Tuesday, September 27, 2005

Shifting The Problem?

'Boundary-shifting' approaches to the Sorites paradox propose that Soritical reasoning only looks convincing because the boundary for the correct application of a vague predicate shifts as we consider different items in the Sorites series. On every occasion, the predicate has some precise boundary, but whenever we consider two successive elements in the series our very doing so makes it the case that the boundary does not lie between those two items. As Delia Graff puts it in this paper, ‘the boundary can never be where we are looking’. This boundary-shifting effect is taken to be responsible for the prima facie plausibility of the (false) major premises in Sorites arguments.

But there is a limited range of possibly-acceptable positions for the boundary of a vague predicate (at least, this is true for many vague predicates). Graff accepts this - she describes constraints of the kind I have in mind here as ‘clear-case constraints’ - and it is very hard to see how anyone could deny it.

However, familiarly, what counts as a ‘clear case’ for the application of a vague predicate is itself a vague matter. So clear-case constraints seem to determine a range of acceptable positions for the boundary of a vague predicate which range is itself vaguely defined. (Of course, there will also be other constraints on the extension of the predicate on any given occasion, but these are not relevant here.)

If we adopt any kind of boundary-shifting view, then, we should consider that one important kind of vagueness associated with a vague predicate is vagueness in the range, across contexts, of acceptable positions for the boundary. And this seems to raise issues. For one thing, it looks as though the full account of the vagueness of our original predicate ('is red', say) will in the end have to make mention of the vagueness of another predicate ('is a clear case of redness'). And a similar thing will happen when we come to give an account of the vagueness of the latter predicate, and so on ad infinitum.

Two questions about this:
1. Do we ever really get a proper account of the vagueness of the original predicate if this infinite regress gets going?
2. Isn't the first step problematic enough by itself? Can we really hope to make progress in understanding the vagueness of 'is red' with an account that invokes the vagueness of 'is a clear case of redness'? Surely our understanding of the latter derives from our understanding of the former, not vice versa?

I'd be interested to hear comments and/or indications of where to look for discussions of this sort of point in the literature. (I know Graff has a paper forthcoming in the Proceedings of the Aristotelian Society on boundary-shifting and higher-order vagueness. Anything else?)

Thursday, September 22, 2005

Time For Fitch

John Burgess has a paper here on a temporal analogue of Fitch's paradox: if whatever is true will be known, then whatever is true is known.

Using 'Kp' to mean 'It is known that p' and 'Fp' to mean 'it sometime will be that p', the analogue of Fitch's paradox is that from:
1: p --> FKp
together with the usual assumptions about knowledge, it appears we can derive 2: p --> Kp
We do this by noting that 1 implies
3: (p&¬Kp) --> FK(p&¬Kp)
but that the consequent of 3 is impossible, so that from 1 we can derive the negation of 3's antecedent, which is (classically) equivalent to 2.

Here, however, an analogue of Edgington's response to the vanilla Fitch paradox looks particularly easy to defend. Just as Edgington's anti-realist says that what's knowable are things of the form 'actually p', the defender of the future-knowledge principle should say that what's knowable are things of the form 'at t, p', where 't' is a name for whatever time it is now. This means that instead of 1 we have
1': p --> FK[p was true at t]
and instead of 3 we get
3': (p&¬Kp) --> FK[(p&¬Kp) was true at t]
the consequent of which is unproblematic.

Given, however, that Edgington's solution to vanilla Fitch is beset with objections, it's not clear how thinking about this temporal analogue can really throw any light on the original puzzle, as Burgess seems to hope it will.

Thursday, September 15, 2005

Relativism and Other Animals

Brian Weatherson has just posted a substantial blog entry on Types of Relativism - something I got interested in here a while ago. Brian offers a taxonomy of 18 logically possible positions, of which he thinks only eight are interesting, consisting of various possible combinations of 'Invariantist', 'Contextualist' and 'Relativist' views on three different issues: utterance content, utterance truth-value and proposition truth-value.

I was hoping I could write a post on how the six positions I talked about in my post relate to Brian's eight positions, but, after working out that Brian's III is not one of my positions - because it's not any kind of relativism-like view - I got confused by the following.

Brian's definitions of 'Invariantism', 'Contextualism' and 'Relativism' are all given in terms of the variation (or lack thereof) of some value (content or truth-value) with what he calls 'context'. I wasn't clear, though, whether this was meant to be the utterer's context, the context of the assessor of the utterance, or whether Brian intends to allow that it could be either (and/or maybe other things besides, such as subject's context). Given that he classes Cohen-DeRose-Lewis contextualism as one of the views definable in terms of his I/C/R classification scheme, I guess that utterer's context must be of importance sometimes. But in the theist graffiti case he explicitly discusses assessor's context. If we don't get clear on whose context it is that matters, surely we overlook an important dimension of variation in the various available views here.

Another point: Brian's contextualist is someone who thinks that:
Any token has the same value in all contexts, but some tokens of the same type take different values
Presumably, though, the reason for calling such a view 'contextualist' is that the explanation of the difference in values is required to have something to do with context (and by my understanding of how the term 'contextualist' is generally used, this would usually be utterer's context).

Monday, September 12, 2005

Most Of Us Prefer Our Own Kind (To Goodhart's)

This is a little off my beaten track, but a bad argument is a bad argument. David Goodhart argues in this month's Prospect that the Human Rights Act is a threat to national security (because it problematizes e.g. the deportation to countries where they may face torture or degrading treatment of individuals perceived to present a terrorist threat, and the detention without trial of such individuals). UK citizens have rights, he says, (mainly) because they are UK citizens. Non-citizens don't share them. ('People are not born with [rights] and, regrettably, many .. have few or none'.) But of course, he acknowledges that 'we would ... like the rights currently enjoyed by people in developed countries extended to the rest of the world too'.

Surely we have two options with rights-talk: we could call 'rights' the things that are actually respected, or we could call 'rights' the things that should be respected. This terminological difference makes no difference to the question of which things should be respected. And as soon as we acknowledge that whatever rights UK citizens enjoy should be extended to everyone, there seems to be no basis of the kind Goodhart wants for an argument that non-UK-citizens should be treated differently to UK citizens.

Goodhart seems to think that non-UK-citizens should not be extended certain rights if they 'hate us and may attempt to harm us'. Whether or not such attitudes and potential behaviours are relevant to the forfeiting of rights, however, no argument is given that UK citizenship is similarly relevant. So it isn't clear why, even if one agrees that one can forfeit rights because of what one might do, the appropriate conclusion is not that anyone who 'hates us and may attempt to harm us' forfeits the rights in question.

(Perhaps, though, it is not so surprising to see an unargued preference for UK citizens in someone who thinks that "[t]o put it bluntly - most of us prefer our own kind").

Thursday, September 08, 2005

Non-Cognitivism and Anti-Realism

Here's a question that's been bothering me for a while. (I seem to remember that someone - it could have been Gideon Rosen - raised something like it in the discussion following my talk at the last Arche Modality Workshop.)

Could one be a non-cognitivist about (say) ethics without thereby being an ethical anti-realist in the sense I favour, i.e. without believing that what it is for an ethical proposition to be true is for us to be some way?

Suppose you're a non-cognitivist about ethics because you think ethical discourse is expressive of our attitudes. Surely you'll therefore agree that what it is for murder to be wrong is for us to have a certain kind of attitude to murder?

One reason why you might not agree is that you might think that nothing is what it is for murder to be wrong. You might think that there is no way for the world to be that would correspond to murder being wrong, since ethical discourse does not correspond to states of affairs or facts in the way a cognitive discourse does. But if someone were to claim that what it is for murder to be wrong is for us to disapprove of it, we would take her as saying that there are ethical facts, it's just that they are facts about our attitudes.

But why should we take 'what it is for' (WIIF) talk as talk about states of affairs or facts, when we're dealing with a non-cognitive discourse?

Presumably one motivation for resisting the anti-realist WIIF claim supposed to be that when we say 'murder is wrong' we aren't asserting that we disapprove of murder. But to claim that what it is for murder to be wrong is for us to disapprove of murder is not to claim that when we say 'murder is wrong' we are asserting that we disapprove of murder. (Similarly, to say that mental states are brain states is not to say that when I say 'I'm happy' I'm asserting that I'm in brain state B. I may never have heard of brain state B.)

Monday, September 05, 2005


I am a bit puzzled by the modal claims often made concerning the relation between a proposition's being true and its truthmaker existing. Here's one of the sources of my puzzlement.

Suppose you think facts (actual worldly states of affairs) make propositions true. In particular, suppose you think that the fact that Mu and Marks purr is what makes true the proposition All Carrie's cats purr.

Why should you think that it is impossible for the same fact to obtain without making proposition true? Consider a world where I have two more cats besides Mu and Marks, and one of these other cats does not purr. In this world, the fact that Mu and Marks purr still obtains, but does not make true All Carrie's cats purr.

I guess it could be said that the truthmaking fact in the actual world is not the fact that Mu and Marks purr but the fact that all Carrie's cats purr. But I wonder whether this sort of fine-grained individuation of facts is in keeping with the conception of them as worldly states of affairs (which, presumably, are supposed to have some degree of independence of the different ways in which we can represent them).

Why do we want a modal tie between the existence of the truthmaker and the truth of the proposition, anyway? We want truthmakers to have some special relationship to the propositions they make true, of course, but why this sort of special relationship? Wouldn't it be better to drop the claim that a proposition p's truthmaker is something that could not exist without making p true, and say instead that p's truthmaker is that thing in virtue of whose existence p is true? (NB: I intend these all as genuine, i.e. not merely rhetorical, questions!)

Sunday, September 04, 2005

Demands of Fairness

Last Friday, Michael Ridge presented a paper at a workshop here in St Andrews on Moral Demandingness.

Ridge discussed obligations entered into collectively by groups of agents - in particular, what happens when one member of the group fails to meet her share of the obligation. He argued that considerations of fairness impose a duty on the remaining parties to divide the extra burden created by this neglect as fairly as possible between them. For instance, suppose I and two friends collectively promise to pay you £9 in return for some service, planning to pay £3 each. Then one of my friends refuses to pay anything. According to Ridge, fairness imposes a duty on you, myself and the remaining friend each to sacrifice the same amount as a result of this refusal. So I and the remaining friend should pay you £4 each, so that you get £8. That way, the cost to each of us of the friend's refusal is £1: you miss out on £1 of your payment and my friend and I pay £1 more than we were supposed to.

There is something appealing about this. But on the other hand there's something appealing about the thought that all that fairness requires of me is that I pay my agreed share of £3. It doesn't seem to be required by fairness (though it may be virtuous and supererogatory) that I pay more than my share (we want to say: more than my fair share) just because someone else has neglected her part in the collective obligation.

So it looks like there's a sense in which fairness requires nothing more of me than that I pay £3, and a sense in which fairness requires that I pay £4. It would be nice to hear more about what these two senses are, in order to lessen the feeling of contradiction. (For what it's worth, my instinct is that the feeling is not genuine.)

Saturday, September 03, 2005

Encore d'ECAP

Michael Devitt offered some thoughts at the ECAP on why referential uses of definite descriptions should not be thought of as conventional implicatures. Were they such, correct referential uses of 'The F is G' would convey both a proposition about whatever is uniquely F and (by implicature) a proposition about a particular thing. But (according to Devitt) in many cases the former is not conveyed at all. Consider for instance 'The book is on the desk'. This usually isn't supposed to convey any claim about some thing which is uniquely a book.

It might be argued in response that the speaker's quantifiers are supposed to be suitably restricted so that there is only one book in their range, or that 'the book' is elliptical for some longer description (such as 'the book in front of us'). But Devitt thinks this can't always be right, because in many cases, an uninformed or misinformed speaker would be unable to supply the required restriction on the quantifier or the required non-elliptical description.

I asked whether it is really fair to demand that the speaker be able to supply these things. Devitt replied that it must be facts about the speaker that determine the range of her quantifiers or the full form of her elliptical descriptions. But I wondered why it needs to be facts which are accessible to the speaker (as opposed to, say, facts about the speaker's causal relation to the world and/or other speakers of her language).

Friday, September 02, 2005


Other interesting ECAP sessions included a talk by David Liggins (PhD Sheffield, shortly to take up a year of Analysis-funded research in Cambridge), fearlessly delivered at 9.30am on the first morning of the conference, entitled Naturalism and Nominalism. David suggested (without endorsing) a new way for nominalists about mathematics to accommodate the fact that mathematical theories seem committed to mathematical objects. They could accept that mathematicians utter lots of sentences which express propositions that entail such commitment, but deny that this means they are committed to theories which contain those propositions. When a sentence of this kind is utterered by mathematicians, on the proposed view, what thereby gets put into the mathematician's theory is not the proposition p expressed by the sentence but some other proposition (David suggested some proposition concerning the provability of p from certain axioms). I'd be interested to hear more about what reasons we could have for thinking that what gets put into the theory is a different proposition from the one expressed, as opposed to thinking that a different proposition was being expressed from the one you might have expected.

I should also mention that I was pleasantly surprised to find myself in a Philosophy of Maths talk later on in the same stream where the women in the room outnumbered the men by five to one. This was unprecedented in my experience!

That afternoon I went to a paper on measures of coherence (of the kind Coherentists would seem to need in order to assess how justified our beliefs are), written jointly by Luca Moretti and Ken Akiba and presented by Moretti. One point that came up here was whether logically equivalent sets of sentences were always equally coherent. The speaker thought so, but I was sceptical. Suppose that P in fact entails Q. Then the set {P, Q, P entails Q} is logically equivalent to {P, Q}, but you might reasonably think it was more coherent.

More paper reports to follow soon, I expect!