Tuesday, March 21, 2006


First we take Manhattan, then we take Berlin

It's going to be an interesting and busy few weeks. Tomorrow I'm speaking to the undergrad association here at UT about vagueness and how it impacts on central debates they'll be familiar with (I hope!) in ethics and other areas of philosophy.

Then early next month the UT first years invade the State of New York. Firstly, John Bengson and I are presenting at the NYU/Columbia grad conference that's running the 1st and 2nd of April. For better or worse, I'm giving my vagueness paper 'The Price of Bivalence' again (hence the posts on Graff last week). Then the weekend after that Briggs Wright AKA Captain Awesome is giving a paper about kidnapping ghosts and stuff like that at the Buffalo conference on the work of Jonathan Lowe.

The weekend after that is the UT grad conference, where it looks like I'll be responding to Kenny's critique of Stanley and Williamson's account of know how. It should be a fun session, and we're expecting Stanley to be there which should ensure things are interesting. We're just finalising the other respondents before we can put the list of papers and schedule up on the website. Watch this space.


Friday, March 17, 2006


To infinity and beyond (maybe)

I noticed tonight that Pioneer - yes, the electronics company - have tamed the infinite.

But before you get all impressed, notice that they don't say how big the set of variations of hues is. For all they say, it might only be countable.

Update: It looks like Pioneer really overshot it with the infinite.


Sunday, March 12, 2006


What Price Bivalence?

(Cross-posted at Arche)

In a talk I've been giving various places recently, I've argued that Delia Graff's theory of vagueness, like other theories which hold onto bivalence, runs into trouble with the forced-march Sorites. Here's the worry in brief. Graff explains our ignorance of where the boundary in a given series lies with the following similarity constraint:

'..if two things are saliently similar [in the relevant respect], then it cannot be that one is in the extension of a vague predicate, or in its anti-extension, while the other is not.' (2000: 57)

The idea is that whenever one is evaluting a pair of items in a suitably constructed Sorites series, both will be saliently similar, and so either both are in the extension of the predicate in question or both are in the anti-extension; the boundary is never where we are looking for it. This also gives an explanation of why we are liable to find Sorites reasoning compelling despite its invalidity (something critics have complained is entirely missing from Williamson-brand Epistemicism, though it's a central concern in Sorensen's Vagueness and Contradiction).

But now imagine a subject shown the items in a Sorites series in order, and asked of each whether it is in the extension of the relevant predicate or the anti-extension. Given the way the series has been constructed, she can neither competently judge all of the items to be in the extension, nor all of the items to be in the anti-extension. So at some point she must 'jump'; that is, judge some item n to be in the extension, yet judge item n + 1 (differing only marginally in the relevant respects from n) to be in the anti-extension. But by the similarity constraint, the boundary in known not to lie between n and n + 1, so how can her judgements be viewed as competent?

As Derek Ball, Geoff Georgi and Crispin Wright all rightly pointed out to me in various discussions, Graff has an answer to that question ready. It's essentially that of Diana Raffman in 'Vagueness without Paradox' (1994); when the subject judges n to be in the extension, n + 1 is too, but when the subject jumps, the boundary shifts so that now both n and n + 1 are in the anti-extension. So the subject's judgements can be seen as competent, yet the similarity constraint is never violated. As Raffman writes (1994: 57):

'There are shifts - events that occur - but these are best viewed as Gestalt like changes of “perspective” or “anchor,” not as boundary crossings - at least not if by ‘boundary’ you mean something that installs a simultaneous and/or fixed category difference between adjacent patches.'

It's clear that my original objection fails to engage with this kind of response, but I've been wondering how it's actually meant to work, given Graff's committment to bivalence - I've reached the conclusion that it doesn't. In presenting the forced-march above, I assumed that the subject only had two available responses. But we should be able to drop this assumption and allow the subject to respond as she likes (see for example Raffman 1994: 45-6). Suppose the subject judges n to be in the extension; then n + 1 is also in the extension. Now suppose when confronted with n + 1, the subjects responds 'I don't know', or 'There's no fact of the matter', or 'It's neither in the extension nor the anti-extension'. How does a shift in the location of the boundary such that both items are now in the anti-extension help to ensure that the subject says something competent? The problem is this; the boundary is supposed to shift so as to accomodate the speakers judgements - that's how we can see the subject who jumps in the face of the forced-march as doing something competent - but while there are a number of judgements a subject might return, the endorser of bivalence only recognises binary options for accomodating them.

(In a recent Analysis note ('How to understand contextualism about vagueness', 2005) Raffman explicitly considers what would happen on her earlier view when a subject switches from judging items to lie in the extension of the relevant predicate to judging them to be borderline. But the issues I raise above don't get into sight, simply because in a parenthetical remark she assumes '[f]or the sake of argument only' that we're working in a three-valued logic (246). With the assumption in place the subject's judgements can be accomodated, but that doesn't help us see how the trick is to be pulled whilst retaining bivalence.)

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Friday, March 03, 2006


Could a priori knowledge be subject-sensitive?

(Cross-posted at Arche. Apologies for overlap with my previous post here.)

Here's a question that arose out of reading Thomas Crisp's recent Analysis note, 'Hawthorne on Knowledge and Practical Reasoning'.

According to Delia Graff's theory of vagueness ('Shifting Sands', 2000), contextualism gets something important wrong, and something important right. Contra the contextualist, vague predicates like 'heap' and 'bald' express the same property throughout their respective suitably constructed Sorites series. Yet changes in the practical interests of a subject making judgements with such predicates determine shifts in their extensions (shifts not attributable to changes in the relevant comparison class, etc), and the resulting picture of the semantics of such expressions i. invalidates Sorites reasoning, ii. explains why we find such reasoning intuitively compelling, and iii. does not require us to give up classical logic or semantics. So the contextualist has something like the right idea, but the hope is Graff's theory delivers the same package whilst neatly avoiding some familiar problems with contextualist approaches.

Now, while the extension of a vague predicate is sensitive to the practical interests of the relevant subject, there are restrictions on such boundary-shifting; just as admissible sharpenings for a supervaluationist must respect the clear polar cases, Graff suggests that on her view the interests of a subject can never determine that the boundary shifts so that, to take an extreme case, a man with no hairs on his head is in the anti-extension of 'bald'. There's something very reasonable about this requirement, but last summer I remember Carrie, Robbie, and other people around the Vagueness project wondering whether Graff really needs or is entitled to it.

Crisp's note suggested to me that there might be a similar issue for interest-relative invariantism (IRI) about knowledge, as defended in Hawthorne and Stanley's recent monographs. According to IRI, contextualism about knowledge gets something important wrong, and something important right. Contra the contextualist, the property expressed in knowledge ascriptions is invariant. Yet changes in the practical interests of a subject determine shifts in whether or not their true beliefs count as knowledge (even keeping their evidence fixed). So whether or not a subject's true belief counts as knowledge depends on non-epistemic (at least as traditionally conceived) features of their circumstances, such as how high the stakes are regarding the possibility that they're wrong.

The parallel question to the one we might want to ask the boundary-shifter about vagueness is this; could it ever be the case that the consequences of being wrong about the truth of a proposition are so disasterous that knowledge attributions are defeated, despite the proposition enjoying some (putatively) priviledged epistemic status (apriority or analyticity, for example)? Crisp's paper suggests that without some Chisholming, Hawthorne's formulation of IRI does indeed allow this possibility. Is there a neat way to avoid such a committment, or is it just a consequence of IRI (unless we do some special-pleading regarding a priori knowledge)? If it is a genuine committment, is that a particuarly bad result? There certainly seems something somewhat counter-intuitive about it, but are there materials for an objection?

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