“Brian Leiter”:http://leiterreports.typepad.com/blog/2007/07/summary-of-majo.html 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.

“John Tierney”:http://www.nytimes.com/2007/07/17/science/17tier.html?8dpc=&_r=1&oref=slogin&pagewanted=all today writes about Richard Gott’s Copernican principle. He has a little more on “his blog”:http://tierneylab.blogs.nytimes.com/2007/07/16/how-nigh-is-the-end-predictions-for-geysers-marriages-poker-streaks-and-the-human-race/#more-103, along with some useful discussion from “Bradley Monton”:http://www.colorado.edu/philosophy/fac/monton.html. 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”:http://spot.colorado.edu/~monton/BradleyMonton/Articles_files/future%20duration%20pq%20final.pdf Monton wrote with Brian Kierland,

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

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

bq. a t_past < t_future < b t_past

is 1/ (a+1) – 1 / (b+1), where t_past is the past life-span of the entity in question, and t_future 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”:http://en.wikipedia.org/wiki/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”:http://en.wikipedia.org/wiki/Demography_of_Australia#Historical_population_estimates 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.

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.

bq. 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.

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I used to read _Analysis_ more or less from cover-to-cover when it came out. For various reasons I’ve stopped doing that, largely because it fell down the priority list than because it seemed like a bad idea. Looking at the latest issue (contents below fold), it seems I might want to return to my old habits. I wish the journal wasn’t so male-dominated, but otherwise it is one of the most valuable philosophy journals we have.

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As many of you will know, Ishani and I were offered positions at Rutgers a while ago. And after a somewhat long negotiating period, we’ve decided to accept them. So we’ll be starting at Rutgers in January 2008.

Part of the reason this was a long negotiation was that Cornell is a pretty good place to work too (to say the least). If you’re reading this blog you probably know how good the faculty are, and the students are really superb. (As many of you will find out as they storm the job market over the next few years.) So I wasn’t exactly feeling a need to leave.

But still, we’re excited about moving to Rutgers. It’s a department that is strong, both at faculty and grad student level, in so many different areas. Having philosophy of language colleagues like Jeff King, Ernie Lepore and Jason Stanley will be a blast. And Rutgers is still the place to be for epistemology. And I’m looking forward to being reunited with former colleagues like Ernie Sosa and Dean Zimmerman. And the NYC/NJ area is home to an insane percentage of the philosophers I’ve learned the most from, and am continuing to learn from. So I’ve both got a lot to look forward to.

I could write a long post on the horse race aspects of this move. (Scarlet Knights trade Arntzenius and Sider for King, Lin, Maitra and Weatherson; Big Red trades Irwin and … you get the idea.) But as fun as that would be, perhaps it is best left for another day.

Ishani and I have each been in upstate NY for five years, so leaving is a big deal. There’s a lot to like about the area, both philosophically and geographically. I think the departments in this area have some very underrated philosophers, many of whom I’ve gotten to know well over the five years here. So as excited as we are about the new jobs, we’ll miss a lot of people here as well.

When I posted my “conditionals and indexical relativism”:http://brian.weatherson.org/CaIR.pdf paper the othe week, I mentioned that part of the motivation for the view came from Tamina Stephenson’s work. Along these lines, I have two updates to report. First, she has a new version of the paper where PRO_J is introduced.

bq. “Judge Dependence, Epistemic Modals, and Predicates of Personal Taste”:http://web.mit.edu/tamina/www/em-ppt-revised-6-05-07.pdf

Second, she has a “handout from a talk on conditionals and relativism”:http://web.mit.edu/tamina/www/CLS-handout.pdf. Happily, it is a slightly different version of relativism to mine. (Diversity is always a philosophic boon!) She takes the propositions expressed by conditionals to be sets of world-judge pairs, and uses this to explain what’s going on in Gibbardian standoff. I think these propositions are (or determine) sets of possible worlds, and I’m not sure there is anything in Gibbardian standoffs that our semantics needs to explain.

Anyway, both links are highly recommended.

In a recent “post about citing papers on the web”:http://metaphysicalvalues.blogspot.com/2007/06/ethics-of-citation.html, Ross Cameron drew the following conclusion.

bq. I’m tempted to think that if you put a paper up on the web, that’s to put it in the public domain, and it’s no more appropriate to place a citation restriction on such a paper than it is on a paper published in a print journal. I’m even tempted to think that conference presentations can be freely cited; i.e.that I shouldn’t have to seek Xs permission to refer in one of my papers to the presentation X gave.

The particular issue here is what to do about papers that the author posts and says at the top “Please don’t quote or cite”. (You occasionally see ‘don’t circulate’ as well, which is a little odd.) I’m not sure how common these notes are outside philosophy, but they are pretty common on philosophy papers posted on people’s websites. Now on the one hand, there is something to be said for following people’s requests like this.

On the other hand, as Ross notes, the requests can lead to annoying situation. One kind of case is where the reader notices an important generalisation of the paper’s argument. Another case is where the conclusion of the paper supplies the missing premise in an interesting argument the reader is developing. Either way, the reader is in a bit of a bind.

I think the main thing to say about these situations is that writers shouldn’t put such requests on their papers.

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Here is one way to run the New Evil Demon argument against externalist theories of justification. Let S be a normal person, with a justified belief that p, and S* her brain-in-vat twin.

1. If S’s belief that p is justified, then S*’s belief that p is justified
2. If S*’s belief that p is justified, then externalism is false.
C. So externalism is false.

Now how might we motivate premise 1? One way is by something like the following argument.

1. The same reactive attitudes are appropriate towards S and S*’s doxastic states.
2. Whether a belief is justified supervenes on the reactive attitudes that are appropriate towards it.
C. So if S’s belief that p is justified, then S*’s belief that p is justified

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