Brian Leiter has a summary of the recent rounds of faculty movement. Here was one interesting statistic from looking at the top 30 US departments.

There were 15 senior hires, 13 male and 2 female.

There were 13 junior hires, 6 male and 7 female.

Having 19 out of 28 hires by top 30 programs be male is not great, but it is promising that so many women are being hired at tenure-track level.

Where the junior hires came from is also interesting. The most successful program by this metric was UCLA, with 3 people hired. After that, NYU, Rutgers and MIT had two graduates each hired, with the other four coming from Princeton, Duke, Freie and Colorado.

Compass Articles

There have been several very high-quality articles come through Compass in recent weeks. As usual, clicking the links takes you to the free abstract. If you want to subscribe, please pressure your institution. (Subscriptions are, I’m told, growing at a very rapid pace for a new journal, so your institution may already subscribe.)

Tierney, Gott and the Philosophers

John Tierney today writes about Richard Gott’s Copernican principle. He has a little more on his blog, along with some useful discussion from Bradley Monton. The principle in question says that you should treat the time of your observation of some entity as being a random point in its lifetime. Slightly more formally, quoting Gott via a paper Monton wrote with Brian Kierland,

Assuming that whatever we are measuring can be observed only in the interval between times tbegin and tend, if there is nothing special about tnow, we expect tnow to be located randomly in this interval.

As Monton and Kierland note, we can use this to argue that the probability of

a tpast < tfuture < b tpast

is 1/ (a+1) – 1 / (b+1), where tpast is the past life-span of the entity in question, and tfuture is its future life-span. Most discussion of this has focussed on the case where a = b = 39. But I think the more interesting case is where a = 0 and b = 1. In this case we get the result that the probability of the entity in question lasting longer into the future than its current life-span is 1/2.

As a rule I tend to be very hostile to these attempts to get precise probabilities from very little data. I have a short argument against Gott’s rule below. But first I want to try a little mockery. I’d like to know anyone who would like to take any of the following bets.

Wikipedia’s History of the Internet dates the founding of the World Wide Web to around the early 1990s, so it is 15 or so years old. Gott’s formula would say that it less than 50/50 that it will survive until around 2025. I’ll take that bet if anyone is offering.

The iPhone has been around for about 3 weeks at this time of writing. Again, Gott’s formula would suggest that it is 50/50 that it will last for more than 3 weeks from now. Again, I’ll take that bet!

Finally, it has been about 100 years since there were over 4,000,000 people on the Australian continent. I’m unlikely to be around long enough to see whether there still will be more than 4,000,000 in 100 years time, but I’m a lot more than 50/50 confident that there will be. I will most likely be around in 10 years to see whether there are more than 4,000,000 people there in 11 years time. Gott’s formula says that the probability of that is around 0.9. I’m a little more optimistic than that, to say the least.

Anyway, here is the argument. Consider any two plays, A and B, that have been running for x and y weeks respectively, with x > y. And consider the following three events.

E1 = Play A is running
E2 = Play B is running
E3 = Plays A and B are both running

Note that E3 has been ongoing for y, just like E2. The Copernican principle tells us that at some time z in the future, the probabilities of these three events are

Pr(E1 at z) = x / (x + z)
Pr(E2 at z) = y / (y + z)
Pr(E3 at z) = y / (y + z)

Now let’s try and work out the conditional probability that A will still be running at z, given that B is running at z. That is, Pr(E1 at z | E2 at z). It is

Pr(E1 at z & E2 at z) / Pr(E2 at z)
= Pr(E3 at z) / Pr(E2 at z)
= (y / (y + z)) / (y / (y + z))
= 1

So using the Copernican formula, we can deduce that the conditional probability of A still running at z given that B is still running at z is 1. And that’s given only the information that z is in the future, and that A has been running at B. That is, to say the least, an absurd result. So I’m sure there is something deeply mistaken with the Copernican formula.

AAP 2007

Daniel and I gave our Backwards Explanation paper at the AAP. It survived well, even convinced a few people, so now it’s full steam ahead for its outing at the BSPC next month, where it will receive the critical attention of Alyssa Ney and Trenton Merricks. Unfortunately our presentation was scheduled up against a bunch of papers that we would have really liked to see. In fact, a downside of the AAP in general was the number of sessions which either had nothing I was particularly interested in or several very interesting papers.

My highlights from the AAP included Josh Parsons‘s talk on Assessment-Contextual Indexicality (draft available from his papers page), which sets out to see what the communicative point of assessment-context indexicals would be and why we might want a language to contain them, and Nic Southwood‘s paper which conjectured that the normativity of rationality is a matter of what we owe to ourselves. In question time I tried to persuade Nic that this view need not engender the rejection of naturalistic reductionism. Daniel Star also raised the question of what distinguises rationality from prudence, which also looks like a matter of what we owe to ourselves. There was an excellent discussion in both sessions.

Some photos should be on their way soon. (Dave Chalmers has posted some already here.)

Nice Doggie

Much friendlier than the Monaco doggies.

There was no way I was going to fly all the way to the south of France and not make (several versions of) that joke.

(Post edited to increase comedic clarity.)


I just found out from the blog of mathematician Terence Tao about Scholarpedia, which is apparently trying to fill in the space between Wikipedia and academic encyclopedias. The goal is to be more authoritative than Wikipedia, and more responsive and current than other academic encyclopedias. Right now, this space is filled quite well in philosophy by the Stanford Encyclopedia of Philosophy, though I can also imagine a use for something in which multiple people can update and edit articles. But right now, Wikipedia seems quite spotty on philosophy (it seems quite good on math and physics, though perhaps not so much so for people who aren’t already well-educated on the relevant topics).

Since it’s quite new, there’s a lot that’s still under development, and there are especially few articles on philosophy so far. But if philosophers get involved in this early enough, it could become quite useful. It looks like they’re commissioning an article on philosophy of mind from Jerry Fodor. The article on the mind-body problem looks like it needs some revision at the moment. And the article on intentionality looks like it could use some philosophical additions – right now it seems to define intentionality as a property only of brains. (Even if this is a technical use of the word, it seems relevant to mention the different but related technical use by philosophers.)

Also, it looks like the way policy is determined depends on who has made edits that previous moderators found useful, so making some good edits now could make sure that some philosophers have a say in how this develops.

A Counterexample to Conditional Countable Additivity

That title should draw the readers in! Here is something that I was prompted to think about by Timothy Williamson’s Analysis piece. Countable additivity is the following principle.

If S is a countable set of propositions, and any two members of S are incompatible, then the probability that one member of S is true is the sum of the probabilities of each member of S. In symbols, if the members of S are p1, p2, …, then Pr(p1 v p2 v …) = Pr(p1) + Pr(p2) + …

One consequence of countable additivity is that it is impossible for it to be certain that one member of S obtains while the probabilities of each member of S are zero. And that implies there cannot be an ‘even’ distribution of probabilities over a countable set. So if you believe countable additivity, you believe that there will be pretty serious constraints on what kinds of sets there can be ‘even’ distributions of probability over. (For example, there can’t be a way of selecting a real number at random in a way that for any two intervals of the same size, the probability of drawing the number from that interval would be the same. It is easy to show that violates countable additivity.) Can we find a counterexample to countable additivity that doesn’t posit such a dubious ‘even’ distribution? I think not, but we can find something similar.

Continue reading “A Counterexample to Conditional Countable Additivity”