Four quick notes.

1. Jeremy Pierce (Syracuse, philosophy) has joined the tide moving from Blogger to MT. His blog is now at: http://parablemania.ektopos.com/.

2. I’ve updated the What I’m Listening To to reflect this Saturday’s SFA show. I am a little excited about this.

3. I didn’t actually watch the half-time show last night, so I didn’t see the big story until I read this morning’s newspapers. The viewer reaction on CNN this morning was hilarious. You’d think Janet and Justin had sex on stage from how outraged some viewers were about the ‘R-ratedness’ of it all.

3a. Go Pats! WooHoo!

4. This is probably one of my craziest philosophical ideas ever, but maybe I can get away with it at the end of a blogpost. It’s a little reflection on the Hansel and Gretel case in Frank, Adam and John’s Bayesianism paper.

Hansel and Gretel start off with a flat probability distribution over a unit square, and over each of the lines within it, and get led by familiar methods to beliefs are problematic at best, and certainly conflict with some widely accepted principles. (Principles like: don’t have beliefs that lead to sure loss.) Frank et al want to either blame the methods, or say that the final beliefs do not violate any epistemic principles. (Well, that’s a crude summary, but close enough for present purposes.) They don’t consider whether the right thing to do would be to blame Hansel and Gretel’s priors.

There is precedent for this. Many of us (though far from all) think that flat distributions over countable sets are bad because they violate similar principles to those Hansel and Gretel end up violating. We respond by adding an axiom, the axiom of countable additivity, that among other things rules out priors with flat distributions over such sets. Is there anything to be said for thinking that Hansel and Gretel’s case shows that we must add yet more axioms to rule out the kind of violation they make, and in particular to rule out a certain kind of flat distribution over continuum-sized sets? My initial reaction is that such a restriction is at least as plausible as the other things we can say here. If that’s wrong, should we (as the paper kinda suggests) think that the usual argument for countable additivity is also wrong?