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29 June, 2009

Monday Links

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.

Posted by Brian Weatherson at 4:29 am

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19 June, 2009

Friday Links

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…)

Posted by Brian Weatherson at 5:00 pm

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17 June, 2009

First and Second Order Epistemic Probability

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.

Posted by Brian Weatherson at 1:00 pm

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Induction and Supposition

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.

Induction and Supposition (PDF)

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

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.

Posted by Brian Weatherson at 11:49 am

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Wednesday Links

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

Posted by Brian Weatherson at 9:07 am

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16 June, 2009

Arché Scepticism Conference

The Arché Scepticism Conference 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.

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. In fact it wasn’t very close. The best title was to Elia’s reply to Anthony Bruekner. Any other participants want to add some more prizes from the conference?

Posted by Brian Weatherson at 10:04 am

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3 June, 2009

Reason and Persuasion

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

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.

Posted by Brian Weatherson at 2:27 pm

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