Monthly Archives: June 2007

The fuzzy link

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

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:

  1. Paradigmatically naturalistic facts (patterns of assent and dissent, causal relationships, dispositions, etc).
  2. Meaning-facts. (Of the form: “+” means addition, “67+56=123” is true, “Dobbin” refers to Dobbin.)
  3. 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)

  1. the meaning-facts to be exactly as we take them to be: i.e. arithmetical truths are determinate “to infinity”; and
  2. the corresponding linguistic norms are determinate “to infinity” as well; and
  3. (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?

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

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…

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


earths
Originally uploaded by blue sometimes

Hee hee

Supervaluations and revisionism once more

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.