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June 27th, 2004

New Paper!

I just wrote a short paper responding to some suggestions by Nick Smith in his paper Vagueness as Closeness. The title is rather utilitarian, and I haven’t checked over the paper greatly (e.g. to check I haven’t left off anyone from the thanks list) but it seems good enough to blog post.

Three Objections to Smith on Vagueness

Posted by Brian Weatherson in Uncategorized

2 Comments »

This entry was posted on Sunday, June 27th, 2004 at 4:43 pm and is filed under Uncategorized. You can follow any responses to this entry through the comments RSS 2.0 feed. Both comments and pings are currently closed.

2 Responses to “New Paper!”

  1. Nick Smith says:

    Wow! When I posted my paper with a request for comments, I never dreamed
    of getting such a detailed and thought-provoking reply. Many thanks indeed.

    Some responses to your three points.

    (1) Vagueness without boundaries.

    I have already been tinkering with my view, to get over some other problems
    in this area. My original response to the Fine (tall or exactly four feet
    in height)/Weatherson (early thirties) problem was to say that a predicate
    is vague simpliciter if it non-vacuously satisfies Closeness across the
    entire domain of discourse, and is in part vague if it is not vague
    simpliciter, but there is some subset of the domain of discourse over
    which it non-vacuously satisfies Closeness. Even apart from your problem,
    however, this will not do, because there is a subset of the domain of
    discourse over which intuitively precise predicates such as ‘is
    greater-than-or-equal-to exactly four feet in height’ non-trivially satisfy
    Closeness: the subset consisting of people less than three feet in height
    or more than seven feet in height (thanks to an anonymous referee for this
    point!).

    My current thought is to avoid this problem as follows. We say that a set
    S is F-connected iff for any two objects in S, either they are very similar
    in F-relevant respects, or they can be linked together by a chain of
    objects, all of which are in S, with adjacent members of the chain being
    very close in F-relevant respects (this can be made precise, but not in
    plain text!). We say that a set S is F-flat iff for every a and b in S,
    ‘Fa’ and ‘Fb’ are very similar in respect of truth. If a set is not F-flat
    we say it is F-tilted. We now say that a predicate F is vague iff there is
    some F-connected, F-tilted subset of the domain of discourse such that F
    satisfies Closeness over this set. (To say that a predicate satisfies
    Closeness over a set S is to say that it satisfies Closeness when the
    initial quantifiers ‘for any objects a and b’ in the Closeness condition
    are taken as ranging over S. Note that we do not now need to include the
    ‘non-vacuousness’ requirement.) A predicate is vague simpliciter iff it is
    vague, and furthermore satisfies Closeness over every F-connected,
    F-tilted subset of the domain of discourse. A predicate is in part vague
    iff it is vague but not vague simpliciter. Thus ‘tall’ is vague
    simpliciter, ‘is tall or exactly four feet in height’ is in part vague, and
    ‘is greater-than-or-equal-to exactly four feet in height’ is not vague.

    Now for your case of F_170. I’m not quite sure how you intended the case,
    i.e. what you mean by saying person A, who is 170cm in height, is tall but
    not definitely tall. Option (a): ‘A is tall’ is true simpliciter/true to
    degree 1/etc., but A is, say, in an epistemic penumbral region for ‘tall’.
    (b) ‘A is tall’ is neither true simpliciter nor false simpliciter/‘A is
    tall’ has a high degree of truth but it’s not equal to 1/etc. Considered
    in turn:

    (a) F_170 is not vague by my definition, but I am happy with that result.
    To my intuitions at least, if everything is a degree-1 instance of F_170,
    then F_170 is not vague, even if we cannot know whether some things A are
    degree-1 instances of F_170.

    (b) F_170 is ‘in part vague’ by my definition, and by my intuitions.

    The only remaining issue is what happens when we get to n such that F_n has
    a jump down in truth value when we cross height n, but such a small jump
    down that ‘B is tall’ (B’s height is n or just under) and ‘C is tall’ (C’s
    height is just over n) are very close in respect of truth. In this case
    F_n is not vague by my definition, but I can live with that.

    (2) Lumpy boundaries.

    You say ‘If He’s late is true to degree 0.6 just before quarter past, and
    degree 0.8 just after, that’s clearly a violation of Closeness. But this
    seems perfectly compatible with the predicate being vague.’

    I don’t see a problem here: If your assumption here (that He’s late is
    true to degree 0.6 just before quarter past, and degree 0.8 just after) is
    granted, then the predicate will be in part vague by my definition, and
    by my intuitions. On the other hand, we might think about ‘late’ that your
    assumption is not true: there is no jump in truth value. Rather, the
    predicate is wholly vague—-the truth value of ‘He’s late’ changes
    continuously as his arrival time increases—-but after quarter-past we
    know that the degree of truth of the claim is now sufficiently high to
    confidently assert ‘He’s late’. So quarter-past does not represent a jump
    in truth value—-just a ‘safe point’ at which we can be quite confident in
    asserting ‘He’s late’.

    (3) Generality.

    I say some stuff in the paper about noun phrases. I do think my view
    handles these smoothly, but I will be saying much more about them in future
    work (near future, I hope). As for very and if, I don’t have any
    intuitions about their vagueness or lack thereof. I have intuitions about
    ‘very tall’ and so on, but no intuitions either way concerning whether
    ‘very’ by itself is vague. I would only be troubled if there were some
    words which intuitively seem akin to vague predicates, but which my
    definition does not cover (e.g. if it only covered one-place predicates,
    not many-place predicates). That would show my definition was worryingly
    specific. But ‘very’ and ‘if’ don’t feel like that. The real question
    about ‘very’ and vagueness seems to be: what in general is the
    relationship between the vagueness of ‘F’ and the vagueness of ‘very F’.
    My view has the resources to make sense of this question. But is there
    really a question as to whether ‘very’ by itself is vague? I just don’t
    feel any force to this question, so I’m not worried that my view does not
    have the resources to make sense of it.

    I think the point about vague pictures is very interesting. There’s an
    important distinction here though. A picture is like a particular
    utterance. When defining vagueness, most people focus on word types. It’s
    one thing to ask what the vagueness of ‘bald’ consists in, another to ask
    what the vagueness of a particular utterance ‘Bob is bald’ consists in. I
    guess I would probably want to say that pictures can be
    indeterminate—-there can be different, equally correct interpretations of
    what a picture is telling us, i.e. different accounts of its content—-but
    maintain this is different from vagueness. On your view of what vagueness
    is, however, pictures could be vague in much (or exactly, depending on the
    details) the same sense as linguistic items.

  2. Brian Weatherson says:

    Just a few quick follow-ups on Nick’s points.

    I wasn’t defining F170 in terms of degrees of truth. I just wanted 170 to be a height where an adult woman that height was tall but not definitely tall. I don’t know how you want to analyse that in terms of degrees of truth. (I know how I analyse it – as such a woman being tall and it being less true than 0=0 that she’s tall.) It seems a bad thing if this isn’t possible on a given analysis (because it seems it means you can’t have a theory of higher-order vagueness) and as soon as its possibility is shown I’ll have a way of creating the example.

    That might (might – I’m really not sure how higher-order vagueness goes on numerical degree theories) be to say I agree with Nick’s second way of putting the problem in the last paragraph, except I do think it’s a problem.

    I do think there’s a hard issue about whether ‘very’, and in particular ‘if’ is vague but maybe there’s not much more than issues of motivation here.

    I have a fair bit more to say on lumpiness, but maybe I’ll leave them for an actual post.