plausible-sounding response to the sorites is easiest if we focus on ‘bald’, ‘tall’, and ‘red’. It would be ironic because those are the cases most theorists work on! I don’t see how to argue that just about every vague term is importantly akin to ‘tall’. Suppose ‘pumpkin’ in my utterance of ‘There is a pumpkin by the tree’ is truth-conditionally synonymous with ‘mature fruit of the pumpkin plant’, or something similar. I don’t see how that helps! Maybe this: x is more of a pumpkin than y iff x has more pure pumpkin stuff than y. But that doesn’t seem promising to me as a way around the arbitrariness difficulties.

I agree that in some sense it’s over-ambitious to demand a fully detailed answer to the pumpkin case. But I’ll settle for a sketch of an answer, and I don’t seem to have even that!

Anonymous said...

Ok, I think I'm seeing that the Pumpkin case is a different sort of beast to the kind of sorites argument that normally gets discussed. Let's call something a straightjacketed sorites series for F if we've identified some dimension of variation such that each member of the series is intuitively "a bit less of an F" than preceding members. Examples: plucking hairs and "bald"; removing grains and "heap"; changing tone and "red". You (Bryan) want the pumpkin case to be a non-straightjacketed sorites: part of what's at issue is whether the changes you make (removing the electrons one by one) makes it any the less a pumpkin.

Of course, for a given predicate, you'd imagine there will be both straightjacketed and non-straightjacketed sorites. It's easy to find straightjacketed sorites for "tall", and reasonably easy to find the same for "pumpkin" (e.g. by considering the pumpkin from bud to fruit: that's what I was thinking of in suggesting that "mature" might be part of it.) And in each case, we'll be able to find non-straightjacketed sorites (as you suggest, by taking a series where it's not clear that the people involved are or are not the same in height).

I'll have a think about the non-straightjacketed case. I'm still suspicious of it.

Here’s one way the concern surfaces. Let’s all agree that we’re ignorant of which electron movements make this thing less of a pumpkin. But we know some of them do. Question is: should we be disturbed just by that? I think not: because, for all we’ve so far said, it may be just because we’re ignorant of what sort of electron-shifts give rise to the sort of microphysical distributions that make a bunch of particles slightly less of a material unity (or whatever).

The thought is that there’s just so much about the relation between pumpkins and the arrangements of its electron parts, that I don’t know about, that it’s entirely unshocking that I’m ignorant of what happens when you move some of the electrons about. If there was a principled story about why this movement of an electron detracts from pumpkinhood of the whole, why that one doesn’t, I’m in absolutely no position to know about it.

The nice thing about straightjacketed sorites, is that they show there’s a distinctive puzzle left even when we’ve got all the information we could reasonably expect about how the features in terms of which the series is described, relates to the property on which we’re running the sorites.

So consider “tall” in connection to 1-dimensional connected lines, for example. Intuitively, once we know what the exact length of the line is, all the information is in regarding facts on which the tallness of such lines depends. But still we’re ignorant about which changes bring a change in alethic status of “tall”. And in such cases (or idealized versions of slightly less artificial cases) it seems there’s nowhere left to pin the blame for our ignorance: it seems the only thing left in play is how tallness relates to length.

p.s. The Unger article “there are no ordinary things” seems also to be dealing in non-straightjacketed sorites (unlike most of the rest of the literature). Would be nice to compare your argument with his.

hazlett said...

Bryan, it seemed at a few places like you were worried how the alethic status of any sentence could change as a result of such a minute physical change - that this would be a "linguistic miracle". Surely not for a sentence like 'The pumpkin by the tree has lost an electron', though. It's not a linguistic miracle how the truth of value of that depends on minute physical changes inside the pumpkin.

So is it this sentence ('There is a pumpkin by the tree') in particular, of which it seems incredible to say that it changes alethic status as a result of a minute physical change? Maybe a moral of the sorites: more sentences than we thought are like 'The pumpkin by the tree has lost an electron', in that their alethic status is subject to minute physical changes.

I second Robbie's point: We shouldn't give up the idea that the object becames less and less of a pumpkin as the atoms are removed. Let's admit that that doesn't happen at first - so let's imagine that the value of the pumpkin claim stays at 1 for a long time, but eventually, all this subtraction of atoms begins to wear on the pumpkin's constitution, so somewhere the pumpkin claim goes from value 1 to value 99.999. Is this incredulous-stare-warranting? Is is still incredulous-stare-warranting when we consider that the continued subtraction of atoms will eventually erode the pumpkin into a pile of mush and seeds, at which point the pumpkin claim will have a much lower truth value? Point: I think it's not hard to accept that the subtraction of atoms, at some point in the series, really does make the pumpkin less of a pumpkin than it was before.

We know something about which atoms matter, don't we? For example, the atoms in the stem don't matter. You could take as many of them as you want, and the pumpkin claim is just as true as it was before. (Worry: this might depend on context, e.g. a bazaar at which pumpkins are being sold for their stems. So scratch that thought for now.)

Bryan Frances said...

Robbie and Allan,

I agree that it’s no surprise how a sentence such as ‘The pumpkin by the tree has lost an electron compared to how it was at time t’ could be false when evaluated with respect to one situation A and then true when evaluated with respect to temporally subsequent situation B even though the only difference between A and B is the movement of an electron. The sentence has parts that make the sensitive truth condition make sense.

But I don’t see anything in the sentence ‘There is a pumpkin by the tree’ that could make it true when evaluated with respect to one situation X and then false (or any alethic status other than true) when evaluated with respect to temporally subsequent situation Y even though the only difference between X and Y is the movement of an electron. So, is there something in the context of utterance, say, that gives it such a discriminating truth condition? We’ve never seen anything that does the job as far as I know.

And I don’t see how the degrees of truth idea helps much. I agree that the degrees of truth idea is attractive on its face, for reasons having nothing to do with the sorites. But what I find incredible is this idea: the utterance of ‘There is a pumpkin by the tree’ has truth-value 1 when evaluated with respect to situations S1 through Strillion and yet it has truth-value .99999 when evaluated with respect to Strillion-plus-one. Again, what I find problematic is the idea that the utterance could have acquired such a discriminating truth condition—given that there is nothing in the sentence itself or the context that could generate the sensitive truth condition.

Could something about 'joints in nature' do the trick? I don't see how, especially when we consider sentences like 'It is noonish' and, more to the point, 'There is something pumpkin-like by the tree'.

I hope that makes sense.