I’ve been meaning to post more over the last week, but I’ve been busy getting ready for my presentation to the “Arché Summer School”:http://www.st-andrews.ac.uk/~arche/ss2009/.

• Speaking of summer schools, the “North American Summer School in Logic, Language and Information”:http://www.indiana.edu/~nasslli/ is returning after a 6 year hiatus. It will be at Indiana in 2010, and two of my esteemed colleagues are on the program committee. Anyone who is interested in presenting a course should get in touch with the organisers.
• I’ve tried to add a Twitter feed to the sidebar. It is meant to track @twtar, which is the Twitter account I opened for TAR. But the software I’m using seems slow and buggy, and I might remove that feed if things don’t improve soon.
• Speaking of the Arché Summer School, I’m about to head off to see “Jonathan Ichikawa”:http://jonathanichikawa.net/ talk about “thought experiments”:http://jonathanichikawa.net/files/summerschool.pdf. First of many fun talks this week I hope!

I’m about to head away for the weekend, so I won’t be responding to (or moderating) comments for the next few days unless I spend some of my vacation time on the internet. (That’s not to say I’ll actually be off the blog…)

• Sinan Dogramaci has “a paper”:http://www.sinandogramaci.net/Site/Sinan_Dogramaci_files/Unabridged,%20March%2017th.pdf forthcoming in Noûs using a similar kind of proof to the one I used in “Induction and Supposition”:http://brian.weatherson.org/IaS.pdf. So I’ve updated my paper to note that he was first! Sinan disagrees with me about where the proof fails. I think it fails when we try to make a statistical inference inside the scope of a supposition. He thinks it fails when we do ∀-introduction in a proof that includes non-deductive steps. So I’ve also extended the discussion in my paper of why I think I’ve diagnosed the error correctly. I don’t think I’ve got to the heart of what Sinan says, but I hope I’ve at least improved my paper.
• I have two posts up at the Arché Methodology Blog. One is on “thought experiments and fictions”:http://www.st-andrews.ac.uk/~armeth/2009/06/two-views-on-thought-experiments/, the other on whether philosophy is inductive or deductive
• Richard Dietz and Igor Douven are putting on a conference on “Conditionals and Conditionalization”:http://formalphilosophy.org/node/333 in Leuven on September 4-6.
• A new “European Journal for Philosophy of Science”:http://listserv.liv.ac.uk/cgi-bin/wa?A2=ind0906&L=philos-l&T=0&P=24272 is being established, though I’m not sure when it will start taking submissions.

Here is an interesting way of making explicit some of the tensions within an externalist account of evidence. I’m drawing here on some points Roger White made at the Arché Scepticism Conference, though I’m not sure Roger is perfectly happy with this way of putting things.

In what follows I’ll use ‘Pr’ for the evidential probability function (and hence assume that one exists), E(a) as a description for a’s evidence, Cr(p, a) for a’s credence in p, and Exp(X, a) as the expected value of random variable X according to probability function Pr conditioned on E(a). Then the following three statements are inconsistent. [There used to be a typo in the previous sentence, which Clayton noted in comments.]

1. If a is perfectly rational, then Cr(p, a) = Pr(p | E(a)).
2. If a is perfectly rational, then Cr(p, a) = Exp(Pr(p| E(a)), a).
3. It is possible for a to be perfectly rational, and for Pr(p | E(a)) to not equal Exp(Pr(p| E(a)), a).

The intuition behind 1 is that for a rational agent, credence is responsive to the evidence.

The intuition behind 2 is that for a rational agent, their credences match up with what they think their credences ought to be. If 2 fails, then rational agents will find themselves taking bets that they (rationally!) judge that they should not take. Roger’s paper at the conference did a really good job of bringing out how odd this option is.

The intuition behind 3 is that not all perfectly rational agents know what their evidence is. So if p is part of a’s evidence, but a does not know that p is part of their evidence, then Pr(p | E(a)) will be 1, although Exp(Pr(p| E(a)), a) will be less than 1. I believe Williamson has some more dramatic violations of this principle in intuitive models, but all we need is one violation to get the example going.

Given that the 3 are inconsistent, we have an interesting paradox on our hands. I think, despite its plausibility, that the thing to give up is 2. Credences should be responsive to evidence. If you don’t know what your evidence is, you can’t know that you’re being responsive to evidence, i.e. being rational. It might be that all of the possible errors are on one side of the correct position. In that case, your best estimate of what you should do will diverge from what you should do. So anyone who thinks evidence isn’t always luminous will think that we will have oddities like the oddities used to motivate 2. So I think we have to learn to live with its failures.

Everyone at the conference seemed to assume that that’s also what Williamson would agree, and say that 2 is what should be given up. I’m not actually sure, as a matter of Williamson interpretation, that that’s correct. Williamson denies that we can interpret evidential probabilities in terms of credences of a hypothetically rational agent. It might be that he would give up both 1 and 2, and deny that there is any simple relationship between rational credence and evidential probability. Or he might accept that Exp(Pr(p| E(a)), a) is a better guide to rational credence than Pr(p | E(a)).

Whatever way we look at it though, I think that this is an interesting little paradox, and one of several reasons I liked the conference at the weekend was that I realised it existed.

Inspired by some things Stewart Cohen and Jonathan Vogel said at the weekend’s scepticism conference, I’ve written a short note on the intersection of inductive reasoning and suppositional reasoning.

bq. “Induction and Supposition”:http://brian.weatherson.org/IaS.pdf (PDF)

Here’s the first paragraph, which gives you a flavour of what I’m arguing against.

bq. Here’s a fairly quick argument that there is contingent a priori knowledge. Assume there are some ampliative inference rules. Since the alternative appears to be inductive scepticism, this seems like a safe enough assumption. Such a rule will, since it is ampliative, licence some particular inference From A infer B where A does not entail B. That’s just what it is for the rule to be ampliative. Now run that rule inside suppositional reasoning. In particular, first assume A, then via this rule infer B. Now do a step of →-introduction, inferring A → B and discharging the assumption A. Since A does not entail B, this will be contingent, and since it rests on a sound inference with no (undischarged) assumptions, it is a priori knowledge.

It has been a while since we’ve had a links post.

• The Stanford Encyclopaedia of Philosophy has started up a “Friends of the Stanford Encyclopaedia Society”:https://leibniz.stanford.edu/friends/. Membership is very cheap, and with it you get access to professionally styled PDFs of SEP articles. And, of course, you’re supporting a good cause.
• There has been a lot of philosophical interest happening over at Crooked Timber recently. I wanted to particularly note “Daniel’s post on throwing eggs at BNP leaders”:http://crookedtimber.org/2009/06/12/the-bnp-and-the-egging-laffer-curve/. Whatever you think of the conclusion, and I think I’m a lot more happy with throwing eggs at fascists than most of the commentators are, the post makes some very insightful points about the role of authority in political discourse. A lot of philosophers have extremely simplistic views about the dynamics of authority in modern societies, and thinking hard about cases like this one is one way to have less simplistic views.
• Robbie Williams has an “excellent paper”:http://www.personal.leeds.ac.uk/%7Ephljrgw/wip/scoring.pdf (PDF) on generalising Joyce’s accuracy argument for probabilism to non-classical contexts. Among other things, the paper has a very nice demonstration of what’s going on in the classical version of the argument. But I’m really excited about the non-classical parts. There is going to be some really interesting work on non-classical probability theory over the next few years.
• Finally, “Cosma Shalizi on Bayesian statistics”:http://cscs.umich.edu/~crshalizi/weblog/612.html, via Brad DeLong.

The “Arché Scepticism Conference”:http://www.st-andrews.ac.uk/~arche/bk2009/ held over the weekend was a great success. Thanks to all the organisers, presenters, commentators and questioners for a great learning experience. For a real-time recap, see the conferences “Twitter feed”:http://twitter.com/#search?q=%23asc2009.

I’ll be posting my paper as soon as I’ve figured out how to respond to objections Martin Smith and Elia Zardini. That should be sometime in 2011-12. (I suspect a few other paper givers will be in the same position when it comes to dealing with objections Elia raised.)

The best slides from the conference were by “Roger White”:http://twitpic.com/7dinp. In fact it wasn’t very close. The best title was to Elia’s “reply to Anthony Bruekner”:http://twitpic.com/7dd51. Any other participants want to add some more prizes from the conference?

John Holbo and Belle Waring, who many of you will know from Crooked Timber and elsewhere, have a new book up in PDF format.

• Reason and Persuasion

The book contains translations of three Platonic dialogues, detailed commentaries on each of them, and illustrations! John has been using versions of it for teaching purposes for several years, and the book looks like it could be very useful for teaching (and research!) purposes.