## Thursday, December 21, 2006

### "Recent comments" function in blogger?

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!

## Tuesday, December 19, 2006

### Eliminating singular quantification

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?

## Thursday, December 14, 2006

### Talks and talks

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

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)

## Thursday, November 16, 2006

### Seduction and the sorites

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.)

## Friday, October 13, 2006

### Eliminating cross-level universals

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"!)

## Thursday, October 05, 2006

### Philosophy Dissertations

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.

## Wednesday, October 04, 2006

### Chances, counterfactuals and similarity

A happy-making feature of today is that Philosophy and Phenomenological 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

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.

## Monday, September 04, 2006

### Primitivism about vagueness

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

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!

## Sunday, September 03, 2006

### Ontic vagueness: the shape of the debate

(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.

## Friday, September 01, 2006

### An argument for conditional excluded middle.

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.)]

## Wednesday, August 30, 2006

### Existence and just more theory

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

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!

## Tuesday, August 29, 2006

### Varities of Rigidity

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.

## Thursday, August 10, 2006

### "Timid modal fictionalism"

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.

## Tuesday, August 08, 2006

### This is the best job in the world

.... because you can do it at the cricket.

England playing Pakistan. In the sun at Headingley (a short bus ride from the office). Sun shining, final day of the test match. Lots of support for both sides. A pile of philosophy papers, books lying around. Lots of interesting stuff about vagueness, composition, monism etc to puzzle about between wickets falling (which they did regularly). I'm particularly intrigued by this paper at the moment.

England won by about 130 runs just before tea, allowing time to come back and sort email and blog before coming home.

## Thursday, August 03, 2006

### Semantics for nihilists

Microphysical mereological nihilists believe that only simples exist---things like leptons and quarks, perhaps. You can be a mereological nihilist without being a microphysical mereological nihilist (e.g. you can believe that ordinary objects are simples, or that the whole world is one great lumpy simple. Elsewhere I use this observation to respond to some objections to microphysical mereological nihilism). But it's not so much fun.

If you're a microphysical mereological nihilist, you're likely to start getting worried that you're committed to an almost universal error-theory of ordinary discourse. (Even if you're not worried by that, your friends and readers are likely to be). So the MMN-ists tend to find ways of sweetening the pill. Van Inwagen paraphrases ordinary statements like "the cat is on the mat" into plural talk (the things arranged cat-wise are located above the things arranged mat-wise"). Dorr wants us to go fictionalist: "According to the fiction of composition, the cat is on the mat"). There'll be some dispute at this point about the status of these substitutes. I don't want to get into that here though.

I want to push for a different strategy. The way to do semantics is to do possible world semantics. And to do possible world semantics, you don't merely talk about things and sets of things drawn from the actual world: you assign possible-worlds intensions as semantic values. For example, the possible-worlds semantic value of "is a cordate" is going to be something like a function from possible worlds to the things which have hearts in those worlds. And (I assume, contra e.g. Williamson) that there could be something that doesn't exist in the actual world, but nevertheless has a heart. I'm assuming that this function is a set, and sets that have merely possible objects in their transitive closure are at least as dubious, ontologically speaking, as merely possible objects themselves.

Philosophers prepared to do pw-semantics, therefore, owe some account of this talk about stuff that doesn't actually exist, but might have done. And so they give some theories. The one that I like best is Ted Sider's "ersatz pluriverse" idea. You can think of this as a kind of fictionalism about possiblia-talk. You construct a big sentence that accurately describes all the possibilities. Statements about possibilia will be ok so long as they follow from the pluriverse sentence. (I know this is pretty sketchy: best to look at Sider's version for the details).

Let's call the possibilia talk vindicated by the construction Sider describes, the "initial" possibila talk. Sider mentions various things you might want to add into the pluriverse sentence. If you want to talk about sets containing possible objects drawn from different worlds (e.g. to do possible world semantics) then you'll want to put some set-existence principles into your pluriverse sentence. If you want to talk about transworld fusions, you need to put some mereological principles into the pluriverse sentence. If you add a principle of universal composition into the pluriverse sentence, your pluriverse sentence will allow you to go along with David Lewis's talk of arbitrary fusions of possibilia.

Now Sider himself believes that, in reality, universal composition holds. The microphysical mereological nihilist does not believe this. The pluriverse sentence we are considering says that in the actual world, there are lots of composite objects. Sider thinks this is a respect in which it describes reality aright; the MMN-ist will think that this is a respect in which it misdescribes reality.

I think the MMN-ist should use the pluriverse sentence we've just described to introduce possibilia talk. They will have to bear in mind that in some respects, it misdescribes reality: but after all, *everyone* has to agree with that. Sider thinks it misdescribes reality in saying that merely possible objects, and transworld fusions and sets thereof, exist---the MMN-ist simply thinks that it's inaccuracy extends to the actual world. Both sides, of course, can specify exactly which bits they think accurately describe reality, and which are artefactual.

The MMN-ist, along with everyone else, already has the burden of vindicating possibilia-talk (and sets of possibilia, etc) in order to get the ontology required for pw-semantics. But when the MMN-ist follows the pluriverse route (and includes composition priniciples within the pluriverse sentence), they get a welcome side-benefit. Not only do they gain the required "virtual" other-worldly objects; they also get "virtual" actual-worldy objects.

The upshot is that when it comes to doing possible-world semantics, the MMN-ist can happily assign to "cordate" an intension that (at the actual world) contains macroscopic objects, just as Sider and other assign to "cordate" an intension that (at other worlds) contain merely possible objects. And sentences such as "there exist cordates" will be true in exactly the same sense as it is for Sider: the intension maps the actual world to a non-empty set of entities.

So we've no need for special paraphrases, or special-purpose fictionalizing constructions, in pursuit of some novel sense in which "there are cordates" is true for the MMN-ist. The flipside is that we can't read off metaphysical commitments from such true existential sentences. Hey ho.

(cross-posted on Metaphysical Values)

## Friday, July 14, 2006

### Illusions of gunk

I've just finished revisions to my "Illusions of gunk" paper. This defends microphysical mereological nihilists (folks who think that the only particulars that exist are microphysical simples) against Ted Sider's argument that they run into gunky trouble.

The paper is up here, and the abstract follows:

The possibility of gunk has been used to argue against mereological nihilism. This paper explores two responses on the part of the microphysical mereological nihilist: (1) the contingency defence, which maintains that nihilism is true of the actual world; but that at other worlds, composition occurs; (2) the impossibility defence, which maintains that nihilism is necessary true, and so gunk worlds are impossible. The former is argued be ultimately unstable; the latter faces the explanatorily burden of explaining the illusion that gunk is possible. It is argued that we can discharge this burden by focussing on the contingency of the microphysicalist aspect of microphysical mereological nihilism. The upshot is that gunk-based arguments against microphysical mereological nihilism can be resisted.

One thing that I argue for in the paper is that microphysical mereological nihilists are committed to a more far reaching error-theory than you might initially have thought: not only are there no cats and dogs (or compound objects), but there could not have been cats and dogs (or compound objects). I mention in a footnote that this seems to me a real problem for the "counterfactual" fictionalist strategy that Cian Dorr favours to explicate nihilism. Basically, if "cat" isn't even assigned an intension (as I argue), then "were things to compose but the arrangement of subatomic particles to be exactly as it actually is, then there'd be cats" will be false.

There are problems for alternatives to Dorr's account too (e.g. I never understood what sense Van Inwagen is supposed to make out of English plural sentences such as "some authors admire only one another"). One future project of mine is to develop a way of doing vanilla possible world semantics in a nihilist world, by tweaking the story about how possible worlds, and possibilia, are constructed...

## Wednesday, July 05, 2006

### Phil studies

Those nice people at Philosophical Studies (NB: no url link, because I haven't found a way to link to specific springerlink journals) have just let me know that they will publish my paper on conversation and conditionals. What makes me particularly happy about this is that I whiled away many happy hours as a phD student playing "hunt the Stalnaker explanation" (Agustin Rayo being the guilty party who introduced me to this strangely addictive game...)

The idea is simple. The idea is to explain as many philosophical puzzles as possible using Bob Stalnaker's conversational dynamics. The consummate player is, of course, Stalnaker himself: read the papers in his Context and Content for the paradigmatic examples, including e.g. compelling explanations of what's going on with Kripke's puzzling Pierre, negative existentials, Referential/attributive distinction.

At the time, I was particularly keen to use it to try and explain some stuff about de re belief reports (for the cogniscienti: I was looking at Kaplan's "youngest spy" counterexample to Quine's principle of universal exportation). To my regret, I couldn't make it work, and fell back in the end on using Gricean stuff rather than Stalnakerian stuff in the paper that resulted (and I always find relying on Grice unsatisfying, since I never understood where the various "cooperative maxims" come from).

Anyway, the conditionals paper makes use of the Stalnakerian framework to explain a couple of puzzles about conditionals: in particular, showing how to explain away "Sobel" and "reverse Sobel sequences" on any account of conditionals at least as strong as the material conditional; and showing how to explain away the "Gibbard phenomenon" on my favoured implementation of the Stalnaker-style "closest-worlds" account of the semantics of the indicative conditional.

### folding up posts on blogger

I've been playing around with a blogger hack that allows short summaries of posts to be displayed on the main blog page: with full posts appearing when you view the main post (they appear "below the fold".

It seems nicer to me: maybe others disagree. The only bit that irritates me is that you don't get any indication, from viewing what appears on the main page, whether or not there's extra content "below the fold". So you have to write this in yourself.

## Thursday, June 29, 2006

### Against against against vague existence

Carrie Jenkins recently posted on Ted Sider's paper "Against Vague Existence".

Suppose you think it's vague whether some collection of cat-atoms compose some further thing (perhaps because you're a organicist about composition, and it's vague whether kitty is still living). It's then natural to think that there'll be corresponding vagueness in the range of (unrestricted) first order quantifier: it might be vague whether it ranges over one billion and fifty five thing or one billion and fifty six things, for example: with the putative one billion and fifty-sixth entity being kitty, if she still exists. Sider thinks there are insuperable problems for this view; Carrie thinks the problems can be avoided. Below the fold, I present a couple of problems for (what I take to be) Carrie's way of addressing the Sider-challenge.

Sider's interested in "precisificational" theories of vagueness, such as supervaluationism and (he urges) epistemicism. The vagueness of an expression E consists in there being multiple ways in which the term could be made precise, between which, perhaps, the semantic facts don't select (supervaluationism), or between which we can't discriminate the uniquely correct one (epistemicism). (On my account, ontic vagueness turns out to be precisificational too). The trouble is alleged to be that vague existence claims can't fit this model. One underlying idea is that multiple precifications of an unrestricted existential quantifier would have to include different domains: perhaps precisification E1 has domain D1, whereas precisification E2 has domain D2, which is larger since includes everything in D1, plus one extra thing: kitty.

But wait! If it is indeterminate whether kitty exists, how can we maintain that the story I just gave is true? When I say "D2 contains one extra thing: kitty", it seems it should be at best indeterminate whether that is true: for it can only be true if kitty exists. Likewise, it will be indeterminate whether or not the name "kitty" suffers reference-failure.

Ok, so that's what I think of as the core of Sider's argument. Carrie's response is very interesting. I'm not totally sure whether what I'm going to say is really what Carrie intends, so following the standard philosophical practice, I'll attribute what follows to Carrie*. Whereas you'd standardly formulate a semantics by using relativized semantic relations, e.g. "N refers to x relative to world w, time t, precification p", Carrie* proposes that we replace the relativization with an operator. So the clause for the expression N might look like: "At world w, At time t, At precisification p, N referes to x". In particular, we'll say:

"At precisfication 1, "E" ranges over the domain D1;
At precisification 2, "E" ranges over the domain D1+{kitty}."

In the metalanguage, "At p" works just as it does in the object language, binding any quantifiers within its scope. So, when within the scope of the "At precisification 2" operator, the metalinguistic name "kitty" will have reference, and, again within the scope of that operator, the unrestricted existential quantifier will have kitty within its range.

This seems funky so far as it goes. It's a bit like a form of modalism that takes "At w" as the primitive modal operator. I've got some worries though.

Here's the first. A burden on Carrie*'s approach (as I'm understanding it) will be to explain under what circumstances a sentence is true. usually, this is just done by quantification into the parameter position of the parameterized "truth", i.e.

"S" is true simpliciter iff for all precisifications p, "S" is true relative to p.

What's the translation of this into the operator account? Maybe something like:

"S" is true simpliciter iff for all precisifications p, At p "S" is true.

For this to make sense, "p" has to be a genuine metalinguistic variable. And this undermines some of the attractions of Carrie*'s account: i.e. it looks like we'll now the burden of explaining what "precisifications" are (the sort of thing that Sider is pushing for in his comments on Carrie's post). More attractive is the "modalist" position where "At p" is a primitive idiom. Perhaps then, the following could be offered:

"S" is true simpliciter iff for all precisification-operators O, [O: "S" is true].

My second concern is the following: I'm not sure how the proposal would deal with quantification into a "precisification" context. E.g. how do we evaluate the following metalanguage sentence?

"on precisification 2, there is an x such that x is in the range of "E", and on precisification 1, x is not within the range of "E""

The trouble is that, for this to be true, it looks like kitty has to be assigned as the value of "x". But the third occurence is within the scope of "on precisification 2". On the most natural formulation, for "on precisification 2, x is F" to be true on the assignment of an object to x, x will have to be within the scope of the unrestricted existential quantifier at precisification 1. But Kitty isn't! There might be a technical fix here, but I can't see it at the moment. Here's the modal analogue: let a be the actual world, and b be a merely possible world where I don't exist. What should the modalist say about the following?

"At a, there is an object x (identical to Robbie) and At b, nothing is identical to x"

Again, for this to be true, we require an open sentence "At b, nothing is identical to x" to be true relative to an assignment where some object not existing at b is the value of "x". And I'm just not sure that we can make sense of this without allowing ourselves the resources to define a "precisification neutral" quantifier within the metalanguage in reference to which Sider's original complaint could be reintroduced.