“Arché”:http://www.st-andrews.ac.uk/~arche now has “a blog”:http://www.archeans.blogspot.com/ where all members of Arché can post. (I’m not exactly sure who is a member in this context. I don’t think I’m one, though I have some connection to the vagueness project.) So far it’s just Robbie Williams and Roy Cook posting, but I’m sure there will be more to come.

bq. “Arché blog”:http://www.archeans.blogspot.com/

HT: “Carrie Jenkins”:http://longwordsbotherme.blogspot.com/2006/02/new-arche-blog.html

I’ve been thinking a bit recently about the following position, and I couldn’t see any obvious reason why it was _incoherent_, so I was wondering whether (a) it might be true or (b) I was missing something obvious about why it was incoherent. So feedback on it is more than welcomed.

Many Bayesians model rational agents using the following two principles

* At any moment, the agent’s credal states are represented by a probability function.
* From moment to moment, the agent’s credal states are updated by conditionalisation on the evidence received.

Of course these are idealisations, and many other people have been interested in relaxing them. One relaxation that has got a lot of attention in recent years is the idea that we should represent agents not by single probability functions, but by _sets_ of probability functions. We then say that the agent regards q as more probable than r iff for all probability functions Pr in the set, Pr(q) > Pr(r). This allows that the agent need not hold that q is more probable than r, or r more probable than q, or that q and r are equally probable, for arbitrary q and r. And that’s good because it isn’t a rationality requirement that agents make pairwise probability judgments about all pairs of propositions.

Now what effect on the model does this relaxation have on the principle about updating? The standard story (one that I’ve appealed to in the past) is that the ideal agent updates by conditionalising all the functions in the set. So if we write Pr_E for the function such that Pr_E(x) = Pr(x | E), and S is the set of probability functions representing the agent’s credal state before the update, then {Pr_E: Pr is in S} is the set we get after updating.

Here’s the option I now think should be taken seriously. Sometimes getting evidence E is a reason for the agent to have more determinate probabilistic opinions than she previously had. (I’m using ‘determinate’ in a sense such that the agent represented by a single probability function has maximally determinate probabilistic opinions, and the agent represented by the set of all probability functions has maximally indeterminate opinions.) In particular, it can be a reason for ‘culling’ the set down a little, as well as conditionalising on what remains. So we imagine that updating on E involves a two-step process.

* Replace S with U(S, E)
* Update U(S, E) to {Pr_E: Pr is in U(S, E)}

In this story, U is a function that takes two inputs: a set of probability functions and a piece of evidence, and returns a set of probability functions that is a subset of the original set. (The last constraint might want to be weakened for some purposes.) Intuitively, it tells the agent that she needn’t have worried that certain probability functions were the ones she should be using. We can put forward formal proposals for U, such as the following

bq. Pr is in U(S, E) iff Pr is in S and there is no Pr* in S such that Pr*(E) > 2Pr(E)

That’s just an illustration, but it’s one kind of thing I have in mind. (I’m particularly interested in theories where U is only knowable a posteriori, so it isn’t specifiable by such an abstract rule that isn’t particularly responsive to empirical evidence. So don’t take that example too seriously.) The question is, what could we say against the coherence of such an updating policy?

One thing we certainly can’t say is that it is vulnerable to a Dutch Book. As long as U(S, E) is always a subset of S, it is easy to prove that there is no sequence of bets such that the agent regards each bet as strictly positive when it is offered and such that the sequence ends in sure loss. In fact, as long as U(S, E) overlaps S, this is easy to show. Perhaps there is some way in which such an agent turns down a sure gain, though I can’t myself see such an argument.

In any case, the original Dutch Book argument for conditionalisation always seemed fairly weak to me. As Ramsey pointed out, the point of the Dutch Book argument was to dramatise an underlying inconsistency in credal states, and there’s nothing inconsistent about adopting any old updating rule you like. (At the Dutch Book symposium last August this point was well made by Colin Howson.) So the threshold for endorsing a new updating rule might be fairly low.

It might be that the particular version of U proposed above is non-commutative. Even if that’s true, I’m not 100% sure it’s a problem, and in any case I’m sure there are other versions of U that are commutative.

In the absence of better arguments, I’m inclined to think that this updating proposal is perfectly defensible. Below the fold I’ll say a little about why this is philosophically interesting because of its connection to externalist epistemologies and to dogmatism.
Continue reading →

“David Chalmers”:http://consc.net/chalmers/, who it seems now has a “wikipedia page”:http://en.wikipedia.org/wiki/David_Chalmers has posted a new paper.

bq. “Scott Soames’ Two-Dimensionalism”:http://consc.net/papers/soames2d.pdf

(Should that be Soames’ or Soames’s?) As the title suggests, Dave thinks Soames has drifted towards _endorsing_ a kind of two-dimensionalism. The paper is for an author meets critics session at the APA Central that will also feature Robert Stalnaker.

The “BBC reports”:http://news.bbc.co.uk/2/hi/science/nature/4679220.stm that Physicists in Cambridge now know a lot more about dark matter than they used to. Here’s Professor Gary Gilmore’s philosophical summary of the discoveries.

bq. These are the first properties other than existence that we’ve been able determine.

HT: “Huw Price”:http://www.usyd.edu.au/time/price/

The “announcement”:http://myweb.facstaff.wwu.edu/nmarkos/BSPC/BSPC7/BSPC7.htm and “call for papers”:http://myweb.facstaff.wwu.edu/nmarkos/BSPC/BSPC7/Guide.htm for this year’s Bellingham conference are now up. This is always one of the more enjoyable conferences of the calendar, as well as being philosophically enlightening, so I’d encourage everyone to inundate the “paper submittee”:http://www.sitemaker.umich.edu/egana with submissions.

I once tried to put together a philosophy trivia quiz together. It was mildly successful, but now that I’ve seen what a “really well done (if somewhat prurient) philosophy trivia quiz”:http://web.mit.edu/philos/www/triviaquiz06/ looks like, I’m glad I won’t be trying again.

This quiz really is the ultimate procrastination device. There are 138 questions to test your knowledge of the history of philosophy and the histories of some philosophers. (I got at least one right – I knew question 12!)

Anyone with sufficient time on their hands is welcome to “try the quiz”:http://web.mit.edu/philos/www/triviaquiz06/ and leave a note in comments saying how many they got right.

Hat tip: “Alex Byrne”:http://web.mit.edu/philos/www/byrne.html

The January 2006 edition of “SGRP”:http://stellar.mit.edu/S/project/sgrp/ (Symposia on Gender, Race and Philosophy) has been published. “SGRP”:http://stellar.mit.edu/S/project/sgrp/ features panel discussions of prominent papers on, as the title suggests, gender, race and philosophy. The papers discussed in this edition are:

* Elizabeth Anderson, “Uses of Value Judgments in Feminist Social Science: A Case Study of Research on Divorce” (Hypatia 19:1 (2004): 1-24.), with comments from Linda Alcoff, Sharyn Clough, Marianne Janack and Charles Mills
* Anita Superson, “Privilege, Immorality, and Responsibility for Attending to the “Facts about Humanity”” (Journal of Social Philosophy, v. 35, n. 1 2004, pp. 34-55), with comments from Louise Antony, Stephen Darwall, Laurence Thomas and Jennifer Uleman

This is the acknowledgments footnote from Timothy Williamson’s “Reference, Inference and the Semantics of Pejoratives”:http://www.philosophy.ox.ac.uk/faculty/members/docs/Reference.pdf.

bq. This paper discusses some of the same phenomena as the fascinating Kaplan 2004, and reaches conclusions that are in some respects quite similar (a difference concerning the notion of validity is noted below). One sign of my general debt to David Kaplan is the difficulty that I have in writing a paper without citing Kaplan 1989, a difficulty that I share with many other philosophers of language. I first encountered his work as an undergraduate, when I read Kaplan 1969, and was immediately impressed by his intellectual fertility, his rigour and his playfulness. Opponents of the scientific spirit in philosophy often associate it with humourless severity, sterility, and indifference to nuance and aesthetic value. David is a wonderful counterexample. Playfulness is one of the best antidotes to that toxin for the scientific spirit, the desire for salvation from philosophy. Precision forces one to respect the subtle distinctions that free-flowing ‘humanistic’ prose pours indifferently over. Rigour provides the constraints that distinguish creativity from arbitrary variation. By precedent rather than precept, logic teaches the value of elegance and a sense of form, even in the search for truth.

Online Papers in Philosophy is now being edited by Jonathan Ichikawa, a Brown University student who many of you will know through his online papers and posts to various blogs. The new address is here:

bq. “http://blogs.brown.edu/other/opp/”:http://blogs.brown.edu/other/opp/

And the new RSS feed is

bq. “http://blogs.brown.edu/other/opp/atom.xml”:http://blogs.brown.edu/other/opp/atom.xml

I’m *very* grateful to Jonathan for taking this over, as it was getting much too much for me, as you probably noticed from the pitiful amount I did on it last semester. So pop on “over there”:http://blogs.brown.edu/other/opp/ and thank Jonathan for taking it on.

While you are there, you might look at a new paper by Igor Douven and Timothy Williamson “Generalizing the Lottery Paradox”:http://www.philosophy.ox.ac.uk/faculty/members/docs/genlot2.pdf. They post a very general critique of a class of solutions to the lottery paradox. As far as I can tell, the criticism doesn’t touch the solution I put forward in “this paper”:http://brian.weatherson.org/cwdwpe.pdf, because my solution (a) has a restricted version of the conjunction principle and (b) because of the functionalism isn’t _structural_ in their sense. But a lot of my rivals do fall by the wayside…

“Brian Leiter”:http://leiterreports.typepad.com/blog/2006/01/secretly_reads_.html recently linked to “the rock star philosopher store”:http://www.cafepress.com/rsphilosopher. There is a lot of good stuff there, especially the titular joke. If you don’t know the joke, you should read “Ted’s paper on maximal properties”:http://fas-philosophy.rutgers.edu/sider/papers/maximal.pdf. (And note Ted’s snazzy icon.) The observations that maximal properties are extrinsic, and that most ordinary predicates denote maximal properties, are to my mind the biggest advances in metaphysics in the last few years, so reading this paper is worthwhile even if you’re looking for more than the context of a joke.