Theories 'n Things

Theories n things moves to wordpress

2008-03-28T09:54:00.002Z

I've decided to follow the recent lead of others and migrate this blog to a new wordpress site.

The big appeal for me of this is added functionality---in particular I'll be able to typeset logical notation using latex commands. Should make things prettier and easier.

Hope to see people over at the new site!

Paracompleteness and credences in contradictions.

2008-03-17T16:53:00.007Z

The last few posts have discussed non-classical approaches to indeterminacy.

One of the big stumbling blocks about "folklore" non-classicism, for me, is the suggestion that contradictions (A&~A) be "half true" where A is indeterminate.

Here's a way of putting a constraint that appeals to me: I'm inclined to think that an ideal agent ought to fully reject such contradictions.

(Actually, I'm not quite as unsympathetic to contradictions as this makes it sound. I'm interested in the dialethic/paraconsistent package. But in that setting, the right thing to say isn't that A&~A is half-true, but that it's true (and probably also false). Attitudinally, the ideal agent ought to fully accept it.)

Now the no-interpretation non-classicist has the resources to satisfy this constraint. She can maintain that the ideal degree of belief in A&~A is always 0. Given that:

p(A)+p(B)=p(AvB)+p(A&B)

we have:

p(A)+p(~A)=p(Av~A)

And now, whenever we fail to fully accept Av~A, it will follow that our credences in A and ~A don't sum to one. That's the price we pay for continuing to utterly reject contradictions.

The *natural* view in this setting, it seems to me, is that accepting indeterminacy of A corresponds to rejecting Av~A. So someone fully aware that A is indeterminate should fully reject Av~A. (Here and in the above I'm following Field's "No fact of the matter" presentation of the nonclassicist).

But now consider the folklore nonclassicist, who does take talk of indeterminate propositions being "half true" (or more generally, degree-of-truth talk) seriously. This is the sort of position that the Smith paper cited in the last post explores. The idea there is that indeterminacy corresponds to half-truth, and fully informed ideal agents should set their partial beliefs to match the degree-of-truth of a proposition (e.g. in a 3-valued setting, an indeterminate A should be believed to degree 0.5). [NB: obviously partial beliefs aren't going to behave like a probability function if truth-functional degrees of truth are taken as an "expert function" for them.]

Given the usual min/max take on how these multiple truth values get settled over conjunction and negation, for the fullyinformed agent we'll get p(Av~A) set equal to the degree of truth of Av~A, i.e. 0.5. And exactly the same value will be given to A&~A. So contradictions, far from being rejected, are appropriately given the same doxastic attitude as I assign to "this fair coin will land heads"

Another way of putting this: the difference between our overall attitude to "the coin will land heads" and "Jim is bald and not bald" only comes out when we consider attitudes to contents in which these are embedded. For example, I fully disbelieve B&~B when B=the coin lands heads; but I half-accept it for B=A&~A . That doesn't at all ameliorate the implausibility of the initial identification, for me, but it's something to work with.

In short, the Field-like nonclassicist sets A&~A to 0; and that seems exactly right. Given this and one or two other principles, we get a picture where our confidence in Av~A can take any value---right down to 0; and as flagged before, the probabilities of A and ~A carve up this credence between them, so in the limit where Av~A has probability 0, they take probability 0 too.

But the folklore nonclassicist I've been considering, for whom degrees-of-truth are an expert function for degrees-of-belief, has 0.5 as a pivot. For the fully informed, Av~A always exceeds this by exactly the amount that A&~A falls below it---and where A is indeterminate, we assign them all probability 0.5.

As will be clear, I'm very much on the Fieldian side here (if I were to be a nonclassicist in the first place). It'd be interesting to know whether folklore nonclassicists do in general have a picture about partial beliefs that works as Smith describes. Consistently with taking semantics seriously, they might think of the probability of A as equal to the measure of the set of possibilities where A is perfectly true. And that will always make the probability of A&~A 0 (since it's never perfectly true); and meet various other of the Fieldian descriptions of the case. What it does put pressure on is the assumption (more common in degree theorists than 3-value theorists perhaps) that we should describe degree-of-truth-0.5 as a way of being "half true"---why in a situation where we know A is halftrue, would we be compelled to fully reject it? So it does seem to me that the rhetoric of folklore degree theorists fits a lot better with Smith's suggestions about how partial beliefs work. And I think it's objectionable on that account.

[Just a quick update. First observation. To get a fix on the "pivot" view, think of the constraint being that P(A)+P(~A)=1. Then we can see that P(Av~A)=1-P(A&~A), which summarizes the result. Second observation. I mentioned above that something that treated the degrees of truth as an expert function "won't behave like a probability function". One reflection of that is that the logic-probability link will be violated, given certain choices for the logic. E.g. suppose we require valid arguments to preserve perfect truth (e.g. we're working with the K3 logic). Then A&~A will be inconsistent. And, for example, P(A&~A) can be 0.5, while for some unrelated B, P(B) is 0. But in the logic A&~A|-B, so probability has decreased over a valid argument. Likewise if we're preserving non-perfect-falsity (e.g. we're working with the LP system). Av~A will then be a validity, but P(Av~A) can be 0.5, yet P(B) be 1. These are for the 3-valued case, but clearly that point generalizes to the analogous definitions of validity in a degree valued setting. One of the tricky things about thinking about the area is that there are lots of choice-points around, and one is the definition of validity. So, for example, one might demand that valid arguments preserve both perfect truth and non-perfect falsity; and then the two arguments above drop away since neither |-Av~A nor A&~A|- on this logic. The generalization to this in the many-valued setting is to demand e-truth preservation for every e. Clearly these logics are far more constrained than the K3 or LP logics, and so there's a better chance of avoiding violations of the logic-probability link. Whether one gets away with it is another matter.]

Regimentation (x-post).

2008-03-17T15:27:00.001Z

Here's something you frequently hear said about ontological commitment. First, that to determine the ontological commitments of some sentence S, one must look not at S, but at a regimentation or paraphrase of S, S*. Second (very roughly), you determine the ontological commitments of S by looking at what existential claims follow from S*.

Leave aside the second step of this. What I'm perplexed about is how people are thinking about the first step. Here's one way to express the confusion. We're asked about the sentence S, but to determine the ontological commitments we look at features of some quite different sentence S*. But what makes us think that looking at S* is a good way of finding out about what's required of the world for S to be true?

Reaction (1). The regimentation may be constrained so as to make the relevance of S* transparent. Silly example: regimentation could be required to be null, i.e. every sentence has to be "regimented" as itself. No mystery there. Less silly example: the regimentation might be required to preserve meaning, or truth-conditions, or something similar. If that's the case then one could plausibly argue that the OC's of S and S* coincide, and looking at the OC's of S* is a good way of figuring out what the OC's of S is.

(The famous "symmetry" objections are likely to kick in here; i.e. if certain existential statements follow from S but not from S*, and what we know is that S and S* have the same OC's, why take it that S* reveals those OC's better than S?---so for example if S is "prime numbers exist" and S* is a nominalistic paraphrase, we have to say something about whether S* shows that S is innocent of OC to prime numbers, or whether S shows that S* is in a hidden way committed to prime numbers).

Obviously this isn't plausibly taken as Quine view---the appeal to synonymy is totally unQuinean (moreover in Word and Object, he's pretty explicit that the regimentation relationship is constrained by whether S* can play the same theoretical role as we initially thought S played---and that'll allow for lots of paraphrases where the sentences don't even have the appearance of being truth-conditionally equivalent).

Reaction (2). Adopt a certain general account of the nature of language. In particular, adopt a deflationism about truth and reference. Roughly: T- and R-schemes are in effect introduced into the object language as defining a disquotational truth-predicate. Then note that a truth-predicate so introduced will struggle to explain the predications of truth for sentences not in one's home language. So appeal to translation, and let the word "true" apply to a sentence in a non-home language iff that sentence translates to some sentence of the home language that is true in the disquotational sense. Truth for non-home languages is then the product of translation and disquotational truth. (We can take the "home language" for present purposes to be each person's idiolect).

I think from this perspective the regimentation steps in the Quinean characterization of ontological commitment have an obvious place. Suppose I'm a nominalist, and refuse to speak of numbers. But the mathematicians go around saying things like "prime numbers exist". Do I have to say that what they say is untrue (am I going to go up to them and tell them this?) Well, they're not speaking my idiolect; so according to the deflationary conception under consideration, what I need to do is figure out whether there sentences translate to something that's deflationarily true in my idiolect. And if I translate them according to a paraphrase on which their sentences pair with something that is "nominalistically acceptable", then it'll turn out that I can call what they say true.

This way of construing the regimentation step of ontological commitment identifies it with the translation step of the translation-disquotation treatment of truth sketched above. So obviously what sorts of constraints we have on translation will transfer directly to constraints on regimentation. One *could* appeal to a notion of truth-conditional equivalence to ground the notion of translatability---and so get back to a conception whereby synonymy (or something close to it) was central to our analysis of language.

It's in the Quinean spirit to take translatability to stand free of such notions (to make an intuitive case for separation here, one might, for example, that synonymy should be an equivalence relation, whereas translatability is plausibly non-transitive). There are several options. Quine I guess focuses on preservation of patterns of assent and dissent to translated pairs; Field appeals to his projectivist treatment of norms and takes "good translation" as something to be explained in projective terms. No doubt there are other ways to go.

This way of defending the regimentation step in treatments of ontological commitment turns essentially on deflationism about truth; and more than that, on a non-universal part of the deflationary project: the appeal to translation as a way to extend usage of the truth-predicate to non-home languages. If one has some non-translation story about how this should go (and there are some reasons for wanting one, to do with applying "true" to languages whose expressive power outstrips that of one's own) then the grounding for the regimentation step falls away.

So the Quinean regimentation-involving treatment of ontological commitment makes perfect sense within a Quinean translation-involving treatment of language in general. But I can't imagine that people who buy into to the received view of ontological commitment really mean to be taking a stance on deflationism vs. its rivals; or about the exact implementation of deflationism.

Of course, regimentation or translatability (in a more Quinean, preservation-of-theoretical-role sense, rather than a synonymy-sense) can still be significant for debates about ontological commitments. One might think that arithmetic was ontologically committing, but the existence of some nominalistic paraphrase that was suited to play the same theoretical role gave one some reassurance that one doesn't *have* to use the committing language, and maybe overall these kind of relationships will undermine the case for believing in dubious entities---not because ordinary talk isn't committed to them, but because for theoretical purposes talk needn't be committed to them. But unlike the earlier role for regimentation, this isn't a "hermeneutic" result. E.g. on the Quinean way of doing things, some non-home sentence "there are prime numbers" can be true, despite there being no numbers---just because the best translation of the quoted sentence translates it to something other than the home sentence "there are prime numbers". This kind of flexibility is apparently lost if you ditch the Quinean use of regimentation.

Arche talks

2008-03-15T00:58:00.005Z

In a few weeks time (31st March-5th April) I'm going to be visiting the Arche research centre in St Andrews, and giving a series of talks. I studied at Arche for my PhD, so it'll be really good to go back and see what's going on.

The talks I'm giving relate to the material on indeterminacy and probability (in particular, evidential probability or partial belief). The titles are as follows:

Indeterminacy and partial belief I: The open future and future-directed belief.
Indeterminacy and partial belief II: Conditionals and conditional belief.
Indeterminacy and partial belief III: Vague survival and de se belief.

A lot of these are based around exploring the consequences of the view that if p is indeterminate, and one knows this (or is certain of it) then one shouldn't invest any probability in p. In the case of the open future, of conditionals, and in vague survival---for rather different reasons in each case---this seems highly problematic.

But why should you believe that key principle about how attitudes to indeterminacy constrain attitudes to p? The case I've been focussing on up till now has concerned a truth-value gappy position on indeterminacy. With a broadly classical logic governing the object language, one postulates truth-value gaps in indeterminate cases. There's then an argument directly from this to the sort of revisionism associated with supervaluationist positions in vagueness. And from there, and a certain consistency requirement on rational partial belief (or evidence) we get the result. The consistency requirement is simply the claim, for example, that if q follows from p, one cannot rationally invest more confidence in p than one invests in q (given, of course, that one is aware of the relevant facts).

The only place I appeal to what I've previously called the "Aristotelian" view of indeterminacy (truth value gaps but LEM retained) is in arguing for the connection between attitudes to determinately p and attitudes to p. But I've just realized something that should have been obvious all along---which is that there's a quick argument to something similar for someone who thinks determinacy is marked by a rejection of excluded middle. Assume, to begin with, that the paracompletist nonclassicist will think in borderline cases, characteristically, one should reject the relevant instance of excluded middle. So if one is fully convinced that p is borderline, one should utterly reject pv~p.

It's dangerous to generalize about non-classical systems, but the ones I'm thinking of all endorse the claim p|-pvq---i.e. disjunction introduction. So in particular, an instance of excluded middle will follow from p.

But if we utterly reject pv~p in a borderline case (assign it credence 0), then by the probability-logic link we should utterly reject (assign credence 0) anything from which it follows.
In particular, we should assign credence 0 to p. And by parallel reasoning, we should assign credence 0 to ~p.

[Edit: there's a question, I think, about whether the non-classicist should take us to utterly reject LEM in a borderline case (i.e. degree of partial belief=0). The folklore non-classicist, at least, might suggest that on her conception degrees of truth should be expert functions for partial beliefs---i.e. absent uncertainty about what the degrees of truth are, one should conform the partial beliefs to the degrees of truth. Nick J. J. Smith has a paper where he works out a view that has this effect, from what I can see. It's available here and is well worth a read. If a paradigm borderline case for the folklore nonclassicist is one where degree of truth of p, not p and pv~p are all 0.5, then one's degree of belief in all of them should be 0.5. And there's no obvious violation of the probability-logic link here. (At least in this specific case. The logic will have to be pretty constrained if it isn't to violate probability-logic connection somewhere).]

If all this is correct, then I don't need to restrict myself to discussing the consequences of the Aristotelian/supervaluation sort of view. Everything will generalize to cover the nonclassical cases---and will cover both the folklore nonclassicist and the no interpretation nonclassicist discussed in the previous cases (here's a place where there's convergence).

[A folklore classicist might object that for them, there isn't a unique "logic" for which to run the argument. If one focuses on truth-preservation, one gets say a Kleene logic; if one focuses on non-falsity preservation, one gets an LP logic. But I don't think this thought really goes anywhere...]

Non-classical logics: the no interpretation account

2008-03-14T23:14:00.004Z

In the previous post, I set out what I took to be one folklore conception of a non-classicist treatment of indeterminacy. Essential elements were (a) the postulation of not two, but several truth statuses; (b) the treatment of "it is indeterminate whether" (or degreed variants thereof) as an extensional operator; (c) the generalization to this setting of a classicist picture, where logic is defined as truth preservation over a range of reinterpretations, one amongst which is the interpretation that gets things right.

I said in that post that I thought that folklore non-classicism was a defensible position, though there's some fairly common maneuvers which I think the folklore non-classicist would be better off ditching. One of these is the idea that the intended interpretation is describable "only non-classically".

However, there's a powerful alternative way of being a non-classicist. The last couple of weeks I've had a sort of road to Damascus moment about this, through thinking about non-classicist approaches to the Liar paradox---and in particular, by reading Hartry Field's articles and new book where he defends a "paracomplete" (excluded-middle rejecting) approach to the semantic paradoxes and work by JC Beall on a "paraconsistent" (contradiction-allowing) approach.

One interpretative issue with the non-classical approaches to the Liar and the like is that a crucial element is a truth-predicate that works in a way very unlike the notion of "truth" or "perfect truth" ("semantic value 1", if you want neutral terminology) that feature in the many-valued semantics. But that's not necessarily a reason by itself to start questioning the folklore picture. For it might be that "truth" is ambiguous---sometimes picking up on a disquotational notion, sometimes tracking the perfect truth notion featuring in the nonclassicists semantics. But in fact there are tensions here, and they run deep.

Let's warm up with a picky point. I was loosely throwing around terms like "3-valued logic" in the last post, and mentioned the (strong) Kleene system. But then I said that we could treat "indeterminate whether p" as an extensional operator (the "tertium operator" that makes "indet p" true when p is third-valued, and otherwise false). But that operator doesn't exist in the Kleene system---the Kleene system isn't expressively complete with respect to the truth functions definable over three values, and this operator is one of the truth-functions that isn't there. (Actually, I believe if you add this operator, you do get something that is expressively complete with respect to the three valued truth-functions).

One might take this to be just an expressive limitation of the Kleene system. After all, one might think, in the intended interpretation there is a truth-function behaving in the way just described lying around, and we can introduce an expression that picks up on it if we like.

But it's absolutely crucial to the nonclassical treatments of the Liar that we can't do this. The problem is that if we have this operator in the language, then "exclusion negation" is definable---an operator "neg" such that "neg p" is true when p is false or indeterminate, and otherwise false (this will correspond to "not determinately p"---i.e. ~p&~indeterminate p, where ~ is so-called "choice" negation, i.e. |~p|=1-|p|). "p v neg p" will be a tautology; and arbitrary q will follow from the pair {p, neg p}. But this is exactly the sort of device that leads to so-called "revenge" puzzles---Liar paradoxes that are paradoxical even in the 3-valued system. Very roughly, it looks as if on reasonable assumptions a system with exclusion negation can't have a transparent truth predicate in it (something where p and T(p) are intersubstitutable in all extensional contexts). It's the whole point of Field and Beall's approaches to retain something with this property. So they can't allow that there is such a notion around (so for example, Beall calls such notions "incoherent").

What's going on? Aren't these approaches just denying us the resources to express the real Liar paradox? The key, I think, is a part of the nonclassicist picture that Beall and Field are quite explicit about and which totally runs against the folklore conception. They do not buy into the idea that model theory is ranging over a class of "interpretations" of the language among which we might hope to find the "intended" interpretation. The core role of the model theory is to give an extensionally adequate characterization of the consequence relation. But the significance of this consequence relation is not to be explained in model-theoretic terms (in particular, in terms of one among the models being intended, so that truth-preservation on every model automatically gives us truth-preservation simpliciter).

(Field sometimes talks about the "heuristic value" of this or that model and explicitly says that there is something more going on than just the use of model theory as an "algebraic device". But while I don't pretend to understand exactly what is being invoked here, it's quite quite clear that the "added value" doesn't consist on some classical 3-valued model being "intended".)

Without appeal to the intended interpretation, I just don't see how the revenge problem could be argued for. The key thought was that there is a truth-function hanging around just waiting to be given a name, "neg". But without the intended interpretation, what does this even mean? Isn't the right thought simply that we're characterizing a consequence relation using rich set-theoretic resources---and in terms of which we can draw differences that correspond to nothing in the phenomenon being modelled.

So it's absolutely essential to the nonclassicist treatment of the Liar paradox that we drop the "intended interpretation" view of language. Field, for one, has a ready-made alternative approach to suggest---a Quinean combination of deflationism about truth and reference, with perhaps something like translatability being invoked to explain how such predicates can be applied to expressions in a language other than ones own.

I'm therefore inclined to think of the non-classicism---at least about the Liar---as a position that *requires* something like this deflationist package. Whereas the folklore non-classicist I was describing previously is clearly someone who takes semantics seriously, and who buys into a generalization of the powerful connections between truth and consequence that a semantic theory of truth affords.

When we come to the analysis of vagueness and other (non-semantic-paradox related) kinds of indeterminacy, it's now natural to consider this "no interpretation" non-classicism. (Field does exactly this---he conceives of his project as giving a unified account of the semantic paradoxes and the paradoxes of vagueness. So at least *this* kind of nonclassicism, we can confidently attribute to a leading figure in the field). All the puzzles described previously for the non-classicist position are thrown into a totally new light. Once we make this move.

To begin with, there's no obvious place for the thought that there are multiple truth statuses. For you get that by looking at a many valued model, and imagining that to be an image of what the intended interpretation of the language must be like. And that is exactly the move that's now illegitimate. Notice that this undercuts one motivation for going towards a fuzzy logic---the idea that one represents vague predicates as some smoothly varying in truth status. Likewise, the idea that we're just "iterating a bad idea" in multiplying truth values doesn't hold water on this conception---since the many-values assigned to sentences in models just don't correspond to truth statuses.

Connectedly, one shouldn't say that contradictions can be "half true" (nor that excluded middle is "half true". It's true that (on say the Kleene approach) that you won't have ~(p&~p) as a tautology. Maybe you could object to *that* feature. But that to me doesn't seem nearly as difficult to swallow as a contradiction having "some truth to it" despite the fact that from a contradiction, everything follows.

One shouldn't assume that "determinately" should be treated as the tertium operator. Indeed, if you're shooting for a combined non-classical theory of vagueness and semantic paradoxes, you *really* shouldn't treat it this way, since as noted above this would give you paradox back.

There is therefore a central and really important question: what is the non-classical treatment of "determinately" to be? Sample answer (lifted from Field's discussion of the literature): define D(p) as p&~(p-->~p), where --> is a certain fuzzy logic conditional. This, Field argues, has many of the features we'd intuitively want a determinately operator to have; and in particular, it allows for non-trivial iterations. So if something like this treatment of "determinately" were correct, then higher-order indeterminacy wouldn't be obviously problematic (Field himself thinks this proposal is on the right lines, but that one must use another kind of conditional to make the case).

"No interpretation" nonclassicism is an utterly, completely different position from the folklore nonclassicism I was talking about before. For me, the reasons to think about indeterminacy and the semantic and vagueness-related paradoxes in the first place, is that they shed light on the nature of language, representation, logic and epistemology. And on these sorts of issues, the no interpretation nonclassicism and the folklore version take diametrically opposed positions on such issues, and flowing from this, the appropriate ways to arguing for or against these views are just very very different.

Non-classical logics: some folklore

2008-03-14T22:03:00.003Z

Having just finished the final revisions to my Phil Compass survey article on Metaphysical indeterminacy and ontic vagueness (penultimate draft available here) I started thinking some more about how those who favour non-classical logics think of their proposal (in particular, people who think that something like the Kleene 3-valued logic or some continuum valued generalization of it is the appropriate setting for analyzing vagueness or indeterminacy).

The way that I've thought of non-classical treatments in the past is I think a natural interpretation of one non-classical picture, and I think it's reasonably widely shared. In this post, I'm going to lay out some of that folklore-y conception of non-classicism (I won't attribute views to authors, since I'm starting to wonder whether elements of the folklore conception are characterizations offered by opponents, rather than something that the nonclassicists should accept---ultimately I want to go back through the literature and check exactly what people really do say in defence of non-classicism).

Here's my take on folklore nonclassicism. While classicists think there are two truth-statuses, non-classicists believe in three, four or continuum many truth-statuses (let's focus on the 3-valued system for now). They might have various opinions about the structure of these truth-statuses---the most common ones being that they're linearly ordered (so for any two truth-statuses, one is truer than the other). Some sentences (say, Jimmy is bald) get a status that's intermediate between perfect truth and perfect falsity. And if we want to understand the operator "it is indeterminate whether" in such settings, we can basically treat it as a one-place extensional connective: "indeterminate(p)" is perfectly true just in case p has the intermediate status; otherwise it is perfectly false.

So interpreted, non-classicism generalizes classicism smoothly. Just as the classicist can think there is an intended interpretation of language (a two valued model which gets the representation properties of words right) the non-classicist can think there's an intended interpretation (say a three valued model getting the representational features right). And that then dovetails very nicely with a model-theoretic characterization of consequence as truth-preservation under (almost) arbitrary reinterpretations of the language. For if one knows that some pattern is truth-preserving under arbitrary reinterpretations of the language, then that pattern is truth-preserving in particular in the intended interpretation---which is just to say that preserves truth simpliciter. This forges a connection between validity and preserving a status we have all sorts of reason to be interested in---truth. (Of course, one just has to write down this thought to start worrying about the details. Personally, I think this integrated package is tremendously powerful and interesting, deserves detailed scrutiny, and should be given up only as an option of last resort---but maybe others take a different view). All this carries over to the non-classicist position described. So for example, on a Kleene system, validity is a matter of preserving perfect truth under arbitrary reinterpretations---and to the extent we're interested in reasoning which preserves that status, we've got the same reasons as before to be interested in consequence. Of course, one might also think that reasoning that preserves non-perfect-falsity is also an interesting thing to think about. And very nicely, we have a systematic story about that too---this non-perfect falsity sense of validity would be the paraconsistent logic LP (though of course not under an interpretation where contradictions get to be true).

With this much on board, one can put into position various familiar gambits in the literature.

One could say that allowing contradictions to be half-true (i.e. to be indeterminate, to have the middle-status) is just terrible. Or that allowing a parity of truth-status between "Jimmy is bald or he isn't" and "Jimmy's both bald and not bald" just gets intuitions wrong (the most powerful way dialectically to deploy this is if the non-classicist backs their position primarily by intuitions about cases---e.g. our reluctance to endorse the first sentence in borderline cases. The accusation is that if our game is taking intuitions about sentences at face value, it's not at all clear that the non-classicist is doing a good job.)
One could point out that "indeterminacy" for the nonclassicist will trivially iterate. If one defines Determinate(p) as p&~indeterminate(p) (or directly as the one-place connective that is perfectly true if p is, and perfectly false otherwise) then we'll quickly see that Determinately determinately p will follow from determinately p; and determinately indeterminate whether p will follow from indeterminate whether p. And so on.
In reaction to this, one might abandon the 3-valued setting for a smooth, "fuzzy" setting. It's not quite so clear what value "indeterminate p" should take (though there are actually some very funky options out there). Perhaps we might just replace such talk with direct talk of "degrees of determinacy" thought of as degrees of truth---with "D(p)=n" being again a one-place extensional operator perfectly true iff p has degree of truth n; and otherwise perfectly false.
One might complain that all this multiplying of truth-values is fundamentally misguiding. Think of people saying that the "third status" view of indeterminacy is all wrong---indeterminacy is not a status that competes with truth and falsity; or the quip (maybe due to Mark Sainsbury?) that one does "not improve a bad idea by iterating it"---i.e. by introducing finer and finer distinctions.

I don't think these are knock-down worries. (1) I do find persuasive, but I don't think it's very dialectically forceful---I wouldn't know how to argue against someone who claimed their intuitions systematically followed, say, the Kleene tables. (I also think that the nonclassicist can't really appeal to intuitions against the classicist effectively). Maybe some empirical surveying could break a deadlock. But pursued in this way the debate seems sort of dull to me.

(2) seems pretty interesting. It looks like the non-classicist's treatment of indeterminacy, if they stick in the 3-valued setting, doesn't allow for "higher-order" indeterminacy at all. Now, if the nonclassicist is aiming to treat determinacy rather than vagueness *in general* (say if they're giving an account of the indeterminacy purportedly characteristic of the open future, or of the status of personal identity across fission cases) then it's not clear one need to posit higher-order indeterminacy.

I should say that there's one response to the "higher order" issues that I don't really understand. That's the move of saying that strictly, the semantics should be done in a non-classical metalanguage, where we can't assume that "x is true or x is indeterminate or x is false" itself holds. I think Williamson's complaints here in the chapter of his vagueness book are justified---I just don't know how what the "non-classical theory" being appealed to here is, or how one would write it down in order to assess its merits (this is of course just a technical challenge: maybe it could be done).

I'd like to point out one thing here (probably not new to me!). The "nonclassical metalanguage" move at best evades the challange that by saying that there's an intended 3-valued interpretation, one is committed to deny higher-order indeterminacy. But we achieve this, supposedly, by saying that the intended interpretation needs to be described non-classically (or perhaps notions like "the intended interpretation" need to be replaced by some more nuanced characterization). The 3-valued logic is standardly defined in terms of what preserves truth over all 3-valued interpretations describable in a classical metalanguage. We might continue with the classical model-theoretic characterization of the logic. But then (a) if the real interpretation is describable only non-classically, it's not at all clear why truth-preservation in all classical models should entail truth-preservation in the real, non-classical interpretation. And moreover, our object-language "determinacy" operator, treated extensionally, will still trivially iterate---that was a feature of the *logic* itself. This last feature in particular might suggest that we should really be characterizing the logic as truth-preservation under all interpretations including those describable non-classically. But that means we don't even have a fix on the *logic*, for who knows what will turn out to be truth-preserving on these non-classical models (if only because I just don't know how to think about them).

To emphasize again---maybe someone could convince me this could all be done. But I'm inclined to think that it'd be much neater for this view to deny higher-order indeterminacy---which as I mentioned above just may not be a cost in some cases. My suggested answer to (4), therefore, is just to take it on directly---to provide independent motivation for wanting however many values that is independent of having higher-order indeterminacy around (I think Nick J.J. Smith's AJP paper "Vagueness as closeness" pretty explicitly takes this tack for the fuzzy logic folk).

Anyway, I take this to be some of the folklore and dialectical moves that people try out in this setting. Certainly it's the way I once thought of the debate shaping up. It's still, I think, something that's worth thinking about. But in the next post I'm going to say why I think there's a far far more attractive way of being a non-classicist.

Metaphysics Conference

2008-02-23T22:44:00.002Z

Announcing: Perspectives on Ontology

A major international conference on metaphysics to be held at the University of Leeds, Sep 5th-7th 2008.

Speakers:
Karen Bennett (Cornell)
John Hawthorne (Oxford)
Gabriel Uzquiano (Oxford)

Jill North (Yale)
Helen Steward (Leeds)
Jessica Wilson (Toronto)

Commentators:
Benj Hellie (Toronto)
Kris McDaniel (Syracuse)
Ted Sider (NYU)
Jason Turner (Leeds)
Robbie Williams (Leeds)

This will be a great conference: so keep your diaries free, and spread the word!

[Update: The conference website is now up.]

"Supervaluationism": the word

2008-02-22T15:53:00.003Z

I've got progressively more confused over the years about the word "supervaluations". It seems lots of people use it in slightly different ways. I'm going to set out my understanding of some of the issues, but I'm very happy to be contradicted---I'm really in search of information here.

The first occurrence I know of is van Fraassen's treatment of empty names in a 1960's JP article. IIRC, the view there is that language comes with a partial intended interpretation function, specifying the references of non-empty names. When figuring out what is true in the language, we
look at what is true on all the full interpretations that extend the intended partial interpretation. And the result is that "Zeus is blue" will come out neither true nor false, because on some completions of the intended interpretation the empty name"Zeus" will designate a blue object, and others he won't.

So that gives us one meaning of a "supervaluation": a certain technique for defining truth simpliciter out of the model-theoretic notions of truth-relative-to-an-index. It also, so far as I can see, closes off the question of how truth and "supertruth" (=truth on all completions) relate. Supervaluationism, in this original sense, just is the thesis that truth simpliciter should be defined as truth-on-all-interpretations. (Of course, one could argue against supervaluationism in this sense by arguing against the identification; and one could also consistently with this position argue for the ambiguity view that "truth" is ambiguous between supertruth and some other notion---but what's not open is to be a supervaluationist and deny that supertruth is truth in any sense.)

Notice that there's nothing in the use of supervaluations in this sense that enforces any connection to "semantic theories of vagueness". But the technique is obviously suggestive of applications to indeterminacy. So, for example, Thomason in 1970 uses the technique within an "open future" semantics. The idea there is that the future is open between a number of currently-possible histories. And what is true about is what happens on all these histories.

In 1975, Kit Fine published a big and technically sophisticated article mapping out a view of vagueness arising from partially assigned meanings, that used among other things supervaluational techniques. Roughly, the basic move was to assign each predicate with an extension (the set of things to which it definitely applies) and an anti-extension (the set of things to which it definitely doesn't apply). An interpretation is "admissible" only if it assigns an set of objects to a predicate that is a superset of the extension, and which doesn't overlap the anti-extension. There are other constraints on admissibility too: so-called "penumbral connections" have to be respected.

Now, Fine does lots of clever stuff with this basic setup, and explores many options (particularly in dealing with "higher-order" vagueness). But one thing that's been very influential in the folklore is the idea that based on the sort of factors just given, we can get our hands on a set of "admissible" fully precise classical interpretations of the language.

Now the supervaluationist way of working with this would tell you that truth=truth on each admissible interpretation, and falsity=falsity on all such interpretations. But one needn't be a supervaluationist in this sense to be interested in all the interesting technologies that Fine introduces, or the distinctive way of thinking about semantic indecision he introduces. The supervaluational bit of all this refers only to one stage of the whole process---the step from identifying a set of admissible interpretations to the definition of truth simpliciter.

However, "supervaluationism" has often, I think, been identified with the whole Finean programme. In the context of theories of vagueness, for example, it is often used to refer to the idea that vagueness or indeterminacy arises as a matter of some kind of unsettledness as to what precise extensions are expressions pick out ("semantic indecision"). But even if the topic is indeterminacy, the association with *semantic indecision* wasn't part of the original conception of supervaluations---Thomason's use of them in his account of indeterminacy about future contingents illustrates that.

If one understands "supervaluationism" as tied up with the idea of semantic indecision theories of vagueness, then it does become a live issue whether one should identify truth with truth on all admissible interpretations (Fine himself raises this issue). One might think that the philosophically motivated semantic machinery of partial interpretations, penumbral connections and admissible interpretations is best supplemented by a definition of truth in the way that the original VF-supervaluationists favoured. Or one might think that truth-talk should be handled differently, and that the status of "being true on all admissible assignments" shouldn't be identified with truth simpliciter (say because the disquotational schemes fail).

If you think that the latter is the way to go, you can be a "supervaluationist" in the sense of favouring a semantic indecision theory of vagueness elaborated along Kit Fine's lines, without being a supervaluationist in the sense of using Van Fraassen's techniques.

So we've got at least these two disambiguations of "supervaluationism", potentially cross-cutting:

(A) Formal supervaluationism: the view that truth=truth on each of a range of relevant interpretations (e.g. truth on all admissible interpretations (Fine); on all completions (Van Fraassen); or on all histories (Thomason)).
(B) Semantic indeterminacy supervaluationism: the view that (semantic) indeterminacy is a matter of semantic indecision: there being a range of classical interpretations of the language, which, all-in, have equal claim to be the right one.

A couple of comments on each. (A) of course, needs to be tightened up in each case by saying which are the relevant range of classical interpretations quantified over. Notice that a standard way of defining truth in logic books is actually supervaluationist in this sense. Because if you define what it is for a formula "p" to be true as it being true relative to all variable assignments, then open formulae which vary in truth value from variable-assignment to variable assignment end up exactly analogous to formulae like "Zeus is blue" in Van Fraassen's setting: they will be neither true nor false.

Even when it's clear we're talking about supervaluationism in the sense of (B), there's continuing ambiguity. Kit Fine's article is incredibly rich, and as mentioned above, both philosophically and technically he goes far beyond the minimal idea that semantic vagueness has something to do with the meaning-fixing facts not settling on a single classical interpretation.

So there's room for an understanding of "supervaluationism" in the semantic-indecision sense that is also minimal, and which does not commit itself to Fine's ideas about partial interpretations, conceptual truths as "penumbral constraints" etc. David Lewis in "Many but also one", as I read him, has this more minimal understanding of the semantic indecision view---I guess it goes back to Hartry Field's material on inscrutability and indeterminacy and "partial reference" in the early 1970's, and Lewis's own brief comments on related ideas in his (1969).

So even if your understanding of "supervaluationism" is the (B)-sense, and we're thinking only in terms of semantic indeterminacy, then you still owe elaboration of whether you're thinking of a minimal "semantic indecision" notion a la Lewis, or the far richer elaboration of that view inspired by Fine. Once you've settled this, you can go on to say whether or not you're a supervaluationist in the formal, (A)-sense---and that's the debate in the vagueness literature over whether truth should be identified with supertruth.

Finally, there's the question of whether the "semantic indecision" view (B), should be spelled out in semantic or metasemantic terms. One possible view has the meaning-fixing facts picking out not a single interpretation, but a great range of them, which collectively play the role of "semantic value" of the term. That's a semantic or "first-level" (in Matti Eklund's terminology) view of semantic indeterminacy. Another possible view has the meaning-fixing facts trying to fix on a single interpretation which will give the unique semantic value of each term in the language, but it being unsettled which one they favour. That's a metasemantic or "second-level" view of the case.

If you want to complain that second view is spelled out quite metaphorically, I've some sympathy (I think at least in some settings it can be spelled out a bit more tightly). One might also want to press the case that the distinction between semantic and metasemantic here is somewhat terminological---what we choose to label the facts "semantic" or not. Again, I think there might be something to this. There are also questions about how this relates to the earlier distinctions---it's quite natural to think of Fine's elaboration as being a paradigmatically semantic (rather than metasemantic) conception of semantic supervaluationism. It's also quite natural to take the metasemantic idea to go with a conception that is non-supervaluational in the (A) sense. (Perhaps the Lewis-style "semantic indecision" rhetoric might be taken to suggest a metasemantic reading all along, in which way it is not a good way to cash out what's the common ground among (B)-theorists is). But there's room for a lot of debate and negotiation on these and similar points.

Now all this is very confusing to me, and I'm sure I've used the terminology confusingly in the past. It kind of seems to me that ideally, we'd go back to using "supervaluationism" in the (A) sense (on which truth=supertruth is analytic of the notion); and that we'd then talk of "semantic indecision" views of vagueness of various forms, with its formal representation stretching from the minimal Lewis version to the rich Fine elaboration, and its semantic/metasemantic status specified. In any case, by depriving ourselves of commonly used terminology, we'd force ourselves to spell out exactly what the subject matter we're discussing is.

As I say, I'm not sure I've got the history straight, so I'd welcome comments and corrections.

Phlox

2008-02-22T15:44:00.002Z

I just found about about Phlox, a (relatively) new weblog in philosophy of logic, language and metaphysics. It's attached to a project at Humboldt University in Berlin. As well as following the tradition of philosophy centres with Greek names (this one means "flame", apparently) "Phlox" is a cunning acronym for the group's research interests.

There's several really interesting posts to check out already. Worth heading over!

Aristotelian indeterminacy and partial beliefs

2008-02-14T02:25:00.002Z

I’ve just finished a first draft of the second paper of my research leave---title the same as this post. There’s a few different ways to think about this material, but since I hadn't posted for a while I thought I'd write up something about how it connects with/arises from some earlier concerns of mine.

The paper I’m working on ends up with arguments against standard “Aristotelian” accounts of the open future, and standard supervaluational accounts of vague survival. But one starting point was an abstract question in the philosophy of logic: in what sense is standard supervaluationism supposed to be revisionary? So let's start there.

The basic result---allegedly---is that while all classical tautologies are supervaluational tautologies, certain classical rules of inference (such as reductio, proof by cases, conditional proof, etc) fail in the supervaluational setting.

Now I’ve argued previously that one might plausibly evade even this basic form of revisionism (while sticking to the “global” consequence relation, which preserves traditional connections between logical consequence and truth-preservation). But I don’t think it’s crazy to think that global supervaluational consequence is in this sense revisionary. I just think that it requires an often-unacknowledged premise about what should count as a logical constant (in particular, whether “Definitely” counts as one). So for now let’s suppose that there are genuine counterexamples to conditional proof and the rest.

The standard move at this point is to declare this revisionism a problem for supervaluationists. Conditional proof, argument by cases: all these are theoretical descriptions of widespread, sensible and entrenched modes of reasoning. It is objectionably revisionary to give them up.

Of course some philosophers quite like logical revisionism, and would want to face-down the accusation that there’s anything wrong with such revisionism directly. But there’s a more subtle response available. One can admit that the letter of conditional proof, etc are given up, but the pieces of reasoning we normally call “instances of conditional proof” are all covered by supervaluationally valid inference principles. So there’s no piece of inferential practice that’s thrown into doubt by the revisionism of supervaluational consequence: it seems that all that happens is that the theoretical representation of that practice has to take a slightly more subtle form than one might except (but still quite a neat and elegant one).

One thing I mention in that earlier paper but don’t go into is a different way of drawing out consequences of logical revisionism. Forget inferential practice and the like. Another way in which logic connects with the rest of philosophy is in connection to probability (in the sense of rational credences, or Williamson’s epistemic probabilities, or whatever). As I sketched in a previous post, so long as you accept a basic probability-logic constraint, which says that the probability of a tautology should be 1, and the probability of a contradiction should be 0, then the revisionary supervaluational setting quickly forces you to a non-classical theory of probability: one that allows disjunctions to have probability 1 where each disjunct has probability 0. (Maybe we shouldn't call such a thing "probability": I take it that's terminological).

Folk like Hartry Field have argued completely independently of this connection to Supervaluationism that this is the right and necessary way to handle probabilities in the context of indeterminacy. I’ve heard others say, and argue, that we want something closer to classicism (maybe tweaked to allow sets of probability functions, etc). And there are Dutch Book arguments to consider in favour of the classical setting (though I think the responses to these from the perspective of non-classical probabilities are quite convincing).

I’ve got the feeling the debate is at a stand-off, at least at this level of generality. I’m particularly unmoved by people swapping intuitions about degrees of belief it is appropriate to have in borderline cases of vague predicates, and the like (NB: I don’t think that Field ever argues from intuition like this, but others do). Sometimes introspection suggests intriguing things (for example, Schiffer makes the interesting suggestion that one’s degree of belief in a conjunction of two vague propositions is typically matches one’s degree of belief in the propositions themselves). But I can’t see any real dialectical force here. In my own case, I don’t have robust intuitions about these cases. And if I'm to go on testimonial evidence on others intuitions, it’s just too unclear what people are reporting on for me to feel comfortable taking their word for it. I'm worried, for example, they might just be reporting the phenomenological level of confidence they have in the proposition in question: surely that needn’t coincide with one’s degree of belief in the proposition (thinking of an exam you are highly nervous about, but are fairly certain you will pass… your behaviour may well manifest a high degree of belief, even in the absence of phenomenological trappings of confidence). In paradigm cases of indeterminacy, it’s hard to see how to do better than this.

However, I think in application to particular debates we might be able to make much more progress. Let us suppose that the topic for the day is the open future, construed, minimally, as the claim that while there are definite facts about the past and present, the future is indefinite.

Might we model this indefiniteness supervaluationally? Something like this idea (with possible futures playing the role of precisifications) is pretty widespread, perhaps orthodoxy (among friends of the open future). It’s a feature of MacFarlane’s relativistic take on the open future, for example. Even though he’s not a straightforward supervaluationist, he still has truth-value gaps, and he still treats them in a recognizably supervaluational-style way.

The link between supervaluational consequence and the revisionionary behaviour of partial beliefs should now kick in. For if you know with certainty that some P is neither true nor false, we can argue that you should invest no credence at all in P (or in its negation). Likewise, in a framework of evidential probabilities, P gets no evidential probability at all (nor does its negation).

But think what this says in the context of the open future. It’s open which way this fair coin lands: it could be heads, it could be tails. On the “Aristotelian” truth-value conception of this openness, we can know that “the coin will land heads” is gappy. So we should have credence 0 in it, and none of our evidence supports it.

But that’s just silly. This is pretty much a paradigmatic case where we know what partial belief we have and should have in the coin landing heads: one half. And our evidence gives exactly that too. No amount of fancy footwork and messing around with the technicalities of Dempster-Shafer theory leads to a sensible story here, as far as I can see. It’s just plainly the wrong result. (One doesn't improve matters very much by relaxing the assumptions, e.g. taking the degree of belief in a failure of bivalence in such cases to fall short of one: you can still argue for a clearly incorrect degree of belief in the heads-proposition).

Where does that leave us? Well, you might reject the logic-probability link (I think that’d be a bad idea). Or you might try to argue that supervaluational consequence isn’t revisionary in any sense (I sketched one line of thought in support of this in the paper cited). You might give up on it being indeterminate which way the coin will land---i.e. deny the open future, a reasonably popular option. My own favoured reaction, in moods when I’m feeling sympathetic to the open future, is to go for a treatment of metaphysical indeterminacy where bivalence can continue to hold---my colleague Elizabeth Barnes has been advocating such a framework for a while, and it’s taken a long time for me to come round.

All of these reactions will concede the broader point---that at least in this case, we’ve got an independent grip on what the probabilities should be, and that gives us traction against the Supervaluationist.

I think there are other cases where we can find similar grounds for rejecting the structure of partial beliefs/evidential probabilities that supervaluational logic forces upon us. One is simply a case where empirical data on folk judgements has been collected---in connection with indicative conditions. I talk about this in some other work in progress here. Another which I talk about in the current paper, and which I’m particularly interested in, concerns cases of indeterminate survival. The considerations here are much more involved than in indeterminacy we find in connection to the open future or conditionals. But I think the case against the sort of partial beliefs supervaluationism induces can be made out.

All these results turn on very local issues. None, so far as see, generalizes to the case of paradigmatic borderline cases of baldness and the rest. I think that makes the arguments even more interesting: potentially, they can serve as a kind of diagnostic: this style of theory of indeterminacy is suitable over here; that theory over there. That’s a useful thing to have in one’s toolkit.

Structured propositions and metasemantics

2007-12-18T17:13:00.000Z

Here is the final post (for the time being) on structured propositions. As promised, this is to be an account of the truth-conditions of structured propositions, presupposing a certain reasonably contentious take on the metaphysics of linguistic representation (metasemantics). It's going to be compatible with the view that structured propositions are nothing but certain n-tuples: lists of their components. (See earlier posts if you're getting concerned about other factors, e.g. the potential arbitriness in the choice of which n-tuples are to be identified with the structured proposition that Dummett is a philosopher.)

Here's a very natural way of thinking of what the relation between *sentences* and truth-conditions are, on a structured propositions picture. It's that metaphysically, the relation of "S having truth-conditions C" breaks down into two more fundamental relations: "S denoting struc prop p" and "struc prop p having truth-conditions C". The thought is something like: primarily, sentences express thoughts (=struc propositions), and thoughts themselves are the sorts of things that have intrinsic/essential representational properties. Derivatively, sentences are true or false of situations, by expressing thoughts that are true or false of those situations. As I say, it's a natural picture.

In the previous posting, I've been talking as though this direction-of-explanation was ok, and that the truth-conditions of structured propositions should have explanatory priority over the truth-conditions of sentences, so we get the neat separation into the contingent feature of linguistic representation (which struc prop a sentence latches onto) and the necessary feature (what the TCs are, given the struc prop expressed).

The way I want to think of things, something like the reverse holds. Here’s the way I think of the metaphysics of linguistic representation. In the beginning, there were patterns of assent and dissent. Assent to certain sentences is systematically associated with certain states of the world (coarse-grained propositions, if you like) perhaps by conventions of truthfulness and trust (cf. Lewis's "Language and Languages"). What it is for expressions E in a communal language to have semantic value V is for E to be paired with V under the optimally eligible semantic theory fitting with that association of sentences with coarse-grained propositions.

That's a lot to take in all at one go, but it's basically the picture of linguistic representation as fixed by considerations of charity/usage and eligibility/naturalness that lots of people at the moment seem to find appealing. The most striking feature---which it shares with other members of the "radical interpretation" approach to metasemantics---is that rather than starting from the referential properties of lexical items like names and predicates, it depicts linguistic content as fixed holistically by how well it meshes with patterns of usage. (There's lots to say here to unpack these metaphors, and work out what sort of metaphysical story of representation is being appealed to: that's something I went into quite a bit in my thesis---my take on it is that it's something close to a fictionalist proposal).

This metasemantics, I think, should be neutral between various semantic frameworks for generating the truth conditions. With a bit of tweaking, you can fit in a Davidsonian T-theoretic semantic theory into this picture (as suggested by, um... Davidson). Someone who likes interpretational semantics but isn't a fan of structured propositions might take the semantic values of names to be objects, and the semantic values of sentences to be coarse-grained propositions, and say that it's these properties that get fixed via best semantic theory of the patterns of assent and dissent (that's Lewis's take).

However, if you think that to adequately account for the complexities of natural language you need a more sophisticated, structured proposition, theory, this story also allows for it. The meaning-fixing semantic theory assign objects to names, and structured propositions to sentences, together with a clause specifying how the structured propositions are to be paired up with coarse-grained propositions. Without the second part of the story, we'd end up with an association between sentences and structured propositions, but we wouldn't make connection with the patterns of assent and dissent if these take the form of associations of sentences with *coarse grained* propositions (as on Lewis's convention-based story). So on this radical interpretation story where the targetted semantic theories take a struc prop form, we get a simultaneous fix on *both* the denotation relation between sentences and struc props, and the relation between struc props and coarse-grained truth-conditions.

Let's indulge in a bit of "big-picture" metaphor-ing. It’d be misleading to think of this overall story as the analysis of sentential truth-conditions into a prior, and independently understood, notion of the truth-conditions of structured propositions, just as it's wrong on the radical interpretation picture to think of sentential content as "analyzed in terms of" a prior, and independently understood, notion of subsentential reference. Relative to the position sketched, it’s more illuminating to think of the pairing of structured and coarse-grained propositions as playing a purely instrumental role in smoothing the theory of the representational features of language. It's language which is the “genuine” representational phenomenon in the vicinity: the truth-conditional features attributed to struc propositions are a mere byproduct.

Again speaking metaphorically, it's not that sentences get to have truth-conditions in a merely derivative sense. Rather, structured propositions have truth-conditions in a merely derivative sense: the structured proposition has truth-conditions C if it is paired with C under the optimal overall theory of linguistic representation.

For all we've said, it may turn out that the same assignment of truth-conditions to set-theoretic expressions will always be optimal, no matter which language is in play. If so, then it might be that there's a sense in which structured propositions have "absolute" truth-conditions, not relative to this or that language. But, realistically, one'd expect some indeterminacy in what struc props play the role (recall the Benacerraf point King makes, and the equally fitness of [a,F] and [F,a] to play that "that a is F" role). And it's not immediately clear why the choice to go one way for one natural language should constrain way this element is deployed in another language. So it's at least prima facie open that it's not definitely the case that the same structured propositions, with the same TCs, are used in the semantics of both French and English.

It's entirely in the spirit of the current proposal that we think of we identify [a,F] with the structured proposition that a is F only relative to a given natural language, and that this creature only has the truth-conditions it does relative to that language. This is all of a piece with the thought that the structured proposition's role is instrumental to the theory of linguistic representation, and not self-standing.

Ok. So with all this on the table, I'm going to return to read the book that prompted all this, and try to figure out whether there's a theoretical need for structured propositions with representational properties richer than those attributed by the view just sketched.

[update: interestingly, it turns out that King's book doesn't give the representational properties of propositions explanatory priority over the representational properties of sentences. His view is that the proposition that Dummett thinks is (very crudely, and suppressing details) the fact that in some actual language there is a sentence of (thus-and-such a structure) of which the first element is a word referring to Dummett and the second element is a predicate expressing thinking. So clearly semantic properties of words are going to be prior to the representational properties of propositions, since those semantic properties are components of the proposition. But more than this, from what I can make out, King's thought is that if there was a time where humans spoke a language without attitude-ascriptions and the like, then sentences would have truth-conditions, and the proposition-like facts would be "hanging around" them, but the proposition-like facts wouldn't have any representational role. Once we start making attitude ascriptions, we implicitly treat the proposition-like structure as if it had the same TCs as sentences, and (by something like a charity/eligibility story) the "propositional relation" element acquires semantic significance and the proposition-like structure gets to have truth-conditions for the first time.

That's very close to the overall package I'm sketching above. What's significant dialectically, perhaps, is that this story can explain TCs for all sorts of apparently non-semantic entities, like sets. So I'm thinking it really might be the Benacerraf point that's bearing the weight in ruling out set-theoretic entities as struc propns---as explained previously, I don't go along with *that*.]

Structured propositions and truth conditions.

2007-12-18T13:15:00.000Z

In the previous post, I talked about the view of structured propositions as lists, or n-tuples, and the Benacerraf objections against it. So now I'm moving on to a different sort of worry. Here's King expressing it:

“A final difficulty for the view that propositions are ordered n-tuples concerns the mystery of how or why on that view they have truth conditions. On any definition of ordered n-tuples we are considering, they are just sets. Presumably, many sets have no truth conditions (eg. The set of natural numbers). But then why do certain sets, certain ordered n-tuples, have truth-conditions? Since not all sets have them, there should be some explanation of why certain sets do have them. It is very hard to see what this explanation could be.”

I feel the force of something in this vicinity, but I'm not sure how to capture the worry. In particular, I'm not sure whether the it's right to think of structured propositions' having truth-conditions as a particularly "deep" fact over which there is mystery in the way King suggests. To get what I'm after here, it's probably best simply to lay out a putative account of the truth-conditions of structured propositions, and just to think about how we'd formulate the explanatory challenge.

Suppose, for example, one put forward the following sort of theory:

(i) The structured proposition that Dummett is a philosopher = [Dummett, being a philosopher].
(ii) [Dummett, being a philosopher] stands in the T relation to w, iff Dummett is a philosopher according to w.
(iii) bearing the T-relation to w=being true at w

Generalizing,

(i) For all a, F, the structured proposition that a is F = [a, F]
(ii) For all individuals a, and properties F, [a, F] stands in the T relation to w iff a instantiates F according to w.
(iii) bearing the T-relation to w=being true at w

In a full generality, I guess we’d semantically ascend for an analogue of (i), and give a systematic account of what structured propositions are associated with which English sentences (presumably a contingent matter). For (ii), we’d give a specification (which there’s no reason to make relative to any contingent facts) about which ordered n-tuples stand in the T-relation to which worlds. (iii) can stay as it is.

The naïve theorist may then claim that (ii) and (iii) amount to a reductive account of what it is for a structured proposition to have truth-conditions. Why does [1,2] not have any truth-conditions, but [Dummett, being a philosopher] does? Because the story about what it is for an ordered pair to stand in the T-relation to a given world, just doesn’t return an answer where the second component isn’t a property. This seems like a totally cheap and nasty response, I’ll admit. But what’s wrong with it? If that’s what truth-conditions for structured propositions are, then what’s left to explain? It doesn't seem that there is any mystery over (ii): this can be treated as a reductive definition of the new term "bearing the T-relation". Are there somehow explanatory challenges facing someone who endorses the property-identity (iii)? Quite generally, I don't see how identities could be the sort of thing that need explaining.

(Of course, you might semantically ascend and get a decent explanatory challenge: why should "having truth conditions" refer to the T-relation. But I don't really see any in principle problem with addressing this sort of challenge in the usual ways: just by pointing to the fact that the T-relation is a reasonably natural candidate satisfying platitudes associated with truth-condition talk.)

I'm not being willfully obstructive here: I'm genuinely interested in what the dialectic should be at this point. I've got a few ideas about things one might say to bring out what's wrong with the flat-footed response to King's challenge. But none of them persuades me.

Some options:

(a)Earlier, we ended up claiming that it was indefinite what sets structured propositions were identical with. But now, we’ve given a definition of truth-conditions that is committal on this front. For example, [F,a] was supposed to be a candidate precisification of the proposition that a is F. But (ii) won’t assign it truth conditions, since the second component isn’t a property but an individual.

Reply: just as it was indefinite what the structured propositions were, it is indefinite what sets have truth-conditions, and what specification of those truth-conditions is. The two kinds of indefiniteness are “penumbrally connected”. On a precisification on which the prop that a is F=[a,F], then the clause holds as above; but on a precisification on which that a is F=[F,a], a slightly twisted version of the clause will hold. But no matter how we precisify structured proposition-talk, there will be a clause defining the truth-conditions for the entities that we end up identifying with structured propositions.

(b) You can’t just offer definitional clauses or “what it is” claims and think you’ve evaded all explanatory duties! What would we think of a philosopher of mind who put forward a reductive account whereby pain-qualia were by definition just some characteristics of C-fibre firing, and then smugly claimed to have no explanatory obligations left.

Reply: one presupposition of the above is that clauses like (ii) “do the job” of truth-conditions for structured propositions, i.e. there won’t be a structured proposition (by the lights of (i)) whose assigned “truth-conditions” (by the lights of (ii)) go wrong. So whatever else happens, the T-relation (defined via (ii)) and the truth-at relation we’re interested in have a sort of constant covariation (and, unlike the attempt to use a clause like (ii) to define truth-conditions for sentences, we won’t get into trouble when we vary the language use and the like across worlds, so the constant covariation is modally robust). The equivalent assumption in the mind case is that pain qualia and the candidate aspect of C-fibre firing are necessarily constantly correlated. Under those circumstances, many would think we would be entitled to identify pain qualia and the physicalistic underpinning. Another way of putting this: worries about the putative “explanatory gap” between pain-qualia and physical states are often argued to manifest themselves in a merely contingent correlation between the former and the latter. And that’d mean that any attempt to claim that pain qualia just are thus-and-such physical state would be objectionable on the grounds that pain qualia and the physical state come apart in other possible worlds.
In the case of the truth-conditions of structured propositions, nothing like this seems in the offing. So I don’t see a parody of the methodology recommended here. Maybe there is some residual objection lurking: but if so, I want to hear it spelled out.

(c)Truth-conditions aren’t the sort of thing that you can just define up as you please for the special case of structured propositions. Representational properties are the sort of things possessed by structural propositions, token sentences (spoken or written) of natural language, tokens of mentalese, pictures and the rest. If truth-conditions were just the T-relation defined by clause (ii), then sentences of mentalese and English, pictures etc couldn’t have truth-conditions. Reductio.

Reply: it’s not clear at all that sentences and pictures “have truth-conditions” in the same sense as do structured propositions. It fits very naturally with the structured-proposition picture to think of sentences standing in some “denotation” relation to a structured proposition, through which may be said to derivatively have truth-conditions. What we mean when we say that ‘S has truth conditions C’ is that S denotes some structured proposition p and p has truth-conditions C, in the sense defined above. For linguistic representation, at least, it’s fairly plausible that structured propositions can act as a one-stop-shop for truth-conditions.

Pictures are a trickier case. Presumably they can represent situations accurately or non-accurately, and so it might be worth theorizing about them by associating them with a coarse-grained proposition (the set of worlds in which they represent accurately). But presumably, in a painting that represents Napolean’s defeat at waterloo, there doesn’t need to be separable elements corresponding to Napolean, Waterloo, and being defeated at, which’d make for a neat association of the picture with a structured proposition, in the way that sentences are neatly associated with such things. Absent some kind of denotation relation between pictures and structured propositions, it’s not so clear whether we can derivatively define truth-conditions for pictures as the compound of the denotation relation and the truth-condition relation for structured propositions.

None of this does anything to suggest that we can’t give an ok story about pairing pictures with (e.g.) coarse-grained propositions. It’s just that the relation between structured propositions and coarse-grained propositions (=truth conditions) and the relation between pictures and coarse-grained propositions can’t be the same one, on this account, and nor is even obvious how the two are related (unlike e.g. the sentence/structured proposition case).
So one thing that may cause trouble for the view I’m sketching is if we have both the following: (A) there is a unified representation relation, such that pictures/sentences/structured propositions stand in same (or at least, intimately related) representation relations to C. (B) there’s no story about pictorial (and other) representations that routes via structured propositions, and so no hope of a unified account of representation given (ii)+(iii).

The problem here is that I don’t feel terribly uncomfortable denying (A) and (B). But I can imagine debate on this point, so at least here I see some hope of making progress.

Having said all this in defence of (ii), I think there are other ways for the naïve, simple set-theoretic account of structured propositions to defend itself that don't look quite so flat-footed. But the ways I’m thinking of depend on some rather more controversial metasemantic theses, so I’ll split that off into a separate post. It’d be nice to find out what’s wrong with this, the most basic and flat-footed response I can think of.

Structured propositions and Benacerraf

2007-12-18T12:59:00.000Z

I’ve recently been reading Jeff King’s book on structured propositions. It’s really good, as you would expect. There’s one thing that’s bothering me though: I can’t quite get my head around what’s wrong with the simplest, most naïve account of the nature of propositions. (Disclaimer: this might all turn out to be very simple-minded to those in the know. I'd be happy to get pointers to the literature (hey, maybe it'll be to bits of Jeff's book I haven't got to yet...)

The first thing you encounter when people start talking about structured propositions is notation like [Dummett, being a philosopher]. This is supposed to stand for the proposition that Dummett is a philosopher, and highlights the fact that (on the Russellian view) Dummett and the property of being a philosopher are components of the proposition. The big question is supposed to be: what do the brackets and comma represent? What sort of compound object is the proposition? In what sense does it have Dummett and being a philosopher as components? (If you prefer a structured intension view, so be it: then you’ll have a similar beast with the individual concept of Dummett and the worlds-intension associated with “is a philosopher” as ‘constituents’. I’ll stick with the Russellian view for illustrative purposes.)

For purposes of modelling propositions, people often interpret the commas as brackets as the ordered n-tuples of standard set theory. The simplest, most naïve interpretation of what structured propositions are, is simply to identify them as n-tuples. What’s the structured proposition itself? It’s a certain kind of set. What sense are Dummett and the property of being a philosopher constituents of the structured proposition that Dummett is a philosopher? They’re elements of the transitive closure of the relevant set.

So all that is nice and familiar. So what’s the problem? In his ch 1. (and, in passing, in the SEP article here) King mentions two concerns. In this post, I’ll just set the scene by talking about the first. It's a version of a famous Benacerraf worry, which anyone with some familiarity with the philosophy of maths will have come across (King explicitly makes the comparison). The original Benacerraf puzzle is something like this: suppose that the only abstract things are set like, and whatever else they may be, the referents of arithmetical terms should be abstract. Then numerals will stand for some set or other. But there are all sorts of things that behave like the natural numbers within set theory: the constructions known as the (finite) Zermelo ordinals (null, {null}, {{null}}, {{{null}}}...) and the (finite) von Neumann ordinals (null, {null}, {null,{null}}…) are just two. So there’s no non-arbitrary theory of which sets the natural numbers are.

The phenomenon crops up all over the place. Think of ordered n-tuples themselves. Famously, within an ontology of unordered sets, you can define up things that behave like ordered pairs: either [a,b]={{a},{a,b}} or {{{a},null},{{b}}}. (For details see http://en.wikipedia.org/wiki/Ordered_pair). It appears there’s no non-arbitrary reason to prefer a theory that ‘reduces’ ordered to unordered pairs one way or the other.

Likewise, says King, there looks to be no non-arbitrary choice of set-theoretic representation of structured propositions (not even if we spot ourselves ordered sets as primitive to avoid the familiar ordered-pair worries). Sure, we *could* associate the words “the proposition that Dummett is a philosopher” with the ordered pair [Dummett, being a philosopher]. But we could also associate it with the set [being a philosopher, Dummett] (and choices multiply when we get to more complex structured propositions).

One reaction to the Benacerrafian challenge is to take it to be a decisive objection to an ontological story about numbers, ordered pairs or whatever that allows only unordered sets as a basic mathematical ontology. My own feeling is (and this is not uncommon, I think) that this would be an overreaction. More strongly: no argument that I've seen from the Benacerraf phenomenon to this ontological conclusion seems to me to be terribly persuasive.

What we should admit, rather, is that if natural numbers or ordered pairs are sets, it’ll be indefinite which sets they are. So, for example, [a,b]={{a},{a,b}} will be neither definitely true nor definitely false (unless we simply stipulatively define the [,] notation one way or another rather than treating it as pre-theoretically understood). Indefiniteness is pervasive in natural language---everyone needs a story about how it works. And the idea is that whatever that story should be, it should be applied here. Maybe some theories of indefiniteness will make these sort of identifications problematic. But prominent theories like Supervaluationism and Epistemicism have neat and apparently smooth theories of what it we’re saying when we call that identity indefinite: for the supervaluationist, it (may) mean that “[a,b]” refers to {{a},{a,b}} on one but not all precisifications of our set-theoretic language. For the epistemicist, it means that (for certain specific principled reasons) we can’t know that the identity claim is false. The epistemicist will also maintains there’s a fact of the matter about which identity statement connecting ordered and unordered sets is true. And there’ll be some residual arbitrariness here (though we’ll probably have to semantically ascend to find it)---but if there is arbitriness, it’s the sort of thing we’re independently committed to to deal with the indefiniteness rife throughout our language. If you’re a supervaluationist, then you won’t admit there’s any arbitriness: (standardly) the identity statement is neither true nor false, so our theory won’t be committed to “making the choice”.

If that’s the right way to respond to the general Benacerraf challenge, it’s the obvious thing to say in response to the version of that puzzle that arises for the Benacerraf case. And this sort of generalization of the indefiniteness maneuver to philosophical analysis is pretty familiar, it’s part of the standard machinery of the Lewisian hoardes. Very roughly, the programme goes: figure out what you want the Fs to do, Ramsify away terms for Fs and you get a way to fix where the Fs are amidst the things you believe in: they are whatever satisfy the open sentence that you’re left with. Where there are multiple, equally good satisfiers, then deploy the indefiniteness maneuver.

I’m not so worried on this front, for what I take to be pretty routine reasons. But there’s a second challenge King raises for the simple, naïve theory of structured propositions, which I think is trickier. More on this anon.

Public service announcements (updated)

2007-12-12T02:47:00.000Z

There's some interesting conferences being announced these days. A couple have caught my eye/been brought to my attention.

First is the Semantics and Philosophy in Europe CFP. This looks really like a really excellent event... one of those events where I think: If I'm not there, I'll be regretting not being there...

The second event is the 2008 Wittgenstein Symposium. It's remit seems far wider than the name might suggest... looks like a funky set of topics. I reproduce the CFP below...

[Update: a third is a one-day conference on the philosophy of mathematics in Manchester. Announcement at the bottom of the post.]

CALL FOR PAPERS:
31st International Wittgenstein Symposium 2008 on

Reduction and Elimination in Philosophy and the Sciences

Kirchberg am Wechsel, Austria, 10-16 August 2008
<http://www.alws.at/>

INVITED SPEAKERS:
William Bechtel, Ansgar Beckermann, Johan van Benthem, Alexander Bird, Elke
Brendel, Otavio Bueno, John P. Burgess, David Chalmers, Igor Douven, Hartry
Field, Jerry Fodor, Kenneth Gemes, Volker Halbach, Stephan Hartmann, Alison
Hills, Leon Horsten, Jaegwon Kim, James Ladyman, Oystein Linnebo, Bernard
Linsky, Thomas Mormann, Carlos Moulines, Thomas Mueller, Karl-Georg
Niebergall, Joelle Proust, Stathis Psillos, Sahotra Sarkar, Gerhard Schurz,
Patrick Suppes, Crispin Wright, Edward N. Zalta, Albert Anglberger, Elena
Castellani, Philip Ebert, Paul Egre, Ludwig Fahrbach, Simon Huttegger,
Christian Kanzian, Jeff Ketland, Marcus Rossberg, Holger Sturm, Charlotte
Werndl.

ORGANISERS:
Alexander Hieke (Salzburg) & Hannes Leitgeb (Bristol),
on behalf of the Austrian Ludwig Wittgenstein Society.

SECTIONS OF THE SYMPOSIUM:
Sections:
1. Wittgenstein
2. Logical Analysis
3. Theory Reduction
4. Nominalism
5. Naturalism &Physicalism
6. Supervenience
Workshops:
- Ontological Reduction & Dependence
- Neologicism

More detailed information on the contents of the sections and workshops can
be found in the "BACKGROUND" part further down.

DEADLINE FOR SUBMITTING PAPERS: 30th April 2008
Instructions for authors will soon be available at <http://www.alws.at/>.
All contributions will be peer-reviewed. All submitted papers accepted for
presentation at the symposium will appear in the Contributions of the ALWS
Series. Since 1993, successive volumes in this series have appeared each
August immediately prior to the symposium.

FINAL DATE FOR REGISTRATION: 20th July 2008
Further information on registration forms and information on travel and
accommodation will be posted at <http://www.alws.at/>.

SCHEDULE OF THE SYMPOSIUM:
The symposium will take place in Kirchberg am Wechsel (Austria) from 10-16
August 2008. Sunday, 10th of August 2008 is supposed to be the day on which
speakers and conference participants are going to arrive and when they
register in the conference office. In the evening, we plan on having an
informal get together. On the next day (11 August, 10:00am) the first
official session of presentations will start with Professor Jerry Fodor's
opening lecture of the symposium. The symposium will end officially in the
afternoon of 16 August 2008.

BACKGROUND:
Philosophers often have tried to either reduce "disagreeable" entities or
concepts to (more) acceptable entities or concepts, or to eliminate the
former altogether. Reduction and elimination, of course, very often have to
do with the question of "What is really there?", and thus these notions
belong to the most fundamental ones in philosophy. But the topic is not
merely restricted to metaphysics or ontology. Indeed, there are a variety
of attempts at reduction and elimination to be found in all areas (and
periods) of philosophy and science.

The symposium is intended to deal with the following topics (among others):

- Logical Analysis: The logical analysis of language has long been regarded
as the dominating paradigm for philosophy in the modern analytic tradition.
Although the importance of projects such as Frege's logicist construction
of mathematics, Russell's paraphrasis of definite descriptions, and
Carnap's logical reconstruction and explicatory definition of empirical
concepts is still acknowledged, many philosophers now doubt the viability
of the programme of logical analysis as it was originally conceived.
Notorious problems such as those affecting the definitions of knowledge or
truth have led to the revival of "non-analysing" approaches to
philosophical concepts and problems (see e.g. Williamson's account of
knowledge as a primitive notion and the deflationary criticism of Tarski's
definition of truth). What role will -- and should -- logical analysis play
in philosophy in the future?

- Theory Reduction: Paradigm cases of theory reduction, such as the
reduction of Kepler's laws of planetary motion to Newtonian mechanics or
the reduction of thermodynamics to the kinetic theory of gases, prompted
philosophers of science to study the notions of reduction and reducibility
in science. Nagel's analysis of reduction in terms of bridge laws is the
classical example of such an attempt. However, those early accounts of
theory reduction were soon found to be too naive and their underlying
treatment of scientific theories unrealistic. What are the state-of-the-art
proposals on how to understand the reduction of a scientific theory to
another? What is the purpose of such a reduction? In which cases should we
NOT attempt to reduce a theory to another one?

- Nominalism: Traditionally, nominalism is concerned with denying the
existence of universals. Modern versions of nominalism object to abstract
entities altogether; in particular they attack the assumption that the
success of scientific theories, especially their mathematical components,
commit us to the existence of abstract objects. As a consequence,
nominalists have to show how the alleged reference to abstract entities can
be eliminated or is merely apparent (Field's Science without Numbers is
prototypical in this respect). What types of "Constructive Nominalism" (a
la Goodman & Quine) are there? Are there any principal obstacles for
nominalistic programmes in general? What could nominalistic accounts of
quantum theory or of set theory look like?

- Naturalism & Physicalism: Naturalism and physicalism both want to
eliminate the part of language that does not refer to the "natural facts"
that science -- or indeed physics -- describes. Metaphysical Naturalism
often goes hand in hand with (or even entails) an epistemological
naturalism (Quine) as well as an ethical naturalism (mainly defined by its
critics), so that also these two main disciplines of philosophy should
restrict their investigations to the world of natural facts. Physicalist
theses, of course, play a particularly important role in the philosophy of
mind, since neuroscientific findings seem to support the view that,
ultimately, the realm of the mental is but a part of the physical world.
Which forms of naturalism and physicalism can be maintained within
metaphysics, philosophy of science, epistemology and ethics? What are the
consequences for philosophy when such views are accepted? Is philosophy a
scientific discipline? If naturalism or physicalism is right, can we still
see ourselves as autonomous beings with morality and a free will?

- Supervenience: Mental, moral, aesthetical, and even "epistemological"
properties have been said to supervene on properties of particular kind,
e.g., physical properties. Supervenience is claimed to be neither reduction
nor elimination but rather something different, but all these notions still
belong to the same family, and sometimes it is even assumed that reduction
is a borderline case of supervenience. What are the most abstract laws that
govern supervenience relations? Which contemporary applications of the
notion of supervenience are philosophically successful in the sense that
they have more explanatory power than "reductive theories" without leading
to unwanted semantical or ontological commitments? What are the logical
relations between the concepts of supervenience, reduction, elimination,
and ontological dependence?

The symposium will also include two workshops on:

- Ontological Reduction & Dependence: Reducing a class of entities to
another one has always been regarded attractive by those who subscribe to
an ideal of ontological parsimony. On the other hand, what it is that gets
reduced ontologically (objects or linguistic items?), what it means to be
reduced ontologically, and which methods of reduction there are, is
controversial (to say the least). Apart from reducing entities to further
entities, metaphysicians sometimes aim to show that entities depend
ontologically on other entities; e.g., a colour sensation instance would
not exist if the person having the sensation did not exist. In other
philosophical contexts, entities are rather said to depend ontologically on
other entities if the individuation of the former involves the latter; in
this sense, sets might be regarded to depend on their members, and
mathematical objects would depend on the mathematical structures they are
part of. Is there a general formal framework in which such notions of
ontological reduction and dependency can be studied more systematically? Is
ontological reduction really theory reduction in disguise? How shall we
understand ontological dependency of objects which exist necessarily? How
do reduction and dependence relate to Quine's notion of ontological
commitment?

- Neologicism: Classical Logicism aimed at deriving every true mathematical
statement from purely logical truths by reducing all mathematical concepts
to logical ones. As Frege's formal system proved to be inconsistent, and
modern set theory seemed to require strong principles of a genuinely
mathematical character, the programme of Logicism was long regarded as
dead. However, in the last twenty years neologicist and neo-Fregean
approaches in the philosophy of mathematics have experienced an amazing
revival (Wright, Boolos, Hale). Abstraction principles, such as Hume's
principle, have been suggested to support a logicist reconstruction of
mathematics in view of their quasi-analytical status. Do we have to
reconceive the notion of reducibility in order to understand in what sense
Neologicism is able to reduce mathematics to logic (as Linsky & Zalta have
suggested recently)? What are the abstraction principles that govern
mathematical theories apart from arithmetic (in particular: calculus and
set theory)? How can Neo-Fregeanism avoid the logical and philosophical
problems that affected Frege's original system -- cf. the problems of
impredicativity and Bad Company?

If you know philosophers or scientists, especially excellent graduate
students, who might be interested in the topic of Reduction and Elimination
in Philosophy and the Sciences, we would be very grateful if you could
point them to the symposium.

With best wishes,

Alexander Hieke and Hannes Leitgeb

********************************************************************************************

Announcing a one-day conference....

Metaphysics and Epistemology: Issues in the Philosophy of Mathematics
Saturday 15 March 2008

Chancellors Hotel and Conference Centre, University of Manchester

Speakers to include:

Joseph Melia (University of Leeds)
Alexander Paseau (University of Oxford)
Philip Ebert (University of Stirling)

For registration details, see
http://www.socialsciences.manchester.ac.uk/disciplines/philosophy/events/conference/index.html

This conference is organised with financial support from the Royal Institute of
Philosophy.

Two problems of the many.

2007-12-04T12:48:00.000Z

Here's a paradigmatic problem of the many (Geach and Unger are the usual sources cited, but I'm not claiming this to be exactly the version they use.) Let's take a moulting cat. There are many hairs that are neither clearly attached, nor clearly unattached to the main body of the cat. Let's enumerate them 1---1000. Then we might consider the material objects which are the masses of cat-arranged matter that include half of the thousand hairs, and exclude to the other half. There are many ways to choose the half that's included. So by this recipe we get many many distinct masses of cat-arranged matter, differing only over hairs. The various pieces of cat-arranged matter change their properties over time in very much the way that cats do: they are now in a sitting-shape, now in a standing-shape, now in a lapping-milk shape, now in an emitting-meows configuration. They each seem to have everything intrinsically required for being a cat.

If you're inclined to think (and I am) that a cat is a material object identical to some piece of cat-arranged matter, then the problem of the many arises: which of the various distinct pieces of cat-arranged matters is the cat? Various answers have been suggested. Some of the most obvious (though not necessarily the most sensible) are: (i) nihilism: none of the cat-candidates are cats. (ii) brutalism: exactly one is a cat, and there is a brute fact of the matter which it is; (iii) vague cat: exactly one is a cat, and it's a vague matter which it is; (iii) manyism: lots of the cat-candidates are cats.

(By the way, (ii) and (iii) may not be incompatible, if you're an epistemicist about vagueness. And those who are fans of many-valued logics for vagueness should have a think about whether they can really support (iii). Consider the best candidates to be a cat, c1....c1000. Suppose these are each cats to an equal degree. Then "one of c1...c1000 is a cat" will standardly have a degree of truth equal to the disjunction=the maximum of the disjuncts=the degree of truth of "c1 is a cat". And the degree of truth of the conjunction: "all of c1...c1000 is a cat" will standardly have a degree of truth equal to the conjunction=the minimum of the conjuncts=the degree of truth of "c1 is a cat". So to the extent that the (determinately distinct) best candidates aren't all cats, to exactly that extent there's no cat among them (and since we chose the best candidates, we won't get a higher degree of truth for "the cat is present" by including extra disjuncts. Conclusion: if you're tempted by response (iii) to the problem of the many, you've got strong reason not to go for many-valued logic. [Edit (see comments): this needs qualification. I think you've reason not to go for many-valued logics that endorse the (fairly standard, but not undeniable) max/min treatment of disjunction/conjunction; and in which the many values are linearly arranged].)

What I'd really like to emphasize is the above leaves open the following question: Is there a super-cat-candidate, i.e. a piece of cat-arranged matter of which every other cat-candidate is a proper part? Take the Tibbles case above, and suppose that the candidates only differ over hairs. Then a potential super-cat-candidate would be the piece of matter that's maximally generous: that includes all the 1000 not-clearly-unattached hairs. If this particular fusion isn't genuinely a cat-candidate, then it's open that if you arrange the cat-candidates by which is a part of which, you'll end up with multiple maximal cat-candidates none of which is a part of the other. Perhaps they each contain 999 hairs, but differ amongst themselves which hair they don't include.

If there is a super-cat-candidate, let's say the problem of the many is of type-1, and if there's no super-cat-candidate, let's say that the problem of the many is of type-2.

My guess is that our description of cases like Tibbles leaves is simply underspecified as to whether it's of type-1 or type-2. But I certainly don't see any principled reason to think that the actual cases of the POM we find around us are always of type-1. There's certainly no a priori guarantee that the sort of criterion that rules in some things as parts of a cat won't also dismiss other things as non-parts. So for example, perhaps we can rank candidates for degrees of integration: some unintegrated parts are ok, but there's some cut-off where an object is just too unintegrated to count as a candidate. One cat-candidate includes some borderline-attached skin cells, and is to that extent unintegrated. Another cat-candidate includes some borderline-attached teeth, and is to that extent unintegrated. But plausibly the fusion that includes both skin cells and teeth is less integrated: enough to disqualify it from being a cat-candidate. It's hard to know how to argue the case further without going deeply into feline biology, but I hope you get the sense of why type-2 POM need to be dealt with.

Now, one response to the standard POM is to appeal to the "maximality" allegedly built into various predicates (like "rock", "cat", "conscious" etc): things that are duplicates of rocks, but which are surrounded by extra rocky stuff, become merely parts of rocks (and so forth). There are presumably intrinisic duplicates of rocks embedded as tiny parts at the centre of large boulders: but there's no intuitive pressure to count them as rocks. Likewise a cat might survive after it's limbs are destroyed by a vengeful deity, but it's unintuitive to think of the duplicate head-and-torso part of Tibbles as itself a cat-candidate. So there's some reasons independently of paradigmatic problem of the many scenarios to think of "cat" and "rock" etc as maximal. (For more discussion of maximality, see Ted Sider's various papers on the topic).

If we've got a type-1 problem of the many, then one might think that the maximality of "cat" or "rock" or whatever gives a principled answer to our original question: the super-cat-candidate (/super-rock-candidate) is the one uniquely qualified to be the cat (/rock). For we've then got an explanation for why all the others, though intrinsically qualified just like cats, aren't cats: being a cat is a maximal property, and all the rival cat-candidates are parts of the one true cat in the vicinity.

But the type-2 problem of the many really isn't addressed by maximality as such. There's no unique super-cat-candidate in this setup, rather a range of co-maximal ones. So maximality won't save our bacon here.

The difference between the two cases is important when we consider other things. For example, in the light of the (fairly widely accepted) maximality of "house" and "cat" and "rock" and the like, few would say that any duplicate of a house must be a house (even setting aside extrinsicality due to social setting). But there's an obvious fall back position, which is floating around the literature: that any duplicate of a house must be a (proper or improper) part of a house (holding fixed social setting etc). That is, any house possesses the property of being part of a house intrinsically (so long as we hold fixed social setting etc). And the same goes for cat: at least holding fixed biological origin, it's plausible that any cat is intrinsically at least part of a cat, and any rock is intrinsically at least part of a rock.

These claims aren't threatened by maximality. But appealing to them in a type-2 problem of the many gets us an argument directly for response (iv): manyism. For plausibly if you took a duplicate of one of the co-maximal cat candidates, T, while eliminating from the scene those bits of matter that are not part of T but are part of one of the other co-maximal cat candidates, then you get something T* that's (determinately) a cat. And so, any duplicate of T* must be at least part of a cat. And since T is a duplicate of T*, T must be at least part of a cat. But T isn't proper part of anything that's even a cat-candidate. So T must itself be a cat.

So the type-2 POM is harder to resolve than the type-1 kind. Maybe some extra weakening of the properties a cat-candidate has intrinsicality are called for. Or maybe (very surprisingly) type-2 POMs never arise. But either way, more work is needed.

Nihilism, maximality, problem of the many

2007-11-27T13:15:00.000Z

Does nihilism about ordinary things help us out with puzzles surrounding maximal properties and the problem of the many? It's hard to see how.

First, maximal properties. Suppose that I have a rock. Surprisingly, there seem to be microphysical duplicates of the rock that are not themselves rocks. For suppose we have a microphysical duplicate of the rock (call it Rocky) that is surrounded by extra rocky stuff. Then, plausibly, the fusion of Rocky and the extra rocky stuff is the rock, and Rocky himself isn't, being out-competed for rock-status by his more extensive rival. Not being shared among duplicates, being a rock isn't intrinsic. And cases meeting this recipe can be plausibly constructed for chairs, tables, rivers, nations, human bodies, human animals and (perhaps) even human persons. Most kind-terms, in fact, look maximal and (hence) extrinsic. Sider has argued that non-sortal properties such as consciousness are likewise maximal and extrinsic.

Second, the problem of the many. In its strongest version, suppose that we have a plentitude of candidates (sums of atoms, say) more or less equally qualified to be a table, cloud, human body or whatever. Suppose further that both the sum and intersection of all these candidates isn't itself a candidate for being the object. (This is often left out of the description of the case, but (1) there seems no reason to think that the set of candidates will always be closed under summing or intersection (2) life is more difficult--and more interesting--if these candidates aren't around.) Which of these candidates is the table, cloud, human body or whatnot?

What puzzles me is why nihilism---rejecting the existence of tables, clouds, human bodies or whatever---should be thought to avoid any puzzles around here. It's true that the nihilist rejects a premise in terms of which these puzzles would normally be stated. So you might imagine that the puzzles give you reason to modus tollens and reject that premise, ending up with nihilism (that's how Unger's original presentation of the POM went, if I recall). But that's no good if we can state equally compelling puzzles in the nihilist's preferred vocabulary.

Take our maximality scenario. Nihilists allow that we have, not a rock, but some things arranged rockwise. And we now conceive of a situation where those things, arranged just as they actually are, still exist (let "Rocky" be a plural term that picks them out). But in this situation, they are surrounded by more things of a qualitatively similar arrangement. Now are the things in Rocky arranged rockwise? Don't consult intuitions at this point---"rockwise" is a term of art. The theoretical role of "rockwise" is to explain how ordinary talk is ok. If some things are in fact arranged rockwise, then ordinary talk should count them as forming a rock. So, for example, van Inwagen's paraphrase of "that's is a rock" would be "those things are arranged rockwise". If we point to Rocky and say "that's a rock", intuitively we speak falsely (that underpins the original puzzle). But if the things that are Rocky are in fact arranged rockwise, then this would be paraphrased to something true. What we get is that "are arranged rockwise" expresses a maximal, extrinsic plural property. For a contrast case, consider "is a circle". What replaces this by nihilist lights are plural predicates like "being arranged circularly". But this seems to express a non-maximal, intrinsic plural property. I can't see any very philosophically significant difference between the puzzle as transcribed into the nihilists favoured setting and the original.

Similarly, consider a bunch of (what we hitherto thought were) cloud-candidates. The nihilist says that none of these exist. Still, there are things which are arranged candidate-cloudwise. Call them the As. And there are other things---differing from the first lot---which are also arranged candidate-cloudwise. Call them the Bs. Are the A's or the B's arranged cloudwise? Are there some other objects, including many but not all of the As and the B's that *are* arranged cloudwise? Again, the puzzle translates straight through: originally we had to talk about the relation between the many cloud-candidates and the single cloud; now we talk about the many pluralities which are arranged candidate-cloudwise, and how they relate to the plurality that is cloudwise arranged. The puzzle is harder to write down. But so far as I can see, it's still there.

Pursuing the idea for a bit, suppose we decided to say that there were many distinct pluralities that are arranged cloudwise. Then "there at least two distinct clouds" would be paraphrased to a truth (that there are some xx and some yy, such that not all the xx are among the yy and vice versa, such that the xx are arranged cloudwise and the yy are arranged cloudwise). But of course it's the unassertibility of this sort of sentence (staring at what looks to be a single fluffy body in the sky) that leads many to reject Lewis's "many but almost one" response to the problem of the many.

I don't think that nihilism leaves everything dialectically unchanged. It's not so clear how many of the solutions people propose to the problem of the many can be translated into the nihilist's setting. And more positively, some options may seem more attractive once one is a nihilist than they did taken cold. Example: once you're going in for a mismatch between common sense ontology and what there really is, then maybe you're more prepared for the sort of linguistic-trick reconstructions of common sense that Lewis suggests in support of his "many but almost one". Going back to the case we considered above, let's suppose you think that there are many extensionally distinct pluralities that are all arranged cloudwise. Then perhaps "there are two distinct clouds" should be paraphrased, not as suggested above, but as:

there are some xx and some yy, such that almost all the xx are among the yy and vice versa, such that the xx are arranged cloudwise and the yy are arranged cloudwise.

The thought here is that, given one is already buying into unobvious paraphrase to capture the real content of what's said, maybe the costs of putting in a few extra tweaks into that paraphrase are minimal.

Caveats: notice that this isn't to say that nihilism solves your problems, it's to say that nihilism may make it easier to accept a response that was already on the table (Lewis's "many but almost one" idea). And even this is sensitive to the details of how nihilism want to relate ordinary thought and talk to metaphysics: van Inwagen's paraphrase strategy is one such proposal, and meshes quite neatly with the Lewis idea, but it's not clear that alternatives (such as Dorr's counterfactual version) have the same benefits. So it's not the metaphysical component of nihilism that's doing the work in helping accommodate the problem of the many: it's whatever machinery the nihilist uses to justify ordinary thought and talk.

There's one style of nihilist who might stand their ground. Call nihilists friendly if they attempt to say what's good about ordinary thought and talk (making use of things like "rockwise", or counterfactual paraphrases, or whatever). I'm suggesting that friendly nihilists face transcribed versions of the puzzles that everyone faces. Nihilists might though be unfriendly: prepared to say that ordinary thought and talk is largely false, but not to reconstruct some subsidiary norm which ordinary thought and talk meets. Friendly nihilism is an interesting position, I think. Unfriendly nihilism is pushing the nuclear button on all attempts to sort out paradoxes statable in ordinary language. But they have at least this virtue: the puzzles they react against don't come back to bite them.

[Update: I've been sent a couple of good references for discussions of nihilism in a similar spirit. First Matt McGrath's paper "No objects, no problem?" argues that the nihilist doesn't escape statue/lump puzzles. Second, Karen Bennett has a forthcoming paper called "Composition, Colocation, and Metaontology" that resurrects problems for nihilists including the problem of the many (though it doesn't now appear to be available online).]

Logically good inference and the rest

2007-11-20T13:43:00.000Z

From time to time in my papers, the putative epistemological significance of logically good inference has been cropping up. I've been recently trying to think a bit more systematically about the issues involved.

Some terminology. Suppose that the argument "A therefore B" is logically valid. Then I'll say that reasoning from "A" is true, to "B" is true, is logically good. Two caveats (1) the logical goodness of a piece of reasoning from X to Y doesn't mean that, all things considered, it's ok to infer Y from X. At best, the case is pro tanto: if Y were a contradiction, for example, all things considered you should give up X rather than come to believe Y; (2) I think the validity of an argument-type won't in the end be sufficient for for the logically goodness of a token inference of that type---partly because we probably need to tie it much closer to deductive moves, partially because of worries about the different contexts in play with any given token inference. But let me just ignore those issues for now.

I'm going to blur use-mention a bit by classifying material-mode inferences from A to B (rather than: "A" is true to "B" is true") as logically good in the same circumstances. I'll also call a piece of reasoning from A to B "modally good" if A entails B, and "a priori good" if it's a priori that if A then B (nb: material conditional). If it's a priori that A entails B, I'll call it "a priori modally good".

Suppose now we perform a competent deduction of B from A. What I'm interested in is whether the fact that the inference is logically good is something that we should pay attention to in our epistemological story about what's going on. You might think this isn't forced on us. For (arguably: see below) whenever an inference is logically good, it's also modally and a priori good. So---the thought runs---for all we've said we could have an epistemology that just looks at whether inferences are modally/a priori good, and simply sets aside questions of logical goodness. If so, logical goodness may not be epistemically interesting as such.

(That's obviously a bit quick: it might be that you can't just stop with declaring something a priori good; rather, any a priori good inference falls into one of a number of subcases, one of which is the class of logically good inferences, and that the real epistemic story proceeds at the level of the "thickly" described subcases. But let's set that sort of issue aside).

Are there reasons to think competent deduction/logically good inference is an especially interesting epistemological category of inference?

One obvious reason to refuse to subsume logically good inference within modally good inferences (for example) is if you thought that some logically good inferences aren't necessarily truth-preserving. There's a precedent for that thought: Kaplan argues in "Demonstratives" that "I am here now" is a logical validity, but isn't necessarily true. If that's the case, then logically good inferences won't be a subclass of the modally good ones, and so the attempt to talk only about the modally good inferences would just miss some of the cases.

I'm not aware of persuasive examples of logically good inferences that aren't a priori good. And I'm not persuaded that the Kaplanian classification is the right one. So let's suppose pro tem that the logically good inference are always modally, a priori, and a priori modally, good.

We're left with the following situation: the logically good inferences are a subclass of inferences that are also fall under other "good" categories. In a particular case where we come to believe B on the basis of A, where is the particular need to talk about its logical "goodness", rather than simply about its modal, a priori or whatever goodness?

To make things a little more concrete: suppose that our story about what makes a modally good inference good is that it's ultra-reliable. Then, since we're supposing all logically good inferences are modally good, just from their modal goodness, we're going to get that they're ultra-reliable. It's not so clear that epistemologically, we need say any more. (Of course, their logical goodness might explain *why* they're reliable: but that's not clearly an *epistemic* explanation, any more than is the biophysical story about perception's reliability.)

So long as we're focusing on cases where we deploy reasoning directly, to move from something we believe to something else we believe, I'm not sure how to get traction on this issue (at least, not in such an abstract setting: I'm sure we could fight on the details if they are filled out.). But even in this abstract setting, I do think we can see that the idea just sketched ignores one vital role that logically good reasoning plays: namely, reasoning under a supposition in the course of an indirect proof.

Familiar cases: If reasoning from A to B is logically good, then it's ok to believe (various) conditional(s) "if A, B". If reasoning from A1 to B is logically good, and reasoning from A2 to B is logically good, then inferring B from the disjunction A1vA2 is ok. If reasoning from A to a contradiction is logically good, then inferring not-A is good. If reasoning from A to B is logically good, then reasoning from A&C to B is good.

What's important about these sort of deployments is that if you replace "logically good" by some wider epistemological category of ok reasoning, you'll be in danger of losing these patterns.

Suppose, for example, that there are "deeply contingent a priori truths". One schematic example that John Hawthorne offers is the material conditional "My experiences are of kind H > theory T of the world is true". The idea here is that the experiences specified should be the kind that lead to T via inference to the best explanation. Of course, this'll be a case where the a priori goodness doesn't give us modal goodness: it could be that my experiences are H but the world is such that ~T. Nevertheless, I think there's a pretty strong case that in suitable settings inferring T from H will be (defeasibly but) a priori good.

Now suppose that the correct theory of the world isn't T, and I don't undergo experiences H. Consider the counterfactual "were my experiences to be H, theory T would be true". There's no reason at all to think this counterfactual would be true in the specified circumstances: it may well be that, given the actual world meets description T*, the closest world where my experiences are H is still an approximately T*-world rather than a T-world. E.g. the nearest world where various tests for general relativity come back negative may well be a world where general relativity is still the right theory, but it's effects aren't detectable on the kind of scales initially tested (that's just a for-instance: I'm sure better cases could be constructed).

Here's another illustration of the worry. Granted, reasoning from H to T seems a priori. But reasoning from H+X to T seems terrible, for a variety of X. (So: My experiences are of H + my experiences are misleading in way W will plausibly a priori supports some T' incompatible with T). But if we were allowed to use a priori good reasoning in indirect proofs, then we could simply argue from H+X to H, and thence (a priori) to T, overall getting an a priori route from H+X to T. the moral is that we can't treat a priori good pieces of reasoning as "lemmas" that we can rely on under the scope of whatever suppositions we like. A priori goodness threatens to be "non-monotonic": which is fine on its own, but I think does show quite clearly that it can completely crash when we try to make it play a role designed for logical goodness.

This sort of problem isn't a surprise: the reliability of indirect proofs is going to get *more problematic* the more inclusive the reasoning in play is. Suppose the indirect reasoning says that whenever reasoning of type R is good, one can infer C. The more pieces of reasoning count as "good", the more potential there is to come into conflict with the rule, because there's simply more cases of reasoning that are potential counterexamples.

Of course, a priori goodness is just one of the inferential virtues mentioned earlier: modal goodness is another; and a priori modal goodness a third. Modal goodness already looks a bit implausible as an attempt to capture the epistemic status of deduction: it doesn't seem all that plausible to classify the inferential move from A and B to B as w the same category as the move from this is water to this is H2O. Moreover, we'll again have trouble with conditional proof: this time for indicative conditionals. Intuitively, and (I'm independently convinced) actually, the indicative conditional "if the watery stuff around here is XYZ, then water is H2O" is false. But the inferential move from the antecedent to the consequent is modally good.

Of the options mentioned, this leaves a priori modal goodness. The hope would be that this'll cut out the cases of modally good inference that cause trouble (those based around a posteriori necessities). Will this help?

I don't think so: I think the problems for a priori goodness resurface here. if the move from H to T is a priori good, then it seems that the move from Actually(H) to Actually(T) should equally be a priori good. But in a wide variety of cases, this inference will also be modally good (all cases except H&~T ones). But just as before, thinking that this piece of reasoning preserves its status in indirect proofs gives us very bad results: e.g. that there's an a priori route from Actually(H) and Actually(X) to Actually (T), which for suitably chosen X looks really bad.

Anyway, of course there's wriggle room here, and I'm sure a suitably ingenious defender of one of these positions could spin a story (and I'd be genuinely interested in hearing it). But my main interest is just to block the dialectical maneuver that says: well, all logically good inferences are X-good ones, so we can get everything we want having a decent epistemology of X-good inferences. The cases of indirect reasoning I think show that the *limitations* on what inferences are logically good can be epistemologically central: and anyone wanting to ignore logic better have a story to tell about how their story plays in these cases.

[NB: one kind of good inference I haven't talked about is that backed by what 2-dimensionalists might call "1-necessary truth preservation": I.e. truth preservation at every centred world considered as actual. I've got no guarantees to offer that this notion won't run into problems, but I haven't as yet constructed cases against it. Happily, for my purposes, logically good inference and this sort of 1-modally good inference give rise to the same issues, so if I had to concede that this was a viable epistemological category for subsuming logically good inference, it wouldn't substantially effect my wider project.]

CEM journalism

2007-11-05T13:45:00.000Z

The literature on the linguistics/philosophy interface on conditionals is full of excellent stuff. Here's just one nice thing we get. (Directly drawn from a paper by von Fintel and Iatridou). Nothing here is due to me: but it's something I want to put down so I don't forget it, since it looks like it'll be useful all over the place. Think of what follows as a bit of journalism.

Here's a general puzzle for people who like "iffy" analyses of conditionals.

No student passes if they goof off.

The obvious first-pass regimentation is:

[No x: x is a student](if x goofs off, x passes)

But for a wide variety of accounts, this'll give you the wrong truth-conditions. E.g. if you read "if" as a material conditional, you'll get it coming out true if all the students goof and succeed! What is wanted, as Higgenbotham urges, is something with the effect:

[No x: x is a student](x goofs off and x passes)

This seems to suggest that under some embeddings "if" expresses conjunction! But that's hardly what a believer in the iffness of if wants.

What the paper cited above notes is that so long as we've got CEM, we won't go wrong. For [No x:Fx]Gx is equivalent to [All x:Fx]~Gx. And where G is the conditional "if x goofs off, x passes", the negated conditional "not: if x goofs off, x passes" is equivalent to "if x goofs off, x doesn't pass" if we have the relevant instance of conditional excluded middle. What we wind up with is an equivalence between the obvious first-pass regimentation and:

[All x: x is a student](if x goofs off, x won't pass).

And this seems to get the right results. What it *doesn't* automatically get us is an equivalence to the Higgenbotham regimentation in terms of a conjunction (nor with the Kratzer restrictor analysis). And maybe when we look at the data more generally, we'll can get some traction on which of these theories best fits with usage.

Suppose we're convinced by this that we need the relevant instances of CEM. There remains a question of *how* to secure these instances. The suggestion in the paper is that rules governing legitimate contexts for conditionals give us the result (paired with a contextually shifty strict conditional account of conditionals). An obvious alternative is to hard-wire in CEM into the semantics, as Stalnaker does. So unless you're prepared (with von Fintel, Gillies et al) to defend in detail fine-tuned shiftiness of the contexts in which conditionals can be uttered then it looks like you should smile upon the Stalnaker analysis.

[Update: It's interesting to think how this would look as an argument for (instances of) CEM.

Premise 1: The following are equivalent:
A. No student will pass if she goofs off
B. Every student will fail to pass if she goofs off

Premise 2: A and B can be regimented respectively as follows:
A*. [No x: student x](if x goofs off, x passes)
B*. [Every x: student x](if x goofs off, ~x passes)

Premise 3: [No x: Fx]Gx is equivalent to [Every x: Fx]~Gx

Premise 4: if [Every x: Fx]Hx is equivalent to [Every x: Fx]Ix, then Hx is equivalent to Ix.

We argue as follows. By an instance of premise 3, A* is equivalent to:

C*. [Every x: student x] not(if x goofs off, x passes)

But C* is equivalent to A*, which is equivalent to A (premise 2) which is equivalent to B (premise 1) which is equivalent to B* (premise 2). So C* is equivalent to B*.

But this equivalence is of the form of the antecedent of premise 4, so we get:

(Neg/Cond instances) ~(if x goofs off, x passes) iff if x goofs off, ~x passes.

And we quickly get from the law of excluded middle and a bit of logic:

(CEM instances) (if x goofs off, x passes) or (if x goofs off, ~ x passes). QED.

The present version is phrased in terms of indicative conditionals. But it looks like parallel arguments can be run for CEM for counterfactuals (Thanks to Richard Woodward for asking about this). For one of the controversial cases, for example, the basic premise will be that the following are equivalent:

D. No coin would have landed heads, if it had been flipped.
E. Every coin would have landed tails, if it had been flipped.

This looks pretty good, so the argument can run just as before.]

Must, Might and Moore.

2007-11-05T12:02:00.000Z

I've just been enjoying reading a paper by Thony Gillies. One thing that's very striking is the dilemma he poses---quite generally---for "iffy" accounts of "if" (i.e. accounts that see English "if" as expressing a sentential connective, pace Kratzer's restrictor account).

The dilemma is constructed around finding a story that handles the interaction between modals and conditionals. The prima facie data is that the following pairs are equivalent:

If p, must be q
If p, q

and

If p, might be q
Might be (p&q)

The dilemma proceeds by first looking at whether you want to say that the modals scope over the conditional or vice versa, and then (on the view where the modal is wide-scoped) looking into the details of how the "if" is supposed to work and showing that one or other of the pairs come out inequivalent. The suggestion in the paper is if we have the right theory of context-shiftiness, and narrow-scope the modals, then we can be faithful to the data. I don't want to take issue with that positive proposal. I'm just a bit worried about the alleged data itself.

It's a really familiar tactic, when presented with a putative equivalence that causes trouble for your favourite theory, to say that the pairs aren't equivalent at all, but can be "reasonably inferred" from each other (think of various ways of explaining away "or-to-if" inferences). But taken cold such pragmatic explanations can look a bit ad hoc.

So it'd be nice if we could find independent motivation for the inequivalence we need. In a related setting, Bob Stalnaker uses the acceptability of Moorean-patterns to do this job. To me, the Stalnaker point seems to bear directly on the Gillies dilemma above.

Before we even consider conditionals, notice that "p but it might be that not p" sounds terrible. Attractive story: this is because you shouldn't assert something unless you know it to be true; and to say that p might not be the case is (inter alia) to deny you know it. One way of bringing out the pretty obviously pragmatic nature of the tension in uttering the conjunction here is to note that asserting the following sort of thing looks much much better:

it might be that not p; but I believe that p

("I might miss the train; but I believe I'll just make it"). The point is that whereas asserting "p" is appropriate only if you know that p, asserting "I believe that p" (arguably) is appropriate even if you know you don't know it. So looking at these conjunctions and figuring out whether they sound "Moorean" seems like a nice way of filtering out some of the noise generated by knowledge-rules for assertion.

(I can sometimes still hear a little tension in the example: what are you doing believing that you'll catch the train if you know you might not? But for me this goes away if we replace "I believe that" with "I'm confident that" (which still, in vanilla cases, gives you Moorean phenomena). I think in the examples to be given below, residual tension can be eliminated in the same way. The folks who work on norms of assertion I'm sure have explored this sort of territory lots.)

That's the prototypical case. Let's move on to examples where there are more moving parts. David Lewis famously alleged that the following pair are equivalent:

it's not the case that: if were the case that p, it would have been that q
if were that p, it might have been that ~q

Stalnaker thinks that this is wrong, since instances of the following sound ok:

if it were that p, it might have been that not q; but I believe if it were that p it would have been that q.

Consider for example: "if I'd left only 5 mins to walk down the hill, (of course!) I might have missed the train; but I believe that, even if I'd only left 5 mins, I'd have caught it. " That sounds totally fine to me. There's a few decorations to that speech ("even" "of course" "only"). But I think the general pattern here is robust, once we fill in the background context. Stalnaker thinks this cuts against Lewis, since if mights and woulds were obvious contradictories, then the latter speech would be straightforwardly equivalent to something of the form "A and I don't believe that A". But things like that sounds terrible, in a way that the speech above doesn't.

We find pretty much the same cases for "must" and indicative "if".

It's not true that if p, then it must be that q; but I believe that if p, q.

("it's not true that if Gerry is at the party, Jill must be too---Jill sometimes gets called away unexpectedly by her work. But nevertheless I believe that if Gerry's there, Jill's there."). Again, this sounds ok to me; but if the bare conditional and the must-conditional were straightforwardly equivalent, surely this should sound terrible.

These sorts of patterns make me very suspicious of claims that "if p, must q" and "if p, q" are equivalent, just as the analogous patterns make me suspicious of the Lewis idea that "if p, might ~q" and "if p, q" are contradictories when the "if" is subjunctive. So I'm thinking the horns of Gillies' dilemma aren't equal: denying the must conditional/bare conditional equivalence is independently motivated.

None of this is meant to undermine the positive theory that Thony Gillies is presenting in the paper: his way of accounting for lots of the data looks super-interesting, and I've got no reason to suppose his positive story won't have a story about everything I've said here. I'm just wondering whether the dilemma that frames the debate should suck us in.

Degrees of belief and supervaluations

2007-11-02T22:35:00.000Z

Suppose you've got an argument with one premise and one conclusion, and you think its valid. Call the premise p and the conclusion q. Plausibly, constraints on rational belief follow: in particular, you can't rationally have a lesser degree of belief in q than you have in p.

The natural generalization of this to multi-premise cases is that if p1...pn|-q, then your degree of disbelief in q can't rationally exceed the sum of your degrees of disbelief in the premises.

FWIW, there's a natural generalization to the multi-conclusion case too (a multi-conclusion argument is valid, roughly, if the truth of all the premises secures the truth of at least one conclusion). If p1...pn|-q1...qm, then the sum of your degrees of disbelief in the conclusions can't rationally exceed the sum of your degrees of disbelief in the premises.

What I'm interested in at the moment is to what extent this sort of connection can be extended to non-classical settings. In particular (and connected with the last post) I'm interested in what the supervaluationist should think about all this.

There's a fundamental choice to be made at the get-go. Do we think that "degrees of belief" in sentences of a vague language can be represented by a standard classical probability function? Or do we need to be a bit more devious?

Let's take a simple case. Construct the artificial predicate B(x), so that numbers less than 5 satisfy B, and numbers greater than5 fail to satisfy it. We'll suppose that it is indeterminate whether 5 itself is B, and that supervaluationism gives the right way to model this.

First observation. It's generally accepted that for the standard supervaluationist

p &~Det(p)|-absurdity;

Given this and the constraints on rational credence mentioned earlier, we'd have to conclude that my credence in B(5)&~Det(B(5)) must be 0. I have credence 0 in absurdity; and the degree of disbelief in the conclusion of this valid argument (1) must not exceed the degree of disbelief in its premises.

Let's think that through. Notice that in this case, my credence in ~Det(B(5)) can be taken to be 1. So given minimal assumptions about the logic of credences, my credence in B(5) must be 0.

A parallel argument running from ~B(5)&~Det(~B(5))|-absurdity gives us that my credence in ~B(5) must be 0.

Moreover, supervaluational entails all classical tautologies. So in particular we have the validity: |-B(5)v~B(5). The standard constraint in this case tells us that rational credence in this disjunction must be 1. And so, we have a disjunction in which we have credence 1, each disjunct of which we have credence 0 in. (Compare the standard observation that supervaluational disjunctions can be non-prime: the disjunction can be true when neither disjunct is).

This is a fairly direct argument that something non-classical has to be going on with the probability calculus. One move at this point is to consider Shafer functions (which I know little about: but see here). Now maybe that works out nicely, maybe it doesn't. But I find it kinda interesting that the little constraint on validity and credences gets us so quickly into a position where something like this is needed if the constraint is to work. It also gives us a recipe for arguing against standard supervaluationism: argue against the Shafer-function like behaviour in our degrees of belief, and you'll ipso facto have an argument against supervaluationism. For this, the probablistic constraint on validity is needed (as far as I can see): for its this that makes the distinctive features mandatory.

I'd like to connect this to two other issues I've been working on. One is the paper on the logic of supervaluationism cited below. The key thing here is that it raises the prospect of p&~Dp|-absurdity not holding, even for your standard "truth=supertruth" supervaluationist. If that works, the key premise of the argument that forces you to have degree of belief 0 in both an indeterminate sentence 'p' and its negation goes missing.

Maybe we can replace it by some other argument. If you read "D" as "it is true that..." as the standard supervaluationist encourages you to, then "p&~Dp" should be read "p&it is not true that p". And perhaps that sounds to you just like an analytic falsity (it sure sounded to me that way); and analytic falsities are the sorts of things one should paradigmatically have degree of belief 0 in.

But here's another observation that might give you pause (I owe this point to discussions with Peter Simons and John Hawthorne). Suppose p is indeterminate. Then we have ~Dp&~D~p. And given supervaluationism's conservativism, we also have pv~p. So by a bit of jiggery-pokery, we'll get (p&~Dp v ~p&~D~p). But in moods where I'm hyped up thinking that "p&~Dp" is analytically false and terrible, I'm equally worried by this disjunction. But that suggests that the source of my intuitive repulsion here isn't the sort of thing that the standard supervaluationist should be buying. Of course, the friend of Shafer functions could just say that this is another case where our credence in the disjunction is 1 while our credences in each disjunct is 0. That seems dialectically stable to me: after all, they'll have *independent* reason for thinking that p&~Dp should have credence 0. All I want to insist is that the "it sounds really terrible" reason for assigning p&~Dp credence 0 looks like it overgeneralizes, and so should be distrusted.

I also think that if we set aside truth-talk, there's some plausibility in the claim that "p&~Dp" should get non-zero credence. Suppose you're initially in a mindset where you should be about half-confident of a borderline case. Well, one thing that you absolutely want to say about borderline cases is that they're neither true nor false. So why shouldn't you be at least half-confident in the combination of these?

And yet, and yet... there's the fundamental implausibility of "p&it's not true that p" (the standard supervaluationist's reading of "p&~Dp") having anything other than credence 0. But ex hypothesi, we've lost the standard positive argument for that claim. So we're left, I think, with the bare intuition. But it's a powerful one, and something needs to be said about it.

Two defensive maneuvers for the standard supervaluationist:

(1) Say that what you're committed to is just "p& it's not supertrue that p". Deny that the ordinary concept of truth can be identified with supertruth (something that as many have emphasized, is anyway quite plausible given the non-disquotational nature of supertruth). But crucially, don't seek to replace this with some other gloss on supertruth: just say that supertruth, superfalsity and gap between them are appropriate successor concepts, and that ordinary truth-talk is appropriate only when we're ignoring the possibility of the third case. If we disclaim conceptual analysis in this way, then it won't be appropriate to appeal to intuitions about the English word "true" to kick away independently motivated theoretical claims about supertruth. In particular, we can't appeal to intuitions to argue that "p&~supertrue that p" should be assigned credence 0. (There's a question of whether this should be seen as an error-theory about English "truth"-ascriptions. I don't see it needs to be. It might be that the English word "true" latches on to supertruth because supertruth what best fits the truth-role. On this model, "true" stands to supertruth as "de-phlogistonated air" according to some, stands to oxygen. And so this is still a "truth=supertruth" standard supervaluationism.)

(2) The second maneuver is to appeal to supervaluational degrees of truth. Let the degree of supertruth of S be, roughly, the measure of the precisifications on which S is true. S is supertrue simpliciter when it is true on all the precisifications, i.e. measure 1 of the precisifications. If we then identify degrees of supertruth with degrees of truth, the contention that truth is supertruth becomes something that many find independently attractive: that in the context of a degree theory, truth simpliciter should be identified with truth to degree 1. (I think that this tendancy has something deeply in common with the temptation (following Unger) to think that nothing that nothing can be flatter than a flat thing: nothing can be truer than a true thing. I've heard people claim that Unger was right to think that a certain class of adjectives in English work this way).

I think when we understand the supertruth=truth claim in that way, the idea that "p&~true that p" should be something in which we should always have degree of belief 0 loses much of its appeal. After all, compatibly with "p" not being absolutely perfectly true (=true), it might be something that's almost absolutely perfectly true. And it doesn't sound bad or uncomfortable to me to think that one should conform one's credences to the known degree of truth: indeed, that seems to be a natural generalization of the sort of thing that originally motivated our worries.

In summary. If you're a supervaluationist who takes the orthodox line on supervaluational logic, then it looks like there's a strong case for a non-classical take on what degrees of belief look like. That's a potentially vulnerable point for the theory. If you're a (standard, global, truth=supertruth) supervaluationist who's open to the sort of position I sketch in the paper below, prima facie we can run with a classical take on degrees of belief.

Let me finish off by mentioning a connection between all this and some material on probability and conditionals I've been working on recently. I think a pretty strong case can be constructed for thinking that for some conditional sentences S, we should be all-but-certain that S&~DS. But that's exactly of the form that we've been talking about throughout: and here we've got *independent* motivation to think that this should be high-probability, not probability zero.

Now, one reaction is to take this as evidence that "D" shouldn't be understood along standard supervaluationist lines. That was my first reaction too (in fact, I couldn't see how anyone but the epistemicist could deal with such cases). But now I'm thinking that this may be too hasty. What seems right is that (a) the standard supervaluationist with the Shafer-esque treatment of credences can't deal with this case. But (b) the standard supervaluationist articulated in one of the ways just sketched shouldn't think there's an incompatibility here.

My own preference is to go for the degrees-of-truth explication of all this. Perhaps, once we've bought into that, the "truth=degree 1 supertruth" element starts to look less important, and we'll find other useful things to do with supervaluational degrees of truth (a la Kamp, Lewis, Edgington). But I think the "phlogiston" model of supertruth is just about stable too.

[P.S. Thanks to Daniel Elstein, for a paper today at the CMM seminar which started me thinking again about all this.]

Supervaluations and logical revisionism paper

2007-11-02T22:13:00.000Z

Happy news today: the Journal of Philosophy is going to publish my paper on the logic of supervaluationism. Swift moral. It ain't logical revisionary; and if it is, it doesn't matter.

This previous post gives an overview, if anyone's interested...

Now I've just got to figure out how to transmute my beautiful LaTeX symbols into Word...

London Logic and Metaphysics Forum (x-posted from MV)

2007-10-24T14:41:00.001+01:00

If you're in London on a Tuesday evening, what better to do than to take in a talk by a young philosopher on logic or metaphysics?

Spotting this gap in the tourist offerings, the clever folks in the capital have set up the London Logic and Metaphysics forum. Looks an exciting programme, though I have my doubts about the joker on the 11th Dec...

Tues 30 Oct: David Liggins (Manchester)
Quantities

Tues 13 Nov: Oystein Linnebo (Bristol & IP)
Compositionality and Frege's Context Principle

Tues 27 Nov: Ofra Magidor (Oxford)
Epistemicism about vagueness and meta-linguistic safety

Tues 11 Dec: Robbie Williams (Leeds)
Is survival intrinsic?

8 Jan: Stephan Leuenberger (Leeds)

22 Jan: Antony Eagle (Oxford)

5 Feb: Owen Greenhall (Oslo & IP)

4 Mar: Guy Longworth (Warwick)

Full details can be found here.

In Rutgers

2007-10-24T13:18:00.001+01:00

As Brian Weatherson reports here, there's a metaphysics/phil physics conference at Rutgers this weekend (26-28th). I'm in Rutgers for the week, and am responding to one of the papers at the event. I'm looking forward to what looks like a really interesting conference.

Tonight (24th) I'm giving a talk to a phil language group at Rutgers. I'm going to be presenting some material on modal accounts of indicative conditionals (a la Stalnaker, Weatherson, Nolan). This piece has evolved quite a bit during the last few weeks as I've been working on it. A bit unexpectedly, I've ended up with an argument for Weatherson's views.

Briefly, the idea is to look at what mileage we can get out of paradigmatic instances of the identification of the probability of a conditional "If A, B" with the conditional probability of B on A (CCCP). We know that in general that identification is highly problematic, due to notorious impossibility results due to David Lewis and more recently Ned Hall and Al Hajek. But I think it's interesting to divide the issue into two halves:

First, what would a modal account of indicative conditionals that obeys (a handful of paradigmatic) instances of CCCP have to look like? I think there's a lot we can say about this: of the salient options, it'll look a lot like Weatherson's theory; it'll have to have a particular take on what kind of vagueness can effect the conditional; it'll have to say that any proposition you know should have probability 1.

Second, is this package sustainable in the face of impossibility results? Al Hajek (in his papers in the Eels/Skyrms probability and conditionals volume) does a really nice job of formulating the challenges here. If we're prepared to give up some instances of CCCP in recherche cases (like left-embedded conditionals, things of the form "if (if A, B), C", then many of the general impossibility results won't apply. But nevertheless, there a bunch of puzzles that remain: in particular, concerning how even the paradigmatic instances can survive when we receive new information.

I'll mostly be talking about the first part of the talk this evening.

Edgington vs. Stalnaker

2007-10-12T17:08:00.000+01:00

One of the things I'm thinking about at the moment is Stalnaker-esque treatments of indicative conditionals. Stalnaker's story, roughly, is that indicative conditionals have almost exactly the same truth conditions as (on his theory) counterfactuals do. That is, A>B is true at w iff B is true at the nearest B-world to w. The difference comes only in the fine details about which worlds count as nearest. For counterfactuals, Stalnaker like Lewis thinks that some sort of similarity does the job. For indicatives, Stalnaker thinks that the nearness ordering is rooted in the same similarity metric, but distorted by the following overriding principle: if A and w are consistent with what we collectively presuppose, then the nearest A-worlds will also be consistent with what we collectively presuppose. In the jargon, all worlds outside the "context set" are pushed further out than they would be on the counterfactual ordering.

I'm interested in this sort of "push worlds" modal account of indicatives. (Others in a similar family include Daniel Nolan's theory, whereby it's knowledge that does the pushing rather than collective presuppositions). Lots of criticisms of Stalnaker's theory don't engage with the fine details of what he says about the closeness ordering, but more general aspects (e.g. its inability to sustain Adams' thesis that the conditional probability is the probability of the conditional; its handling of Gibbard cases; its sensitivity to fine factors of conversational context). An exception, however, is an argument that Dorothy Edgington puts forward in her SEP survey article (which, by the way, I very much recommend!)

Here's the case. Let's suppose that Jill is uncertain how much fuel is in Jane's car. The tank has a capacity for 100-miles'-worth, but Jill has no knowledge of what level it is at. Jane is
going to drive it until it runs out of fuel. For Jill, the probability of the car being driven for n miles, given that it's driven for no more than fifty, is 1/50. (for n<51).

Suppose that in fact the tank is full. The most similar worlds to actuality, arguably, are those where the tank is 50 per cent full, and so where Jane drives 50 miles. The same goes for any world where the tank is more than 50 per cent full. So, if nearness of worlds is determined by similarity, the conditional is true as uttered at each of the worlds where the tank is more than 50 per cent full. So without knowing the details of the level of the tank, we should be at least 50 per cent confident that if it goes for under 50 miles, it'll go for exactly 50 miles. But this seems all wrong. Varying the numbers we can make the case even worse: we should be almost sure of "If it goes for no more than 3 miles, it'll go for exactly 3 miles", even though we regard 3, 2, 1 as equiprobable fuel levels.

Of course, that's only to take into account the comparative similarity of worlds in determining the ordering, and Stalnaker and Nolan have the distorting factor to appeal to: worlds that are incompatible with something we presuppose/know to be true, can be pushed further out. But it doesn't seem in this case that anything relevant is being presupposed/known.

I don't think this objection works. To see that something is going wrong, notice that the argument, if successful, would work against other theories too. Consider, for example, Stalnaker's theory of the counterfactual conditional. Take the case as before, but suppose we're a day later and Jill doesn't know how far Jane drove. Consider the counterfactual "Had it stopped after no more than 50 miles, it'd have gone for exactly 50 miles". By the previous reasoning, the most similar worlds to over-50 worlds are exactly-50 worlds; so we should be half confident of the truth of that conditional. Varying the numbers, we should be almost sure that "If it had gone no more than 3, it'd go exactly 3", despite regarding the probabilities of 3, 2 and 1 as equally likely. But these all seem like bizarre results.

Moral: the counterfactual ordering of worlds isn't fixed by the kind of similarity that Edgington appeals to: the sort of similarity whereby a world in which the car stops after 53 miles is more similar to one in which the car stops after 50 miles than one in which the car stops after 3 miles. Of course, in some sense (perhaps an "overall" sense) those similarity judgements are just right. But we know from the Fine/Bennett cases that the sense of similarity that supports the right counterfactual verdicts can't be all in cases (those cases are ones concerning counterfactuals starting "if Nixon had pushed the nuclear button in the 70's..." All-in similarity arguably says that closest such worlds are ones where no missiles are released, leading to the wrong results).

Spelling out what the right notion of similarity is is tricky. Lewis gave us one recipe. In effect, we look for a little miracle that'll suffice to let the counterfactual world diverge from actual history to bring about the antecedent. Then we let events run on according to actual laws, and see what happens. So in worlds where the tank is full, say, let's look for the little miracle required to to make it run for no more than 50 miles, and run things on. What are the plausible candidates? Perhaps Jane's decides to take an extra journey yesterday, or forgets to fill up her car two days ago. Small miracles could suffice to get us into those sorts of worlds. But those sorts of divergences don't really suggest that she'll end up with exactly 50 miles worth of fuel in the tank, and so this approach undermines the case for "If were at most 50, then exactly 50" being true in antecedent-false worlds. (Which is a good thing!)

If that's the right thing to say in the counterfactual case, the indicative case too will be sorted. For it's designed to be a case where presuppositions/knowledge don't have a relevant distorting effect. And so, once more, the case for "If the car goes for at most 50, then it'll go for exactly 50" doesn't work.

I think that the basic interest of push-worlds theories of indicatives like Stalnaker's and Nolan's is to connect up the counterfactual and indicative ordering: whether there's anything informative to say about the counterfactual ordering of worlds itself is an entirely different matter. So if the glosses of the position lead to problems, it's best to figure out whether the problems lie withthe gloss of the counterfactual ordering (which then should be assessed in connection with that familiar and worked through literature) or with the push-worlds maneuver itself (which has, I think, been less fully examined). I think Edgington's objection is really connected with the first facet, and I've tried to say why I think a more detailed theory will make the problem dissolve. But even if it did turn out to be a problem, the push-worlds thesis itself is still standing.

(Incidentally, I do think Edgington's setup (which she attributes to a student, James Studd) has wider interest. It looks to me like Jackson's modal theory of counterfactuals, and Davis' modal theory of indicatives, both deliver the wrong results in this case.)

[Actually, now I've written this out, it strikes me that maybe the anti-Stalnaker argument is fixable. The trick would be to specify the background state of the world to make the result for counterfactual probabilities seem plausible, but such that (given Jill's ignorance of the background conditions) the indicative probabilities still seem wrong. So maybe the example is at least a recipe for a counterexample to Stalnaker, even if the original case is resistable as described.]

UK job market

2007-09-18T09:26:00.001+01:00

As the next crop of PhDers gear up for the job market, I thought I’d try to systematize some info about the UK system that might not be transparent to outsiders. It's not always totally transparent to insiders either, but I’m hoping that everything I say below is accurate, at least as a rule of thumb. I’d very much welcome queries, corrections and supplements.

Basics:

The UK job market has no unified system for applications. Jobs come out in dribs and drabs, and you apply individually to each one you fancy going for at the appropriate time.
Three main categories of job that PhDers look for:

“Lectureships”. Usually these jobs comes with responsibilities to teach, to do research, and to do certain amounts of administrative work. These come with the equivalent of tenure. These are sometimes called “permanent” or “continuing” lectureships to distinguish them from (c) below.
People sometimes think of these---very roughly---as US assistant professorships (though coming with the equivalent of tenure).
“Postdocs”: (normally) full time research positions, often held for two or three years.
“Fixed term lectureships” (including “teaching fellowships” and “replacement lectureships”). These are usually positions covering teaching needs within a department. Pay and conditions vary wildly: some of them are de facto full-time teaching positions, some of them will have the same conditions as the non-fixed term lectureships.

It’s far more common in the UK than in the US for PhD-ers aiming for a research career to try for a postdoc position for a few years. Postdocs are pretty prestigious things to get. However, over the last few years quite a few PhD leavers have moved straight into continuing lectureships, which offers the extremely nice feature of instant job security, if less upfront time to spend on research.
Lectureships come in grades: Lecturer A and lecturer B are the entry-level grades (lecturer Bs getting a bit more money than lecturer As). Then come senior lectureships and “readerships”; then professorships. You can roughly map the UK lecturer/senior lecturer/prof divisions onto US assistant/associate/full prof. But I don’t have enough familiarity with the US system to know how closely it matches---and of course there isn’t a tenured/untenured line to be drawn as there is in the US.
Fixed term lectureships are the equivalent, I guess, of US visiting professorships.
Sometimes but not always UK jobs will be advertised according to US norms (e.g. specified with AOS/AOC, advertised in JFP). But to get the full whack, the best thing to do is to sign up for the most popular UK academic job website, www.jobs.ac.uk.

Appointments procedure

What’s asked for in a UK application will vary. There’s often an application form to be given out, writing samples will be asked for (perhaps with a specified wordlimit) and of course you need to include a CV. References aren’t typically required at the initial application stage. But often US applicants find it easiest to send their standard application pack, including references, teaching reports and whatever. This’ll probably mean that US applicants end up providing a *lot* more info than their rivals at the initial stages. Obviously you can contact the dept for guidance if you’re worried your application pack will be out of sync with what’s officially requested.
If you’re invited for interview, you should be aware that the setup will differ markedly from US norms. Often, there’ll be a shortlist of 4 or 5 for a continuing lectureship, and often all candidates will be interviewed on the same day, and even taken out for dinner together. Some people find this totally awkward, and hate it. I sort of enjoyed the camaraderie. But it is standard practice, so don’t be surprised by having to socialize with your competitors. (Remember: there's nothing like the APA smoker to go through in the UK system: the interview days are a one-stop-shop). The institution will tell you what to expect, but often the formal proceedings will include a presentation and an interview, carried out over one or two days.
Any presentation will typically be to the whole department, who’ll give feedback to the appointments committee who run the interview and who actually make the hiring decisions. Presentations can be of various formats: from 20 min presentations with 10 mins for questions, to hour-long presentations with substantial discussion time. For fixed term lectureships, you might be asked for a teaching-based presentation (“give a presentation suitable for a first-year course”). For postdocs, obviously a research presentation is appropriate. For continuing lectureships, it’ll probably veer towards the research. The institution will give guidance, and don’t be afraid to ask for clarification/advice if you’re unsure what they’re wanting (particularly if they ask for something totally impossible e.g. “a twenty minute presentation accessible by second year undergraduates that gives an overview of your research programme”).
As mentioned, UK appointments are made by appointments committees, not by individual departments. The makeup of appointments committees can vary, but it isn’t atypical for there to be just two philosophers in a committee of five or more for a philosophy-only post. Obviously, these philosophers have an influential voice, both in the interview itself (you can expect them to ask the majority of the questions) and in the hiring decisions. But for continuing positions probably also be asked questions by non-philosophers. For obvious reasons “are there interdisciplinary aspects to your research?” is a question often heard at that stage of the interview.

Finally, the Oxbridge section:

Oxford and Cambridge are exceptions to almost every UK rule. Their unique college-based setup means that their jobs are titled differently and graded differently: [for example, in Oxford] CUFs and University Lectureships are the main continuing jobs they offer. Those are, again, both tenured positions. See this discussion on Leiter (by Michael Rosen) for the lowdown. Oxford and Cambridge also have a vast stock of postdoc positions (called in Oxbridge “junior research fellowships” or JRFs) and a vast stock of fixed term appointments “lectureships”. All terribly confusing even to UK folk.
Not all Oxford and Cambridge JRFs are advertised on jobs.ac.uk, though I believe all continuing positions will be. I found the only way to get comprehensive listings for JRFs is by looking at the Oxford Gazette: http://www.ox.ac.uk/gazette/ (this comes out weekly, and you can sign up for email notification). From the homepage, click on “weekly issues”, then an issue, then “appointments”. Amusingly under “positions outside Oxford”, it lists all and only positions available at Cambridge. That’s quantifier restriction for you. Two warnings: these positions are often (though not always) advertised across disciplines, so that a philosopher will be competing with biologists and mathematicians and whatever. Also, at least when I applied, each JRF position that came up (and there are lots) seemed to require it’s own research statement, of varying lengths with varying requirements. That’s hugely time-consuming for the applicant (Oxbridge: please introduce some uniformity!)

[updated in the light of Brian's queries in the comments about whether the Cambridge continuing positions are relevantly like those in Oxford or relevantly like those in the rest of the UK. I don't know about this. Be very pleased to receive information.]

Sleeping bookie

2007-09-06T14:54:00.000+01:00

I've spent more of this week than is healthy thinking about the Sleeping Beauty puzzle (thanks in large part to this really interesting post by Kenny). I don't think I've got anything terribly novel to say, but I thought I'd set out my current thinking to see if people agree with my take on what the dialectic is on at least one aspect of the puzzle.

Sleeping Beauty is sent to sleep by philosophical experimenters. He (for, in a strike for sexual equality, this Beauty is male) will be woken up on Monday morning, told on Monday afternoon what day it is, and sent to sleep again after being given a drug which will mean that the next time he wakes up, he will have no memories of what transpired. Depending on the result of a fair coin flip, he will either be woken up in exactly similar circumstances on Tuesday morning, or be left to sleep through the day. Beauty is aware of the setup.

How confident should Beauty be on Monday morning that the coin to be flipped in a few hours will land heads (remember, he knows it’s a fair coin). Halfers say: he should have credence 1/2 that it’ll be heads. Thirders say: the credence should be 1/3. (All sides agree that on Sunday his credence should be 1/2).

What I’m interested in is whether there are Dutch book arguments for either view. The very simplest takes the following form. Sell Beauty a [$30,T] bet for $15 on Sunday evening. Then, if Beauty’s a halfer, on Monday and (if awoken) Tuesday mornings, sell him [$20,H] bets on each awakening for $10.

If H obtains, Beauty loses the first bet but wins the sole remaining bet (on Monday morning), for a net loss of $5. If T obtains, Beauty wins the first bet, but loses the next two, for a net loss of $5 again. So Beauty is guaranteed to lose money.

This is in some sense a diachronic dutch book. But as several people note, it’s not a particularly convincing argument that there’s something wrong with Beauty being a halfer. For notice that the information here is asymmetric: the bookie offering the bets needs to have more information than Beauty, since it is crucial to their strategy to offer twice as many bets if the result of the coin flip is tails, than if it is heads.

Hitchcock aims to give a revised Dutch book argument for the same conclusion that avoids this problem. He suggests that the experimenters put the bookie through the same procedure as they put Beauty through, and the bookie’s strategy should then simply be to offer Beauty the bets every time they both wake. That has the net effect of offering the same set of bets as above for a sure loss for Beauty, but the bookie and Beauty are in the same epistemic state. This is the sleeping bookie argument.

What I’d like to claim (inspired by Bradley and Leitgeb) is that if we concentrate too much on the epistemic state of hypothetical bookies, we’ll get led astray. Looking at the overall mechanism whereby bets are offered to Beauty, we initially described this as one where an agent (bookie) is offering bets to Beauty each time they are both awake. But I’d prefer to describe this as a case where a complex agency (the bookie and the experimenters in cahoots) are offering bets to Beauty. The second description seems at least as good as the first: after all, without the compliance of the experimenters, the bookie’s dutch book strategy can’t be implemented. But the system constituted by the experimenters and the bookie clearly has access to the information about the result of the coin toss, and arranges for the bets to be made appropriately, even though the bookie alone lacks this information.

Now dutch book arguments are only as good as the results we can extract from them about what credences are rational to have in given circumstances. And clearly, if Beauty knows that the bets coming at him encode information about the outcome on which the bet turns, then he needn’t (perhaps shouldn't) simply bet according to his credences, but adjust them to take into account the encoded information. That’s why, to get a fix on what Beauty’s credences are, we put a ban on the bookie having excess information. That's why the first dutch book argument for thirding looks like a bad way to get a fix on what Beauty's credences are. But this rationale for forbidding the bookie from having excess information generalizes, so that we shouldn't trust dutch books in any situation where the mechanism whereby bets are offered (whether in the hands of a single individual, or a system) relies on information about the outcome on which the bet turns. (Equally, if the bookie had extra information, but the system of bets doesn’t exploit this in any way, there's as yet no case against trusting the dutch book argument, it seems to me.)

The moral I take from all this is that what’s going on in the head of some individual we deign to call “bookie” is neither here nor there: what matters is the pattern of bets and whether that pattern exploits information about the outcomes on which the bet turns. This is effectively what I take Bradley and Leitgeb to argue for in their very nice article. What they suggest (roughly) is that a necessary condition on taking a dutch book argument to give a fix on rational credences, is that the pattern of bets be uncorrelated with the outcomes on which the bets turn. I conjecture (tentatively), that this is really what the ban on bookie’s having extra information was trying to get at all along. The upshot is that Hitchcock's sleeping bookie argument is problematic in the same way as the initial dutch book argument against halfers.

But more than this. If we refocus attention on the issue of the goodstanding of the pattern of bets, rather than the epistemic states of hypothetic bookies, we can put together a dutch book argument against thirders. For suppose that the experimenters offer Beauty a [$30,H] bet for $15 on Sunday, and then a genuine bet of [$30,T] for $20 on Monday morning no matter what happens, and (so he can’t tell what’s going on) a fake bet where he’ll automatically get his stake returned, apparently of [$30,T] for $20 on Tuesday. Then he’ll be guaranteed a loss of $5 no matter what happens. Of course, the experimenters here have knowledge of the outcomes. But (arguably) that doesn’t matter, because the bets they offer are uncorrelated with the outcomes of the event on which the bets turn: the system of bets offered is the same no matter what the outcome is, so (it seems to me) the information that the experimenters have isn’t implicit in the pattern of bets in any sense. So I think there’s a better dutch book argument against thirding, than there is against halfing. (Or at least, I'd be interested in seeing the case against this in detail).

All this is not to say that the halfer is out of the woods. A quite different dutch book argument is given in a paper by Draper and Pust, which exploits the standard halfer’s story (Lewis’s) about what happens on Monday afternoon, once Beauty has been told what day it is. The Lewisian halfer thinks that once Beauty realizes its Monday, he should have credence 2/3 that Heads is the result. And that, it appears, is a dutch-bookable situation.

Notice that this isn’t directly an argument against the thesis that Beauty should have credence 1/2 in Heads on Monday morning. It is, in effect, an argument that he should also have credence 1/2 in Heads on Tuesday. And, with a few other widely accepted assumptions, these combine to give rise to a contradiction (see for example, Cian Dorr's presentation of the Beauty case as a paradox).

If this is all we say, then we should conclude that we really do have here a puzzling argument for a contradiction, where all the premises look pretty plausible and the two crucial ones both seem prima facie defensible via dutch book strategies. Maybe, as some suggest, we should revise our claims about updating of credences to make halfing in both circumstances appropriate: or maybe there’s something unavoidably irrational in Beauty’s predicament. What will finally come out in the wash as the best response to the puzzle is one matter; whether the dutch book considerations support halfing or thirding on Monday morning is another; and it is only on this narrow point that I’m claiming that there is a pro tanto case to be a halfer.

Thoughts?

Emergence, Supervenience, and Indeterminacy

2007-08-17T03:01:00.000+01:00

While Ross Cameron, Elizabeth Barnes and I were up in St Andrews a while back, Jonathan Schaffer presented one of his papers arguing for Monism: the view that the whole is prior to the parts, and the world is the one "fundamental" object.

An interesting argument along the way argued that contemporary physics supports the priority of the whole, at least to the extent that properties of some systems can't be reduced to properties of their parts. People certainly speak that way sometimes. Here, for example, is Tim Maudlin (quoted by Schaffer):

The physical state of a complex whole cannot always be reduced to those of its parts, or to those of its parts together with their spatiotemporal relations… The result of the most intensive scientific investigations in history is a theory that contains an ineliminable holism. (1998: 56)

The sort of case that supports this is when, for example, a quantum system featuring two particles determinately has zero total spin. The issues is that there also exist systems that duplicate the intrinsic properties of the parts of this system, but which do not have the zero-total spin property. So the zero-total-spin property doesn't appear to be fixed by the properties of its parts.

Thinking this through, it seemed to me that one can systematically construct such cases for "emergent" properties if one is a believer in ontic indeterminacy of whatever form (and thinks of it that way that Elizabeth and I would urge you to). For example, suppose you have two balls, both indeterminate between red and green. Compatibly with this, it could be determinate that the fusion of the two be uniform; and it could be determinate that the fusion of the two be variegrated. The distributional colour of the whole doesn't appear to be fixed by the colour-properties of the parts.

I also wasn't sure I believed in the argument, so posed. It seems to me that one can easily reductively define "uniform colour" in terms of properties of its parts. To have uniform colour, there must be some colour that each of the parts has that colour. (Notice that here, no irreducible colour-predications of the whole are involved). And surely properties you can reductively define in terms of F, G, H are paradigmatically not emergent with respect to F, G and H.

What seems to be going on, is not a failure for properties of the whole to supervene on the total distribution of properties among its parts; but rather a failure of the total distribution of properties among the parts to supervene on the simple atomic facts concerning its parts.

That's really interesting, but I don't think it supports emergence, since I don't see why someone who wants to believe that only simples instantiate fundamental properties should be debarred from appealing to distributions of those properties: for example, that they are not both red, and not both green (this fact will suffice to rule out the whole being uniformly coloured). Minimally, if there's a case for emergence here, I'd like to see it spelled out.

If that's right though, then application of supervenience tests for emergence have to be handled with great care when we've got things like metaphysical indeterminacy flying around. And it's just not clear anymore whether the appeal in the quantum case with which we started is legitimate or not.

Anyway, I've written up some of the thoughts on this in a little paper.

Fundamental and derivative truths

2007-08-15T17:43:00.000+01:00

I've posted a new version of my paper "Fundamental and derivative truths". The new version notes a few more uses for the fundamental/derivative distinction, and clears up a few points.

As before, the paper is concerned with a way of understanding the---initially pretty hard to take---claim that tables exist, but don't really exist. I think that that claim at least makes good sense, and arguably the distinction between what is really/fundamentally the case and what is merely the case is something we should believe in whether or not we endorse the particular claim about tables. I think in particular that it leads to a particularly attractive view on the nature of set theory, since it really does seem that we do want to be able to "postulate sets into existence" (y'know how things form sets? well consider the set of absolutely everything. On pain of contradiction that set can't be something that existed beforehand...) The framework I like lets us make sober sense of that.

The current version tidies up a bunch of things, it pinpoints more explicitly the difference between comparatively "easy cases"---defending the compatibility of set theoretic truths with a nominalist ontology----and "hard cases"---defending the compatibility of the Moorean corpus with a microphysical mereological nihilist ontology. I've got another paper focusing on some of the technicalities of the composition case.

This project causes me much grief, since it involves many many different philosophically controversial areas: philosophy of maths, metaphysics of composition, theory of ontological commitment, philosophy of language and in particular metasemantics, and so forth. That makes it exciting to work on, but hard to present to people in a digestible way. Nevertheless, I'm going to have another go at the CSMN workshop in Olso later this month, focusing on the philosophy of language/theory of meaning aspects.

A couple of bits of news.

2007-08-09T21:42:00.000+01:00

First, I've finished a (much extended) draft of the reply I gave to Hugh Mellor's paper "Microcomposition" at the Leeds RIP Being conference (the name still amuses: that's the Royal Institute of Philosophy, folks, not a metametaphysical jibe). The paper's called "Working parts" and presents some arguments against the view that mereological relations are metaphysical primitive. Hugh's position is that they should be analyzed in terms of locational and causal relations, and I think there's a lot to be said for that view. Comments, as ever, very welcome. The paper is available here.

Second, from the end of this month I'm going to be taking over as secretary of the Analysis Committee. The trust does all sorts of good things: from awarding Analysis studentships to giving out conference grants, and of course, and are the figures in the background of the fantastic journal Analysis. I'm really excited to be involved.

A puzzle about supervenience arguments for dualism

2007-07-24T19:05:00.000+01:00

Suppose there's a qualitative duplicate of the actual world (It might be a world with haecceitistic differences from the actual one, but it doesn't have to be). Call the actual world A, and its duplicate, B.

I'm conscious in world A. Call the extension at the actual world of the things which are conscious S. There are cauliflowers in world B. Call the extension at B of the things which are cauliflowers, S*. Now consider the gruesome intension cauli-consc, which has S as its extension at world A, and S* as its extension in world B (it doesn't matter what its extension is in other worlds: maybe it applies to all and only conscious cauliflowers).

Is there a property that things have iff they are cauli-consc? So long as "property" is intended in an ultra-lightweight sense (a sense in which any old possible-worlds intension corresponds to a property) then there shouldn't be an trouble with this.

However. Cauli-consc is a property that doesn't supervene on the pattern of instantiation of fundamental physical properties. After all, A and B are alike in all physical respects. But they differ as to where cauli-consc is instantiated.

Cauli-consc is a property, instantiated in the actual world, that doesn't supervene on physical properties! Does that mean that the fact that I'm cauli-consc is a "further fact about our world, over and above the physical facts" (Chalmers 1996 p.123)? That is, do we have to say that, if there are such qualitive duplicates of the actual world, then materialism is shown to be wrong by cauli-consc?

Surely not. But the interesting question is: if some properties (like cauli-consc) can fail to supervene on the physical features of the world, what is that blocks the inference from failure of supervenience on physical features of the world, to the refutation of materialism? For what principled reason is this property "bad", such that we can safely ignore its failure to supervene?

Here's a way to put the general worry I'm having. Supervenience physicalism is often formulated as follows (from Lewis, I believe): any physical duplicate of the actual world is a duplicate simpliciter. But if duplication is understood (again following Lewis) as the sharing of natural properties by corresponding parts, then to get a counterexample to physicalism you'd need not only to demonstrate that a certain property fails to supervene on the physical features of the world, but also that some natural property fails to supervene: otherwise you won't get a failure of duplication among physical duplicates. The case of cauli-consc is supposed to dramatize the gap here. Sometimes it looks like you can get properties which fail to supervene, but which don't seem to threaten materialism.

However, when you look at the failure-to-supervene arguments for dualism, you find that people stop once they take themselves to establish that a given property fails to supervene, and not, in addition, that some natural property does so (For example, Chalmers 1996 p132 assumes that it's enough to show that the 1-intension of "consciousness" fails to supervene, without also arguing that it's a natural property) .

Now, I think in particular cases I can see how to run the arguments to address this issue. Add as a premise that e.g. the 1-intensions of the words of our language supervene on the total qualitative character of the world, so that we're guaranteed that if there's a world in which "1-consciousness" is instantiated and another where it isn't, those can't be qualitative duplicates. If now we find a failure of 1-consciousness to supervene on physical features of the world, we'll be able to argue for the existence of physical duplicate worlds differing over 1-consciousness, we now know can't be qualitative duplicates. (In effect, the suggestion is that the sense in which cauli-consc is bad is exactly that it fails to supervene on the total qualitative state of the world).

That all seems reasonable to me, but it does start to add potentially deniable premises to the argument against materialism. (For example, I'm not sure it should be uncontroversial that consciousness supervenes on the total qualitative state of the world. Is it really so clear, for example, that there are no haecceitistic elements to consciousness: that a world containing me might contain a conscious being, but a qualitiative duplicate containing some other individual doesn't?)

So I'm not sure whether the elaboration of the Zombie argument for dualism I've just sketched is the way Chalmers et al want to go. I'd be interested to know how they have/would respond (references welcome, as ever).

Metametaphysics in Barcelona/some distinctions (x-post from MV)

2007-07-24T11:11:00.001+01:00

Logos are holding a meta-metaphysics conference in Barcelona in 2008. The CFP is now out: with deadline being April 1st 2008.

I went to a Logos conference back in 2005, when I was just finishing up as a graduate student. It was a great experience: Barcelona is an amazing city to be in, Logos were fantastic hosts, and the conference was full of interesting people and talks. I also had what was possibly the best meal of my life at the conference dinner. This time, the format is preread, which I've really enjoyed in the past.

Here's a quick note on the "metametaphysics" stuff. Following the Boise conference on this stuff, it seemed to me that under the label "metametaphysics" go a number of interesting projects that need a bit of disentangling. Here's three, for starters.

First, there's the "terminological disputes" project. Consider a first-order metaphysical question like: "under what circumstances do some things make up a further thing" (van Inwagen's special composition question). This notes the range of seemingly rival answers to the question (all the time! some of the time! never!) and asks about whether there's any genuine disagreement between the rival views (and if so, what sort of disagreement this is). The guiding question here is: under what conditions is a metaphysical/philosophical debate merely terminological (or whatever).

Note that the question here really doesn't look like it has much to do with metametaphysics per se, as opposed to metaphilosophy in general. Metaphysics is just a source of case studies, in the first instance. Of course, it might turn out that metaphysics turns out to be full of terminological disputes, whereas phil science or epistemology or whatever isn't. But equally, it might turn out that metaphysics is all genuine, whereas e.g. the Gettier salt mines are full of terminological disputes.

In contrast to this, there's the "first order metametaphysics" (set of) project(s). This'd take key notions that are often used as starting points/framework notions for metaphysical debates, and reflect philosophically upon those. E.g.: (1) The notion of naturalness as used by Lewis. Is there such a notion? If so, are their natural quantifiers and objects and modifiers as well as natural properties? Does appeal to naturalness commit one to realism about properties, or can something like Sider's operator-view of naturalness be made to work? (2) Ontological commitment. Is Armstrong right that (at least in some cases) to endorse a sentence "A is F" is to commit oneself to F-ness, as well as to things which are F? Might the ontological commitments of our theories be far less than Quine would have us believe (as some suggest)? (3) unrestricted existential quantifier. Is there a coherent such notion? How should its semantics be given? Is such a quantifier a Tarskian logical constant?

These debates might interest you even if you have no interesting thoughts in general about how to demarcate genuine vs. terminological disputes. Thinking about this stuff looks like it can be carried out in very much first-order terms, with rival theories of a key notion (naturalness, say) proposed and evaluated. Of course, this sort of first-order examination might be a particularly interesting kind of first-order philosophy to one engaged in the terminological disputes project.

The third sort of project we might call "anti-Quine/Lewis metametaphysics". You might think the following. In recent years, there's been a big trend for doing metaphysics with a Realist backdrop; in particular, the way that Armstrong and Lewis invite us to do metaphysics has been very influential among the young and impressionable. A bunch of presuppositions have become entrenched, e.g. a Quinean view of ontological commitment, the appeal to naturalness etc. So, without in the first instance attacking these presuppositions, one might want to develop an alternative framework in comparable detail which allows the formulation of alternatives. One natural starting point is to go with neoCarnapian thoughts about what the right thing to say about the SCQ is (e.g. it can be answered by stipulation). That sort of line is incompatible with the sort of view on these questions that Quine and Lewis favour. What's the backdrop relative to which it makes sense? What are the crucial Quine-Lewis assumptions that need to be given up?

Now, this sort of project differs from the first kind of project in being (a) naturally restricted to metaphysics; and (b) not committed to any sort of demarcation of terminological disputes vs. genuine disputes. It differs from the second kind of project, since, at least in the first instance, we needn't assume that the differences between the frameworks will reduce to different attitudes to ontological commitment, or naturalness, or whatever. On the other hand, it's attractive to look for some underlying disagreement over the nature of ontological commitment, or naturalness, or whatever, to explain how the worldviews differ. So it may well be that a project of this kind leads to an interest in the first-order metametaphysics projects.

I'm not sure that these projects form a natural philosophical kind. What does seem to be right is that investigation of one might lead to interest in the others. There's probably a bunch more distinctions to be drawn, and the ones I've pointed to probably betray my own starting points. But in my experience of this stuff, you do find people getting confused about the ambition of each other's projects, and dismissing the whole field of metametaphysics because they identify it with some one of the projects that they themselves don't find particularly interesting, or regard as hard to make progress with. So it'd probably be helpful if someone produced an overview of the field that teased the various possible projects apart (references anyone?).

Williamson on vague states of affairs

2007-07-12T22:11:00.000+01:00

In connection with the survey article mentioned below, I was reading through Tim Williamson's "Vagueness in reality". It's an interesting paper, though I find its conclusions very odd.

As I've mentioned previously, I like a way of formulating claims of metaphysical indeterminacy that's semantically similar to supervaluationism (basically, we have ontic precisifications of reality, rather than semantic sharpenings of our meanings. It's similar to ideas put forward by Ken Akiba and Elizabeth Barnes).

Williamson formulates the question of whether there is vagueness in reality, as the question of whether the following can ever be true:

(EX)(Ex)Vague[Xx]

Here X is a property-quantifier, and x an object quantifier. His answer is that the semantics force this to be false. The key observation is that, as he sets things up, the value assigned to a variable at a precisification and a variable assignment depends only on the variable assignment, and not at all on the precisification. So at all precisifications, the same value is assigned to the variable. That goes for both X and x; with the net result that if "Xx" is true relative to some precisification (at the given variable assignment) it's true at all of them. That means there cannot be a variable assignment that makes Vague[Xx] true.

You might think this is cheating. Why shouldn't variables receive different values at different precisifications (formally, it's very easy to do)? Williamson says that, if we allow this to happen, we'd end up making things like the following come out true:

(Ex)Def[Fx&~Fx']

It's crucial to the supervaluationist's explanatory programme that this come out false (it's supposed to explain why we find the sorites premise compelling). But consider a variable assignment to x which at each precisification maps x to that object which marks the F/non-F cutoff relative to that precisification. It's easy to see that on this "variable assignment", Def[Fx&Fx'] comes out true, underpinning the truth of the existential.

Again, suppose that we were taking the variable assignment to X to be a precisification-relative matter. Take some object o that intuitively is perfectly precise. Now consider the assignment to X that maps X at precisification 1 to the whole domain, and X at precisification 2 to the null set. Consider "Vague[Xx]", where o is assigned to x at every precisification, and the assignment to X is as above. The sentence will be true relative to these variable assignments, and so we have "(EX)Vague[Xx]" relative to an assignment of o to x which is supposed to "say" that o has some vague property.

Although Williamson's discussion is about the supervaluationist, the semantic point equally applies to the (pretty much isomorphic) setting that I like, and which is supposed to capture vagueness in reality. If one makes the variable assignments non-precisification relative, then trivially the quantified indeterminacy claims go false. If one makes the variable assignments precisification-relative, then it threatens to make them trivially true.

The thought I have is that the problem here is essentially one of mixing up abundant and natural properties. At least for property-quantification, we should go for the precisification-relative notion. It will indeed turn out that "(EX)Vague[Xx]" will be trivially true for every choice of X. But that's no more surprising that the analogous result in the modal case: quantifying over abundant properties, it turns out that every object (even things like numbers) have a great range of contingent properties: being such that grass is green for example. Likewise, in the vagueness case, everything has a great deal of vague properties: being such that the cat is alive, for example (or whatever else is your favourite example of ontic indeterminacy).

What we need to get a substantive notion, is to restrict these quantifiers to interesting properties. So for example, the way to ask whether o has some vague sparse property is to ask whether the following is true "(EX:Natural(X))Vague[Xx]". The extrinsically specified properties invoked above won't count.

If the question is formulated in this way, then we can't read off from the semantics whether there will be an object and a property such that it is vague whether the former has the latter. For this will turn, not on the semantics for quantifiers alone, but upon which among the variable assignments correspond to natural properties.

Something similar goes for the case of quantification over states of affairs. (ES)Vague[S] would be either vacuously true or vacuously false depending on what semantics we assign to the variables "X". But if our interest is in whether there are sparse states of affairs which are such that it is vague whether they obtain, what we should do is e.g. let the assignment of values to S be functions from precisifications to truth values, and then ask the question:

(ES:Natural(S))Vague[S].

Where a function from precisifications to truth values is "natural" if it corresponds to some relatively sparse state of affairs (e.g. there being a live cat on the mat). So long as there's a principled story about which states of affairs these are (and it's the job of metaphysics to give us that) everything works fine.

A final note. It's illuminating to think about the exactly analogous point that could be made in the modal case. If values are assigned to variables independently of the world, we'll be able to prove that the following is never true on any variable assignment:

Contingently[Xx].

Again, the extensions assigned to X and x are non-world dependent, so if "Xx" is true relative to one world, it's true at them all. Is this really an argument that there is no contingent instantiation of properties? Surely not. To capture the intended sense of the question, we have to adopt something like the tactic just suggested: first allow world-relative variable assignment, and then restrict the quantifiers to the particular instances of this that are metaphysically interesting.

Ontic vagueness

2007-07-12T18:40:00.000+01:00

I've been frantically working this week on a survey article on metaphysical indeterminacy and ontic vagueness. Mind bending stuff: there really is so much going on in the literature, and people are working with *very* different conceptions of the thing. Just sorting out what might be meant by the various terms "vagueness de re", "metaphysical vagueness", "ontic vagueness", "metaphysical indeterminacy" was a task (I don't think there are any stable conventions in the literature). And that's not to mention "vague objects" and the like.

I decided in the end to push a particular methodology, if only as a stalking horse to bring out the various presuppositions that other approaches will want to deny. My view is that we should think of "indefinitely" roughly parallel to the way we do "possibly". There are various disambiguations one can make: "possibly" might mean metaphysical possibility, epistemic possibility, or whatever; "indefinitely" might mean linguistic indeterminacy, epistemic unclarity, or something metaphysical. To figure out whether you should buy into metaphysical indeterminacy, you should (a) get yourself in a position to at least formulate coherently theories involving that operator (i.e. specify what its logic is); and (b) run the usual Quinean cost/benefit analysis on a case-by-case basis.

The view of metaphysical indeterminacy most opposed to this is one that would identify it strongly with vagueness de re, paradigmatically there being some object and some property such that it is indeterminate whether the former instantiates the latter (this is how Williamson seems to conceive of matters in a 2003 article). If we had some such syntactic criterion for metaphysical indeterminacy, perhaps we could formulate everything without postulating a plurality of disambiguations of "definitely". However, it seems that this de re formulation would miss out some of the most paradigmatic examples of putative metaphysical vagueness, such as the de dicto formulation: It is indeterminate whether there are exactly 29 things. (The quantifiers here to be construed unrestrictedly).

I also like to press the case against assuming that all theories of metaphysical indeterminacy must be logically revisionary (endorsing some kind of multi-valued logic). I don't think the implication works in either direction: multi-valued logics can be part of a semantic theory of indeterminacy; and some settings for thinking about metaphysical indeterminacy are fully classical.

I finish off with a brief review of the basics of Evans' argument, and the sort of arguments (like the one from Weatherson in the previous post) that might convert metaphysical vagueness of apparently unrelated forms into metaphysically vague identity arguably susceptable to Evans argument.

From vague parts to vague identity

2007-07-12T01:04:00.000+01:00

(Update: as Dan notes in the comment below, I should have clarified that the initial assumption is supposed to be that it's metaphysically vague what the parts of Kilimanjaro (Kili) are. Whether we should describe the conclusion as deriving a metaphysically vague identity is a moot point.)

I've been reading an interesting argument that Brian Weatherson gives against "vague objects" (in this case, meaning objects with vague parts) in his paper "Many many problems".

He gives two versions. The easiest one is the following. Suppose it's indeterminate whether Sparky is part of Kili, and let K+ and K- be the usual minimal variations of Kili (K+ differs from Kili only in determinately containing Sparky, K- only by determinately failing to contain Sparky).

Further, endorse the following principle (scp): if A and B coincide mereologically at all times, then they're identical. (Weatherson's other arguments weaken this assumption, but let's assume we have it, for the sake of argument).

The argument then runs as follows:
1. either Sparky is part of Kili, or she isn't. (LEM)
2. If Sparky is part of Kili, Kili coincides at all times with K+ (by definition of K+)
3. If Sparky is part of Kili, Kili=K+ (by 2, scp)
4. If Sparky is not part of Kili, Kili coincides at all times with K- (by definition of K-)
5. If Sparky is not part of Kili, Kili=K- (by 4, scp).
6. Either Kili=K+ or Kili=K- (1, 3,5).

At this point, you might think that things are fine. As my colleague Elizabeth Barnes puts it in this discussion of Weatherson's argument you might simply think at this point that only the following been established: that it is determinate that either Kili=K+ or K-: but that it is indeterminate which.

I think we might be able to get an argument for this. First our all, presumably all the premises of the above argument hold determinately. So the conclusion holds determinately. We'll use this in what follows.

Suppose that D(Kili=K+). Then it would follow that Sparky was determinately a part of Kili, contrary to our initial assumption. So ~D(Kili=K+). Likewise ~D(Kili=K-).

Can it be that they are determinately distinct? If D(~Kili=K+), then assuming that (6) holds determinately, D(Kili=K+ or Kili=K-), we can derive D(Kili=K-), which contradicts what we've already proven. So ~D(~Kili=K+) and likewise ~D(~Kili=K-).

So the upshot of the Weatherson argument, I think, is this: it is indeterminate whether Kili=K+, and indeterminate whether Kili=K-. The moral: vagueness in composition gives rise to vague identity.

Of course, there are well known arguments against vague identity. Weatherson doesn't invoke them, but once he reaches (6) he seems to think the game is up, for what look to be Evans-like reasons.

My working hypothesis at the moment, however, is that whenever we get vague identity in the sort of way just illustrated (inherited from other kinds of ontic vagueness), we can wriggle out of the Evans reasoning without significant cost. (I go through some examples of this in this forthcoming paper). The over-arching idea is that the vagueness in parthood, or whatever, can be plausibly viewed as inducing some referential indeterminacy, which would then block the abstraction steps in the Evans proof.

Since Weatherson's argument is supposed to be a general one against vague parthood, I'm at liberty to fix the case in any way I like. Here's how I choose to do so. Let's suppose that the world contains two objects, Kili and Kili*. Kili* is just like Kili, except that determinately, Kili and Kili* differ over whether they contain Sparky.

Now, think of reality as indeterminate between two ways: one in which Kili contains Sparky, the other where it doesn't. What of our terms "K+" and "K-"? Well, if Kili contains Sparky, then "K+" denotes Kili. But if it doesn't, then "K+" denotes Kili*. Mutatis Mutandis for "K-". Since it is is indeterminate which option obtains, "K+" and "K-" are referentially indeterminate, and one of the abstraction steps in the Evans proof fail.

Now, maybe it's built into Weatherson's assumptions that the "precise" objects like K+ and K- exist, and perhaps we could still cause trouble. But I'm not seeing cleanly how to get it. (Notice that you'd need more than just the axioms of mereology to secure the existence of [objects determinately denoted by] K+ and K-: Kili and Kili* alone would secure the truth that there are fusions including Sparky and fusions not including Sparky). But at this point I think I'll leave it for others to work out exactly what needs to be added...

The fuzzy link

2007-06-14T23:39:00.000+01:00

Following up on one of my earlier posts on quantum stuff, I've been reading up on an interesting literature on relating ordinary talk to quantum mechanics. As before, caveats apply: please let me know if I'm making terrible technical errors, or if there's relevant literature I should be reading/citing.

The topic here is GRW. This way of doing things, recall, involved random localizations of the wavefunction. Let's think of the quantum wavefunction for a single particle system, and suppose it's initially pretty wide. So the amplitude of the wavefunction pertaining to the "position" of the particle is spread out over a wide span of space. But, if one of the random localizations occurs, the wavefunction collapses into a very narrow spike, within a tiny region of space.

But what does all this mean? What does it say about the position of the particle? (Here I'm following the Albert/Loewer presentation, and ignoring alternatives, e.g. Ghirardi's mass-density approach).

Well, one traditional line was that talk of position was only well defined when the particle was in an eigenstate of the position observable. Since on GRW the particles' wavefunction is pretty much spread all over space, on this view talking of a particle's location would never be well-defined.

Albert and Loewer's suggestion is that we alter the link. As previously, think of the wavefunction as giving a measure over different situations in which the particle has a definite location. Rather than saying x is located within region R iff the set of situations in which the particle lies in R is measure 1, they suggest that x is located within region R iff the set of situations in which the particle lies in R is almost measure 1. The idea is that even if not all of a particle's wavefunction places it right here, the vast majority of it is within a tiny subregion here. On the Albert/Loewer suggestion, we get to say on this basis, that the particle is located in that tiny subregion. They argue also that there are sensible choices of what "almost 1" should be that'll give the right results, though it's probably a vague matter exactly what the figure is.

Peter Lewis points out oddities with this. One oddity is that conjunction-introduction will fail. It might be true that marble i is in a particular region, for each i between 1 and 100; and yet it fail to be true that all these marbles are in the box.

Here's another illustration of the oddities. Take a particle with a localized wavefunction. Choose some region R around the peak of the wavefunction which is minimal, such that enough of the wavefunction is inside for the particle to be within R. Then subdivide R into two pieces (the left half and the right half) such that the wavefunction is nonzero in each. The particle is within R. But it's not within the left half of R. Nor is it within the right half of R (in each case by modus tollens on the Albert/Loewer's biconditional). But the R is just the sum of the left half and right half of R. So either we're committed to some very odd combination of claims about location, or something is going wrong with modus tollens.

So clearly this proposal is looking like it's pretty revisionary of well-entrenched principles. While I don't think it indefensible (after all, logical revisionism from science isn't a new idea) I do think it's a significant theoretical cost.

I want to suggest a slightly more general, and I think, much more satisfactory, way of linking up the semantics of ordinary talk with the GRW wavefunction. The rule will be this:

"Particle x is within region R" is true to degree equal to the wavefunction-measure of the set of situations where the particle is somewhere in region R.

On this view, then, ordinary claims about position don't have a classical semantics. Rather, they have a degreed semantics (in fact, exactly the degreed-supervaluational semantics I talked about in a previous post). And ordinary claims about the location of a well-localized particle aren't going to be perfectly true, but only almost-perfectly true.

Now, it's easy but unwarranted to slide from "not perfectly true" to "not true". The degree theorist in general shouldn't concede that. It's an open question for now how to relate ordinary talk of truth simpliciter to the degree-theorist's setting.

One advantage of setting up things in this more general setting is that we can "off the peg" take results about what sort of behaviour we can expect the language to exhibit. An example: it's well known that if you have a classically valid argument in this sort of setting, then the degree of untruth of the conclusion cannot exceed the sum of the degrees of untruth of the premises. This amounts to a "safety constraint" on arguments: we can put a cap on how badly wrong things can go, though there'll always be the phenomenon of slight degradations of truth value across arguments, unless we're working with perfectly true premises. So there's still some point of classifying arguments like conjunction introduction as "valid" on this picture, for that captures a certain kind of important information.

Say that the figure that Albert and Loewer identified as sufficient for particle-location was 1-p. Then the way to generate something like the Albert and Loewer picture on this view is to identify truth with truth-to-degree-1-p. In the marbles case, the degrees of falsity of each premise "marble i is in the box" collectively "add up" in the conclusion to give a degree of falsity beyond the permitted limit. In the case

An alternative to the Albert-Loewer suggestion for making sense of ordinary talk is to go for a universal error-theory, supplemented with the specification of a norm for assertion. To do this, we allow the identification of truth simpliciter with true-to-degree 1. Since ordinary assertions of particle location won't be true to degree 1, they'll be untrue. But we might say that such sentences are assertible provided they're "true enough": true to the Albert/Loewer figure of 1-p, for example. No counterexamples to classical logic would threaten (Peter Lewis's cases would all be unsound, for example). Admittedly, a related phenomenon would arise: we'd be able to go by classical reasoning from a set of premises all of which are assertible, to a conclusion that is unassertible. But there are plausible mundane examples of this phenomenon, for example, as exhibited in the preface "paradox".

But I'd rather not go either for the error-theoretic approach, nor for the identification of a "threshold" for truth, as the Albert-Loewer inspired proposal suggests. I think there are more organic ways to handle utterance-truth within a degree theoretic framework. It's a bit involved to go into here, but the basic ideas are extracted from recent work by Agustin Rayo, and involve only allowing "local" specifications of truth simpliciter, relative to a particular conversational context. The key thing is that on the semantic side, once we have the degree theory, we can take "off the peg" an account of how such degree theories interact with a general account of communication. So combining the degree-based understanding of what validity amounts to (in terms of limiting the creep of falsity into the conclusion) and this degree-based account
of assertion, I think we've got a pretty powerful, pretty well understood overview about how ordinary language position-talk works.

Kripkenstein's monster

2007-06-14T11:35:00.000+01:00

Though I've thought a lot about inscrutability and indeterminacy (well, I wrote my PhD thesis on it) I've always run a bit scared from the literature on Kripkenstein. Partly this is because the literature is so huge and sometimes intimidatingly complex. Partly it's because I was a bit dissatisfied/puzzled with some of the foundational assumptions that seemed to be around, and was setting it aside until I had time to think things through.

Anyway, I'm now thinking about making a start on thinking about the issue. So this post is something in the way of a plea for information: I'm going to set out how I understand the puzzle involved, and invite people to disabuse me of my ignorance, recommend good readings or where these ideas have already been worked out.

To begin with, let's draw a rough divide between three types of facts:

Paradigmatically naturalistic facts (patterns of assent and dissent, causal relationships, dispositions, etc).
Meaning-facts. (Of the form: “+” means addition, “67+56=123” is true, "Dobbin" refers to Dobbin.)
Linguistic norms. (Of the form: One should utter “67+56=123” in such-and-such circs).

Kripkenstein’s strategy is to ask us to show how facts of (A) can constitute facts of kind (B) and (C). (An oddity here: the debate seems to have centred on a “dispositionalist” account of the move from A to B. But that’s hardly a popular option in the literature on naturalistic treatments of content, where variants of radical interpretation (Lewis, Davidson), of causal (Fodor, Field) and teleological (Millikan) theories are far more prominent. Boghossian in his state of the art article in Mind seems to say that these can all be seen as variants of the dispositionalist idea. But I don't quite understand how. Anyway...)

One of the major strategies in Kripkenstein is to raise doubts about whether this or that constitutive story can really found facts of kind (C). Notice that if one assumes that (B) and (C) are a joint package, then this will simultaneously throw into doubt naturalistic stories about (B).

In what sense might they be a joint package? Well, maybe some sort of constraint like the following is proposed: unless putative meaning-facts make immediately intelligible the corresponding linguistic norms, then they don’t deserve the name “meaning facts” at all.

To see an application, suppose that some of Kripke’s “technical” objections to the dispositionalist position were patched (e.g. suppose one could non-circularly identify a disposition of mine to return the intuitively correct verdicts to each and every arithmetical sum). Still, then, there’s the “normative” objection: why are those the verdicts the ones one should return in those circumstances? And (right or wrongly) the Kripkenstein challenge is that this normative explanation is missing. So (according to the Kripkean) these ain’t the meaning-facts at all.

There's one purely terminological issue I'd like to settle at this point. I think we shouldn’t just build it into the definition of meaning-facts that they correspond to linguistic norms in this way. After all, there’s lot of other theoretical roles for meaning other than supporting linguistic norms (e.g. a predicative/explanatory role wrt understanding, for example). I propose to proceed as follows. Firstly, let’s speak of “semantic” or “meaning” facts in general (picked out if you like via other aspects of the theoretical role of meaning). Secondly, we'll look for arguments for or against the substantive claim that part of the job of a theory of meaning is to subserve, or make immediately intelligible, or whatever, facts like (C).

Onto details. The Kripkenstein paradox looks like it proceeds on the following assumptions. First, three principles are taken as target (we can think of them as part of a "folk theory" of meaning)

the meaning-facts to be exactly as we take them to be: i.e. arithmetical truths are determinate “to infinity”; and
the corresponding linguistic norms are determinate “to infinity” as well; and
(1) and (2) are connected in the obvious way: if S is true, then in appropriate circumstances, we should utter S.

The “straight solutions” seem to tacitly assume that our story should take the following form. First, give some constitutive story about what fixes facts of kind (B). Then (supposing there’s no obvious counterexamples, i.e. that the technical challenge is met). Then the Kripkensteinian looks to see whether this “really gives you meaning”, in the sense that we’ve also got a story underpinning (C). Given our early discussion, the Kripkensteinian challenge needs to be rephrased somewhat. Put the challenge as follows. First, the straight solution gives a theory of semantic facts, which is evaluated for success on grounds that set aside putative connections to facts of kind (C). Next, we ask the question: can we give an adequate account of facts of kind (C), on the basis of what we have so far? The Kripkensteinian suggests not.

The “sceptical solution” starts in the other direction. It takes as groundwork facts of kind (A) and (C) (perhaps explaining facts of kind (C) on the basis of those of kind (A)?) and then uses this in constructing an account of (something like) (B). One Kripkensteinian thought here is to base some kind of vindication of (B)-talk on the (C)-style claim that one ought to utter sentences involving semantic vocabulary such as " '+' means addition".

The basic idea one should be having at this point is more general however. Rather than start by assuming that facts like (B) are prior in the order of explanation to facts like (C), why not consider other explanatory orderings? Two spring to mind: linguistic normativity and meaning-facts are explained independently; or linguistic normativity is prior in the order of explanation to meaning-facts.

One natural thought in the latter direction is to run a “radical interpretation” line. The first element of a radical interpretation proposal is identify a “target set” of T-sentences, which the meaning-fixing T-theory for a language is (cp) constrained to generate. Davidson suggests we pick the T-sentences by looking at what sentences people de facto hold true in certain circumstances. But, granted (C)-facts, when identifying the target set of T-sentences one might instead appeal to what person’s ought to utter in such and such circs.

There’s no obvious reason why such normative facts need be construed as themselves “semantic” in nature, nor any obvious reason why the naturalistically minded shouldn’t look for reductions of this kind of normativity (e.g. it might be a normativity on a par with that involved with weak hypothetical imperatives, e.g. in the claim that I should eat this food, in order to stay alive, which I take to be pretty unscary.). So there's no need to give up on reductionist project in doing things this way. Nor is it only radical interpretation that could build in this sort of appeal to (C)-type facts in the account of meaning.

One nice thing about building normativity into the subvening base for semantic facts in this way is that we make it obvious that we’ll get something like (a perhaps restricted and hedged) form of (iii). Running accounts of (B) and (C) separately would make the convergence of meaning-facts and linguistic norms seem like a coincidence, if it in fact holds in any form at all.)

Is there anything particularly sceptical about the setup, so construed? Not in the sense in which Kripke’s own suggestion is. Two things about the Kripke proposal (as I suggested we read it): it’s clear that we’ve got some kind of projectionist/quasi-realist treatment of the semantic going on (it’s only the acceptability of semantic claims that’s being vindicated, not "semantic facts" as most naturalistic theories of meaning would conceive them). Further, the sort of norms to which we can reasonably appeal will be grounded in practices of praise and blame in a linguistic community to which we belong, and given the sheer absence of people doing very-long sums, there just won't be a practice of praise and blaming people for uttering "x+y=z" for sufficiently large choices of x, y and z. The linguistic norms we can ground in this way might be much more restricted than one might at first think: maybe only finitely many sentences S are such that something of the following form holds: we should assert S in circs c. Though there might be norms governing apparently infinitary claims, there is no reason to suppose in this setup that there are infinitely many type-(C) facts. That'll mean that (2) and (3) are dropped.

In sum, Kripke's proposal is sceptical in two senses: it is projectionist, rather than realist, about meaning-facts. And it drops what one might take to be a central plank of folk-theory of meaning, (2) and (3) above.

On the other hand, the modified radical interpretation or causal theory proposal I’ve been sketching can perfectly well be a realist about meaning-facts, having them “stretch out to infinity” as much as you like (I’d be looking to combine the radical interpretation setting sketched earlier with something like Lewis’s eligibility constraints on correct interpretation, to secure semantic determinacy). So it's not "sceptical" in the first sense in which Kripke's theory is: it doesn't involve any dodgy projectivism about meaning-facts. But it is a "sceptical solution" in the other sense, since it gives up the claims that linguistic norms "stretch out" to infinity, and that truth-conditions of sentences are invariably paired with some such norm.

[Thanks (I think) are owed to Gerald Lang for the title to this post. A quick google search reveals that others have had the same idea...]

Why preserve the letter of Humean supervenience?

2007-06-13T15:12:00.000+01:00

Today in the phil physics reading group here at Leeds we were discussing Tim Maudlin's paper "Why be Humean?".

The question arose about why we should accord to the letter of the Humean supervenience principle. What that requires is that everything there is should supervene on the distribution of fundamental (local, monadic) properties and spatio-temporal relations. Why not e.g. allow further perfectly natural relations holding between pointy particles, so long as they are physically motivated and don't enter into necessary connections with other fundamental properties or relations?

Brian Weatherson's Lewis blog addressed something like this question at one point. His suggestion (I take it) was that the interest of tightly-constrained Humean supervenience was methodological: roughly, if we can fit all important aspects of the manifest image (causality, intentionality, consciousness, laws, modality, whatever) into an HS world, then we should be confident that we could do the same in non-HS worlds, worlds which are more generous with the range of fundamentals they commit us to. If Brian's right about this, the motivation for going for the strongest formulation of HS, is that allowing any more would make our stories about how to fit the manifest image into the world as described by science, more dependent on exactly what science delivers.

If that's the motivation for HS, then it's not so interesting whether physics contradicts HS: what's interesting is whether the stories about causality, intentionality and the rest that Lewis describes with the HS equipment in mind, go through in the non-HS worlds with minimal alteration.

Jobs at Leeds

2007-06-13T10:17:00.000+01:00

Just to note that there are currently a bunch of jobs in philosophy/history and philosophy of science being advertised at Leeds. These are fixed-term (one year) lecturerships, and are pretty nice. While some places make temporary positions into teaching drudgery, Leeds has a policy of appointing full lecturer replacements, and so people appointed to these posts have in the past got exactly the teaching/admin load as the rest of us. Importantly for people looking to get out publications and secure permanent jobs, this means you got the same time to do research as a permanent lecturer. (Recent occupants of these roles have just secured permanent jobs and postdoc positions in the UK).

And of course you get to hang out with the lovely Leeds folk. So apply!

converting LaTeX into word...

2007-06-13T10:06:00.000+01:00

I write (most) of my research in LaTeX format. But journals often demand .rtf or even .doc formats for the final version of my paper. Sometimes by speaking to them very nicely you can get them to accept tex versions (Phil Studies and Phil Perspectives both did this). But sometimes that's just not an option.

This leads to hours of heartache and potentially lots of typos, as I try ten ways of transferring the stuff over to my word processor. And I have to deal with getting logic into word, which is never nice. I used to use a special compiler to get it into html format, and then "save as" word. But that didn't actually save much time, so I've recently begun to just cut-and-paste the raw tex file, and reformat it and rewrite any code I've put in. I've downloaded a couple of trial applications that promise to convert stuff directly into doc, but with no success (they throw a wobbly whenever they meet any dollar signs, it seems).

Does anyone know what the best way to do this is? Would it help to get scientific word (more money to the man, I know, but at this stage I'm desperate).

Worlds

2007-06-08T21:21:00.001+01:00

earths
Originally uploaded by blue sometimes

Hee hee

Supervaluations and revisionism once more

2007-06-08T15:53:00.000+01:00

I've just spent the afternoon thinking about an error I found in my paper "supervaluational consequence" (see this previous post). I've figured out how to patch it now, so thought I'd blog about it.

The background is the orthodox view that supervaluational consequence will lead to revisions of classical logic. The strongest case I know for this (due to Williamson) is the following. Consider the claim "p&~Determinately(p)". This (it is claimed) cannot be true on any serious supervaluational model of our language. Equivalently, you can't have both p and ~Determinately(p) both true in a single model. If classical reductio were an ok rule of inference, therefore, you'd be able argue from ~Determinately(p) to ~p. But nobody thinks that's supervaluationally valid: any indeterminate sentence will be a counterexample to it. So classical reductio should be given up.

This is stronger than the more commonly cited argument: that supervaluational semantics vindicates the move from p to Determinately(p), but not the material conditional "if p then Determinately(p)" (a counterexample to conditional proof). The reason is that, if "Determinately" itself is vague, arguably the supervaluationist won't be committed to the former move. The key here is the thought that as well as things that are determinately sharpenings of our language, their may be interpretations which are borderline-sharpenings. Perhaps interpretation X is an "admissible interpretation of our language" on some sharpenings, but not on others. If p is true at all the definite sharpenings, but false at X, then that may lead to a situation where p is supertrue, but Determinately(p) isn't.

But orthodoxy says that this sort of situation (non-transitivity in the accessibility relation among interpretations of our language) does nothing to undermine the case for revisionism I mentioned in the first paragraph.

One thing I do in the paper is construct what seems to me a reasonable-looking toy semantics for a language, on which one can have both p and ~Determinately p. Here it is.

Suppose you have five colour patches, ranging from red to orange (non-red). Call them A,B,C,D,E.

Suppose that our thought and talk makes it the case that only interpretations which put the cut-off between B and D are determinately "sharpenings" of the language we use. Suppose, however, that there's some fuzziness around in what it is to be an "admissible interpretation". For example, an interpretation that places the cut-off between B and C, thinks that both interpretations placing the cut-off between C and D, and interpretations placing the cut-off between A and B, are admissible. And likewise, an interpretation that place the cut-off between C and D think that interpretations that place the cut-off between B and C are admissible, but also thinks that interpretations that place the cut-off between D and E are admissible.

Modelling the situation with four interpretations, labelled AB, BC, CD, DE, for where they place the red/non-red cut-off, we can express the thought like this: each intepretation accesses (thinks admissible) itself and its immediate neighbours, but nothing else. But BC and CD are the sharpenings.

My first claim is that all this is a perfectly coherent toy model for the supervaluationist: nothing dodgy or "unintended" is going on.

Now let's think about the truths values assigned to particular claims. Notice, to start with, that the claim "B is red" will be true at each sharpening. The claim "Determinately, B is red" will be true at the sharpening CD, but it won't be true at the sharpening BC, for that accesses an interpretation on which B counts as non-red (viz. AB).

Likewise, the claim "D is not red" will be true at each sharpening, but "Determinately, D is not red" will be true at the sharpening BC, but fails at CD, due to the latter seeing the (non-sharpening) interpretation DE, at which D counts as red.

In neither of these atomic cases do we find "p and ~Det(p)" coming out true (that's where I made a mistake previously). But by considering the following, we can find such a case:

Consider "B is red and D is not red". It's easy to see that this is true at each of the sharpenings, from what's been said above. But also "Determinately(B is red and D is not red)" is false at each of the sharpenings. It's false at BC because of the accessible interpretation AB at which B counts as non-red. It's false at CD because of the accessible interpretation DE at which D counts as red.

So we've got "B is red and D is not red, & ~Determinately(B is red and D is non-red)." And we've got that in a perfectly reasonable toy model for a language of colour predicates.

(Why do people think otherwise? Well, the standard way of modelling the consequence relation in settings where the accessibility relation is non-transitive is to think of the sharpenings as *all the interpretations accessible from some designated interpretation*. And that imposes additional structure which, for example, the model just sketch doesn't satisfy. But the additional structure seems to me totally unmotivated, and I provide an alternative framework in the paper for freeing oneself from those assumptions. The key thing is not to try and define "sharpening" in terms of the accessibility relation.).

The conclusion: the best extant case for (global) supervaluational consequence being revisionary fails.

Bohm and Lewis

2007-06-06T14:11:00.000+01:00

So I've been thinking and reading a bit about quantum theory recently (originally in connection with work on ontic vagueness). One thing that's been intriguing me is the Bohmian interpretation of non-relativistic quantum theory. The usual caveats apply: I'm no expert in this area, on a steep learning curve, wouldn't be terribly surprised if there's some technical error in here somewhere.

What is Bohmianism? Well, to start with it's quite a familiar picture. There are a bunch of particles, each supplied with non-dynamical properties (like charge and mass) and definite positions, which move around in a familiar three-dimensional space. The actual trajectories of those particles, though, are not what you'd expect from a classical point of view: they don't trace straight lines through the space, but rather wobbly ones, if if they were bobbing around on some wave.

The other part of the Bohmian picture, I gather, is that one appeals to a wavefunction that lives in a space of far higher dimension: configuration space. As mentioned in a previous post I'm thinking of this as a set of (temporal slices of) possible worlds. The actual world is a point in configuration space, just as one would expect given this identification.

The first part of the Bohmian picture sounds all very safe from the metaphysician's perspective: the sort of world at which, for example, Lewis's project of Humean supervenience could get off and running, the sort of thing to give us the old-school worries about determinism and freedom (the evolution of a Bohmian world is totally deterministic). And so on and so forth.

But the second part is all a bit unexpected. What is a wave in modal space? Is that a physical thing (after all, it's invoked in fundamental physical theory)? How can a wave in modal space push around particles in physical space? Etc.

I'm sure there's lots of interesting phil physics and metaphysics to be done that takes the wave function seriously (I've started reading some of it). But I want to sketch a metaphysical interpretation of the above that treats it unseriously, for those of us with weak bellies.

The inspiration is Lewis's treatment of objective chance (as explained, for example, in his "Humean supervenience debugged"). The picture of chance he there sketches has some affinities to frequentism: when we describe what there is and how it is in fundamental terms, we never mention chances. Rather, we just describe patterns of instantiation: radioactive decay here, now, another radioactive decay there, then (for example). What one then has to work with is certain statistically regularities that emerge from the mosaic of non-chancy facts.

Now, it's very informative to be told about these regularities, but it's not obvious how to capture that information within a simple theory (we could just write down the actual frequencies, but that'd be pretty ugly, and wouldn't allow us to to capture underlying patterns among the frequencies). So Lewis suggests, when we're writing down the laws, we should avail ourselves of a new notion "P", assigning numbers to proposition-time pairs, obeying the usual probability axioms. We'll count a P-theory as "fitting" with facts (roughly) to the extent that the P-values it assigns to propositions match up, overall, to the statistically regularities we mentioned earlier. Thus, if we're told that a certain P-theory is "best", we're given some (cp) information on what the statistical regularities are. At not much gain in complexity, therefore, our theory gains enormously in informativeness.

The proposal, then, is that the chance of p at t is n, iff overall best theory assigns n to (p,t).

That's very rough, but the I hope the overall idea is clear: we can be "selectively instrumentalist" about some of the vocabulary that appears in fundamental physical theory. Though many of the physical primitives will also be treated as metaphysically basic (as expressing "natural properties") some bits that by the lights of independently motivated metaphysics are "too scary" can be regarded as just reflections of best theory, rather than part of the furniture of the world.

The question relevant here is: why stop at chance? If we've been able to get rid of one function over the space of possible worlds (the chance measure), why not do the same with another metaphysically troubling piece of theory: the wavefunction field.

Recall the first part of the Bohmian picture: particles moving through 3-space, in rather odd paths "as if guided by a wave". Suppose this was all there (fundamentally) was. Well then, we're going to be in a lot of trouble finding a decent way of encapsulating all this data about the trajectories of particles: the theory would be terribly unwieldy if we had to write out in longhand the exact trajectory. As before, there's much to be gained in informativeness if we allow ourselves a new notion in the formulation of overall theory, L, say. L will assign scalar values (complex numbers) to proposition-time pairs, and we can then use L in writing down the wavefunction equations of quantum mechanics which elegantly predicts the future positions of particles on the basis of their present positions. The "best" L-theory, of course will be that one whose predictions of the future positions of particles fits with the actual future-facts. The idea is that wavefunction talk is thereby allowed for: the wave function takes value z at region R of configuration space at time t iff Best L-theory assigns z to L(R,t).

So that's the proposal: we're selectively instrumentalist about the wavefunction, just as Lewis is selectively instrumentalist about objective chance (I'm using "instrumentalist" in a somewhat picturesque sense, by the way: I'm certainly not denying that chance or wavefunction talk has robust, objective truth-conditions.) There are, of course, ways of being unhappy with this sort of treatment of basic physical notions in general (e.g. one might complain that the explanatory force has been sucked from notions of chance, or the wavefunction). But I can't see anything that Humeans such as Lewis should be unhappy with here.

(There's a really nice paper by Barry Loewer on Lewisian treatments of objective chance which I think is the thing to read on this stuff. Interestingly, at the end of that paper he canvasses the possibility of extending the account to the "chances" one (allegedly) finds in Bohmianism. It might be that he has in mind something that is, in effect, exactly the position sketched above. But there are also reasons for thinking there might be differences between the two ideas. Loewer's idea turns on the idea that one can have something that deserves the name objective chance, even in a world for which there are deterministic laws underpinning what happens (as is the case for both Bohmianism, and for the chancy laws of statistically mechanics in a chancy world). I'm inclined to agree with Loewer on this, but even if that were given up, and one thought that the measure induced by the wavefunction isn't a chance-measure, the position I've sketched is still a runner: the fundamental idea is to use the Lewisian tactics to remove ideological commitment, not to use the Lewisian tactics to remove ideological commitment to chance specifically. [Update: it turns out that Barry definitely wasn't thinking of getting rid of the wavefunction in the way I canvass in this post: the suggestion in the cited paper is just to deal with the Bohmian (deterministic) chances in the Lewisian way])

[Update: I've just read through Jonathan Schaffer's BJPS paper which (inter alia) attacks the Loewer treatment of chance in Stat Mechanics and Bohm Mechanics (though I think some of his arguments are more problematic in the Bohmian case than the stat case.) But anyway, if Jonathan is right, it still wouldn't matter for the purposes of the theory presented here, which doesn't need to make the claim that the measure determined by the wavefunction is anything to do with chance: it has a theoretical role, in formulating the deterministic dynamical laws, that's quite independent of the issues Jonathan raises.]

Academic careers

2007-06-06T13:38:00.000+01:00

Others have already pointed this out, but it's worth highlighting.

Terence Tao - recent winner of the Field's medal (a sort of Nobel prize for mathematics) - has written some really interesting career advice. It's aimed at mathematicians, but lots of it is more generally applicable, and certainly lots of strikes a chord with academic philosophy. It's also not just for graduates: e.g. I'm a recent-graduate, and I'm sure there's lots there that I'm not doing, which it's good to be reminded of.

The advice to "use the wastebasket" is going to be more difficult now that the University of Leeds has decided to remove all wastebackets from our offices...

HT: Shawn Standefer, Richard Zach

p.s. here's one thing that struck me as particularly transferable:

"Don't prematurely obsess on a single "big problem" or "big theory". This is a particularly dangerous occupational hazard in this subject - that one becomes focused, to the exclusion of other mathematical activity, on a single really difficult problem in a field (or on some grand unifying theory) before one is really ready (both in terms of mathematical preparation, and also in terms of one career) to devote so much of one's research time to such a project. When one begins to neglect other tasks (such as writing and publishing one's "lesser" results), hoping to use the eventual "big payoff" of solving a major problem or establishing a revolutionary new theory to make up for lack of progress in all other areas of one's career, then this is a strong warning sign that one should rebalance one's priorities. While it is true that several major problems have been solved, and several important theories introduced, by precisely such an obsessive approach, this has only worked out well when the mathematician involved (a) has a proven track record of reliably producing significant papers in the area already, and (b) has a secure career (e.g. a tenured position). If you do not yet have both (a) and (b), and if your ideas on how to solve a big problem still have a significant speculative component (or if your grand theory does not yet have a definite and striking application), I would strongly advocate a more balanced approach instead: keep the big problems and theories in mind, and tinker with them occasionally, but spend most of your time on more feasible "low-hanging fruit", which will build up your experience, mathematical power, and credibility for when you are ready to tackle the more ambitious projects. "

Pictures from St Andrews (with added commentary)

2007-06-06T11:53:00.001+01:00

Courtesy of Brit over at Lemmings

you can find the originals from the link here

We had a great time in St Andrews, by the way. Two good conferences, lots of fun time spent with interesting people. And conference-accommodation to die for...

AJP paper

2007-06-06T11:31:00.000+01:00

My paper on a certain kind of argument for structural universals has just appeared in AJP. Very exciting from my perspective: I've had things "forthcoming" for so long, I think I thought they'd always have that status.

FWIW, the paper discusses a certain argument for the existence of structural universals (that is, universals "made out of" other universals, as "being water" might be thought to be made out of "being Hydrogen" "being Oxygen" etc.) The argument is based on the (alleged) possibility of worlds with no fundamental physical layer: where things "go down forever". Quite a few people use this argument in print, and many more raise it in conversation when you're pressing a microphysicalist metaphysics.

This is part of a wider project exploring a ontological microphysicalism, where the only things that really exist are the physical fundamentals. The recent stuff on ontological commitment is, in part, a continuation of that project.

On a more practical note, I can't figure out how you access AJP articles these days: my institution is supposed to have a subscription, but the links that take you to the pdf don't seem live. Any ideas of how to get into it would be gratefully received!

Vagueness and quantum stuff

2007-06-06T09:30:00.000+01:00

I've finally put online a tidied up version of my ontic vagueness paper, which'll be coming out in Phil Quarterly some time soon. One idea in the paper is to give an account of truths in an ontically vague world, making use of the idea that more than one possible world is actual. The result is a supervaluation-like framework, with "precisifications" replaced with precise possible worlds. For some reason, truth-functional multi-valued settings seem to have a much firmer grip on the ontic vagueness debate than in the vagueness debate more generally. That seems a mistake to me.

(The idea of having supervaluation-style treatments of ontic vagueness isn't unknown in the literature however: in a couple of papers, Ken Akiba argues for this kind of treatment of ontic vagueness, though his route to this framework is pretty different to the one I like. And Elizabeth Barnes has been thinking and writing about the the kind of modal treatments of ontic vagueness for a while, and I owe huge amounts to conversations with her about all of these issues. Her take on these matters is very close to the one I like (non-coincidentally) and those interested should check out her papers for systematic discussion and defense of the coherence of ontic vagueness in this spirit.)

The project in my paper wasn't to argue that there was ontic vagueness, or even tell you what ontic vagueness (constitutively) is. The project was just to set up a framework for talking about, and reasoning about, metaphysically vague matters, with a particular eye to evaluate the Evans argument against ontically vague identity. In particular, the framework I gave has no chance of giving any sort of reduction of metaphysical indeterminacy, since that very notion was used in defining up bits of the framework. (I'm actually pretty attracted to the view that the right way to think about these things would be to treat indeterminacy as a metaphysical primitive, in the way that some modalists might treat contingency. See this previous blog post. I was later pointed to this excellent paper by David Barnett where he works out this sort of idea in far more detail.)

One thing that I've been thinking about recently is how the sort of "indeterminacy" that people talk about in quantum mechanics might relate to this setting. So I want to write a bit about this here.

Some caveats. First, this stuff clearly isn't going to be interpretation neutral. If you think Bohm gave the right account of quantum ontology, then you're not going to think there's much indeterminacy around. So I'll be supposing something like the GRW interpretation. Second, I'm not going to be metaphysically neutral even given this interpretation: there's going to be a bunch of other ways of thinking about the metaphysics of GRW that I don't consider here (I do think, however, that independently motivated metaphysics can contribute to the interpretation of a physical theory). Third, I'm only thinking of non-relativistic quantum theory here: Quantum field theory and the like is just beyond me at the moment. Finally, I'm on a steep learning curve with this stuff, so please excuse stupidities.

You can represent the GRW quantum ontology as a wave function over a certain space (configuration space). Mathematically speaking, that's a scalar field over a set of points (which then determines a measure over those points) in a high-dimensional space. As time rolls forward, the equations of quantum theory tell you how this field changes its values. Picture it as a wave evolving through time over this space. GRW tells you that at random intervals, this wave undergoes a certain drastic change, and this drastic change is what plays the role of "collapse".

That's all highly abstract. So let me try parlaying that into something more familiar to metaphysicians.

Suppose you're interested in a world with N particles in it, at time t. Without departing from classical modes of thinking yet, think of the possible arrangements of those particles at t: a scattering of particles equipped with mass and charge over a 3-dimensional space, say (think of the particles haecceistically for now). Collect all these possible-world-slices together into a set. There'll be a certain implicit ordering on this set: if the worlds contain nothing but those N massy and chargey particles located in space-time, then we can describe a world-slice w by giving, for each of the N particles, the coordinates of its location within w: that is, by giving a list of 3N coordinates. What this means is that each world can be regarded as a point in a 3N dimensional space (the first 3 dimensions giving the position of the first particle in w, the second 3 dimensions the position of the second, etc). And this is what I'm taking to be the "configuration space". So what is the configuration space, on the way I'm thinking of it? It's a certain set of time-slices of possible worlds.

One Bohmian picture of quantum ontology fits very naturally into the way that we usually think of possible worlds at this point. For Bohm says that one point in configuration space is special: it gives the actual positions of particles. And this fits the normal way of thinking of possible worlds: the special point in configuration space is just the slice of the actual world at t. (Bohmian mechanics doesn't dispense with the wave across configuration space, of course: just as some physical theories would appeal to objective chance in their natural laws, which we can represent as a measure across a space of possible worlds, Bohmianism appeals to a scalar field determining a measure across configuration space: the wavefunction).

But on the GRW interpretation, we don't get anything like this trad picture. What we have is configuration space and the wave function over it. Sometimes, the amplitude of that wave function is highly concentrated on a set of world-slices that are in certain respects very similar: say, they all contain particles arranged in a rough pointer-shaped in a certain location. But nevertheless, no single world will be picked out, and some amplitude will be given to sets of worlds which have the particles in all sorts of odd positions.

But of course, the framework for ontic vagueness I like is up for monkeying around with the actuality of worlds. There needn't be a single designated actual world, on the way I was thinking of things. But the picture I described doesn't exactly fit the present situation. For I supposed (following the supervaluationist paradigm) that there'd be a set of worlds, all of which would be "co-actual".

Yet there are other closely related models that'd help here. In particular, Lewis, Kamp and Edgington have described what I'll call a "degree supervaluationist" picture that looks to be exactly what we need. Here's the story, in the original setting. Your classical semantic theorist looks at the set of all possible interpretations of the language, and says that one among them is the designated (or "intended") one. Truth is truth at the unique, designated, interpretation. Your supervaluationist looks at the same space, and says that there's a set of interpretations with equal claim to be "intended": so they should all be co-designated. Truth is truth at each of the co-designated interpretations. Your degree-supervaluationist looks at the set of all interpretations, and says that some are better than others: they are "intended" to different degrees. So the way to describe the semantic facts is to give a measure over the space of interpretations that (roughly) gives in each case the degree to which a given interpretation is designated. Degree supervaluationism will share some of the distinctive features of the classical and standard supervaluational setups: for example, since classical tautologies are true at all interpretations, the law of excluded middle and the like will be "true to degree 1" (i.e. true on a set of interpretations of designation-measure 1).

I don't see any reason why we can't take this across to the worlds setting I favoured. Just as the traditional view is that there's a unique actual world among the space of possible worlds, and I argued that we can make sense of there sometimes being a set of coactual worlds among that space (with something being true if it is true at all of them), I now suggest that we should be up for there being some measure across the space of possible worlds, expressing the degree to which those worlds are actual.

The suggestion this is building up to is that we regard the measure determined by the wavefunction in GRW as the "actuality measure". Things are determinately the case to the extent that the set of worlds where they're true is assigned a high measure.

So, for example, suppose that the amplitude of the wavefunction is concentrated on worlds where Sparky is located within region R (suppose the measure of that space of world-slices is 0.9). Then it'll be determinately the case to degree 0.9 that Spark is in location R. Of course, in a set of worlds of measure 0.1, Sparky will be outside R. So it'll be determinately the case to degree 0.1 that Sparky is outside R. (Of course, it'll be determinate to degree 1 that Sparky is either inside R or outside R: at all the worlds, Sparky is located somewhere!)

I don't expect this to shed much light at all on what the wavefunction means. Ontic indeterminacy, many think, is a pretty obscure notion taken cold, and I'm not expecting metaphysicians or anyone else to find the notion of "degrees of actuality" something they recognize. So I'm not saying that there's any illuminating metaphysics of GRW here. I think the illumination is likely to go in the other direction: if you've can get a pre-philosophical grip on the "determinacy" and "no fact of the matter" talk in quantum physics, we've got a way of using that to explain talk of "degrees of actuality" and the like. Nevertheless, I think that, if this all works technically, then a bunch of substantive results follow. Here's a few thoughts in that direction:

We've got a candidate for vagueness in the world, linked to a general story about how to think about ontic vagueness. Given ontic vagueness isn't in the best repute in the philosophical community, there's an important "existence result" in the offing here.
Recall the idea canvassed earlier that "determinacy" or an equivalent might just be a metaphysical primitive. Well, here we have the suggestion that what amounts to (degrees of) determinacy being taken as a *physical* primitive. And taking the primitives of fundamental physics as a prima facie guide to metaphysical primitives is a well-trodden route, so I think some support for that idea could be found here.
If there is ontic vagueness in the quantum domain, then we should be able to extract information about the appropriate way to think and reason in the presence of determinacy, by looking at an appropriately regimented version of how this goes in physics. And notice that there's no suggestion here that we go for a truth-functional degree theory with the consequent revisions of classical logic: rather, a variant of the supervaluational setup seems to me to be the best regimentation. If that's right, then it lends the support for the (currently rather hetrodox) supervaluational-style framework for thinking about metaphysical vagueness.
I think that there's a bunch of alleged metaphysical implications of quantum theory that don't *obviously* go through if we buy into the sort of metaphysics of GRW just suggested. I'm thinking in particular about the allegation that quantum theory teaches us that certain systems of particles have "emergent properties" (Jonathan Shaffer has been using this recently as part of his defence of Monism). Bohmianism already shows, I guess, that this sort of claim won't be interpretation-neutral. But the above picture I think complicates the case for holism even within GRW.

(Thanks are owed to a bunch of people, particularly George Darby, for discussion of this stuff. They shouldn't be blamed for any misunderstands of the physics, or indeed, philosophy, that I'm making!)

Gavagai again again

2007-04-25T17:06:00.000+01:00

A new version of my discussion of Quine's "argument from below" is now up online (shorter! punchier! better!) Turns out it was all to do with counterpart theory all along.

Here's the blurb: Gavagai gets discussed all the time. But (unless I'm missing something in the literature) I've never seen an advocate of gavagai-style indeterminacy spell out in detail what exactly the deviant interpretations or translations are, that incorporating the different ways of dividing reference (over rabbits, rabbit-stages or undetached rabbit-parts). And without this it is to say the least, a bit hard to evaluate the supposed counterexamples to such interpretations! So the main job of the paper is to spell out, for a significant fragment of language, what the rival accounts of reference-division amount to.

One audience for the paper (who might not realize they are an audience for it initially) are folks interested in the stage theory/worm theory debate in the philosophy of persistence. The neuvo-Gavagai guy, according to me, is claiming that there's no fact of the matter whether our semantics is stage-theoretic or worm-theoretic. I think there's a reasonable chance that that he's right.

Stronger than this: so long as there are both 4D worms and instantaneous temporal parts thereof around (even if they're "dependent entities" or "rabbit histories" or "mere sums" as opposed to Real Objects), the Gavagai guy asks you to explain why our words don't refer to those worms or stages rather than whatever entity you think *really are* rabbits (say, enduring objects wholly present at each time).

By the way, even if these semantic indeterminacy results were right, I don't think that this forecloses the metaphysical debate about which of endurance, perdurance or exdurance is the right account of *persistence*. But I do think that it forces us to think hard about what the difference is between semantic and metaphysical claims, and what sort of reasons we might offer for either.

Parsimony and the fundamental (x-posted from metaphysical values)

2007-04-25T17:04:00.000+01:00

A bit cross-posting this one...

In his APA comments on Jonathan Schaffer, Ross asks about some of Jonathan's ideas about the applicability of Ockham's razor. The question arises if you buy into some robust distinction between "fundamental" and "derivative" existents. Candidate fundamental existents: quarks, electrons, maybe organisms (or maybe just THE WORLD). Candidate derivative existents: weirdo fusions, impure sets, maybe tables and chairs (or maybe everything except THE WORLD).

Let's call the idea that "derivative" as well as "fundamental" entities are (thump table) existing things the expansivist interpretation of the fundamental/derivative distinction. Call the idea that only the fundamental (thump table) exists the restrictivist interpretation of that distinction.

Jonathan's position is that Ockham's razor, rightly understood, tells us to minimize the number of fundamental entities. Ross's idea (I think?) is that this is right iff one has a restrictivist understanding of the fundamental/derivative distinction. But Jonathan, pretty clearly, has an expansivist understanding of that distinction: he doesn't want to say that the only thing that (thump table) exists is the world, just that the world is ontologically prior to everything else. So if Ross is right, his application of parsimony is in trouble.

I can see what the idea is here: after all, understanding parsimony as the instruction to minimize (thump table) existents or to minimize the (thump table) kinds of existents is surely close to the traditional understanding. Whereas the idea that we need only minimize (kinds of) existents of such-and-such a type, seems to come a bit out of the blue, and at minimum we need some more explanation before we could accept that revision to our theoretical maxims.

However... One thing that seems important is to consider what sort of principles of parsimony might be present in more ordinary theorizing (e.g. in the special sciences). The appeal of appealing to parsimony in metaphysics is in large part that it's a general theoretical virtue, applicable in all sorts of areas that are paradigms of good, productive fields of inquiry. Now, theoretical virtues in the sciences is not a topic that I'm in a position to speak with authority on. But one thing that seems to me important in this connection: if you think that the entities of special sciences aren't fundamental entities, then principles of parsimony restricted to the fundamentals aren't going to be in a position to give you much bite. (NB: I think that this was raised by someone in comments on Jonathan's paper in Boise, but I can't remember who it was...).

If that's right, then whether you're an expansivist or a restrictivist about the fundamental/derivative distinction seems beside the point. Any theorist who gives a story about what the fundamentals are that's unconstrained by what the special sciences say, is going to be in trouble with the idea that principles of parsimony should be restricted to constraints on fundamental existents: for such principles of parsimony won't then be able to get much bite on theorizing in the special sciences. I'd like to think that quarks, leptons etc are going to populate the fundamental, rather than Jonathan's WORLD. This point bites me as much as Jonathan.

There's plenty of room for further discussion here, particularly the interaction of the above with what you take to be evidence for some entities being fundamental. E.g. if you thought that various types of emergentism in special science would be evidence for "higher level" fundamental entities, then maybe the above parsimony principle would still have application to special sciences: it'd tell you to reduce to the number of emergent entities you postulate (i.e. it'd be a methodological imperative towards reductionism).

Also, it seems to me that there is something to the thought that some entities are simply "don't cares" when applying parsimony principles. If I'm concerned with theorizing about the behaviour of various beetles in front of me, I care about how many kinds of beetles my theory is giving me, but not with how many kinds of mathematical entities I need to invoke in formulating that theory. Now, maybe that differential attitude can be explained away by pointing to the generality of the mathematica involved (e.g. that total science is "already committed to them"). But one natural take would be to look for restrictions to principles of parsimony/Ockham's razor, making them sensitive to the subject-matter under investigation.

To speculate wildly: If principles of parsimony do need to be sensitized in this way, and if the study of what fundamentally exists is a genuine investigation, maybe the principle of parsimony, in application to that study, really would tell us to minimize the number of, and kinds of, fundamental entities we posit.

APA return

2007-04-09T00:53:00.000+01:00

Back in Atlanta waiting to reboard a flight to the UK. Trying not to miss the flight this time (interestingly, the plane from SF was an hour out on the "local time" it displayed on board, which might explain the previous problems).

The APA was really fun. Highlights for me included the Hudson-fest, featuring comments from Josh Parsons, Mark Heller and Michael Rae, and interesting replies to each from Hud. Also the author-meets-critics session on dialethism which Brit mentions here. I've been thinking a lot about open futures following Brit's talk on sea battle semantics, and may have some thoughts to post soon (on the plane over to Atlanta, my frantic drawing of dots and arrows trying to figure out how counterfactuals interact with open future semantics convinced my neighbour I was an astrophysicist. Must be the big axes with "time" and "reality" on them...). Andy Egan gave two really interesting papers, on fragmented minds and aesthetic disagreement, and I really enjoyed Alyssa Ney's talk on how different theories of causation fit together (or not). And lots more nice people met and good stuff talked about!

It was fun also meeting various bloggers for the first time in the flesh.

The tale of the 14 philosophers and the limousine is already legendary, I gather (I wasn't there).

San Francisco

2007-04-03T04:04:00.000+01:00

San Francisco! I'm staying at a hotel with a very posh lobby, the Sir Francis Drake, just down the street from the APA venue. I've enjoyed a hour-long double-decker train journey, and am just being struck once more about the strangeness of being in a different country.

I think food may be in order, then recovery before the hard philosophical slog restarts...

To the APA

2007-04-02T22:08:00.000+01:00

The Boise metametaphysics conference finished today. A really fun event! I gave quick versions of my comments on Ted's naturalness paper this morning.

One thing that was kind of surprising to me is that there weren't many people defending the sort of "realist Quinean" view that I (along with a lot of people) took to be the orthodoxy. Carnapians (of various flavours), Aristotelians, and the like were more in evidence.

I found the framework and ideas in Dave Chalmers' "Ontological anti-realism" paper particularly stimulating. It suggests to me some nice ways of extending some of the views I have on ontic vagueness. Lots to think about.

Anyway, I'm now about to get on a plane for San Francisco, for the Pacific APA. It was very exciting seeing the Pacific for the first time as I flew in to SF on the way to Boise; I'm really looking forward to seeing the city and attending the conference.

West coast journeying

2007-03-30T01:12:00.000+01:00

I'm currently in Atlanta airport.

I didn't mean to be still here. A combination of tiredness, lack of care with a watch, and (I suspect) there being different timezones in different terminals, mean that I missed my connecting flight.

On the positive side, I was happily making notes on excellent metametaphysics papers while missing my flight. Still, an all-things-considered bad, I think.

But the nice people at Delta rebooked me, and (modulo a taxi journey and quite possibly sleeping at San Jose airport) my travel plans are back in the swing.

So long as I don't miss another flight through blogging...

Probabilistic multi-conclusion validity

2007-03-26T00:26:00.000+01:00

I've been thinking a bit recently about how to generalize standard results relating probability to validity to a multi-conclusion setting.

The standard result is the following (where the uncertainty of p is 1-probability of p):

An argument is classically valid
iff
for all classical probability functions, the sum of the uncertainties of the premises is at least as great as the uncertainty of the conclusion.

It'll help if we restate this as follows:

An argument is classically valid
iff
for all classical probability functions, the sum of the uncertainties of the premises + the probability of the conclusion is at least 1.

Stated this way, there's a natural generalization available:

A multi-conclusion argument is classically valid
iff
for all classical probability functions, the sum of the uncertainties of the premises + the probabilities of the conclusions is greater than or equal to 1.

And once we've got it stated, it's a corollary of the standard result (I believe).
It's pretty easy to see directly that this works in the "if" direction, just by considering classical probability functions which only assign 1 or 0 to propositions.

In the "only if" direction (writing u for uncertainty and p for probability)

Consider A,B|=C,D. This holds iff A,B,~C,~D|= holds by a standard premise/conclusion swap result. And we know u(~C)=p(C), u(~D)=p(D). By the standard result, the sum of uncertainties of the premises of a single-conclusion argument must be greater than that of the conclusion. That is, the single-conc argument holds iff u(A)+u(B)+u(~C)+u(~D) is greater than equal to 1. But by the above identification, this holds iff u(A)+u(B)+p(C)+p(D) is greater than or equal to 1. This should generalize to arbitrary cases. QED.

Naturalness in Idaho (x-post from MV)

2007-03-25T23:11:00.001+01:00

I'm off very soon to the INPC metametaphysics conference in Boise. Many other fun people will be there (not least fellow CMM-er Andy McGonigal, fresh from a spell at Cornell).

Together with Iris Einheuser, I'm going to be responding to Ted Sider's paper "Which disputes are substantive?". It's been great to have a serious think about the way that Ted thinks of this stuff, and how it relates to the Kit Fine inspired setting that I've been working on lately.

Anyway, the whole writing-a-response thing got way out of hand, and I've ended up with a 7,500 word first draft. I do think there's a couple of substantive issues raised therein for the kind of framework (otherwise really really attractive) that he's been pushing here and in recent work. The worry centres around quantification into the scope of Ted's "naturalness" operator. For any who are interested, I've put the draft response up online.

After the INPC, I'll be in San Fran for the Pacific APA, along with many other CMM and Leeds folks.

Fundamental and derivative truths

2007-03-09T12:37:00.000Z

After a bit of to-ing and fro-ing, I've decided to post a first draft of "Fundamental and derivative truths" on my work in progress page.

I've been thinking about this material a lot lately, but I've found it surprisingly different to formulate and explain. I can see how everything fits together: just not sure how best to go about explaining it to people. Different people react to it in such different ways!

The paper does a bunch of things:

offering an interpretation of Kit Fine's distinction between things that are really true, and things that are merely true. (So, e.g. tables might exist, but not really exist).
using Agustin Rayo's recent proposal for formulating a theory of requirements/ontological commitments in explication.
putting forward a general strategy for formulating nihilist-friendly theories of requirements (set theoretic nihilism and mereological nihilisms being the illustrative cases used in the paper).
using this to give an account of "postulating" things into existence (e.g. sets, weirdo fusions).
sketching a general answer to the question: in virtue of what do our sentences have the ontological commitments they do (i.e. what makes a theory of requirements *the correct one* for this or that language?)

This is exploratory stuff: there's lots more to be said about each of these, and plenty more issues (e.g. how does this relate to fictionalist proposals?) But I'm at a stage where feedback and discussion are perhaps the most important things, so making it public seems a natural strategy...

I'm going to be talking in more detail about the case of mereological nihilism at the CMM structure in metaphysics workshop.

Thresholds for belief

2007-03-09T12:19:00.000Z

I’m greatly enjoying reading David Christensen’s Putting logic in its place at the moment. Some remarks he makes about threshold accounts of the relationship between binary and graded beliefs seemed particularly suggestive. I want to use them here to suggest a certain picture of the relationship between binary and graded belief. No claim to novelty here, of course, but I’d be interested to hear about worries about this specific formulation (Christensen himself argues against the threshold account).

One worry about threshold accounts is that they’ll make constraints on binary beliefs look very weird. Consider, for example, the lottery paradox. I am certain that someone will win, but for each individual ticket, I’m almost certain that it’s a loser. Suppose that having belief of degree n sufficed for binary belief. Then, by choosing a big enough lottery, we can make it that I believe a generalization (there will be a winner) while believing the negation of each of its premises. So I believe each of a logically inconsistent set.

This sort of situation is very natural from the graded belief perspective: the beliefs in question meet constraints of probabilistic coherence. But there’s a strong natural thought that binary beliefs should be constrained to be logically consistent. And of course, the threshold account doesn’t deliver this.

What Christensen points to is some observations by Kyburg about limited consistency results that can be derived from the threshold account. Minimally, binary beliefs are required to be weakly consistent: for any threshold above zero, one cannot believe a single contradictory proposition. But there are stronger results too. For example, for any threshold above 0.5, one cannot believe a pair of mutually contradictory propositions. One can see why this is if one remembers the following result: that a logically valid argument is such that the improbability of its conclusion cannot be greater than the sum of the improbabilities of its premises. For the case where the conclusion is absurd (i.e. the premises are contradictory) we get the the sum of the improbabilities of the premises must be less than or equal to 1.

In general, then, what we get is the following: if the threshold for binary belief is at least 1-1/n, then one cannot believe each of an inconsistent set of n propositions.

Here’s one thought. Let’s suppose that the threshold for binary belief is context dependent in some way (I mean here to use this broadly, rather than committing to some particularly potentially controversial semantic analysis of belief attributions). The threshold that marks the shift to binary belief can vary depending on aspects of the context. The thought, crudely put, is that there’ll be the following constraint on what thresholds can be set: in a context where n propositions are being entertained, then the threshold for binary belief must be at least 1-1/n.

There is, of course, lots to clarify about this. But notice that now relative to every context, we’ll get logical consistency as a constraint on the pattern of binary belief (assuming that to belief that p is in part to entertain that p).

[As Christensen emphasises, this is not the same thing as getting closure holding in every context. Suppose we consider the three propositions, A, B, and A&B. Consistency means that we cannot accept the first two and accept the negation of the last. And indeed, with the threshold set at 2/3, we get this result. But closure would tell us that every situation in which we believe the first two, we should believe the last. But it’s quite consistent to believe A and B (say, by having credence 2/3 in each) and to fail to believe A&B (say, by having credence 1/3 in this proposition). Probabilistic coherence isn’t going to save the extendability of beliefs by deduction, for any reasonable choice of threshold.

Of course, if we allow a strong notion of disbelief or rejection, such that someone disbelieves that p iff their uncertainty of p is past the threshold (the same threshold as for belief), then we’ll be able to read off from the consistency constraint that in a valid argument, if one believes the premises, one should abandon disbelief in the conclusion. This is not closure, but perhaps it might sweeten the pill of giving up on closure.]

Without logical consistency being a pro tanto normative constraint on believing, I’m sceptical that we’re really dealing with a notion of binary belief at all. Suppose this is accepted. Then we can use the considerations above to argue (1) that if the threshold account of binary belief is right, then thresholds (if not extreme) must be context dependent, since for no choice of threshold less than 1 will consistency be upheld. (2) that there’s a natural constraint on thresholds in terms of the number of propositions obtained.

The minimal conclusion, for this threshold theorist, is that the more propositions they entertain, the harder it will be for them to count as beliefs. Consider the lottery paradox construed this way:

1 loses

2 loses

…

N loses

So: everyone loses

Present this as the following puzzle: We can believe all the premises, and disbelieve the conclusion, yet the latter is entailed by the former.

We can answer this version of the lottery paradox using the resources described above. In a context where we’re contemplating this many propositions, the threshold for belief is so high that we won’t count as believing the individual props. But we can explain why it seems so compelling: entertain each individually, and we will believe it (and our credences remain fixed throughout).

Of course, there’s other versions of the lottery paradox that we can formulate, e.g. relying on closure, for which we have no answer. Or at least, our answer is just to reject closure as a constraint on rational binary beliefs. But with a contextually variable threshold account, as opposed to a fixed threshold account, we don’t have to retreat any further.

Supervaluational consequence again

2007-03-08T12:18:00.000Z

I’ve just finished a new version of my paper supervaluational consequence. A pdf version is available here. I thought I'd post something explaining what's going on therein.

Let’s start at the beginning. Classical semantics requires, inter alia, the following. For every expression, there has to be a unique intended interpretation. This single interpretation will assign to each name, a single referent. To each predicate, it will assign a set of individuals. Similarly for other grammatical categories.

But sometimes, the idea that there are such unique referents, extensions and so on, looks absurd. What supervaluationism (in the liberal sense I’m interested in) gives you is the flexibility to accommodate this. Supervaluationism requires, not a single intended interpretation, but a set of interpretations.

So if you’re interested in the problem of the many, and think that there’s more than one optimal candidate referent for “Kilimanjaro”; if you’re interested in theory change, and think that relativist and rest mass are equi-optimal candidate properties to be what “mass” picks out; if you are interested in inscrutability of reference, and think that rabbit-slices, undetached rabbit parts as well as rabbits themselves are in the running to be in the extension of “rabbit”; if you’re interested in counterfactuals, and think that it’s indeterminate which world is the closest one where Bizet and Verdi were compatriots; if you think vagueness can be analyzed as a kind of multiple-candidate indeterminacy of reference; if you find any of these ideas plausible, then you should care about supervaluationism.

It would be interesting, therefore, if supervaluationism undermined the tenants of the kind of logic that we rely on. For either, in the light of the compelling applications of supervaluationism, we will have to revise our logic to accommodate these phenomena; or else supervaluationism as a theory of these phenomena is itself misconceived. Either way, there’s lots at stake.

Orthodoxy is that supervaluationism is logically revisionary, in that it involves admitting counterexamples to some of the most familiar classical inferential moves: conditional proof, reductio, argument by cases, contraposition. There’s a substantial hetrodox movement which recommends a hetrodox way of defining supervaluational consequence (so called “local consequence”) which is entirely non-revisionary.

My paper aims to do a number of things:

to give persuasive arguments against the local consequence heterodoxy
to establish, contra orthodoxy, that standard supervaluational consequence is not revisionary (this, granted a certain assumption)
to show that, even if the assumption is refused, the usual case for revisionism is flawed
to give a final fallback option: even if supervaluational consequence is revisionary, it is not damagingly so, for it in no way involves revision of inferential practice.

It convinces me that supervaluationists shouldn't feel bad: they probably don't revise logic, and if they do, it's in a not-terribly-significant way.

Back!

2007-02-19T17:20:00.000Z

Things have been very slow on the blogging front recently: a product of hecticity in all aspects of life over the last few weeks. Apologies in particular to those who have left comments

On the research side, I was down in Oxford on Friday giving a talk to the departmental Philosophical Society on "Semantics for nihilists". This is a paper that's turning into a more general project of showing how to get truths about macro-objects, or sets, say, without having to having to admit macro-objects into ones ontology. As I think of these things, the real issue here concerns the nature of ontological commitment (Agustin Rayo's recent papers convinced me of this). I'm planning to write up this stuff at the next available opportunity. I'm giving it again at a "Structure in Metaphysics" workshop here in Leeds, soon.

I'm also in the process of organizing my trip to Boise, Idaho, for the metametaphysics conference there.

Finally, on the news front: I'm going to be on research leave next year, courtesy of those nice people of the AHRC. It's for a project called "Intrinsic survival, multiple survival, vague survival", which takes on a cluster of issues, including intrinsicality, ontic vagueness, fission cases, and the problem of the many. One part of the application was to give regular research updates on this blog, so I'm committed to keep this active while on leave!

"Recent comments" function in blogger?

2006-12-21T16:50:00.000Z

I've noticed that many of my favourite blogs (e.g. here here and here) have in their sidebar a list of the most recent comments. This is probably stupid of me, but I can't find how to set up my template to do this! Anybody got any pointers?

Update: with a bit of scratching around I found a widget that'd do something like the job. I'm not totally happy with it, though, so alternatives still welcome!

Eliminating singular quantification

2006-12-19T18:45:00.001Z

I've been thinking idly about plural quantification over the last day or so (the things one does on ones holidays...).

The general idea is that we can go beyond standard first-order predicate logic, by adding distinctively plural quantification. So, in addition to quantifying by saying "there is something such that it is Mopsy"; we may also say "there are some things such that Mopsy is one of them". Oystein Linnebo has a really nice summary of plural logics in the Stanford Encyclopedia.

The setting I was thinking of is less expansive than the systems that Oystein concentrates on (those he calls PFO and PFO+). The way it is less expansive is this. the languages of PFO and PFO+ includes both singular quantification/singular terms and plural quantification/plural terms in its primitives. I want a system that has only plural quantification/terms as primitive. This means that rather than taking the relational primitive "is one of", holding between singular terms and plural terms, as primitive, I'll take "are among", which holds between pairs of plural terms. The payoff may be this: singular terms, variables and predication may turn out to be "dispensible", in the same sense that Russell's theory of descriptions showed that individual constants were dispensible. This may well be stuff that is already covered by the literature (or just obvious). If so, I'd be very happy to get references!

I will be taking it that the language of plurals contains predicates of plural terms. In this way, we follow what Linnebo calls L_PFO+ rather than L_PFO. Now generally we can distinguish between plural predicates that are distributive; and those that are non-distributive. Linnebo's examples are: the distributive predicate "is on the table" (if some things are on the table, then each one of those things is individually on the table); and the non-distributive predicate "forms a circle" (Some things can form a circle, even though there is no sense in which each individually forms a circle). Linnebo says that he does this to allow for non-distributive predications; but part of my motivation is to allow also for distributive plural predications. Syntactically, we need not pay attention to this (though if the semantic treatment of distributive and non-distributive plural predicates is to differ, we might want to differentiate them syntactically: introducing two sets of predicates. I'm going to ignore such refinements for now.)

Here's the language:

1. L_Plural has the following plural terms (where i is any natural number):

* plural variables xxi;
* plural constants aai.

2. L_Plural has the following predicates:

* a dyadic logical predicate <. (to be thought of as are among);
* non-logical predicates Rni (for every adicity n and every natural number i).

3. L_Plural has the following formulas:

* Rni(t1, …, tn) is a formula when Rni is an n-adic predicate and tj are plural terms;
* t < t' is a formula when t and t' are plural terms;
* ~φ and φ&ψ are formulas when φ and ψ are formulas;
* (Ev)v.φ is a formula when φ is a formula and vv a plural variable.
* the other connectives are regarded as abbreviations in the usual way.

What I'm interested in is whether we can develop a natural logic of plurals on the basis of this language: and if so, what its expressive power would be.

An immediate task would be to reintroduce singular quantification. The intuitive thought is that singular quantification can be thought of as a special case of plural quantification, where we somehow ensure that there is just one of them. The trick is to show how this can be done without circular appeal to singular quantification.

My thought (roughly) is to treat this as the following restricted quantifier [Exx : (yy)(if yy < xx then xx < yy].

Why will this play the role of singular quantification? Well, just because if you've got a plurality of things, which is such that every subplurality is also a superplurality, it's got to be a plurality consisting of just one thing (I'm assuming that there are no "null" pluralities). Now, of course, L_plural doesn't contain restricted quantifiers. But it's easy enough to find things that play the role of restricted quantifiers (formally, we'll define a paraphrase from L_PFO+ into L_plural that'll play this role). In parallel fashion, we can get a paraphrase of sentences containing singular terms, and paraphrase them into something that only uses plural vocabulary.

E.g. "(Ex)Elephant(x)" may go to: "(Exx)((yy)(if yy < xx then xx < yy)& Elephant(xx))". And "Runs(Susan)" may go to: "(yy)(if yy < Susan then Susan < yy)& Runs(Susan) )

Now, it seems to me that there are some interesting questions of detail about how best to formalize the "intuitive" logical theory for L_plural that I've been working with. But let me leave the this for now. Question is: does the above elimination of singular quantification and terms in favour of plural quantification and terms seem tenable? Does the paraphrase work on the "intuitive" reading of L_plural. Can people see any obstacles to formalizing this intuitive logic for L_plural?

Talks and talks

2006-12-14T13:09:00.000Z

Last weekend, I gave a talk at a philosophy of mathematics conference up in St Andrews: the Arche "Status Belli" conference. The conference marked the end of a major AHRC-funded project on the philosophy of mathematics at the Arche centre. I was a PhD student within that project for many years, and though I kept getting distracted into other areas (notably the other Arche projects, in Vagueness and Modality), it has a great big place in my heart. One thing I note with approval: Arche PhD students now seem to be doing loads of (linguistics-informed) philosophy of language. Since Herman Cappelan has just been appointed to a professorship there, no doubt this will continue. In my time, the centre was dominated by phil logic, epistemology and metaphysics: as my interests run centrally to phil language (as well as phil logic and metaphysics), I heartily approve of the current emphasis!

Working in the project was a really great experience, and seems to have been an objective success, to judge by all the philosophy that came out of it. It certainly gave me an appreciation of how much sheer work there is to be done in philosophy: the whole of philosophy exists in microcosm in a well-chosen problem. Over the years, the project got me working and thinking about the theory of truth and liar-like paradoxes, higher-order and plural logics, issues in the epistemology of basic knowledge and their relation to skepticism, Quinean and rival takes on ontological commitment, metaphysics of abstract objects, the applicability of mathematics, and (what I ended up writing my thesis on) the putative determinacy of reference and arguments for various forms of inscrutability.

Anyway, my paper at the conference was on the issue that I had intended to work on when I first arrived at St Andrews: the philosophy of the complex numbers, neofregean treatments of them and special issues of determinacy of reference that arise.

Following the conference, Agustin Rayo who was giving also giving a talk at the conference, travelled down to Leeds, presenting a paper drawn from his current project "On specifying content". The basic idea is that we should distinguish between the metalinguistic resources we need in order to give a (systematic, compositional) specification of the content of some belief (about the number of planets, or macroscopic objects, or higher-order quantification, or whatever) and the ontological/other commitments we build into the content as a prerequist for that content being true at a world. He gives a really detailed treatment of how this might work.

I think this stuff looks really exciting, with potential applications all over the place (for example, as I read him, Joseph Melia has been arguing for a while that something like the expressive resources/metaphysical demands distinction is crucial in a series of debates in modality, philosophy of mathematics, and elsewhere). I'm hoping to get to grips with it well enough to present and evaluate an application of it to defend mereological nihilism in the upcoming Structure in Metaphysics event here in Leeds.

Perspectives and magnets

2006-12-14T10:11:00.000Z

As Brian Weatherson notes, the new Philosophical Perspectives is now out. This includes a paper of mine called "Illusions of gunk". The paper defends mereological nihlism (the view that no complex objects exist) against a certain type of worry: (1) that mereological nihlism is necessary, if true; and (2) that "gunk-worlds" (worlds apparently containing no non-complex objects) are possible. (See this paper of Ted Sider's for the worry) I advise the merelogical nihilist to reject (2). There are various possibilities that the nihilist can admit, that plausibly explain the illusion that gunk is possible.

The volume looks to be full of interesting papers, but there's one in particular I've read before, so I'll write a little about that right now.

The paper is Brian Weatherson's "Asymmetric Magnets Problem". The puzzle he sets out is based on a well-entrenched link between intrinsicality and duplication: a property is intrinsic iff necessarily, it is shared among duplicate objects. Weatherson examines an application of this principle to a case where some of the features of the objects we consider are vectorial.

In particular, consider an asymmetric magnet M: one which has a pointy-bit at one end, and is such that the north pole of the magnet "points out" of the pointy end. Intuitively, the following is a duplicate of another magnet M*: one with the same shape, but simply rotated by 180 degrees so that both the north pole and the pointy end are both orientated in the opposite direction to M. (Weatherson has some nice pictures, if you want to be clear about the situation).

Though M and M* seem to be duplicates, their vectorial features differ: M has its north pole pointing in one direction, M* has its north pole pointing in the opposite direction. Moral: given the link, we can't take vectorial properties "as a whole" (i.e. building in their directions) as intrinsic, for they differ between duplicates.

What if we think that only the magnitude of a vectorial feature is intrinsic? Then we get a different problem: for their are pointy magnets whose north pole is directed out of the non-pointy end. Call one of these M**. But in shape properties, and so on, it matches M and M*. And ex hypothesi, in all intrinsic respects, their vectorial features are the same. So M, M* and M** all count as duplicates. But that's intuitively wrong (it's claimed).

Such is the asymmetric magnets problem. The challenge is to say something precise about how to think about the duplication of things with vectorial features, that'd preserve both intuitions and the duplication-intrinsicality link.

Weatherson's response is to take a certain relationship between parts of the pointy magnet its vectorial feature, as intrinsic to the magnet. In effect, he takes the relative orientation of the north-pole vector, and a line connecting certain points within the magnet, as intrinsic.

Ok, that's Weatherson's line in super-quick summary, as I read him. Here are some thoughts.

First thing to note: the asymmetric magnets problem looks like a special case of a more general issue. Suppose point particles a, b, c each have two fundamental vectoral features F and G, with the same magnitude in each case. Suppose in a's case they point in different directions, whereas in b and c's cases they point in the same direction (in b's case they both point north, in c's case they both point south). The intuitive verdict is that a and b are not duplicates, but b and c are. But, if you just demand that duplicates preserve the magnitudes of the quantities, you'll get a, b, and c as duplicates of one another; and if you demand that duplicates preserve direction of vectoral quantities, you'll get none of them as duplicates. That sounds just like the asymmetric magnets problem all over again. Let me call it the vector-pair problem.

What's the natural Weathersonian thought about the vector-pair problem? The natural line is to take the relative orientation ("angle") between the instances of F and G as a perfectly natural relation. (I think that Weatherson might go for this line now: see his comment here).

It seemed to me that a natural response to the problem just posed might be this: require that the magnitude of any quantities is invariant under duplication; also that the *relative orientation* of vectoral properties be invariant under duplication. Thus we build into the definition of duplication the requirement that any angles between vectors are preserved. There's thus no easy answer to the question of whether vectorial features of objects are intrinsic: we can only say that their magnitudes and relative orientations are, but their absolute orientation is not.

This leads to a couple of natural questions:

(A) Why do we demand absolute sameness of magnitude, and only relative sameness of direction, when defining what it takes for something to be a duplicate of something else?

I'm tempted to think that there's no deep answer to this question. In particular, consider a possible world with an "objective centre", and where various natural laws are formulated in terms of whether objects have properties "pointing towards" the centre or away from it. E.g. suppose two objects both with instantaneous velocity towards the centre will repel each other with a force proportional to the inverse of their separation; while two objects both with instantaneous velocity away from the centre will attract each other with a similar force (or something like that: I'm sure we can cook something up that’ll make the case work). Anyway, since the behaviour of objects depends on the "direction in which they're pointing", I no longer have strong intuitions that particles like b and c should count as duplicates (with that world considered counteractually).

I find it harder to imagine worlds where only relative magnitudes matter to physical laws, but I suspect that with ingenuity one could describe such a case: and maybe (considering such a scenario counteractually again) we'd be happier to demand only relative sameness of magnitudes, in addition to relative sameness of orientation of vectoral properties, among duplicates.

(B) The above proposal demands invariance of relative orientation of vectoral properties among duplicate entities. But that doesn't straightaway deal with the original asymmetric magnet case. For there we had the orientation of the shape-properties of the object to consider, not just the orientation of the vectoral quantities that the (parts of) the object has.

I'm tempted by the following way of subsuming the original problem under the more general treatment just given: say that some perfectly natural spatial properties are actually vectoral in character. E.g. the spatial property that holds between my hand and my foot is not simply "being separated by 1m" but rather "being separated by 1m downwards" (with, of course, the converse relation holding in the other direction). After all, if in giving the spatial properties that I currently have, we just list the spatial separations of my parts, we leave something out: my orientation. And that is a spatial property that I have (and is coded into the usual representations of location, e.g. Cartesian or polar coordinates. Of course, such representations are all relative to a choice of axes, just as the representation of spatial separation is relative to a choice of unit.)

Now, there might be ways of getting this result without saying that spatial-temporal relations among particulars are fundamentally vectorial. But I'm not seeing exactly how this would work.

(Incidentally, if we do allow fundamentally vectorial spatio-temporal relations, then it's not clear that we need to appeal to spatio-temporal relations among parts of an object to solve the asymmetric magnets problem: appealing to the angle between the "north pole" and the (vectorial) spatio-temporal properties of the pointy magnet may be enough to get the intuitive duplication verdicts. If so, then the Weathersonian solution can be extended to the case where the magnets are extended simples, which is (a) a case he claims not to be able to handle (b) a case he claims to be impossible. But I disagree with (b), so from my perspective (a) looks like a serious worry!)

(x-posted on metaphysical values)

Seduction and the sorites

2006-11-16T13:41:00.000Z

Consider a red-yellow sorites sequence. Famously, "There is a red patch right next to a non-red patch" looks awful. But deny it (assert its negation) and you have the major premise of the sorites paradox. Plenty of theorists want to say that the "sharp boundary" sentence turns out to be true. They then face the burden of saying why it's unacceptable. Call that the burden of explaining the seductiveness of the sorites paradox.

There is a fair amount of discussion of this kind of thing, and I have my own favourites. But in reading the literature, I keep coming across one particular line. It is to explain, on the basis of your favoured theory of vagueness, why we should think that each instance of the existential is false. So, theorists explain why we'd be confident that this isn't a red patch next to a non-red patch, and that isn't a red patch next to a non-red patch. And so on throughout the series.

However, there's something suspicious about that strategy. Consider the situation that generates the preface "paradox". Of each sentence I write in my book, I'm highly confident that it's true. But on the basis of general considerations, I'm highly confident that there's some sentence somewhere in it that's false.

Suppose we accept that, of each pair in the sorites series, we have grounds for thinking that the red/non-red boundary is not located there. Still, we have excellent general grounds (e.g. a short logical proof, from obvious premises using apparently uncontroversial principles) for the truth of the existential claim that the boundary is located somewhere. So far, it looks like we should be something like the preface situation. We should be comfortable with the existential claim that there is a cut-off somewhere (/there is an error somewhere in the book) while disbelieving each instance, that the cut-off is here (/the error occurs in this sentence).

But, of coures, the situation with the sorites is strikingly not like this. Despite the apparently compelling general grounds we can give for the truth of the existential, most of us find it really hard to believe.

The trouble is this: the simple fact that each instance of an existential appears false does not in general lead us to believe that the existential itself is false (the preface situation illustrates this). So there must be something special about the sorites case that makes the move seem compelling in this case. And I can't see that the authors that I've been reading explain what that is.

(A variation on this theme occurs in Graff Fara's "Shifting sands". Roughly, she gives a contextualist(-ish) story about why each instance asserting that the cut-off is not here will be true. She then says that it is "no wonder" will count universal generalization (the major premise of the sorites) as true.

But again, it's hard to see what general pattern of inferring this falls into (remembering that it has to be one so compelling that it survives confrontation with a short proof of the truth of the existential). After all, as I look around my room, the following are successively true: "my chair is currently visible" "my table is currently visible", "my cabinet is currently visible" etc. I feel no temptation to generalize to "all of the medium sized objects in my room are currently visible". I have reasons to think this general statement false, and that totally swamps my tendancy to generalize from the various instances. So again, the real question here is to explain why something similar doesn't happen in the sorites. And I don't see that question being addressed.)

Eliminating cross-level universals

2006-10-13T11:35:00.000+01:00

I've just come back from a CMM discussion of Lewis on Quantities (built around John Hawthorne's paper of that title).

One thing that came up was the issue of what you might call potentially "cross level" fundamental properties. These are properties that you might expect to find instantiated at the "bottommost" microphysical level, but also instantiated "further up". For example, electrons have negative charge; but so do ions. But ions are composite entities, which (from what I remember of A-level chemistry) are charged in virtue of the charges of their parts.
Clearly in some sense, electrons and ions can have the same determinate property: e.g. "charge -1". But, when giving e.g. a theory of universals, I'm wondering whether we have to say that they share the same Universal.

On Armstrong's theory of quantities, it looks to me that we won't say that the ion and the electron both instantiate the same Universal. The "charge -1" we find instantiated by the ion will be a structural universal, composed of the various charge Universals instantiated by the basic parts of the ion. The "charge -1" we find instantiated by an electron, on the other hand, looks like it'll be a basic, non-structural universal. So, it seems to me, it'll then be a challenge to Armstrong's account to say why these two universals resemble each other in a tight enough way that we apply to them the same predicate. (To avoid confusion, let's call the former "ur-charge -1" and leave "charge -1" as a predicate that applies to both ions and electrons, though not, on this view, in virtue of them instantiating the same Universal).

Let's suppose we're looking at a theory of universals (such as the one Lewis seems to contemplate at various points) which is just like Armstrong's except for ditching all the structural universals. Electrons get to instantiate the Universal "ur-charge -1". But ions, as actual-worldly complex objects, instantiate no Universals at all. Of course, again there's the challenge to spell out exactly what the conditions are under which we'll apply the predicate "charge -1" to things (roughly: when the various ur-charges instantiated by their parts "balance out"---though the details get tricksy).

What goes for charge can go for various other types of property. So we may find it useful to distinguish ur-mass 1kg (which will be a genuine basic universal) from the set of things "having mass 1kg".

A last thought. What is the relation between mass properties and ur-masses? In particular, is it the case that things can only ever have masses when their basic parts have ur-masses? I don't see any immediate reason to think so. Perhaps the actual world is one where things have mass in virtue of their parts having ur-mass. But why shouldn't we think that "having parts that have ur-masses" is but one *realization* of mass: and that at other worlds quite different ur-properties may underlie mass (say, ur-mass-densities, rather than ur-masses). That's potentially significant for discussions of modality and quantities: for two worlds that intially seem to be share the same stock of fundamental properties (spin, charge, mass, etc) may turn out to actual contain alien properties from each others point of view: if one contains ur-masses underlying the (non-fundamental) mass properties, while the other contains ur-mass-densities underlying those same properties.

(Thanks to all those at CMM for the discussion that led to this. This is x-posted at Metaphysical Values. And thanks to an anonymous commentator, who pointed out in an early version of this post that by "free radicals" I meant "ions"!)

Philosophy Dissertations

2006-10-05T09:45:00.000+01:00

Just to continue the shout outs for Josh Dever's excellent project of putting philosophy dissertations up online. I learned lots from reading dissertations when I was a graduate student (in particular, from John MacFarlane's and Cian Dorr's). The best dissertations not only give you not only a bunch of cutting-edge ideas, but also hugely useful surveys of the philosophical backdrop. They also give ideas of the "big picture" that's informing interesting people's work. I found them more interesting than most books (though I guess I was looking at a biased sample!)

A final thought. It's being suggested that online dissertations can be put in for the latest RAE exercise in the UK (any "public domain" paper is allowed to be put in, but obviously not too sensible to put in any old scrap: but dissertations that have gone through viva-ing are a natural candidate to be put in). Perhaps we'll see more dissertations going online because of this.

Chances, counterfactuals and similarity

2006-10-04T22:45:00.000+01:00

A happy-making feature of today is that Philosophy and Phenomenological Research have just accepted my paper "Chances, Counterfactuals and Similarity", which has been hanging around for absolutely ages, in part because I got a "revise and resubmit" just as I was finishing my thesis and starting my new job, and in part because I got so much great feedback from a referee that there was lots to think about.

The way I think about it, it is a paper in furtherance of the Lewisian project of reducing counterfactual facts to similarity-facts between worlds, which feeds into a general interest in what kinds of modal structure (cross-world identities, metrics and measures, stronger-than-modal relations etc) you need to appeal to for metaphysical purposes. Lewis has a distinctive project of trying to reduce all this apparent structure to the economical basis of de dicto modality --- what's true at this world or that --- and (local) similarity facts. Counterpart theory is one element of this project: showing how cross-world identities might be replaced by similarity relations and de dicto modality. Another element is the reduction of counterfactuals to closeness of worlds, and closeness of worlds is ultimately cashed out in terms of one world's fitting another's laws, and there being large areas where the local facts in each world match exactly. Again, we find de dicto modality of worlds and local similarity at the base.

Lewis's main development of this view looks at a special case, where the actual world is presupposed to have deterministic laws. But to be general (and presumably, to be applicable to the actual world!) we want to have an account that holds for the situation where the laws of nature are objective-chance-laws. Lewis does suggest a way of extending his account to the chancy case. It's attacked by Hawthorne in a recent paper---ultimately successfully, I think. In any case, Lewis's ideas in this area always looked (to me) like a bit of a patch-up job, so I suggest a more principled Lewisian treatment, which then avoids the Hawthorne-style objections to the Lewis original.

The basic thought (which I found in Adam Elga's work on Humean laws of nature) is that "fitting" chancy laws of nature is not just a matter of not violating those laws. Rather, to fit a chancy law is to be objectively typical relative to the probability function those laws determine. Given this understanding, we can give a single Lewisian account of what comparative similarity of worlds amounts to, phrased in terms of fit. The ambition is that when you understand "fit" in the way appropriate to deterministic laws, you get Lewis's original (unextended) account. And when you understand "fit" in the way I argue is appropriate to chancy laws, you get my revised suggestion. All very satisfying, if you can get it to work!

Update

2006-10-04T22:20:00.001+01:00

Things have been pretty crazy around here: semester is starting, teaching is being prepared and the long summer days seem a long time ago.

I'm currently working on the ideas about primitive vagueness I talked about in a post below. I'm giving a "work in progress" seminar here in Leeds on these next week, and hopefully then I'll give a fuller paper on some of this stuff at York and Durham later in the year. I'm pretty excited about this stuff, not least because it gives me a chance to think about modalism, temporalism and other funky things.

Currently, I'm trying to work out what Evans' argument looks like to the primitivist. After that, next on the agenda is vague existence (after all, why can't it just *be the case* that it is vague whether Tibbles exists, for the primitivist?) Sider has some interesting way of making precise a worry about this, and I think the primitivist is able to buy into enough of his premises to make the debate interesting.

In the end though, primitivism doesn't need vague existence or identity to be coherent in order to be good: not unless we have arguments that take us from metaphysical vagueness in general to those particular kinds of metaphysical vagueness. And that's my other project at the moment: to try and survey those kind of connections for the Ontic Vagueness paper.

On that note, I just found some really interesting discussion of vague survival (in the context of personal fission cases) in a classic Bernard Williams paper "The self and the future". I'll be trying to get my head around this stuff soon.

Primitivism about vagueness

2006-09-04T12:13:00.000+01:00

One role this blog is playing is allowing me to put down thoughts before I lose them.

So here's another idea I've been playing with. If you think about the literature on vagueness, it's remarkable that each of the main players seems to be broadly reductionist about vagueness. The key term here is "definitely". The Williamsonian epistemicist reduces "definitely" to a concept constructed out of knowability. The supervaluationist typically appeals to semantic indecision, on one reading, that reduces vagueness to semantic facts; on another reading, that reduces vagueness to metasemantic facts concerning the link between semantic facts and their subvening base. Things are a little less clear with the degree theorist, but if "definite truth" is identified with "truth to degree 1", then what they're doing is reducing vagueness to semantic facts again.

If you think of the structure of the debate like this, then it makes sense of some of the dialectic on higher-order vagueness. For example, if vagueness is nothing but semantics, then the question immediately arises: what about those cases where semantic facts themselves appear to be vague? The parallel question for the epistemicist is: what about cases where it's vague whether such-and-such is knowable? The epistemicists look like they've got a more stable position at this point, though exactly why this is is hard to spell out.

Consider other debates, e.g. in the philosophy of modality. Sure, there are reductionist views: Lewis wanting to reduce modality to what goes on in other concrete space-times; people who want to reduce it to a priori consistency; and so on. But a big player in that debate is the modalist, who just takes "possibility" and "necessity" as primitive, and refuses to offer a reductive story.

It seems to me pretty clear that a position analogous to modalism should be a central part of the vagueness literature; but I'm not aware of any self-conscious proponents of this position. Let me call it "primitivism" about vagueness. I think that perhaps some self-described semantic theorists would be better classified as primitivists.

At the end of ch 5 of the "Vagueness" book, Tim Williamson has just finished beating up on traditional supervaluationism, which equates truth with supertruth. He then briefly considers people who drop that identification. Here's my take on this position. Proponents say that semantically, there's a single precisification of our language which is the intended one, but which one it is is (semantically) vague. Truth is truth on the intended precisification; but definite truth is defined to be truth on all the precisifications which aren't determinately unintended. Definite truth (supertruth) and truth come apart. This position, from a logical point of view, is entirely classical; satisfies bivalence; and looks like it thereby avoids many of Williamson's objections to supervaluationism.

I think Williamson puts exactly the right challenge to this line. In what sense is this a semantic theory of vagueness? After all, you haven't characterized "Definitely" in semantic terms: rather, what we've done is characterized "Definitely" using that very notion again in the metalanguage. One might resist this, claiming that "Definitely" should be defined using the term "admissible precisification" or some such. But then one wonders what account could be made of "admissible": it plays no role in defining semantic notions such as "true" or "consequence" for this theorist. What sense can be made of it?

I think the challenge can be met by metasemantic versions of supervaluationism, who give a substantive theory of what makes a precisification admissible. I take that to be something like the McGee/McLaughlin line, and I spent a chapter of my thesis trying to lay out precisely what was involved. But that's another story.

What I want to suggest now is that Primitivism about vagueness gives us a genuinely distinct option. This accepts Williamson's contention that when we drop supertruth=truth, "nothing articulate" remains of the semantic theory of vagueness. But it questions the idea that this should lead us towards epistemicism. Let's just take determinacy (or lack of it) as a fundamental part of reality, and then use it in constructing theories that make sense of the phenomenon of vagueness. Of course, there's nothing positive this theorist has to say that distinguishes her from reductive rivals such as the epistemicist; but she has plenty of negative things to say disclaiming various reductive theses.

The present time

2006-09-04T09:59:00.000+01:00

One notorious issue for presentists (and other kinds of A-theorist) is the following: special relativity tells us (I gather) that among the slices of space-time that "look like time slices", there's no one that is uniquely privileged as "the present" (i.e. simulataneous with what's going on here-now). But the presentist says that only the present exists. So it looks like her metaphysics entails that there is a metaphysically privileged time-slice: the only one that exists. (Of course, I suppose the science is just telling us that there's no physically significance sense in which one is privileged, and it's not obvious the presentist is saying anything that conflicts with that. But it does seem worrying...)

One option is to retreat into "here-now"ism: the only things that exist are those that exist right here right now. No problems with relativity there.

I was idly wondering about the following line: say that it's (ontically) vague which time-slice is present, and so (for the presentist) say that it's ontically vague what exists. As I'm thinking of it, there'll be some kind of here-now-ish element to the metaphysics. From the point of view of a certain position p in space time, all that exists are those "time-like" slices of space time that contain the point, then it will be determinately the case that p exists. But for every other space-time point q, there will (I take it) be a reference frame according to which p and q are non-simultaneous. So it won't determinately be the case that q exists.

The details are going to get quite involved. I think some hard thinking about higher-order indeterminacy will be in order. But here's a quick sketch: choose a point r such that there's a choice of reference-frame that make q and r simultaneous. Then it sort of seems to me that, from p's perspective, the following should hold:

r doesn't exist
determinately, r doesn't exist
not determinately determinately r doesn't exist

The idea is that while r isn't "present" (and so fails to exist), relative to the perspective of some of the things that are present, it is present.

What I'd like to do is model this in a "supervaluation-style" framework like that one I talk about here. First, consider the set of all centred time-like-slices. It'll end up determinate that one and only one of these exists: but it'll be a vague matter which one. Let centred time-like-slice x access centred time-slice y iff the centre of y is somewhere in the time-slice x.

Now take a set of time-slices P which are all and only those with common centre p. These are the ontic candidates for being the present time. Next, consider the set P*, containing a set of time-slices which are all and only those accessed by some time-slice in P. And similarly construct P**, P*** etc etc etc.

Now, among space-time points, only the "here-now" point p determinately exists. All and only points which are within some some time-slice in P don't determinately fail to exist. All and only points which are within some time-slice in P* don't determinately determinately fail to exist. All and only points which are within some time-slice in P* don't determinately determinately determinately fail to exist. And so on. (If you like, existence shades of into greater and greater indeterminacy as we look further away from the privileged here-now point).

Well, I'm no longer sure that this deserves the name "presentism". Kit Fine distinguishes some versions of A-theory in a paper in "Modality and tense" which this view might fit better with (the Fine-esque way of setting this up would be to have the whole of space-time existing, but only some time-slices really or fundamentally existing. The above framework then models vagueness in what really or fundamentally exist). It is anyway up to it's neck in ontic vagueness, which you might already dislike. But I've no problem with ontic vagueness, and insofar as I can simulate being a presentist, I quite like this option.

There should be other variants too for different forms of A-theory. Consider, for example, the growing block view of reality (the time-slices in the model can be thought of as the front edges of a growing block: as we go through time, more slices get added to the model). The differences may be interesting: for the growing block, future space-time points determinately don't exist, but they don't det ...det fail to exist for some amount of iterations of "det"; while past space-time points determinately exist, but they don't det .... det exist for some amount of iterations of "det".

Any thoughts most welcome, and references to any related literature particularly invited!

Ontic vagueness: the shape of the debate

2006-09-03T23:23:00.000+01:00

(cross-posted on metaphysical values)

One of my projects at the moment is writing a survey article on ontic vagueness. I've been working on this stuff for a while now, but it's time to pull things together. (And writing up comments on Hugh Mellor's paper "Micro-composition" at the RIP Being conference got me puzzling about some of these issues all over again.)

One thing I'd like to achieve is to separate out different types of ontic vagueness. The "big three", for me, are vague identity, vague existence, vague instantition. But there also might be: vagueness in the parthood relation, vague locations, vague composition, vagueness in "supervening" levels (it being ontically vague whether x is bald); vagueness at the fundamental level (it being ontically vague whether that elementary particle is charged). These all seem prima facie different, to me. And (as Elizabeth Barnes told me time and again until I started listening) it's just not obvious that e.g. rejecting vague identity for Evansian reasons puts in peril any other sort of ontic vagueness, since it's not obvious that any other form of ontic vagueness requires vague identity.

[Digression: It's really not very surprising that ontic vagueness comes in many types, when you think about it. For topic T in metaphysics (theory of properties, theory of parts, theory of persistence, theory of identity, theory of location etc etc), we could in principle consider the thesis that the facts discussed by T are vague. End Digression]

Distinguish (a) the positive project of giving a theory of ontic vagueness; and (b) the negative project of defending it against its many detractors. The negative project I guess has the lion's share of the attention in the literature. I think it helps to see the issues here as a matter of (i) developing arguments against particular types of ontic vagueness (ii) arguing that this or that form of ontic vagueness entails some other one.

Regarding (i), Evans' argument is the most famous case, specifically against vague identity. But it won't do what Evans claimed it did (provide an argument against vagueness in the world per se) unless we can argue that other kinds of ontic vagueness give rise to vague identity (and Evans, of course, doesn't say anything about this). Vague existence is another point at which people are apt to stick directly. I think some of Ted Sider's recent arguments against semantically or epistemically vague existence transfer directly to the case of ontically vague existence. And we shouldn't forget the "incredulous stare" maneuver, often deployed at this point.

Given these kind of answers to (i), I think the name of the game in the second part of the negative project is to figure out exactly which forms of ontic vagueness commit one to vague existence or vague identity. So, for example, one of the things Elizabeth does in her recent analysis paper is to argue that vague instantiation entails vague existence (at least for a states-of-affairs theorist). Implicit in an argument due to Katherine Hawley are considerations seemingly showing that vague existence entails vague identity (at least if you have sets, or unrestricted mereological composition, around). (I set both of these out briefly and give references in this paper).
Again, you can think of Ted Sider's argument against vague composition as supporting the following entailment: vague composition entails vague existence. And so on and so forth.

[A side note. Generally, all these arguments will have the form:

Ontic vagueness of type 1
Substantive metaphysical principles
Therefore:
Ontic vagueness of type 2.

What this means is that these debates over ontic vagueness are potentially extemely metaphysically illuminating. For, suppose that you think that ontic vagueness of type 2 occurs, but that ontic vagueness of type 1 is impossible (say because it entails vague identity). Then, you are going to have to reject the substantive metaphysical principles that provide the bridge from one to the other. For example, if you want vague instantiation, but think vague existence is, directly or indirectly, incoherent, then you have an argument against states-of-affairs-theorists. The argument from vague existence to vague identity won't worry someone who doesn't believe in or in unrestricted mereological fusion. Hence, if cogent, it can be turned into an argument against sets and arbitrary fusions (actually, it's in that form --- as an argument against the standard set theoretic axioms --- that Katherine Hawley first presented it). And so forth.]

So that's my view on what the debate on ontic vagueness is, or should be. It has the advantage of unifying what at first glance appear to be a load of disparate discussions in the literature. It does impose a methodology that's not in keeping with much of the literature by defenders of ontic vagueness: in particular, the way I'm thinking of things, classical logic will be the last thing we give up: though non-classical logics are often the first tool reached for by defenders of ontic vagueness (notable exceptions are the modal-ish/supervaluation-ish characterizations of ontic vagueness favoured in various forms by Ken Akiba, Elizabeth Barnes and, erm, me). I'll have to be up front about this.

Still, I'd like to use the above as a way of setting up the paper. It can only be 5000 or so words long, and it has to be comprehensible to advanced undergraduates, so I may not be able to include everything, particularly if the issues allude to complex areas of metaphysics. But I'd like to have an as-exhaustive-as-possible taxonomy, of which I can extract a suitable sample for the paper. I'd be really interested in collecting any discussions of ontic vagueness that can fit into the project as I've sketched it. And I'd also be really grateful to hear about other parts of the literature that I'm in danger of missing out or ignoring if I go this route, and any comments on the strategy I'm adopting.

Some examples to get us started:

If composition is identity, then it looks like vague parthood entails vague identity. For if it's vague whether the a is part of b, then it'll be vague whether the a's are identical to b.

Indeed, if classical mereology holds, then it looks like vague parthood entails vague identity. For if it's vague whether the aa's are all and only the parts of b, then mereology will give us that that object which is the fusion of the aa's is identical to b iff the aa's are all and only the parts of b. Since the RHS here is ex hypothesi vague, the LHS will be too.

If the Wigginsean "individuation criteria" for Fs are vague, it looks like vague existence will follow when it's vague whether the conditions are met.

An argument for conditional excluded middle.

2006-09-01T10:08:00.000+01:00

Conditional excluded middle is the following schema:

if A, then C; or if A, then not C.

It's disputed whether everyday conditionals do or should support this schema. Extant formal treatments of conditionals differ on this issue: the material conditional supports CEM; the strict conditional doesn't; Stalnaker's logic of conditionals does, Lewis's logic of conditionals doesn't.

Here's one consideration in favour of CEM (inspired by Rosen's "incompleteness puzzle" for modal fictionalism, which I was chatting to Richard Woodward about at the Lewis graduate conference that was held in Leeds yesterday).

Here's the quick version:

Fictionalisms in metaphysics should be cashed out via the indicative conditional. But if fictionalism is true about any domain, then it's true about some domain that suffers from "incompleteness" phenomena. Unless the indicative conditional in general is governed in general by CEM, then there's no way to resist the claim that we get sentences which are neither hold nor fail to hold according to the fiction. But any such "local" instance of a failure of CEM will lead to a contradiction. So the indicative conditional in general is governed by CEM

Here it is in more detail:

(A) Fictionalism is the right analysis about at least some areas of discourse.

Suppose fictionalism is the right account of blurg-talk. So there is the blurg fiction (call it B). And something like the following is true: when I appear to utter , say "blurgs exist" what I've said is correct iff according to B, "blurgs exist". A natural, though disputable, principle is the following.

(B) If fictionalism is the correct theory of blurg-talk, then the following schema holds for any sentence S within blurg-talk:

"S iff According to B, S"

(NB: read "iff" as material equivalence, in this case).

(C) The right way to understand "according to B, S" (at least in this context) is as the indicative conditional "if B, then S".

Now suppose we had a failure of CEM for an indicative conditional featuring "B" in the antecedent and a sentence of blurg-talk, S, in the consequent. Then we'd have the following:

(1) ~(B>S)&~(B>~S) (supposition)

By (C), this means we have:

(2) ~(According to B, S) & ~(According to B, ~S).

By (B), ~(According to B, S) is materially equivalent to ~S. Hence we get:

(3) ~S&~~S

Contradiction. This is a reductio of (1), so we conclude that

(intermediate conclusion):
No matter which fictionalism we're considering, CEM has no counterinstances with the relevant fiction as antecedent and a sentence of the discourse in question as consequent.

Moreover:

(D) the best explanation of (intermediate conclusion) is that CEM holds in general.

Why is this? Well, I can't think of any other reason we'd get this result. The issue is that fictions are often apparently incomplete. Anna Karenina doesn't explicitly tell us the exact population of Russia at the moment of Anna's conception. Plurality of worlds is notoriously silent on what is the upper bound for the number of objects there could possibly be. Zermelo Fraenkel set-theory doesn't prove or disprove the Generalized Continuum Hypothesis. I'm going to assume:

(E) whatever domain fictionalism is true of, it will suffer from incompleteness phenomena of the kind familiar from fictionalisms about possibilia, arithmetic etc.

Whenever we get such incompleteness phenomena, many have assumed, we get results such as the following:

~(According to AK, the population of Russia at Anna's conception is n)
&~(According to AK, the population of Russia at Anna's conception is ~n)

~(According to PW, there at most k many things in a world)
&~(According to PW, there are more than k many things in some world)

~(According to ZF, the GCH holds)
&~(According to ZF, the GCH fails to hold)

The only reason for resisting these very natural claims, especially when "According to" in the relevant cases is understood as an indicative conditional, is to endorse in those instances a general story about putative counterexamples to CEM. That's why (D) seems true to me.

(The general story is due to Stalnaker; and in the instances at hand it will say that it is indeterminate whether or not e.g. "if PW is true, then there at most k many things in the world" is true; and also indeterminate whether its negation is true (explaining why we are compelled to reject both this sentence and its negation). Familiar logics for indeterminacy allow that p and q being indeterminate is compatible with "p or q" being determinately true. So the indeterminacy of "if B, S" and "if B, ~S" is compatible with the relevant instance of CEM "if B, S or if B, ~S" holding.)

Given (A-E), then, I think inference to the best explanation gives us CEM for the indicative conditional.

[Update: I cross-posted this both at Theories and Things and Metaphysical Values. Comment threads have been active so far at both places; so those interested might want to check out both threads. (Haven't yet figured out whether this cross-posting is a good idea or not.)]

Existence and just more theory

2006-08-30T23:13:00.000+01:00

I've been spending much time recently in coffee shops with colleagues talking about the stuff that's coming up in the fantastically named RIP Being conference (happening in Leeds this weekend). Hopefully I won't be treading on toes if I draw out one strand of those conversations that I've been finding particularly interesting.

(continued below the fold)

The story for me begins with an old paper by Hartry Field. His series of papers in the 70's is one of the all-time great runs: from "Tarski's theory of truth" through "Quine and the correspondance theory", "Theory Change", "Logic, meaning and conceptual role", "Conventionalism and Instrumentalism in semantics" and finishing off with "Mental representation". (All references can be found here). Not all of them are reprinted in his collection Truth and the absence of fact, which seems a pity. The papers I mentioned above really seemed to me to lay out the early Fieldian programme in most of the details. Specifically, in missing out the papers "Logic, meaning ..." and "Conventionalism and instrumentalism...", you miss out on the early-Field's take on how the cognitive significance of language relates to semantic theory; and the most interesting discussion I know of concerning what Putnam's notorious "just more theory" argument might amount to.

The "just more theory" move is supposed to be the following. It's familiar that you can preserve sensible truth conditions, by assigning wildly permuted reference-schemes to language (see my other recent posts for more details and links). But, prima facie, these permuted reference schemes are going to vitiate some plausible conditions of what it takes for a term to refer to something (e.g. that the object be causally connected to the term). Now, some theorists of meaning don't build causal constraints into their metasemantic account. Davidson, early Lewis and the view Putnam describes as "standard" in his early paper, are among these (I call these "interpretationisms" elsewhere). But the received view, I guess, is to assume that some such causal constraint will be in play.

Inscrutability argument dead-in-the-water? No, says Putnam. For look! the permuted interpretation has the resources to render true sentences like "reference is a relation which is causally constrained". For just as, on the permuted interpretation "reference" will be assigned as semantic value some weirdo twisted relation Reference*, so on the same interpretation "causation" will be assigned some weirdo twisted relation Causation. And it'll turn out to be true that Reference* and Causation* match up in the right way. So (you might think), how can metasemantic theories tell you rule in favour of the sensible interpretation over this twisted one? For whichever no matter which of these we imagine to be the real interpretation of our language, everything we say will come out true.

Well, most people I speak to think this is a terrible argument. (For a particularly effective critique of Putnam---showing how badly things go if you allow him the "just more theory" move---see this paper by Tim Bays.) I'll take it the reasons are pretty familiar (if not, Lewis's "Putnam's paradox" has a nice presentation of a now-standard response). Anyway, what's interesting about Field's paper is that it gives an alternative reading of Putnam's challenge, which makes it much more interesting.

Let's start by granting ourselves that we've got a theory which really has tied down reference pretty well. Suppose, for example, that we say "Billy" refers to Billy in virtue of appropriate causal connections between tokenings of that word and the person, Billy. The "Wild" inscrutability results threatened by permutation arguments simply don't hold.

But now we can ask the following question: what's special about that metasemantic theory you're endorsing? Why should we be interested in Reference (=Causal relation C)? What if we tried to do all the explanatory work that we want semantics for, in terms of a different relation Reference*? We could then have a metasemantic* theory of reference*, which would explain that it is constrained to match a weirdo relation causation*. But, notice, that the relation "S expresses* proposition* p" (definable via reference*) and "S expresses proposition p" (definable via reference*) are coextensional. Now, if all the explanatory work we want semantics to do (e.g. explaining why people make those sounds when they believe the world is that way) only ever makes appeal to what propositions sentences express, then there just isn't any reason (other than convenience) to talk about semantic properties rather than semantic* ones.

The conclusion of these considerations isn't the kind of inscrutability I'm familiar with. It's not that there's some agreed-upon semantic relation, which is somehow indeterminate. It's rather that (the consideration urges) it'll be an entirely thin and uninteresting matter that we choose to pursue science via appeal to the determinate semantic properties rather than the determinate semantic* properties. You might think of this as a kind of metasemantic inscrutability, in contrast to the more usual semantic inscrutability: setting aside mere convenience, there's no reason why we ought to give this metasemantic theory rather than that one.

Now, let's turn to a different kind of inscrutability challenge. For one reason or another, lots of people are very worried over whether we can really secure determinate quantification over an absolutely unrestricted domain. Just suppose you're convinced that there are no abstracta. Suppose you're very careful to never say anything that commits you to their existence. However, suppose you're wrong: abstracta exist. Intuitively, when you say "There are no abstracta, and I'm quantifying over absolutely everything!" you're speaking falsely. But this is only so if your quantifiers range over the abstracta out there as well as the concreta: and why should that be? In virtue of what can your word "everything" range over the unrestricted domain? After all, what you say would be true if I interpreted the word as ranging over only concreta. I'd just take you to be saying that no concreta exist (within your domain; and that you were quantifying over absolutely everything in your domain. Both of these are true, given that your domain happens to contain only concreta!

Bring in causality doesn't look like it helps here; neither would the form of reference-magnetism that Lewis endorsed, which demands that our predicates latch onto relatively natural empirical kinds, help. Ted Sider, in a paper he's presenting at the RIP conference, advocates extending the Lewis point to make appeal to logical "natural kinds" (such as existence) at this point. However, let me sketch instead a variant of the Sider thought that seems more congenial to me (I'll sketch at the end how to transfer it back).

My take on Lewis's theory is the following. First, identify a "meaning building language". This will contain only predicates for empirical natural kinds, plus some other stuff (quantifiers, connectives, perhaps terms for metaphysically basic things such as mereological notions). Now, what it is for a semantic theory for a natural language to be the correct one, is for there to be a semantic theory phrased in the meaning-building language, which (a) assigns to sentences of the natural language truth-conditions which fit with actual patterns of assent and dissent; and (b) is as syntactically simple as possible. (I defend this take on what Lewis is doing here).

Now, clearly we need to use some logical resources in constructing the semantic theory. Which should we allow? Sider's answer: the logically natural ones. But for the moment let's suppose we don't want to commit ourselves to logically natural kinds. Well, why don't we just stipulate that the meaning building language is going to contain this, that, and the next logical operator/connective? In the case of predicates, there's the worry that our meaning-building theory should contain all the empirical kinds there are or could be: since we don't know what these are, we need to give a general definition such as "the meaning building language will contain predicates for all and only natural kinds". But there seems no comparible reason not simply to lay it down that "the meaning building language will contain negation, conjunction and the existential quantifier).

Indeed, we could go one further, and simply stipulate that the existential quantifier it contains is the absolutely unrestricted one. The effect will be just like the one Sider proposes: this metasemantic proposal has a built-in-bias towards ascribing truly unrestricted generality to the quantifiers of natural language, because it is syntactically simpler to lay down clauses for such quantifiers in the meaning-building language, than for the restricted alternatives. You quantify over everything, not just concreta, because the semantic theory that ascribes you this is more eligible than one that doesn't, where eligibility is a matter of how simple the theory is when formulated in the meaning-building language just described.

Ok. So finally finally I get to the point. It seems to me that Field's form of Putnam's worries can be put to work here too. Let's grant that the metasemantic theory just described delivers the right results about semantic properties of my language; and shows my unrestricted quantification to be determinate. But why choose just that metasemantic theory? Why not, for example, describe a metasemantic theory where semantic properties are determined by syntactic simplicity of a semantic theory in a meaning building language where the sole existential quantifier is restricted to concreta? Maybe we should grant that our way picks out the semantic properties: but we've yet to be told why we should be interested in the semantic properties, rather than the semantic* properties delivered by the rival metasemantic theory just sketched. Metasemantic inscrutability threatens once more.

(I think the same challenge can be put to the Sider-style proposal: e.g., consider the Lewis* metasemantic theory whereby the meaning-building language contains expressions for all those entities (of whatever category) which are natural*: i.e. are the intersection of genuinely natural properties (emprical or logical) with restricted domain D.)

I have suspicians that metasemantic inscrutability will turn out to be a worrying thing. That's a substantive claim: but it's got to be a matter for another posting!

(Major thanks here go to Andy and Joseph for discussions that shaped my thoughts on this stuff; though they are clearly not to be blamed..).

Rigidity and inscrutability

2006-08-30T13:36:00.000+01:00

In response to something Dan asks in the comments in the previous post, I thought it might be worth laying out one reason why I'm thinking about "rich" forms of rigidity at the moment.

Vann McGee published a paper on inscrutability of reference recently. The part of it I'm particularly interested in deals with the permutation argument for radical inscrutability. The idea of the permutation arguments, in brief, is: twist the assignments of reference to terms as much as you like. By making compensating twists to the assignments of extensions to predicates, you'll can make sure the twists "cancel out" so that the distribution of truth values among whole sentences matches exactly the "intended interpretation". So (big gap) there's no fact of the matter whether the twisted-interpretation or rather the intended-interpretation is the correct description of the semantic facts. (For details (ad nauseum) see e.g. this stuff)

Anyway, Vann McGee is interested in extending this argument to the intensional case. V interesting to me, since I'd be thinking about that too. I started to get worried when I saw that McGee argued that permutation arguments go wrong when you extend them to the intensional case. That seemed bad, coz I thought I'd proved a theorem that they go over smoothly to really rich intensional settings (ch.5, in the above). And, y'know, he's Vann McGee, and I'm not, so default assumption was that he wins!

But actually, I think what he was saying doesn't call into question the technical stuff I was working on. What it does is show that the permuted interpretations that I construct do strange things with rigidity. Hence my now wanting to think about rigidity a little more.

McGee's nice point is this: if you permute the reference scheme wrt each world in turn, you end up disrupting facts about rigidity. To illustrate suppose that A is the actual world, and W a non-actual one. Choose a permutation for A that sends Billy to the Taj Mahal, and a permutation for W that sends Billy to the Great Wall of China. Then the permuted interpretation of the language will assign to "Billy" an intension that maps A to the Taj Mahal, and W to the Great Wall of China". In the familiar way, we make compensating twists to the extension of each predicate wrt each world, and the intensions of sentences turn out invariant. But of course, "Billy" is no longer a rigid designator.

(McGee offers this as one horn of a dilemma concerning how you extend the permutation argument to the intensional case. The other horn concerns permuting the reference scheme for all worlds at once, with the result that you end up assigning objects as the reference of e in w, when that object doesn't exist in w. I've also got thoughts about that horn, but that's another story).

McGee's dead right, and when I looked at (one form of) my recipe for extending the permutation argument to waht I called the "Carnapian" intensional case, I saw that this is exactly what I got. However, the substantial question is whether or not the non-rigidity of "Billy" on the permuted interpretation gives you any reason to rule out that interpretation as "unintended". And this question obviously turns on the status of rigidity in the first place.

Now, if the motivation for thinking names were rigid, were just that assigning names rigid extensions allows us to assign the right truth conditions to "Billy is wise", then it looks like the McGee point has little force against the permutation argument. Because, the permuted interpretation does just as well at generating the right truth conditions! So what we should conclude is that it becomes inscrutable whether or not names are rigid: the argument that names are rigid is undermined.

However, maybe there's something deeper and spookier about rigidity, above and beyond getting-the-truth-conditions-right. Maybe, I thought, that's what people are onto with the de jure rigidity stuff. And anyway, it'd be nice to get clear on all the motivations for rigidity that are in the air, to see whether we could get some (perhaps conditional) McGee-style argument against permutation inscrutability going.

p.s. one thing that I certainly hadn't realized before reading McGee, was that the permuted interpretations I was offering as part of an inscrutability argument had non-rigid variables! As McGee points out, unless this were the case, you'd get the wrong results when looking at sentences involving quantification over a modal operator. I hadn't clicked this, since I was working with Lewis's general-semantics system, where variables are handled via an extra intensional index: it had quite passed me by that I was doing something so kooky to them. You live and learn!

Varities of Rigidity

2006-08-29T13:49:00.000+01:00

This post over on metaphysical values by Ross Cameron has got me thinking about reference and rigidity.

There's a familiar distinction between singular terms that are "de facto" rigid and those that are "de jure" rigid. Paradigm example of the former: "the smallest prime"; paradigm example of the latter: "Socrates" (or, variables).

I'm not sure exactly how "de jure" rigidity is typically characterized. I've seen it done through slogans such as: what the name contributes to the truth conditions expressed by sentences in which it figures is just the object it stands for. I've seen it done like this: a name is de jure rigid if its rigidity is "due to" the semantics of language, and not to metaphysical facts about the world.
Those two definitions seem to come apart: "the actual inventer of the zip" is plausibly de jure rigid in the second, but not the first, sense.

Let's concentrate on the first sense of de jure rigidity (so a constraint on getting this right is that actualized descriptions won't count as de jure rigid in this sense). How could we tighten it up? Well, the task is pretty easy if your semantic theory takes the right shape. For example, suppose you have a semantic theory which in the first instance assigns structured propositions to sentences, and then says what truth conditions these propositions (and thus sentences) have. Then you can say precisely what it is for "name to contribute an object" to the truth conditions of sentences in which it figures: it's for you to shove an object into the structured prop associated with the sentence.

Notice two things:
(1) this is a semantic characterization: you can read off from the semantics of the language whether or not a given term is de jure rigid. (In this sense, it's like the characterization of "rigidity" as "referring to the same thing wrt every world").
(2) this is a local characterization: it only works if you're working within the right semantic framework (the structured-props one). You can't use it if you're working e.g. with Davidsonian truth theories, or possible world semantics.

This raises a natural question: how can we capture de jure rigidity in this, that and the next semantic framework? What interests me is what we can do to this end, working with a general semantics in the sense of Lewis (1970). I can't see any way to read off de jure rigidity from semantic theory.

But if we appeal to metasemantics (i.e. the theory of how semantic facts get fixed) it looks like we have some options. Suppose, for example you're one of the word-first guys: that is, like early Field, Fodor, Stalnaker et al, you think that the metasemantic story operates first at the level of lexical items (names, predicates), and then we can offer a reduction of the semantic properties of complex expressions (e.g. definite descriptions, sentences) to the semantic properties of their parts. The de jure rigid terms will be those whose semantic properties are fixed in the following way:

(1) term T refers (simpliciter) to an object X.
(2) term T has the as intension that function from worlds to objects, which, at each world w, will pick out the entity that is identical to what T refers to (simpliciter).

So here's my puzzle: this looks like a characterization that's turns essentially on the word-first metasemantic theory. Fair do's, if you like that kind of thing. But I'm more sympathetic to metasemantic theories like Lewis's, where the semantic properties of language get determined holistically. If you're an "interpretationist" (and if you haven't got the semantic characterizations to help you out, because you're working with a trad possible world semantics), is there any content in the notion of de jure rigidity? More on this to follow.

"Timid modal fictionalism"

2006-08-10T16:38:00.000+01:00

Just reading this very interesting paper by Brit Brogaard comparing timid modal fictionalism with "holistic ersatzism" a la Nolan, Sider, et al (I've just noted that Sider credits this paper by Leeds' very own Joseph Melia as one source of the idea). Still thinking about the content at the moment, something about the terminology in this area re-struck me.

As currently used, modal fictionalisms are positions that endorse something like the following biconditional

Possibly P iff According to the fiction of possible worlds, P*

Strong modal fictionalism is the natural thought that we see this biconditional as in the service of possibility-talk to talk about what holds according to a fiction. That is a fictionalism about modality.

Timid modal fictionalism is a view that denies this. Rather, we take modality as primitive (or reduce it in some other way), and read the biconditional left-to-right as partially defining the content of the fiction.

But is this really a modal fictionalism at all (in the sense of a fictionalism about modality)? When I first read this stuff, this issue threw me totally---I didn't understand what the point or purpose of timid fictionalism was meant to be---until I realized that it is really a kind of fictionalism about possibilia and worlds-talk. So it's not a modal fictionalism (/fictionalism about the modal operators), timid or otherwise; it's a possibilia-fictionalism, as strong as you like.

I guess I can see why Rosen chose those names (you might take the domain of modality to cover modal operators+worlds-talk+possiblia-talk, and then modal fictionalism is strong or timid to the extent that it's a fictionalism about all or only some of those bits of modal talk). The cogniscienti will be well aware of what's intended: but it wasn't what the terminology suggested to me at first.