Sound and Fury

I’ve just got back from a philosophy of probability conference in Oxford. It was very interesting.

Here are some thoughts I had about Hilary Greaves’ talk. The project is to flesh out an idea of epistemic rationality by analogy to practical rationality and practical decision theory. The idea is that in the “Cognitive Decision Theory” the sort of acts you are interested in are various beliefs you could adopt. Or various belief functions you could adopt. There is an idea of cognitive utility which is supposed to be a measure of how epistemically good you think a certain belief state is. Greaves and Wallace 2006 show that it is rational to update by conditionalisation when some conditions are satisfied.

The thing is, their theory starts by assuming that belief is represented by a probability function. This is a fairly standard, but perhaps too restrictive assumption. To paraphrase from Greaves’ talk yesterday: there are various intuitions we have about epistemic rationality. If we can derive lots of these from the theory, without building them in to the theory, then that’s a good thing. The less we have to start with and still get back all (or most) of our intuitions, the better.

So let’s apply that to the issue of presupposing that belief is probabilistically coherent. Why not start with some more general belief function set up and see under what circumstances probability measures are the uniquely rational way to structure your beliefs? The answer to this question is, I imagine, “because it’s really hard to prove anything about any more general framework”. True enough. But what about the case where belief is represented by a set of probability measures? How much of the argument of Greaves and Wallace goes through in the case where you just replace every instance of “probability measure, ” with “set of probability measures ” and replace every with .

A large spread of probability measures in an agent’s representor can be seen as indicating that agent’s desire to withhold judgment pending more conclusive evidence. I think that’s a valuable thing to want to model formally. The probability measure representation of belief requires that the agent has to be maximally probabilistically opinionated, which I don’t think is epistemically rational…

Presumably in this broader context it is no longer possible to prove that conditionalise is the best updating rule, but perhaps some analogue of conditionalise which incorporates a method for conditionalising on sets of probability measures still works.

Here’s a suggestion as to when it would be rational to have probabilistic credences. If your epistemic utility function were close to the scoring rules of Joyce 1998 then perhaps probabilism would be uniquely rational.

In general however, I think that as well as accuracy (which moves you towards probabilism), there is another source of epistemic utility. Or rather, a source of epistemic disutility which you want to avoid. Accuracy means you derive utility from being close to the truth. You derive disutility from being far from the truth.

Here’s a kind of geometrical analogy to illustrate the sources of utility in contention. Alice’s credence in an event is represented by some subinterval while Bob’s credence is some one point in the unit interval. The event is actually some value . While the vagueness of Alice’s credence is itself a source of epistemic disutility, the fact that is a good thing and gives Alice some positive utility. Bob, on the other hand, gets no “vagueness penalty”, but he does get some disutility proportional to how far wrong he was, i.e. proportional to . So, if an agent does not have enough information to pin down the actual value, it might be epistemically rational to take the hit from the “vagueness penalty” in order to avoid Bob’s “wrongness penalty”. In the same way, paucity of information might make vague interval valued credences preferable to probabilistic point values.

A long time ago, I decided to see if I could rewrite an essay I’d written as an undergrad in Open Office in LaTeX. I gave up soon after because (1) it was pointless since I had since then written a better paper (in LaTeX) on the same subject (the conventionality of spacetime geometry, if you must know) and (2) it was really irritating going through doing things like changing “…” into “…”  and so on.

Now, recently I was again recovering old ground and I wanted to write something similar to something I mentioned in an essay I wrote (in LaTeX) as an MA student (About coin flipping and partitioning the space of initial conditions…). I was surprised to discover that even that was laborious to update. I had to do things like go through and replace \citet and \citep with \textcite and \parencite as appropriate. This is because I moved to using biblatex rather than bibtex. I know about the natbib=true compatibility option, but it doesn’t behave properly all the time, particularly with multiple citations… And I had to add signposts to my \labels. That is, write \label{fig:zebra} rather than \label{zebra}. OK, “had to” is probably a bit strong. I wanted to, because I think it’s a good idea to signpost whether it’s a figure or an equation or a section or what have you that you’re referring to.

Today I discovered that it is reccommended that I use \(…\) instead of $…$ for inline maths in LaTeX. This means that even a paper I wrote a couple of months ago (about the principle of indifference) which I now want to work on again has to be updated in a non trivial way before I can use it. (This is a change I can’t just do Find and Replace for… On the other hand, it’s an aesthetic thing rather than a functionality thing. $…$ still works fine, but I like to follow proper practice…)

So I suppose that means I should stick to writing about new stuff rather than recovering old ground if I want to avoid having to laboriously fix minor pseudoproblems with my LaTeX code…

This story is thoroughly ridiculous.

I’m no anti-modern-art type, but Hirst is doing himself no favours with his reaction to this stuff. Seriously, grow a sense of humour.

I’ve recently started actually using twitter. It’s amusing. I like the hashtags thing. Two current favourites #hirstisacock and #lacklustreblockbusters

I recently changed from using boring old BibTeX to exciting new BibLaTeX. There have been some slight problems with the transition (aren’t there always!). First, citations started appearing as: “Name, Year” instead of “Name (Year)” like I wanted them to. I got around this by adding the option “natbib=true” to the \usepackage{biblatex} command and replaced all my \cite commands with \citet commands. Not the most elegant solution, I’ll grant you, but it works. So I was casting around for a better solution. I thought I’d try the APA standards packages. They didn’t work at all until I did a “sudo texhash” and after that they didn’t solve the problem. (Though they did fix an annoying bibliography quirk: the biblatex standard authoryear bibliography style writes things as “Author, Year, Paper-title In: Journal” The APA packages do at least get rid of that annoying “In:” Tomorrow I’m going to see if Harvard or Chicago bbx and cbx files can get me out of that mess.

Two other outstanding gripes with biblatex. First is that I can’t have “X et al” appear in the citation while still having “X, Y and Z” appear in the bibliography. This was standard with whatever set-up I was using before (natbib and chicago probably). This is because the “maxnames” option controls both citations and bibliography. Not ideal.

Second gripe, I want my bibliography to be titled “References” rather than “bibliography” I had a work around for this using the memoir class and bibtex, but it no longer works with biblatex. I suppose I will explore this issue further tomorrow.

And why am I spending so much time playing with my bibliography? Well, because it’s a superb displacement activity and I have a huge project due in next week, that’s why!