A quick illustration of the fixity of clichéd expressions. H. R. Block (a tax return company) currently is running a promotion that if you don’t get the maximum possible tax return using them, the tax return is free. Here’s the slogan they use (at least on bus shelters in downtown Providence.)

Get every penny you deserve, or don’t pay a dime

I was sort of stunned to notice how much more natural that sounds, even to my foreign ears, than

Get every nickel you deserve, or don’t pay a quarter

While on this theme, a couple of Google spellchecks that don’t really help.

judgment: 8,190,000
judgement: 2,760,000

busses: 417,000
buses: 3,660,000

The last one of these amuses me every time I walk past the corner in downtown Providence where there are two signs opposite each other with a word for more than one bus, and no other word containing ‘s’, and five ‘s’s between them. (Disclaimer: At least there were such signs last I looked – they might have been replaced/repaired by now.)

Matt Weiner writes:

I don’t think we want it to be the case that, once you open the first envelope, you have a reason to switch. Now, one issue here is the mathematical impossibility of defining a probability distribution on which every rational number is equally likely–probabilities are supposed to be countably additive, which makes it impossible to assign the same value to an infinite number of different ones. [Afterthought: Anyone know if non-standard analysis can do any work here?]

Actually you don’t even need non-standard analysis. As John Broome (1995) pointed out you can get just the result that Matt doesn’t want within standard probability theory. To be sure, you can’t get the result that whatever you see in the envelope it is equally likely that there is twice as much in the other envelope as half as much. But we can get the result that whatever you see, you should switch. Here’s one way. (It could be Broome’s exact method for all I remember – I don’t have the paper in front of me. And the numbers feel familiar from what I remember of Broome’s paper.)

Let’s assume we have a red and blue envelope, a currency denominated in utils, and a God, Eris seems appropriate, who chooses how much to put in the envelopes as follows. She takes a coin that has a 2/3 probability of falling tails, and tosses it repeatedly until it falls heads. Let n be the number of tosses this takes. (If it falls tails infinitely often, stipulate that n=1.) She then takes a fair coin and tosses it once to determine what goes in the envelopes by the following rules.

If heads, then 2ⁿ utils in the red envelope and 2ⁿ⁺¹ utils in the blue envelope.

If tails, then 2ⁿ utils in the blue envelope and 2ⁿ⁺¹ utils in the red envelope.

Let’s assume she now gives you the red envelope and you somehow (presumably with the help of another God – this part sort of defeats Eris’s purposes) get to see what’s in it. It turns out there are only two cases worth considering.

Case 1: You see 2 utils. In this case you know that there are 4 utils in the other envelope, so the expected gain from switching is 2.

Case 2: You see 4 utils. In this case you know that there are either 2 utils in the other envelope or 8. The prior probability (i.e. before Eris tosses any coins, which we can assume is when she stops telling you what happens) that the red envelope would end up with 4 and the blue envelope with 2 is 1/9. The prior probability that the red envelope would end up with 4 and the blue envelope with 8 is 2/27. So by a quick application of Bayes’s theorem, the posterior probability that the blue envelope has 2 is 0.6, and that it has 8 is 0.4. So the expected value of the blue envelope is 2 * 0.6 + 8 * 0.4 = 4.4. So the expected gain from swapping is 0.4.

What about all the other cases you ask? Well I won’t try doing the algebra in HTML, but it isn’t too hard to prove that for any x larger than 2 that you see, the expected gain from swapping is x/10. So whatever you see, you should not only prefer to swap, you should be prepared to pay at least 0.4 to swap. And note that we’ve only used standard (countably additive) probability functions here and standard reasoning.

By the way, although I’ll leave the proof for another day, I’m pretty sure that the expected utility of receiving one of the envelopes does not have to be infinite for a two-envelope paradox style situation to arise, i.e. a situation where you will want to swap whatever you see in your envelope, whichever envelope you are given. (No one I know of has ever said that it has to be, but it’s easy to misread David Chalmers as saying that it must be.) In the case here, the expected value of Eris’s gift is infinite. (Well, until she starts getting you to pay to switch envelopes.) But I’m pretty sure that by mixing positive and negative payouts in the distribution it’s possible to produce a paradoxical distribution with each envelope having a strictly undefined expected utility.

My colleague (and head of department) David Estlund has a blog! It’s Occasionalities. It’s not designed to be a philosophy blog, though philosophers are always tempted to put a philosophical spin on things. I’m tempted to comment on the “What good are blogs” post, but maybe another time. There’s a long post I’ve been thinking about about how sometimes it would be nice to post something that didn’t go to everyone in philosophy. But that post ends up sounding fairly platitudinous, because the examples are all, well you get the picture. Anyway,while talking about Blogger…

Kaye Trammell and James Russell have noted that Blogger now has an inbuilt RSS feed – details here. Third-party RSS feeds for Blogger blogs have been pretty bad in the past, so hopefully this will be better. If you don’t know why RSS is good for you, read Kaye and Dave Winer. Let me add another reason – I don’t read blogs without RSS feeds. Anyone who is running a Blogger blog should turn on this feature and display the feed link prominently. (And if you’re a blog I’ve discussed before, leave a comment here saying that you’ve turned the feed on, so I might start reading you again!)

Opiniatrety is off to a flying start – leaving my light posting to shame. I hope Matt doesn’t catch Zadie Smith syndrome: put all your ideas down on paper all at once and then struggle to come up with a follow-up. Of course, if I could write a book as good as White Teeth I’d be happy to trade that for a few years of mediocrity, so maybe the syndrome is not all that bad.

One of Matt’s posts picks up on this question posed by Geoff Pullum a while ago. Jonathan Ichikawa also chimes in. I feel less bad about not replying to it now. I think I agree with what Matt and Jonathan say.

If I had a horse in the Democratic Primary I think I’d be so nervous today that I couldn’t think. Even without having any strong preferences the excitement of it all is a little overwhelming. For what it’s worth, I think my preference ordering right now is Edwards, Clark, Dean, Kerry, (gasping chasm), Lieberman, Kucinich, Sharpton. They won’t finish that way today, but there’s actually a slim chance (very slim) that they will finish that way in the overall delegate count, especially if Kerry collapses next Tuesday.

This one should be obvious, but I can’t quite see how to answer it.

The following principle is, I think, beyond serious dispute: If being F is an intrinsic property then having a part that is F is intrinsic.[1]

At first glance I would have this principle was just as safe: If being F is extrinsic then having a part that is F is also extrinsic. But I can’t find a quick proof of this that is completely universal. Here’s my initial thoughts.

Take an object that has an F part. Since F is extrinsic, it has a duplicate that is not F. Match that duplicate with duplicates of all the other parts of the object and voila a duplicate of the original object that has no parts that are F. Well obviously this won’t work because (a) we don’t know that the duplicate part could be not F while surrounded by all those other duplicate parts. (Remember F is extrinsic – surrounding it with other things is potentially relevant.) And of course now one of the other parts could be F. So that won’t work at all.

My second thought was to start with an object that is itself F although none of its parts are, and consider non-F duplicates of it. But this might be impossible, e.g. if F is the property of being a gunky object in a world that contains a G. So I’m a bit stuck for a proof here.

The principle sure looks sound, but I suppose that’s what Frege said about Axiom V.

Here’s an interesting specific instance of the principle to close with. Many people say that being negatively charged is extrinsic, because it’s defined in terms of its relational properties or some such. Is the property of having a part that is negatively charged extrinsic? Is it an extrinsic property of the universe we live in?

[1] I don’t mean it is beyond dispute – I just reserve the right to treat the disputants as less than serious.

UPDATE: No wonder I couldn’t prove this – it isn’t true. See David Chalmers’s comment below, or if you’d prefer the exposition version read on. An object is accompanied, in Langton and Lewis’s sense, if there is something in the world it does not overlap. Let F be “accompanied or simple”. This is pretty clearly extrinisic. (Our universe is not F but a duplicate of it in a larger world is F, for example.) But having a part that is F is a necessary property. Every simple has it in virtue of being itself simple and having itself as a part. And every non-simple can be divided into two parts, and each of the parts are F, so it has the property too. And the necessary property is intrinsic. So that settles that. Much thanks to David Chalmers for the example.

Frequent TAR and CT commentator Matt Weiner has (finally!) set up his own blog: Opiniatrety. Still early days, but to be checked out.

And Matt Brown, a grad student at UCSD, has The Hanged Man, which I probably should have noticed long ago.

Here’s a question that came up at BAPHLD the other day, to which I might now have an answer. It’s impossible to interpret (1) as (2) – it has to be read as (3)

(1) Three or four jobs interest me.
(2) Three interests me or four jobs interest me
(3) Some jobs, three or four to be more precise, interest me

This point is made by Thomas Hofweber in Number Determiners, Numbers, and Arithmetic, and he uses it to make a point about the possible meanings of ‘three’. I thought there should be a simple explanation for this. (More precisely, various theoretical claims I believe commit me to there being a simple explanation, and I believe the consequences of my theoretical beliefs, even when this is hard work.)

I was trying to argue that (2) was a genuine disambiguation, and it just wasn’t preferred for pragmatic reasons. Normally pragmatic explanations are a little ad hoc, but this one looked like a no-brainer. Among the possible pragmatic explanations are

(a) Who’s interested in the number three anyway?
(b) If you were interested in the number three, wouldn’t you put that by sayings “The number three interests me”, not “Three interests me”?
(c) Under what circumstances would you be unsure whether you were interested in the number three or four jobs?
(d) How do the number three and four jobs fit into a common enough group that they could be conjoined?

Well, maybe I could go on, but you see the drill. The problem (allegedly) is that a pragmatic explanation is too weak. All of these are reasons why (3) should be the default interpretation, not the only possible interpretation.

Fortunately there’s a simpler explanation, one that I managed to miss the first time around. Note that to get from (1) to (2) I had to change ‘interest’ to ‘interests‘. If we interpret (1) as something like (2), there will be a plurality disagreement. So (3) is the only acceptable interpretation, I think.

More generally, “three or four” is an interesting phrase. It would be decidedly odd to say “Three or five jobs interest me”, although one could imagine circumstances under which that is true. It’s not that “three or four” is an idiom, but there is something odd about the construction. Maybe one for the Language Loggers, though it’s probably wrong of me to suggest that since I haven’t responded to their last philosophy challenge.

While on the “good blogs I should have spotted long ago” theme, here’s K and A, an Oxford flavoured philosophy blog that’s been running for a month now.

This should be fun.

Issue on Ordinary Objects: October 2005

Editor: Barry Smith (University at Buffalo)
Advisory Editor: L. A. Paul (University of Arizona & ANU)

Ordinary objects such as apples, statues and cats can be understood philosophically in different ways: as bundles of properties, as Aristotelian substances, as substrates having attributes, or as hunks of matter. There are familiar puzzles associated with each of these alternative conceptions. Consider: Is my apple identical to the matter it is made of? My apple could not, after all, survive being squashed, yet its matter could. This difference in modal properties suggests that the apple and its matter are not identical. Some have suggested that the matter constitutes, but is not identical to, the apple. But what, then, is the apple? If it is merely a bundle of properties, does it have all its properties essentially? And if so, then how does this square with the common-sense opinion that the apple could have had a slightly different color or shape? And if the apple is a bundle of properties or a substrate that has properties, then are these properties themselves universals, or tropes, or something else? Perhaps we must find out what concept my apple falls under before these questions can be answered. But would then our concept of the apple determine what the apple is? Or would the apple still exist independently of whatever concepts we apply to it?

Papers are invited on the metaphysics of objects which provide an analysis of what objects such as apples, statues and cats are in a way which will yield solutions to problems of these sorts, including problems concerning material constitution, the identity of indiscernibles, essentialism, and the role of ordinary objects in cognition.

Contributors will include Michael Ayers, John Hawthorne, Mark Heller and E.J. Lowe.

Deadline for submissions: October 31, 2004.
Submissions should be emailed to L.A. Paul at arizona dot edu or mailed to L.A. Paul, Department of Philosophy, University of Arizona, Tucson, AZ 85721.

If I’m not too lazy I might send the growing individuals paper in. It’s all about ordinary things. Or at least if it’s right it is.

Katherine at Obsidian Wings has several more excellent posts on the Maher Arar case. Here’s the editorial

We don’t know all the details or explanations, but we know that something terrible happened. Our government took a man from an airport in New York City and handed him over to Syria, where he was tortured for 10 months. I think I’ve made a decent case that he was probably innocent; that this was done with the knowledge and approval of fairly important government officials; and that this was not some freak accident or isolated occurrence. …
As Ted Barlow said last November, “I support the vigorous investigation and prosecution of terrorists and terrorist suspects. But if this isn’t over the line, then there is no line.” It is not acceptable to me for my country to send people to be tortured on scant evidence, or on evidence gained from other torture sessions.

Since whatever happens to Canadians can happen to Australians, and whatever can happen to Australians can happen to me, I have a selfish interest in taking this a bit seriously. (On that note, I saw in yesterday’s Washington Post that David Hicks has finally got to have one meeting with a lawyer. After two years in custody. Hooray for due process!) Of course hideous behaviour by governments is hideous behaviour by governments whether the victims are people like me or not, but when they are it’s a little easier to feel appalled by it all.

Back on Arar, today it seems that Juliet O’Neill has (or perhaps will be) arrested over this story she wrote on Arar’s case. In more ficticious news the Feds have arrested Robert Novak for his role in leaking Valerie Plame’s name.

Another linguistics blog, Semantic Compositions has opened for business, and it’s well worth reading. I’m a little late to the party with this one, but then I always took “fashionably late” to mean arriving just as the host has started forcibly evicting the stragglers.