the boundaries of language

Apologies for the lack of posts recently. I spent most of last week up in St Andrews for the Arche Vagueness Conference, which unsurprisingly turned out to be a very fun trip.

Let me take the chance to thank Andreas, Ole, Ralf and Andri, who very kindly put me up, and enabled me to be part of an effort to break the world record for the number of male philosophy graduate student bloggers simultaneously living under one roof. Cosmic. (Dan was also in town for the conference, and I got the chance to meet Avery, so, to adapt Nick Asher's joke, St Andrews seemed blogger-dense; between any two philosophy bloggers there was another one.)

The talks themselves were a slightly mixed bag, as always. I don't have much to add to the exchange between Andreas and Dan on Nathan Salmon's paper. I found myself very dissatisfied with Scott Soames' attempt to respond to the Dummett-Glanzberg challenge to the possibility of truth-value gaps (see here for links and discussion). Basically (and no doubt wildly oversimplified) the challenge is this. The intrinsic aim of assertion is truth, and either an assertion achieves that aim or it doesn't. So there are only two possible verdicts concerning whether an assertion achieved its aim; the idea that there might be assertions which fit into some third bracket is just incoherent. The suggested upshot is that a third truth-value is, at best, radically unmotivated.

I'm not really sure what to make of the Dummett-Glanzberg line of reasoning. Soames, however, attributed to them the thesis that truth is the norm of assertion, in the sense that Williamson has given that phrase; the thesis that it's constitutive of the speech act of assertion that one must only assert the true. He then recycled Williamson's arguments for favoring the knowledge rule of assertion over the truth rule, concluding that all the Dummett-Glanzberg argument showed is that his position is inconsistent with an incorrect account of the norm of assertion. But there wasn't even so much as a comment on the switch from talking of the aim of assertion to talking of the constitutive norm of assertion, and the two are quite different. It might well be true that the intrinsic aim of an assertion is to hit the truth, and the argument that truth is a binary notion can then proceed in the envisaged manner from the observation that whether that aim has been achieved is itself a binary matter. But that is, so far as I can tell, consistent with holding that the norm governing the making of assertions is more demanding than truth (for instance, the knowledge rule) or even less demanding (like the reasonably- or rationally-believed rules). Certainly there's some work to be done getting clear on the idea of an 'intrinsic aim' of assertion. But Soames' take seemed utterly uncharitable - aside from any other issues, the attribution of the thesis that only truth warrants assertion to the Dummett of 'Truth' should have raised alarm bells concerning Soames' interpretation of the challenge. And even putting aside these doubts about whether Soames had correctly identified his target, it was difficult to feel he'd really engaged the issues; there was simply no discussion whatsoever of the many powerful criticisms that have been made of the Williamsonian account of assertion in the literature (including Matt's excellent defense of the truth account over the knowledge account). It just seemed to be taken for granted that Williamson's arguments must be cogent, something I think noone has the right to assume in the current climate.

We had a characteristically high-altitude discussion from John MacFarlane and Dorothy Edgington, acting as his commentator, on how to motivate degree-theoretic accounts of vagueness. The main sticking point between them was whether we should endorse Stephen Schiffer's suggestion that confronted with a borderline case of baldness, tallness and thinness, we should have just as much (or nearly as much) credence in the truth of 'x is bald and x is tall and x is thin' as we should have in each of the conjuncts, contrary to what would be the case if credences about borderline cases obeyed the axioms of classical probability theory. The case against Schiffer and MacFarlane, led by Edgington and Roy Sorensen, turned on the observation that our credence in the truth of 'y is bald and y is tall and y is thin' should be higher than the analogous claim about x, when y is a borderline case of thinness and tallness but a absolutely clear case of baldness. While the standard picture can accommodate this point easily, the alternative pictures proposed by Schiffer and MacFarlane both (more or less) assigned a conjunction the min of the three conjuncts, and so both claims would be assigned the same value.

Roy Sorensen's talk probably supplied the most entertainment value, and gave what, for me, was the quote of the conference:

'Epistemicism is a pie-eating competition, and the prize is more pie.'

The highlight, however, was the final session, with Crispin Wright giving his paper 'The Illusion of Higher-Order Vagueness', and Mark Sainsbury responding. I'd heard Crispin's paper last year in Austin, so there weren't any real surprises. But as Mark pointed out in his closing remarks on the conference, Crispin has been thinking about this issue for over 40 years, and we got a little bit of that distilled into 40 minutes in his talk. It left me looking forward even more to his collected papers on the topic, The Riddle of Vagueness.

Anyway, it was a real pleasure to be back in St Andrews; it was great to catch up with everyone, and I'm very glad I got to see the last official moments of the Vagueness project.

Labels: Conferences, Crispin Wright, Mark Sainsbury, Vagueness

In my earlier post, I argued that commitments one takes on in accepting that superassertibility is a genuine truth-predicate for some domain of discourse (at least if one holds, as Crispin does, that any genuine truth-predicate sustains a full disquotational schema) rules out the possibility of what I'll call "iceberg ahead!" states of information; states of information such that they warrant the assertion of some sentence P, but also warrant the assertion that one of the other necessary conditions for superassertibility isn't met (so either the grounds that confer warranted assertibility upon P would not withstand arbitrarily exacting scrutiny, or there is some extension to one's state of information which no longer warrants an assertion of P).

I was reading Wright's 'Intuitionism, Realism, Relativism and Rhubarb' after I wrote the original post, and it suggested to me an example of an "iceberg ahead!" state of information. Focus on 'disputes of inclination', so, for example, a dispute over whether rhubarb is delicious. Suppose that one holds firstly that 'Rhubarb is delicious' is warrantedly assertible by subject S just in case S likes the taste of rhubard; likewise, 'Rhubarb is not delicious' is warrantedly assertible by S just in S does not like the taste of rhubarb (Wright 2006: 57). Suppose also that one holds that truth regarding expressions of inclination is constituted by superassertibility (as Wright proposes in his paper, though he does not wholeheartedly endorse the proposal).

Finally, suppose that I do not at present like the taste of rhubarb, but I have resolved to eat it every day for at least the next forty days. I also have very good (perhaps inductive or testimonial) grounds for holding that if one tastes a food-stuff forty times one will come to like it. Given the above commitments, isn't this a case in which 'Rhubarb is not delicious' is warrantedly assertible by me, but assuming the credentials of my belief that my dislike of rhubarb will not survive the next 40 days to be sufficiently good, the claim that 'Rhubarb is not delicious' is not superassertible is also warrantly assertible (since my current state of information is such that I know that there is an extension of that state of information which will not warrant my asserting 'Rhubarb is not delicious')?

It might be a little unlikely that I'd ever find myself in quite this epistemic condition. But I don't find it a really bizarre case, and all I really need is that it strikes us as coherent.

Labels: Anti-Realism, Crispin Wright, Rhubarb

I've fallen behind with reading LanguageLog of late. Had I been more attentive, I would have known sooner that Professor Carlota Smith, of the linguistics department at UT, died a little over a week ago. I was fortunate enough to be her student for one semester, and the level of dedication she put into that one class, despite coping with constant bouts of chemotherapy, was astonishing. She will be missed by all those she taught.

David's post is here, and the department's page for her is here.

Labels: Linguistics

I haven't spent as long as I'd like on the details here, but I don't really have the time just now, so I thought I'd post and let the more logically competent point out in what way I'm misguided (on this, or some other issue of their choosing).

A number of philosophers (Brueckner, Kvanvig, etc.) have argued against Crispin Wright's suggestion that superassertibility is a truth predicate. I'm wondering if Church-Fitch reasoning doesn't give us a very quick route to the conclusion that they're right to challenge Crispin on this point.

A sentence 'P' is superassertible (SA 'P') iff it is warrantly assertible (WA 'P') and that warrant i. will 'survive arbitrarily close and extensive investigation' and ii. is not defeasible (that is, there is no extension, i', to our current information state i such that i' fails to warrant the assertion of 'P').

To set up the problem, we need the following three principles:

1. SA 'P' iff P
2. If SA 'P&Q', then SA 'P' and SA 'Q'
3. If WA 'P' and WA 'Q', then WA 'P&Q'

These are all pretty straightforward. (1) is just the disquotation principle for SA, which Crispin thinks has to hold if SA is genuinely to count as a truth-predicate. (2) says that SA is closed under &-elimination, which follows from the closure of SA under logical implication (which again seems pretty compelling if SA is a genuine truth-predicate). Lastly, (3) says that WA is closed under &-introduction, which again seems compelling (at least when we're restricting attention to sentences with only two conjuncts; perhaps the preface and lottery paradoxes should make us doubt this principle in its full generality).

Now, the objection I have in mind starts from the observation that SA is strictly logically stronger than WA; that is, SA 'P' -> WA 'P' but not vice versa. This doesn't imply, but seems to leave open the possibility of a sentence 'X' and state of information such that:

i. WA 'X' & WA '~SA 'X''

By (3), it immediately follows that,

ii. WA 'X & ~SA 'X''

But we have,

iii. ~WA 'X & ~SA 'X''

Contradiction.

The sub-argument for iii. is just standard Church-Fitch reasoning, with (1) in place of factivity and the knowability principle. Suppose,

iv. X & ~SA 'X'

Then by (1),

v. SA 'X & ~SA 'X''

Whence by (2),

vi. SA 'X' and SA '~SA 'X''

But then, by (1) again,

vii. SA 'X' and ~SA 'X'

So we can conclude,

viii. ~(X & ~SA 'X'),

which presumably suffices for iii.

I'm not spotting any gapping holes in this, though I'm sure others will be quick to point them out. (1) isn't a legitimate supposition if we endorse the following variant of the reflection principle for WA:

4. If WA '~SA 'P'', then ~WA 'P'

But I'm not seeing any good reason to adopt (4). My supposition in i. does seem to be a legitimate possibility; it might be unusual to be in a state of information which both warrants the assertion of a particular sentence and warrants the assertion that some expansion of that information state fails to warrant that sentence, but (in empirical discourse) the idea does not seem incoherent. Yet if I haven't messed up, it is incoherent if superassertibility is a truth-predicate (given the closure of WA under &-introduction).

Labels: Anti-Realism, Crispin Wright, Philosophy of Logic

In a footnote in her 'How to understand contextualism about vagueness: reply to Stanley', Diana Raffman writes:

'[Stanley] cites Scott Soames (2002: 445) as claiming that vague predicates are indexicals. I am sceptical of this reading of Soames, but I won't press the point here.' (Raffman 2005: 244fn)

I'd really like to have seen her press the point, since as it stands, I'm hugely confused. The first line of the passage from p445 of Soames 2002 (which is his PPR precis of Understanding Truth), quoted by Jason (in his 2003 Analysis piece which Raffman is replying to) is:

'To say that vague predicates are context-sensitive is to say that they are indexical.' (Quoted at Stanley 2003: 270)

And the final line is:

'If, as I believe, vague predicates are context-sensitive, then this is the model on which they must be understood.' (Quoted at Stanley 2003: 271)

Sandwiched in between is what appears to be an elaboration of the claim that vague expressions are indexicals. I'm intrigued to know what might support scepticism about Jason's reading of Soames here.

Labels: Jason Stanley, Vagueness