I’ve been reading John Burgess’s book “Fixing Frege”:http://www.amazon.com/Fixing-Frege-Princeton-Monographs-Philosophy/dp/0691122318/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1205369760&sr=8-1, and I have to say, it’s one of the best books I’ve read in ages. Burgess’s subject is recent attempts to rescue from the inconsistent theory Frege proposed, theories that are consistent and strong enough in which to do serious mathematics. Burgess is somewhat sceptical of the project’s ultimate success, but the main aim here is to set out the state of play. And I would never have thought it was possible to do it as clearly as Burgess does. It’s quite hard, for instance, to give novice readers an approximate guide to what someone is saying, and to say quite clearly in what respects you are approximating. Usually if you can do that, you can state the non-approximate statement just as clearly. But Burgess does this kind of thing with apparent ease. Really highly recommended if you want to know what’s been going on in this field.

In other news, Vincent Hendricks’ new philosophy show on prime-time Danish TV has started, and you can see episodes “here”:http://www.ruc.dk/cuid/tankensmagt/. And you can see pictures of him receiving the Elite Science Prize from a famous Australian “here”:mms://media.xstream.dk/dk4_2006/eliteforsker_v_f_hendricks_2008.wmv.

I’ve been thinking again about the issues about knowledge justified belief and practical interests that I explored a bit in “this old paper”:http://brian.weatherson.org/cwdwpe.pdf. In that paper I have a rather complicated example that’s meant to show that a principle Jeremy Fantl and Matthew McGrath endorse, namely (PC) is false. Here is the principle.

(PC) S is justified in believing that _p_ only if S is rational to prefer as if _p_.

The rough outline of why (PC) is wrong is that whether one is rational to prefer as if _p_ might depend not only on whether one has justified attitudes towards _p_, but on whether one’s other attitudes are justified. Here is one example in which that distinction matters.

S justifiably has credence 0.99 in _p_. She unjustifiably has credence 0.9999 in _q_. (She properly regards _p_ and _q_ are probabilistically independent.) In fact, given her evidence, her credence in _q_ should be 0.5.

S is offered a bet that pays $1 if _p_v_q_ is true, and loses $1000 otherwise. Assume S has a constant marginal utility for money. It is irrational for S to prefer to take the bet. Given her evidence, it has a negative expected value. Given her (irrational) beliefs, it has a positive expected value, but if she properly judged the evidence for _q_, then she would not take the bet.

Of course, given _p_ the bet is just a free grant of $1, so she should take it.

So this is a case where it is not rational to prefer as if _p_. She should prefer to decline the bet, but to accept the bet given _p_.

If we accept (PC), it follows that S is not justified in believing _p_. But this conclusion seems wrong. S’s credence in _p_ is perfectly justified. And on any theory of belief that seems viable around here, S’s credence in _p_ counts as a belief. (On my preferred view, S believes _p_ iff she prefers as if _p_. And she does. The main rival to this view is the “threshold view”, where belief requires a credence above the threshold. And the usual values for the threshold are lower than 0.99.)

So this is a counterexample to (PC). In a recent paper, Fantl and McGrath defend a weaker principle, namely (KA).

(KA) S knows that _p_ only if S is rational to act as if _p_.

Is this case a counterexample to (KA) as well? (Assume that _p_ is true, so the agent could possibly know it.) I don’t believe that it is a counterexample. I think the things that an agent knows are the things she can use to frame a decision problem. If the agent knows _p_, then the choice between taking or declining the bet just is the choice between taking a dollar and refusing it. So she should take the bet. This would be irrational, so that must be the wrong way to frame the bet. Hence she doesn’t know that _p_.

The upshot of this is that these practical cases give us a new kind of counterexample to K = JTB. In the case I’ve described, the agent has a justified true belief that _p_, but does not know _p_.

Fresh off his winning the Elite Research Prize, Vincent Hendricks has “a TV show”:http://www.dk4.dk/?p=plug-side-item;id=2619. Here’s a rough-and-ready translation of the text on that link.

bq. The Power of Mind is a TV-series on philosophy which attempts to show how fundamental philosophical questions and issues show themselves everywhere – in science as well as everyday life.

bq. The show is hosted by Professor Vincent F. Hendricks who in each program will have a new guest in the studio to discuss ethics, religion, science, aestetics, politics mathematics, logic, knowledge and other themes making up the fundamental disciplines of philosophy.

And Joshua Knobe is featured on “Bloggingheads”:http://www.bloggingheads.tv/diavlogs/8796 discussing experimental philosophy.

Personally I much prefer getting philosophy in text form rather than over video or audio. But it’s very exciting to see philosophy being presented to a broader audience, particularly on prime time national TV as Vincent is doing!

Somewhat related to one another…

• Barnard Center for Research on Women report on Women, Work and the Academy
• Gender, Race and Philosophy: The Blog

A couple of congratulations, and an announcement.

• Congratulations first to Vincent Hendricks for winning the Elite Research Prize from the Danish government. See here for more info on the prize, and here for a very cool shot of Vincent receiving the prize from a well known Australian.
• Congratulations to Leeds for once again making some excellent junior hires. This year they’ve hired Jason Turner, currently at Rutgers, and Pekka Vayrynen, recently of Davis and before that Cornell. Leeds hiring record, especially their junior hiring record, in recent years is quite remarkable.
• Arche has two new PhD studentships, these attached to the newly funded Intuitions and Methodology project. They also have 6 other studentships currently being advertised. More details here.

I’ve been trying to think through how various puzzles in formal epistemology look from certain externalist perspectives. This is a little harder than I think it should be, because there’s so little written on what formal externalist epistemology might look like. (And I haven’t exactly done a great job of chasing down what has been written I guess.) Tim Williamson has quite a bit, though most of it doesn’t seem to have been absorbed into the formal mainstream.

So what I’m trying to figure out at the first stage is a very simple question. Bayesian epistemology is based around the idea of updating by conditionalising on evidence. So what should count as evidence, in the salient sense, for various kinds of externalists?
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As “Joe Salerno”:http://knowability.blogspot.com/2008/01/both-kinds-of-philosophy-country-and.html reports, John MacFarlane gave a really nice paper on “ought” (co-written with Nico Kolodny) at the recent Arizona Ontology Conference. In the questions Adam Elga raised a really nice case that I think deserves some thinking about. At the very least it makes me worried about my preferred theories of “ought”.

NB: John’s paper isn’t online yet, so I’m not linking to it, nor directly discussing it. The puzzle raised here is a puzzle for his particular view, but it’s also a puzzle for a view like I like, which is quite unlike John’s.
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Because we haven’t done these for a while.

• APA Pacific Schedule.
• Wo has a really great argument for the halfer solution to the Sleeping Beauty problem. This is one of those nice occasions where a blog post is more philosophically valuable than your average journal article.
• Brian Leiter has a nice thread going on recommendations for where to start reading about LEMMing philosophy.

I was looking around trying to find flights to the APA Pacific, and I noticed that it is possible to get Continental flights starting at the “Lower Manhattan Heliport”:http://en.wikipedia.org/wiki/Downtown_Manhattan_Heliport. They’re a little more expensive than just getting the train (or for that matter a cab) to Newark and flying from there. But not by as much as I expected – I think about $125 each way. And it would be pretty nice to simply fly back into the city after a long trip. Sadly, I’m not sure my research budget covers such little luxuries.

So as many of you will know, Ishani and I recently moved to start new jobs at Rutgers. One of the nice features of the move, which I hadn’t appreciated in advance, was how much more like home it would be. I knew about “Little Australia”:http://www.timeout.com/newyork/restaurants/chinatown-little-italy/3322/rubys, but I hadn’t quite appreciated how South Asian the area was. One cute sign of this is that the deli across the street from me features (enormous) trophies won in local cricket tournaments. Another was that the bus stop across from the department in New Brunswick is currently festooned with fliers recruiting players for the Rutgers Cricket Club.

If only I was half as good at playing cricket as watching it, I’d have plenty to do around here. As it is, I have to hope that the “Indian Premier League”:http://en.wikipedia.org/wiki/Indian_premier_league will be broadcast on some convenient American TV channel.