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!

It might already be apparent that I like anagrams. Well, I have just discovered this website. Which is much better at finding cool anagrams than trawling through all the hits on this website. Anyway, for your enjoyment I present you some anagrams of people’s names that I think are amusing.

• SEAMUS BRADLEY = A RUDE ASSEMBLY
• IMMANUEL KANT = AM MAN-LIKE NUT
• RENE DESCARTES = EARNED SECRETS
• WILLIAM HENRY GATES = THE MARGINALLY WISE
• ALBERT EINSTEIN = TEN ELITE BRAINS
• ARTHUR SCHOPENHAUER = SHEER CRAP HUN AUTHOR

I might even change the name of this blog to “a rude assembly”…

I posted a while ago about a conversation I had in a pub about global warming. Well, I was recently back in that pub, not even with the same people and we ended up talking global warming again, briefly. But that wasn’t what I wanted to write about today. We also talked about the future of gadgets. It’s a platitude now to say that several gadgets are converging into the smartphone: phone (obviously), camera, PDA, music player… The netbook will soon be included in this gadget. That is, if all you want from your netbook is a little browsing and the odd note-taking, then your next-gen smartphone will probably do this… Next steps might involve your smartphone acting as a credit card or a house key. Obviously there are security issues there, but why not have everything you normally carry in your pockets coalescing into one chunk of high-techery?

So what other classes of consumer electronics will there be? The home desktop computer, TV and entertainment systems (games consoles, hifi…) could converge into one super-entertainment hub. This big computer system could also then perform those tasks associated with the idea of “smart” houses that generate some part of their electricity themselves and sell any surplus back to the grid.

So we have two classes of consumer electronics. The super portable pocket tech-chunk, and the super-unportable home HAL. There is, I think a middle ground. There is room for a gadget that is portable, but that doesn’t need to fit in your pocket. This gadget would essentially be a convergence of netbook (if you actually use your netbook for stuff you can’t get out of your smartphone) the laptop proper and the ebook reader.

So the point of all this uninformed speculation is basically that I guess the netbook is a transient phase of consumer electronics. It’s a kind of middle ground between laptop and smartphone. People buy them either for portability or price. Eventually, smartphones will be smart enough to claw away some of the netbook market (those who want portability), and laptop/ebook reader type devices will fall in price enough to take the rest of the market (those who bought a netbook for the price).

So that’s how things will look some time in the future. But further in the future we will be able to PLUG COMPUTERS DIRECTLY INTO OUR BRAINS! THE SINGULARITY IS NEAR! AND THEN THE MACHINES TAKE OVER! STEP FORWARD JOHN CONNOR! AAAAAAH!

I’ve not posted for a while: I’ve been busy doing things other than procrastinating! OK that’s a lie, but the procrastination hasn’t taken the form of blog posts for a while. My website looks much the same as ever, but lots has changed under the hood, as it were. It now validates as XHTML and the columns are the same height and extend to accommodate as much text as needed. Hoorah. I also have an essay I’m rather proud of. (Actual work, shock horror!) It is probably over long and not all that much of it can be adapted to fit into my literature review, but I’m still happy with the (almost) finished product. On an unrelated note, here are some poems that appealed to the geek in me.

Here is the halting problem proven in poem form.

A poem composed entirely of punctuation. (I may have linked to this before.)

I remember a maths lecturer at Warwick starting a lesson by telling us:
Integral t-squared dt
from 1 to the cube root of 3
times the cosine
of three pi over 9
equals log of the cube root of ‘e’.

More maths limericks here.

A history of Western philosophy in limerick form you say? Well why not?

And of course there’s limerickdb. The marked geeky charm of the top 150 indicates that this project is from the chap behind xkcd.

And while it’s not a poem, it’s certainly the same ballpark.

And finally my own contribution thanks to getting bored during measure theory lectures. I give you a haiku about basic measure spaces:

A finite union
of disjoint rectangles is
elementary

I have tons more of these on some scrap of paper in my old notes folder. I also wrote a limerick about Rene Magritte once… (I rhymed “Rene Magritte” with “ceci n’est pas une pipe”)

Recently I’ve noticed a few newspaper headlines that are equal parts hilarious and intriguing. Maybe it’s because not much real news happens in the summer? Anyway, all of the following are genuine news stories, though I have neglected to record where I saw these actual headlines.

• Drunk badger disrupts traffic
• Ozzy Osbourne’s dog eaten by coyote
• Pablo Escobar’s fugitive hippo shot dead
• Man blows up apartment in attempt to repair bed

My favourite is that third one. It sounds like something straight out of The Day Today…

Hugh Pennington attributes the aphorism “Making predictions about the future is difficult, especially about the future” to Sam Goldwyn. (It’s in the second last paragraph) This is a phrase I’ve always thought was due to Neils Bohr, though a little digging shows that this phrase has been attributed to a number of other sources.

I’ve seen this happen with a couple of other pithy phrases. For example the phrase “The mere absurdity of a proposition is no guarantee that some philosopher will not endorse it” has been attributed to a number of people. The form of the sentence as it appears above is due to John Burgess. I’ve seen a similar sentiment attributed to Descartes and even to Cicero.

A third example is the idea of God as a circle whose centre is everywhere. I had it in my head that this was due to Spinoza, though it certainly seems to pop up in a variety of places…

I wonder what explains this multiple attribution? More examples or “canonical” attributions to any of these quotations are more than welcome!

When I went for an interview at Oxford for my undergrad degree one of the things we had to do was a kind of logic test. It had things like “All men wear hats, some men wear ties” and you were asked what it was possible to conclude from that. Presumably they were looking for something like “Some men wear ties and hats”. One of the questions was “Most men wear ties, most men wear hats”. I said that it wasn’t possible to conclude anything from this. But it was then explained to me that if hat-wearers and tie-wearers are both in a majority, then there must be some who are both: the proper conclusion is that “Some men wear ties and hats”.

“All men” is standing in for the universal quantifier (x) and “Some men” stands for the existential quantifier (Ex). But “Most men” is awkward to put in similar terms without resorting to some sort of logic enriched with predicates relating to numerical proportions. But that sort of “statistical logic” is too complex. The fact that some predicate applies not to all but to a majority of some domain is an easily understood fact that does not need a whole logic of proportions behind it. Let’s make “Most of” a new kind of quantifier: (Mx). What properties does (Mx) have?

This is the property my interviewer at Oxford was exploiting. If most x’s are P’s and most x’s are Q’s, then some x’s must be both.

These two properties simply say that if all men wear hats then most men wear hats and if most men wear hats then some men wear hats.

Do we really need a third quantifier here? Is there some way to express “most of” in terms of universal and existential quantifiers? I’m not sure there is. Here’s a first stab. When you say “(Mx)Px” what you are really saying is:

But that’s no good, because that expression still contains an “Mx”. We are kind of going beyond standard predicate logic, but only a little bit. Perhaps Mx shouldn’t be a quantifier, but a property of predicates? But I don’t think that is a particularly satisfying suggestion. A property of predicates would be a third-order entity, and that seems extravagant given the modest goal of formalising the easily understood concept of a majority.

Soon I’ll post again and discuss the “dual” of (Mx): “Only a few men wear hats” “Hat-wearers are in a minority”.

A note on the symbolism: I wanted to use and but I couldn’t think of a way to “invert” the letter “M” in a similar fashion. It shares the vertical symmetry of “A” but when reflected around a horizontal axis as is, you get a “W”, which is no good if the idea is to come up with a new symbol. So I reverted to old-style quantifiers. Suggestions regarding how to “symbolise” majority are most welcome.