Thoughts Arguments and Rants

Announcement

As of July 8 I will be posting on Crooked Timber. This blog will keep running, but it will be more focussed on metaphysics, epistemology and philosophy of language than it used to be, with other posts going to Crooked Timber.

Friday

I’ve been looking back over the blog entries from the last month or two, and I noticed a disturbing trend. Just as readership is going up, the blog entries are getting more snarky and less well-reasoned. Any one of these, or even any two of these, would be fine. But the three in combination is a disaster. The upshot is that now lots of people read the blog, see that I make cheap cracks at people without, say, reasons to support them, and could well conclude that I’m a jerk. Now if what I cared about was the spread of true beliefs throughout the world, I may or may not care about that. But I don’t. What I care about is how pleasant a place the world is for Brian. And if the Brian is a jerk meme spreads, the world becomes a less pleasant place for Brian. So we’ll be making some improvements around here. No more postings after several beers and midnight for starters.

Onto more serious matters, I’m sitting in this semester on a seminar on focus, run by Polly Jacobson. I’m rather excited to take a course on focus, because last semester I seemed to get into too many debates with Jeff King and/or Jason Stanley that ran this way

BW: Your theory can’t account for the following phenomena. [Insert long description of said phenomena, complete with carefully constructed example to illustrate the exact point at issue, and which has often been the only thing I’ve worked on for the previous 24 to 36 hours.]

JK/S: You’re ignoring focus.

BW: My bad.

At least I won’t make that mistake again after a whole semester on focus.

I might write a long-ish post on focus later, but I was wondering for now whether anyone has intuitions about the following sentence.

(1) Morgan only believes that ALEX and SAM voted for Chris.

Presumably (1) means that for all (salient?) people other than Alex and Sam, Morgan does not believe they voted for Chris. But it’s not easy to see how that follows on Rooth’s ‘alternative semantics’. Roughly, the idea is that every alternative to (1) is false, where alternatives are generated by replacing one or more of the focussed words with an alternative, and dropping ‘only’. So here are a couple of alternatives to (1)

(1a) Morgan believes that Sam and Alex voted for Chris.

(1b) Morgan believes that Sam and Sam voted for Chris.

But presumably each of these could be true, yet (1) is still true. Am I missing something obvious here?

posted by Brian Weatherson 1/31/2003 06:03:00 PM

The latest philosophy papers blog is up. The main news is that Ted Sider has a paper Against Vague Existence. I trust his arguments are at least a little more rigorous than the ‘arguments’ I put forward in my Problem of the Many paper. There is also a double issue of Synthese on mathematical proof, and as mentioned below entry number five in the NDPR “There’s no crying in philosophy” series.

posted by Brian Weatherson 1/31/2003 02:29:00 PM

Another negative review in NDPR. This is getting almost out of hand. No real money quote, but this one comes close.
Despite his considerable innovations, however, I believe that much more work is needed to show that Ostrow’s interpretation is correct.
Will we ever see nice reviews again?

posted by Brian Weatherson 1/31/2003 11:56:00 AM

Thursday

David Chalmers noticed that in the December 2002 edition of Ratio there is an article by Michael Brearley on psychoanalysis and the mind-body problem. It’s all rather Wittgensteinian, and there isn’t a lot that is philosophically new, but two things about the article standout.

Nowadays, Brearley is a psychoanalyst, and he has some interesting comments comparing symptoms of patients to views of philosophers. The main message is that the philosophers are not as crazy as you might think. Philosophers have philosophical beliefs that mimic all sorts of conditions that psychologists have to treat, but philosophers don’t let that take over their daily lives. So here is an example of F. H. Bradley being mentally healthy.

In this lecture I have proved that Space does not exist. In next week's lecture I will show that Time does not exist. Next week's lecture will be in room 6 at 10 o'clock.

The other point to note is that Michael Brearley the psychoanalyst who writes for Ratio is the same Michael Brearley who was not so long ago captain of the English cricket team, most famously during the 1981 Ashes series, site of possibly the least notorious instance of professional sportsmen openly betting against their own team. And the paper has a few cricketing references, particularly an interesting dream involving Geoff Boycott (and a rather nuanced depiction of Boycott for a dream, I thought) that’s all a symbol for, well I don’t know what it is a symbol for and I suspect Brearley doesn’t either, but it’s all good clean fun.

An earlier draft of the paper was presented at this conference in Brisbane in 2001, and that draft of the paper is available here. Unfortunately that version leaves out some of the most philosophically juicy bits, so if you can track down the version in Ratio, you should.

Thanks again to David Chalmers for spotting this piece.

posted by Brian Weatherson 1/30/2003 04:08:00 PM

The latest philosophy papers blog entry is up. There are three new papers, a couple of journals, and a new NDPR review that, despite being mostly negative, lacks a killer pullout quote. Something must be done about this!

posted by Brian Weatherson 1/30/2003 01:32:00 PM

I made the news today oh boy.

posted by Brian Weatherson 1/30/2003 11:03:00 AM

Wednesday

In light of all the talk about heaven and hell the last few days or so here, I decided to look again at Ted Sider’s paper on hell. Ted, most of you probably know, argued that the following problem poses a serious challenge for several popular theistic theories. On whatever criteria God decides who goes to heaven and who goes to hell, there will be people who just make it over the threshold needed to get into heaven, and people who just miss and get sent to hell. By all accounts, the difference in lifestyle quality between heaven and hell is quite noticable, and it seems unfair that people who only differ by a small amount, one prayer not said, one small charitable donation not made, could be justly treated in such different manners.

So I was thinking of a couple of ways God might deal with the problem. First, He might use lotteries. When each person gets to judgement, he or she is assigned a probability of going to heaven, depending on those features of their life in which we normally think getting to heaven depends upon. Roughly, the better she has been, the higher the probability. God then runs a chance process which has that probability of resulting in ‘success’, and one minus that probability of resulting in ‘failure’. If it turns out to be a success, the judgee goes to heaven, otherwise it’s downstairs.

This avoids Ted’s problem, at least at one level. As far as God’s role in the judgement goes, like cases are treated very much alike. If x and y are very much alike in their heavenly virtues, the probabilities of each of them going to heaven will be very similar. Of course, this doesn’t mean that one of them won’t end up in heaven while the other ends up in hell. For this reason, David Lewis somewhere describes similar (if less dramatic) systems of using lotteries for reward and punishment as being intuitively barbaric. But, you know, this looks a lot like those old librul complaints about the fact that we don’t have equality of outcomes in a just society. For some people, equality of inputs, equality of opportunity if you will, is less important than equality of outputs, or equality of outcomes. And here we have equality of inputs — it’s a great conservative scheme!

A more serious problem, perhaps, is what happens to people at the extremes. Imagine the case of some degenerate sinner who has just enough redeeming features to be awarded a 0.1% probability of winning the lottery actually beating the odds and going up. A little unfair, no? Or some almost perfect person having just one little flaw that means their probability of going to heaven is 99.9% rather than 100% losing the lottery. This seems a little bad. Reminds me of that man-on-the-Clapham-omnibus quote the Onion found after the last election: “You know, they say people get the government they deserve, but I don't recall knife-raping any retarded nuns.” (The link isn’t to the Onion because they seem to not have complete archives.) Of course here it is afterlife rather than government, but the sentiment carries across.

So perhaps we need another way. My second solution is a little more radical. Traditional versions of the afterlife have everyone going to one or other destination for all of eternity, with perhaps a change of planes in purgatory. But why have this? Perhaps some people deserve some time in heaven and some time in hell. God could just decide that for every day or so, each person will spend a certain amount of time in heaven, and the rest of the day in hell. This way slight differences in the quality of the person’s life will lead to slight differences in the percentage of each day that that person spends in heaven and hell.

Of course, this will mean that hell loses a few of its characteristically nasty features. For one thing, it will hard to feel abandoned by God if he’s flicking you back and forth between the two supernatural realms. For another, the company of the damned won’t be quite so bad in these circumstances. Father Arnall put it this way.

The damned howl and scream at one another, their torture and rage intensified by the presence of beings tortured and raging like themselves. All sense of humanity is forgotten. The yells of the suffering sinners fill the remotest corners of the vast abyss. The mouths of the damned are full of blasphemies against God and of hatred for their fellow sufferers and of curses against those souls which were their accomplices in sin. ... They turn upon [their] accomplices and upbraid them and curse them. But they are helpless and hopeless: it is too late now for repentance.

Well, actually on my plan I guess it wouldn’t be. I imagine some of the conversations would be less like the rightfield bleachers at Yankee Stadium and more like this.

  • So how long are you down here for?
  • Twenty minutes a day. And you?
  • Twenty-five.
  • A fair cop?
  • Oh very fair. Very fair. Though I wouldn’t complain if this worm stopped gnawing at my eye.
  • I know what you mean, but it’s only for a while, and what we have to go back to...
  • Ah, yes, just thinking of that almost makes me forget the blistering heat of this here eternal fire.
  • Yes, rather hot that. My skin seems to be peeling off. Good thing they patch us back together every day.
  • So, was it worth the pain for you?
  • Was what worth it?
  • What you did to get here? You know, nudge nudge wink wink.
  • Say no more!

Still, I think there’s something to be said for this solution to Ted’s problem.

I should mention that the solution Ted mentions towards the end of his paper, and attributes to Jesus, doesn’t strike me as particularly bad either. At the very least, it’s a very intersting solution, probably more worthy of consideration than my little proposals. And it’s a better example of Jesus being a philosopher than Douglas Groothuis finds. The Groothuis article is kind of odd actually. He’s trying to defend the chimp’s claim that Jesus was a first-class political philosopher. And he doesn’t mention a single instance of political philosophy in the whole piece. From memory, the most prominent bit of political philosophy in the gospels is the Give Unto Caeser passage. And this passage suggests that the state owns all money in virtue of having its logo on it. This isn’t an unheard of opinion in political philosophy. Hobbes believed something similar, for example, though his reasons were a little more sophisticated. But it’s hard to square it with the GOP policies nowadays. (Amusing challenge: find the second occurrence of the word ‘political’, or any of its cognates in Groothius’s article.)

I’d talked to Ted about his article a bit while it was being drafted, but I hadn’t read the final draft until recently. And when I did what struck me was how much attention was now being paid to views on which whether one gets to Heaven depends on whether one has sufficient faith, rather than on how morally worthy one is. And I guess this is because it was pointed out to Ted that on lots of the theologies that he at least appears to be attacking, whether one gets to heaven really does depend on faithfulness rather than goodness.

This is probably just a consequence of a Catholic upbringing, but I find these theological views very hard to fathom. It’s very hard for me to see what’s praiseworthy about a God who rewards those who believe in Him for believing in Him, and punishes those who do not for not so believing. If God behaved that way it would seem, well, petty. Of course, this is no evidence that such a God doesn’t exist, but it is a reason to not praise such a God. I’m simplifying a lot here, I know, but I don’t see how a faith-based admissions procedure becomes more defensible, let alone praiseworthy, by being tempered with morally salient characteristics.

Of course, even on Catholic teaching good faith is a component of getting to heaven as well as good works. And I think that’s not laudable, but at least it’s better than all faith all the time. (I have a kind of biased view here because the order that ran my high school was even more focussed on good works, particularly education, than most.) And of course this doesn’t mean that the Catholic church has it entirely right about what counts as good works. If I had to bet (and according to some I do) I’d say God is less sex-obsessed than a sixteen year old with a Viagra habit. But maybe I should leave the last word to Joyce’s resident theologians Kernan and Cunningham. (This passage is from Grace.)

—Tell me, Martin, he said, weren’t some of the popes -- of course, not our present man, or his predecessor, but some of the old popes -- not exactly ... you know... up to the knocker?

There was a silence. Mr. Cunningham said,

—O, of course, there were some bad lots... But the astonishing thing is this. Not one of them, not the biggest drunkard, not the most... out-and-out ruffian, not one of them ever preached ex cathedra a word of false doctrine. Now isn’t that an astonishing thing?

How could you not like a church with that track record?

posted by Brian Weatherson 1/29/2003 10:46:00 PM

I’ve posted the papers for the day to the philosophy papers blog. The main points to note are a couple of papers on contextualism in Grazer Philosophische Studien, two papers related to consciousness by (inter alia) Kevin O’Regan (who gets to work in Paris, the lucky so-and-so) and a new paper on the Semantics Archive by Angelika Kratzer. Actually, it’s an update of a paper first posted there three months ago, but since we weren’t tracking the semantics archive then, I’m posting it now. If you haven’t looked at the Semantics Archive, you should. It’s a great service, both to readers and to writers. I imagine most people who write on semantics know about it, but if you don’t you should see if you want to post works in progress there.

posted by Brian Weatherson 1/29/2003 11:18:00 AM

Tuesday

The philosophy papers updates are posted for the day. Lots of interesting journals, and as already noted the third and most intensive smackdown in the hopefully continuing NDPR Making Authors Weep Since January 2003 series.

posted by Brian Weatherson 1/28/2003 01:52:00 PM

It’s smackdown week at NDPR. Do you detect a pattern here?

This is another instance of the first worry that I noted above, viz., the feeling that there is nothing substantially new on offer here, but rather a theory put together out of a selection of what is currently on offer.

What results is a farrago that does not advance the current debate about moral realism and the moral sentiments, and indeed does not even seem to have caught up with it.

Thus it is surprising and disappointing to find a carelessness and ineptness of argument and critical analysis as well as a succession of trivial verbal solutions to serious problems.

And this isn’t biased sampling. (Well, it isn’t very biased sampling!) These are from the last three reviews posted. Heaven knows what I’d have to say if I had to rewrite my Wiggins review to keep up with the trash talking.

Now that the name Mighty Midwestern Metaphysical Mayhem has been retired from the conference circuit, I think it would have been fine to use as the title of the last review.

Thanks to Fritz Warfield for the tip about the last review.

posted by Brian Weatherson 1/28/2003 11:58:00 AM

Untitled Document

Sometimes even the good guys screw up. From Justice Breyer’s dissent in FCC v Nextwave

The statute before us says that the Government may not revoke a license it has granted to a person who has entered bankruptcy “solely because [the bankruptcy debtor] . . . has not paid a debt that is dischargeable in [bank-ruptcy].” 11 U. S. C. §525(a). The question is whether the italicized words apply when a govern-ment creditor, having taken a security interest in a license sold on an installment plan, revokes the license not because the debtor has gone bankrupt, but simply because the debtor has failed to pay an installment as promised. The majority answers this question in the affirmative. It says that the italicized words mean

“nothing more or less than that the failure to pay a dissenting dischargeable debt must alone be the proximate cause of the cancellation—the act or event that triggers the agency’s decision to cancel, whatever the agency’s ultimate motive . . . may be.”

Hence, if the debt is a dischargeable debt (as virtually all debts are), then once a debtor enters bankruptcy, the Government cannot revoke the license—irrespective of the Government’s motive. That, the majority writes, is what the statute says. Just read it. End of the matter.

It is dangerous, however, in any actual case of interpretive difficulty to rely exclusively upon the literal meaning of a statute’s words divorced from consideration of the statute’s purpose. That is so for a linguistic reason. Gen-eral terms as used on particular occasions often carry with them implied restrictions as to scope. “Tell all customers that . . .” does not refer to every customer of every business in the world. That is also so for a legal reason. Law as expressed in statutes seeks to regulate human activities in particular ways. Law is tied to life. And a failure to understand how a statutory rule is so tied can undermine the very human activity that the law seeks to benefit. “No vehicles in the park” does not refer to baby strollers or even to tanks used as part of a war memorial. See Fuller, Positivism and Fidelity to Law—A Reply to Professor Hart, 71 Harv. L. Rev. 630, 663 (1958).

I think Breyer’s right, but he shouldn’t have picked this example to try and make his point. “Tell all customers that . . .” does not have as part of its literal meaning that the instructee (whomever that happens to be here) is to tell every customer in the world something. The number of serious theorists who think that it does is miniscule, and some of them have yet further positions that are kinda wacky (though we can forgive Bay Area people a lot after what they’ve been through the last four months) and this position rides roughshod over fairly strong semantic intuitions every single day of the week. (—You mean the salient days of the week. —Exactly.)

I probably should try and back this up with an argument, but it’s late and I’m not likely to influence the Supreme Court in any case. So I’ll just recite some clichés. If I look in the fridge and say, panicking, “There’s no beer”, Breyer’s position is that I say something literally false, that there is no beer in the entire world, but one should interpret my intended message as the true claim that there is no beer in the fridge. And this is the latest battleground between interpretavists and literalists. And most every theorist who looks at this question, not all but almost all, says that I just don’t literally say that, I literally say that there is no beer in the fridge. Cheap rhetorical argument that you shouldn’t take seriously: Would you really say that someone routinely said things that are false, or even literally false, just because they say omit quantifier domain restrictions as in “There’s no beer” or “All customers should be told that...”?

The point is, Breyer can play along with the interpretative literalists and still have his implicit quantifier domain restrictions, because those restrictions are part of the literal meaning of the sentence. Well, he sort of can at least, because it’s not obvious how one is to read a quantifier domain restriction into this particular statute. Which is to say, Stephens was probably right to agree with Breyer in principle and the majority in practice.

posted by Brian Weatherson 1/28/2003 12:09:00 AM

Monday

The fact that New York English lets negations that syntactically appear to have narrow scope in fact take wide scope with respect to quantifiers never ceases to amuse me. (I am, to be sure, easily amused by language from time to time.) This is from this morning’s Super Bowl coverage.

The Super Bowl has been known to canonize its quarterbacks, but sometimes it buries them. Everyone can't be Joe Montana and Joe Namath.

Not even Joe Montana?! Not even Joe Namath?!!

posted by Brian Weatherson 1/27/2003 03:33:00 PM

There were people working on Superbowl weekend after all! Dave Chalmers has updated his responses to critics page. There are lots of summaries of and responses to lots of criticisms of his theories.

posted by Brian Weatherson 1/27/2003 11:18:00 AM

I’ve been a bit busy with the start of semester to get much posted here, but the weekend’s philosophy papers updates are up. There’s no update today because, as best I could tell, no one spent Superbowl Sunday writing and posting new papers. I guess Superbowl fever even extends to philosophers!

posted by Brian Weatherson 1/27/2003 09:47:00 AM

Friday

The latest philosophy papers blog entry is up. Nothing much to report about. A Susanna Siegel paper which was previously only available in HTML is now available in PDF. Not that it is not a good paper, but this makes it less newsworthy today. The Notre Dame review about which I posted below, and a fairly interesting entry on causal determinism in the Stanford Encyclopaedia. So only slightly more than most of us have time to read, not lots more.

posted by Brian Weatherson 1/24/2003 03:44:00 PM

Normally when I’m posting reviews from Notre Dame to the philosophy papers blog, I post the first paragraph as a kind of blurb. But in this case I think I’m going to have to make an exception. It’s from David Sussman’s review of Praise and Blame by Daniel Robinson. The first paragraph is relatively uneventful, but here is the last paragraph.

Praise and Blame is a strangely unfocussed work that flits back and forth amongst a wide array of philosophical topics but fails to sustain any substantive line of argument for very long. Despite all the ground he covers, Robinson leaves us with conclusions that are either fairly jejune versions of familiar positions or hopelessly vague if high-minded gestures. The “moral realism” of the title turns out to be something of a red herring, as there is no serious discussion anywhere in the book about the objectivity, rationality, or epistemology of morality so construed. Rather, such realism seems to be merely an excuse for treating a variety of loosely related (if interesting) topics together. What results is a farrago that does not advance the current debate about moral realism and the moral sentiments, and indeed does not even seem to have caught up with it.

I guess that review won’t be going in the folio.

posted by Brian Weatherson 1/24/2003 09:40:00 AM

Question for anyone who knows a bit about copyright law.

Imagine, for the sake of argument, that I wanted to write a philosophy paper as a ‘Platonic’ dialogue, but rather than have the characters be Socrates etc I wanted the characters to be the characters from the Harry Potter books. Do you think that using these characters would be a violation of copyright?

I’m guessing it would be, but that the violation is so inconsequential that no one should be bothered. I think it might be amusing to write to the publishers of the Potter books and ask for permission, maybe even including the relatively abtruse argument I want to put in the mouths of the heroes and villains. If I do write such a letter I’ll be sure to post it here.

posted by Brian Weatherson 1/24/2003 01:20:00 AM

Thursday

From Heather Dyke’s review of Katherine Hawley’s How Things Persist.

Stage theory combines elements of both its rivals. It shares perdurance theory’s commitment to a four-dimensional metaphysical framework but denies that theory’s account of predication and adopts instead something like endurance theory’s account of predication. It is not four-dimensional objects which satisfy predicates like ‘is a chair’ and which change by having some parts that are clean and some parts that are coffee-stained. Instead, it is the momentary stages that make up the four-dimensional objects which are chairs and which are clean or coffee-stained.

Let’s work backwards through this. The last sentence is entirely true. The penultimate sentence is I think true, though one might quibble with the claim that in stage theory stages are the things that change. (Do you Ted, if you’re reading this?) But how does the ante-penultimate sentence follow from those? In what way is the stage theory’s account of predication something like the endurance theory’s? In what way is a raven like a writing desk? In what way is a conversation on a Dublin street like a fight with a Trojan soldier? I’m puzzled.

I think what’s going on here is that both the endurance theory and the stage theory say that x is a chair is true just in case x itself is a chair, but the traditional perdurance theory is thought to say that this is true just in case x’s current temporal part is a chair. But this isn’t really comparing apples with apples. The perdurantist doesn’t reject the T-schema, she can say x satisfies is a chair, i.e. x is a chair is true, just in case x is a chair. She goes on to say something else about how x’s being a chair depends on features of x’s current temporal part, but she isn’t disagreeing yet. So is the difference that the stage theorist doesn’t go on to say anything like that. Er, not obviously. If you think that whether or not something is a chair depends on, say, the intent with which it was constructed, then when the stage theorist goes to say what x’s being a chair depends on, it will include (something like) a story about how x bears a counterpart relation to certain of its temporal counterparts, and how those parts were created for the intent of being sat upon, or something to this effect. In other words, temporal parts seem to come into the story about predication at more or less exactly the same time. I still think it’s a ravens and writing desks comparison.

In other news, the day’s philosophy papers blog entry is up. It’s much less exciting than yesterday, but there is still some stuff there of note.

posted by Brian Weatherson 1/23/2003 10:36:00 AM

I realised earlier this week that an example of Jamie Dreier’s might be related to my objections to Adam Elga’s indifference principle, and my continuing war against indifference in all its manifestations. So let me tell you Jamie’s example, get your opinion on it, and then tell you my variant on it. (I’m not sure how similar my example will look to Jamie’s, but it really is pretty much the same case, so I don’t want to claim any credit for it. On the other hand, blame for misappropriation is appropriate.)

The world consists of infinitely many people (or at least morally salient agents) who live forever without moving. The people are arranged in a lattice-like pattern - relative to a suitable co-ordinate system the people are set up so that a point (x, y, z) is occupied iff x, y and z are integers. (We assume our ‘people’ are point-sized!) There is a small sphere, currently of radius < 1, centred at (0,0,0). Over time, the radius of this sphere will grow at some constant rate. (It won’t matter what the rate is, but feel free to pick a value for its expansion if it helps you visualise the example.)

A less than belevolent god gives us a choice about what will happen to the people in the world throughout the rest of time. If we pick option A, call it pain in, then at every point in time, those inside the sphere will be in pain, and those outside the sphere will be in pleasure, or at least happy. If we pick option B, call it pain out, then at every point in time, those inside the sphere will be happy, those outside will be in pain. Which should we choose?

Jamie points out some odd features of the case. If we poll people in that world, we’ll find overwhelming support for option B. Every person in the world should prefer we pick B, because it means they will be in pain for a finite amount of time, then happy for an infinite duration, rather than the reverse. (Some agents far from the centre with a high discount rate might dissent, but they are irrational dolts, so let’s ignore them.) On the other hand, if we come back to look at the world at any time after choosing B, we’ll see many more people in pain as a result of our decision than in pleasure. And while the the sphere with the pained people in it is expanding, it isn’t really clear that we are buying some future happiness as the result of present suffering. At every point in the future of the world, there will be more suffering than pain.

So, which will it be, option B or option A?

Now for the application to Elga, which surprisingly enough doesn’t turn on your answer there. Dr Evil creates infinitely many (a countable infinity) duplicates of Alex, and tweaks their biology a little so that (a) each of them will live forever and not age, and have the same experiences as all the others (b) every fifty years they will forget everything they have experienced for the last fifty years and be reverted to the epistemic state of the person who right now is being told by Dr Evil that she will live forever and by the way she has countable many like situated Sissyphusians.

These immortals are epistemically alike, but they are different from each other in two small respects. First, they each have a ‘serial number’ written on their chest in noumenal pen (so they can’t get any evidence about what it says). This number records how many Alexes existed before this Alex was made. So the original Alex is 0, the first duplicate is 1, the second is 2 and so on. (Since there are a countable infinity of them, Evil could have created them in a linear order.) Secondly, on their back they have a ‘version number’ which records how many times their memories have been erased. (I just wrote that this too was in noumenal ink, but I think I used the wrong pen, so let me say it again.) So they are born/created with 0 on their back, and this is replaced with 1 after fifty years, 2 after a hundred, and so on and so forth ad infinitum ad infinitum.

Each of these souls is told about their numbers, S and V, when they are created or having their memories wiped. And each of them occasionally wonders whether she is such that S > V, or S = V, or S < V. As best I can tell, Adam’s theory says nothing at all about what they should think about this question. Not even, surprisingly enough, that Pr(S = V) = 0, which you might expect.

The point is that all he says is that any two hypotheses S = s & V = v and S = s´ & V = v´ should receive the same credence. And same credence in the strong sense of same probability that the conditional probability of a particular one of these being true given that one or other of them is is 1/2, not just in the weak sense that the probability of each equals zero, although that would be problem enough. One issue with this, which I may have noted once or twice before, is that it commits Adam to denying countable additivity. For Pr(S = s) = 0 for all s, but Pr($x S = x) = 1, which is impossible if Pr($x S = x) is just equal to Pr(S = 0) + Pr(S = 1) + Pr(S = 2) + ..., which countable additivity says that it is. Now countable additivity is not a golden calf, many smart people have rejected it. Indeed, many smart people have rejected it for just the reason that Adam is implicitly adopting. Intuitvely, they say, it is possible to have an even distribution of credences over a countably additive set, and if countable additivity is inconsistent with that (which it is) then so much the worse for wear for countable additivity. But with countable addivity gone, so go a lot of other things which we might have expected. One of them is the ability to get from what premises we have (that any two hypotheses about the value of S and V are strongly equiprobable) to conclusions like Pr(S = V) = 0.

So Adam’s theory doesn’t compel Alex to take any particular attitude towards S > V. But he does seem to assume that a particular Alex should assign some number or other to the probability that, for her, SV. And therein lies the problem. For the theory does imply the following constraints.

  • "x Pr(SV | V = x) = 1
  • "y Pr(SV | S = y) = 0

So Alex is in the following awkward position. If her credence in SV is less than 1, then by the first constraint, she knows that there is a partition of the possibility space (specifically, {<V = n>: Î N} where I use angle brackets to represent de se propositions, and N for the set of natural numbers) such that conditional on every member of that partition, her conditional credence in SV is higher than her actual credence. That’s often taken to be a bad thing. But perhaps all it means is Pr(S > V) = 1. Perhaps. On the other hand, if her credence in SV is greater than 0, then by the second constraint there is a partition of the possibility space (specifically {<V = n>: Î N}) such that conditional on every member of that partition, her conditional credence in SV is higher than her actual credence. That is not good.

So I think as long as Alex follows Adam’s advice, she is in trouble, and that’s bad news for Adam’s theory.

Some people would try and spell out the particular kind of trouble that Alex is in by using some kind of Dutch Book argument, or in some other way get an epistemological conclusion from decision theory. But that would be mistaken thrice over.

First, those ‘pragmatic’ arguments generally aren’t very good, although I won’t go into the reasons why they aren’t very good here. (Quick summary of the reasons, if you care. There’s no obvious connection between stupid actions and stupid doxastic states. The pragmatic arguments for various conclusions within probability theory all presuppose some particular theory about how the connection is supposed to hold. But these presuppositions are often (a) false, (b) not things that people who don’t believe the arguments conclusions would want to believe or (c) both. And unsound question-begging arguments aren’t worth the electrons they’re reflected from.)

Secondly, we already know from the two-envelope problem that once infinities come into play, then the kind of position Alex will find herself in with respect to bets on S > V, there being some bets such that she prefers them and she knows that when she learns which member of a partition is actual she will no longer prefer them, is a position that anyone could find themselves in. What is distinctive about Alex is that we don’t need to bring in decision-theoretic considerations to embarrass her. There’s a distinction between Alex’s problem (if she takes Adam’s advice) and the problem facing someone facing a two-envelope paradox, and bringing decision theory in blurs that distinction.

Thirdly, Alex knows that she won’t find out which member of the partition is true, for to do that would require that she have different evidence to her twins, and as the problem clearly states, she has the same evidence as all the others, so really that’s not very likely. This matters, because the kind of argument that would be used here to show that Alex’s position is embarrassing would be to get her to buy or sell a bet on S > V, and then depending on what she did release to her the info about the value of S or V, and get her to reverse the transaction she just made with interest. Since Alex knows this can’t happen, I don’t see how her decision making apparatus is noticably faulty.

None of this is to say that Alex gets off the hook. I think the awkward position I laid out really is awkward, and it’s a bug not a feature of Adam’s indifference principle that it leads his advisees there. But I can’t conclusively demonstrate that using arguments from decision theory.

So what should Alex do? Well, I think that she should assign a non-numerical credence to S > V that is neither less than 1 nor greater than 0. Could Adam say the same thing? Possibly, though there’s a worry once he opens the door to this kind of move. Often the situations that he thinks call for application of an indifference principle I think call for non-numerical probabilities. I think that some of the cases he brings up in his paper are like this, for example. That’s a post for another day, but the quick version of that post will be that if Adam adopts non-numerical probabilities to get out of the Alex problem, he wins (or at least not loses) the battle, but he loses the war. But it’s late and I need to work tomorrow, so I’ll leave that for now.

posted by Brian Weatherson 1/23/2003 12:44:00 AM

Wednesday

Philosophy papers for the day is half-up.

posted by Brian Weatherson 1/22/2003 03:01:00 PM

I’ve been slow getting the philosophy papers blog done today because I’ve been doing a headless chook impersonation trying to get my classes ready. Hopefully it will be up by early afternoon. Apologies for the delay.

In the meantime, I’ve been thinking about these Purgatory problems some more (scroll down for details) and I’ve been wondering what the consequences are of adopting the following rule: Leopold should accept a deal iff were the deal to be offered repeatedly, the probability that he would be making a profit by accepting it every time would tend to 1 as the number of times the deal is accepted tends to infinity.

Discuss.

posted by Brian Weatherson 1/22/2003 11:35:00 AM

Serenity Now!

posted by Brian Weatherson 1/22/2003 12:16:00 AM

Tuesday

Blog Entry

I should start listing more of the academic blogs that I come across. Anyway, two worth noting today. Kai von Fintel has a blog that focusses so far mainly on news alerts for linguists. He promises that it will contain scholarship, with it seems as much focus on other people’s work as his. (—But we want to know what Kai is doing? —Settle down. Blogs are big things. It is possible to report on other people’s work and on your own.)

He also has a really interesting paper on his website about epistemic containment (co-authored with Sabine Iatridou). Apparently, epistemic modals have different patterns of interaction with quantifiers to other modals. So, for instance, (7) is inappropriate in the following setting.

We are standing in front of an undergraduate residence at the Institute. Some lights are on and some are off. We don’t know where particular students live but we know that they are all conscientious and turn their lights off when they leave. So, we clearly know that not all of the students are out (some lights are on and they wouldn’t be on if the students were away). It could in fact be that all of them are home (the ones whose lights are off may already be asleep). But it is also possible that some of them are away. Since we don’t know which student goes with which light, we have that for every particular student it is compatible with our evidence that he or she has left.

(7)*Every student may have left but not every one of them has.

Compare (7´) (not from their paper but motivated by it).

(7´)Every student could have won but not every one of them could have.

(7´) is awkward, to be sure, but it has a true reading, that while for any given student it was possible that they won, it was not possible that every student won. Von Fintel and Iatridou have more natural examples, but they aren’t as close a match in form to (7).

I think this is fascinating stuff, but I should put in a word about why it matters for those of you who don’t find semantics to be intrinsically interesting. It’s often a source of contention in debates about epistemology and metaphysics whether the modal operator in a particular sentence is epistemic or, in some sense, metaphysical. Previously it was difficult to find a fully operational test for determining this, and so people relied on rules of thumb. (Might is usually epistemic, contingent is usually metaphysical, and so on, with added debates about how these modalities interact with conditionals.) It seems possible, and I’m not saying it can be done but possible that this observation will lead to an operational test. We shall see.

Mark Kleiman is a Professor of Policy Studies at UCLA. So his work tends to be much more focussed on politics than most of what I cover here. Not that focusing on politics is a bad thing, but there are I don’t know, about six and a half billion politics blogs in the world right now, and only a handful of active philosophy blogs, so I think we’re more likely to be approaching the point of diminshing returns in politics rather than philosophy now in the blogworld.

So why am I bringing this up? Well, because Kleiman also does political philosophy, and occasionally it creeps onto the blog. Today, as a follow-up to the amusing discussion of Jonah Goldberg and Mark Twain on censorhip , Kleiman posted this:

Not so fast. No doubt you, dear reader, are aware that Plato was an advocate of censorship, believing that his young “guardians” should be brought up hearing only martial music and bombastic patriotic poetry. So we were taught by Bertrand Russell and Karl Popper.

But now take a look, if you will, at Republic II, 376c-385. Plato's Socrates, talking to a group of young intellectual conservatives, has no problem convincing them that censorship of reading material for the young is a good thing. He then immediately introduces as examples Homer and Hesiod, the closest thing to canonical sacred texts known to Athenian society, and they're so thick they just keep saying “Yes, Socrates.”

It's the very same joke Mark Twain made, and for two millennia now people a lot smarter than Jonah Goldberg have been reading Plato's irony as if it were sober prescription. What makes this misreading even more astonishing is that Plato, later in the same text, makes a famous claim that the ideal polity would ban dramatic poetry altogether, and does so in a dialogue, a species of dramatic poetry.

As I was taught this material by Paul Desjardins, the ironies go much deeper, starting with the fact that the polity constructed in the dialogue is not in fact the city that embodies justice, but instead a luxurious city to meet the luxurious taste of Glaucon and his rich, idle friends. (372c-375). The “guardians” -- not, in the text, rulers, but warriors -- are necessary only because the city-in-speech being built is unlimited in its desire for wealth, and therefore will fall into conflict with its similarly intemperate neighbors.

Personally, I can't imagine writing or speaking without the use of irony in its various degrees, starting with the sarcastic “r-i-i-i-i-i-i-i-ght!” and moving up the scale of subtety. But the warning is there. Even a supreme literary artist -- which Plato undoubtedly was -- proved unable to overcome the natural thick-headedness of his readers, and wound up being identified with the very position he was satirizing. “Against stupidity, the gods themselves contend in vain.”

I did a little digging around this afternoon and found that, well, it’s not taken to be settled beyond doubt, but some much better Plato scholars than Russell and Popper are prepared to take Plato at his word here. I don’t know enough about Plato to have an opinion one way or the other, but I’m prepared to defer to my authorities. It does look like an interesting question of scholarly interpretation, but that is so far from my area of expertise (—Which is what, philosophy of language? —I do theoretical philosophy, not applied, don’t bug me) that I won’t try and get personally involved.

UPDATES: Kai von Fintel has a long list of people with online papers in semantics. I made a quick policy decision that semantics is part of philosophy, and included those links on the list of webpages to be checked every day. So the philosophy papers blog is now tracking changes to around 650 web pages daily. I also added a link to this post two hours after it was written, and two hours after the link should have been added.

posted by Brian Weatherson 1/21/2003 07:24:00 PM

I was listening to this song yesterday and didn’t notice the first line of the lyrics. If you remember watching Manchester United play a few years ago it should sound humourously sensible.

posted by Brian Weatherson 1/21/2003 06:33:00 PM

I’ve posted the days changes to the philosophy papers blog. There’s quite a lot there, but for me the highlight was seeing Bill Lycan post a different version of a forthcoming paper to that forthcoming. That in itself isn’t entirely unusual, but normally the web version doesn’t have a different conclusion to the dead-tree version, unless the dead-tree version is on trees that have been dead some time.

posted by Brian Weatherson 1/21/2003 09:47:00 AM

Monday

Here’s another puzzle about infinite decision theory. (Although I haven’t been flooded with responses to the last one yet, but I like making these up.)

The background is the same as last week. Leopold is in purgatory. He occasionally gets to spend days in Heaven or Hell depending on how various gambles with angels turns out. Recently these have all involved St. Petersburg type gambles.

Some quick terminology will help us along. (This is all from the previous story.) A rock is an envelope with a number inside it, called its number. The number is chosen by a St. Petersburg style process. A coin is flipped until it lands tails. If it lands tails the first time, the number is 1, the second time the number is 2, the third time the number is 4, and so on doubling ad infinitum. An x-rock is a rock where the number generated by this process is multiplied by x. So if the coin lands tails on the third trial when building a five-rock, the number written would be 20. (4, for the third coin toss, by 5, the multiplier for the rock.) A green rock entitles the bearer to spend its number of days in Heaven, a yellow rock condemns the bearer to spend that many days in hell. We won’tbe using this here, but in the previous story I also defined an x-rock minus y, whose number is determined by working out what its number would be were it an x-rock, then subtracting y. (The main issue in the previous post was whether rationality demanded one prefer a ten-rock to a ten-rock minus ten.)

Leopold’s preferences are such that the marginal utility of days in Heaven and Hell are equal, opposite and constant. So he’s indifferent between the status quo and accepting a pair of gambles, one of which gives him a days in Heaven with probability b, and the other sends him to c days in Hell with probability d iff ab = cd.

Today two angels came by and offered him some deals. The first offered him two green rocks if he would also take a yellow two-rock. The second offered him a green two-rock if he would also take two yellow rocks. What should he do?

posted by Brian Weatherson 1/20/2003 12:07:00 PM

Sunday

Blog Entry

In the latest Analysis, Darren Bradley and Brandon Fitselsen argue that using confirmation theory can assist understand what happens in the Monty Hall problem. The idea is that by assuming that “the degree to which E confirms H is properly measured by the ration Pr(H | E):Pr(H) of the posterior to the prior probability of H” we get the nice conclusion that in all but a very special case Monty’s action provides better evidence that you chose the wrong door than that you chose the right door. (I assume some familiarity with the Monty Hall problem. If not, read Bradley and Fitselsen’s paper — it’s a nice problem.)

The problem with all this is that we don’t need to bring out anything so heavy duty as a contentious theory of confirmation to get this. Assume that you choose door 3. There are four options remaining.

  1. Monty will open door 1 and the prize is behind door 2.
  2. Monty will open door 1 and the prize is behind door 3.
  3. Monty will open door 2 and the prize is behind door 1.
  4. Monty will open door 2 and the prize is behind door 3.

When Monty opens, say, door 2, options 1 and 2 are removed. That is, one of the ways in which the prize could have been behind door 3, one of the ways in which you could have made the right choice, is taken away, but all of the ways in which the prize could have been behind (what is now) the other door, door 1, are still live options. Unless that way in which the prize could have been behind door 3, that is option 2, was not a live possibility, which I suppose it isn’t ridiculous to equate with Pr(Option 2) = 0, it isn’t at all surprising that Monty’s action better confirms the hypothesis that you’re wrong than the hypothesis that you’re right.

(And, interestingly, Bradley and Fitselsen also note that if Pr(Option 2) = 0 then by their lights Monty’s action doesn’t differentially confrm the hypothesis that you’re wrong.)

So in this case I’m not sure what the heavy duty confirmation theory is doing, except perhaps to confirm something entirely expected.

This approach is also held to validate a version of the Doomsday argument, but not I think the most interesting version of the Doomsday argument. What we care about in Doomsday is a de se proposition, how long it is from now until Doom. What most versions of the argument, and Bradley and Fitselsen are no different to most here, is show that evidence that we are not that far from the beginning of time differentially confirms certain pessimistic looking de dicto hypotheses about how many people that will ever live. But, in their case at least, everything they say is consistent with evidence that we are not that far from the beginning of time having no effect whatsoever on our future-directed de se beliefs, and only affecting the de dicto attitudes by altering our past-directed de se attitudes.

It isn’t too hard to see this is exactly what their argument must show, when we notice that their reasoning in support of Doomsday arguments would apply equally well to an agent who had been told by God that there would be exactly 100 billion more people in the future of the world as it would to agents like us with no such knowledge.

posted by Brian Weatherson 1/19/2003 01:03:00 PM

Saturday

Grice on web design. No really.

posted by Brian Weatherson 1/18/2003 08:32:00 PM

There were two things I wanted to do with the following post. First, I wanted to get people's feedback about a tricky decision problem. Secondly, I wanted to tell a story, just for the sake of adding some story-telling to the site. If you want to skip the story, and have the example given in a more traditionally philosophical format, feel free to jump to the end of the story, which is clearly marked with a horizontal line. There are many allusions to various themes from economics, literature, philosophy and theology in the story. Most of them are obscure, to sy the least. In some cases, you might reasonably think that the most salient property the alluser and allusee have in common is that they are members of a particular pair set. Despite that, I'm not going to explain all of them, but there are some footnotes explaining some, particuarly where I directly borrow ideas without clear citation in the story.


Walking out of the bar, Leopold and Stephen turned right onto Upper Ormond Quay. It was a long walk to the park, especially in the snow, but they seemed resigned to it. Stephen stopped at a cart selling old books and picked up a tattered journal.

—This is the most bizarre theory of the afterlife I've ever read, said Stephen. It claims that some of the people that are sentenced to purgatory are occasionally moved around between heaven and hell because of games they play with gods and angels. And it says that the values of days in heaven and hell are equal, opposite and constant.

—Opposite relative to what, asked Leopold?

—Relative to time in purgatory, said Stephen. So two days in heaven followed by two days in hell is exactly as good as four days in purgatory. What I can't believe is the constancy. It seems to me that as you got used to heaven it would be less pleasurable than when you first arrive, but as your pain tolerance diminished, hell would just get worse and worse.

—That's a very depressing view of the afterlife. I remember Pascal argued eloquently for the constant marginal utility of extra days in heaven.

—Are you sure? I recall Jevons arguing finely that everything has a constant marginal utility.

—Jevons? Don't believe everything you read by Australians.

—No, I think he made a very plausible case.

—LOTTERY TICKETS!

—What? asked Stephen, turning around to see a small boy holding out a small book.

—Lottery tickets, said the boy. First prize a week in paradise.

—We've just been talking about paradise, haven't we Leopold? Maybe we should buy and if we win we can go and see if the seventh day is as good as the first.

—I think the seventh day is normally better than the first, said Leopold.

—Where, pray tell, is paradise boy? asked Stephen.

—Margate, said the boy.

—Paradise is in England? snorted Stephen. I doubt even God can see through the clouds that hover over England.

At that Stephen and Leopold turned around to walk off. But they never made it, as at that moment a runaway horse came tearing up the path, trampling over Stephen and Leopold, killing them both.

Instants later, they were in Purgatory, with instructions ringing in their ears that that was where they were to stay the afterlife. Stephen thought it was a fair cop, but Leopold was understandably aggrieved at the injustice of it all.

They were rather surprised to learn that the theories of heaven and hell Stephen had recited just before their deaths were entirely true. It took them a while to discover this, and it was mainly through Leopold's work that they learned it was true. At first, Leopold accepted every deal offered by a passing angel. One day in hell followed by six in heaven. Sixteen days in hell, with a day in heaven after the seventh. Four days in heaven for free. The last deal from the angel who felt he must make up to Leopold for exploiting his curiosity in the previous deal. Leopold took everything that came by, and concluded that the value of days in heaven and hell really was equal, opposite and constant.

Stephen disparaged all these journeys. Heaven isn't all it was cracked up to be. Life is a journey, and once you've arrived in heaven you've got nowhere to go, so you may as well be dead. The chase, he'd say, is always better than the kill. Leopold noted that Stephen disliked being reminded of this little morsel of wisdom after another failed sexual adventure. But eventually Stephen agreed with the common wisdom that the value of time in heaven and hell is equal opposite and constant.

Purgatory was a dull and dreary place. A failed seaside resort, perhaps, but even then there was something missing. So Leopold became heavily involved with the gambling scene in Purgatory. He found it hard to follow all the terminology sometimes. He didn't understand how a shilling was a thousand pounds, except when it was a shilling, which it almost never was because a shilling didn't buy you anything nowadays. So a shilling was a thousand pounds. And there were some new currencies to learn. A hundred pounds made a cent, and a hundred cents made a roam. And roams were very important, because you could trade a roam for a day in heaven, and if you went into debt you had to buy back roams from the bankruptcy court at one roam per day spent in hell. It was all very painful, but it meant all debts got paid, which was nice. No one knew how this currency came into being, nor how the bank could transfer roams for days in heaven, or the bankruptcy court repay debts in this way, but when pushed most experts turned out to be Boussetians.

—Oh look! There's Buck, said Stephen. Should we go and see what he's up to?

—I suppose it can't hurt, said Leopold, thinking mostly of how he could trick Buck out of some roams.

When they wandered over, Buck was talking with an angel called Daniele. Or at least that's what Buck said the name was, though Leopold and Stephen were suspicious, for the angel didn't look Italian. Daniele was explaining a particular deal Buck was being offered.

—A rock is an envelope with a number written inside it. I figure out what number to write in it by flipping a coin repeatedly until it lands tails.

—A fair coin? asked Buck suspiciously.

—Yes, it's all perfectly fair, said Daniele. If it lands tails the first time, I write 1, if it lands tails the second time I write 2, if it lands tails the third time I write 4, the fourth time I write 8, and so on.

—And if it never lands tails? asked Buck, seeming to recall something from his past.

—I tear up the envelope and start again, said Daniele.

—Doesn't that take a while? asked Stephen.

—I flip the coins pretty fast, said Daniele. So, that's a standard rock. A tenrock is just like a normal rock, except I multiply the numbers by ten. And for a hundredrock I multiply the numbers by one hundred. And that, Buck my lad, is just what I have here. Two shiny hundred rocks, one green and one gold.

—It looks more yellow than gold to me, said Buck, still not trusting Daniele.

—Well, it's faded a bit over time. So let's call it yellow. Here's the deal. If you agree as many days in hell as is written in the yellow envelope, you can spend as many days in heaven as is written in the green envelope. What do you think?

—I don't like that deal, said Buck, I don't trust those rocks.

—Hmmm, said Daniele meaningfully. What about this deal then? If you agree to spend one billion days in hell, you can spend the number of days in heaven written in the yellow envelope.

—NO! screamed Buck.

—That sounded fairly definite to me, said Daniele, and started to drift off.

Leopold and Stephen, intrigued by the last exchange, followed in pursuit.

—Why did you offer him that last deal? asked Stephen.

—I'm allowed to do anything I like to your poor souls as long overall you're better off having me around than not having me around. So now in the future I can make up some rules for our Buck to break, and then send him to hell for a decade or two for breaking them.

Stephen didn't follow this at all, but he couldn't help but be impressed by the majesty of the apparent smile on Daniele's face.

Meanwhile, Leopold was busy calculating what Buck had been offered. How much and how many and how much and how many and how much and how many and, oh this is going to take a while. Stephen always thought how much and how many and so on was a foolish way to choose how to bet, but he had to admit that Leopold had been doing fairly well since he started using it. So if it's going to take so long, is it worth even doing? Perhaps. How much and how many, that's 100 and a half, that's 50, and how much and how many, that's 200 and a quarter, that's another 50, and 400 and an eight, that's another 50, and oh these rocks could be worth quite a bit. But how many fifties does it take to make a billion?

—So, here's four tenrocks, two green and two yellow. Will you each take one of each colour? asked Daniele.

Stephen agreed, and so did Leopold.

—I'll offer you each the same deal I offered Buck. Well, perhaps with a twist. For you Leopold I'll make your yellow envelope a tenrock minus ten.

And, snapping his fingers, he did just that.

—What's a tenrock minus ten? asked Leopold.

—It's just like a tenrock, except I take ten off the answer. So if your envelope previously said forty, it now says thirty. And for you Stephen, I think I'll make that yellow envelope a tenrock minus twenty.

Leopold started to splutter. Daniele ignored him and clicked his fingers.

—What if my yellow rock only said ten, asked Stephen? Now it says minus ten, but I can't spend minus ten days in hell.

—If it's negative they'll be extra days in heaven, said Daniele.

—Why does he get twenty off and I only get ten off? asked Leopold who managed to regain his voice.

Ten roam was more than a man could make in a year of good gambling, and here Stephen was being given it on a whim.

—I like Catholics, said Daniele. Besides, you're doing better than ugly Buck.

Nobody noticed that Leopold rudely resumed spluttering as loudly as ever. Stephen started twirling his envelope around aimlessly while trying to think about the deal.

—Oh disaster, said Daniele. Stephen's green rock seems to be a window envelope. I do hope you haven't seen the number inside there before you made the decision.

Stephen had stopped twirling the green envelope, and was now staring at it in shocked disbelief. Daniele, in a rare feat of interpretative genius, took that to be a negative answer, and pressed on for an answer.

—What'll it be boys? Green days and yellow days for a while, or no?

—I'm in, said Leopold, though I think it's rotten how you gave him a better deal than I.

Stephen went to speak, but was clearly struggling to produce words.

—I, I, I suppose I must, I have to, that is, I can't, I'm sure it's a very generous offer, well almost sure that is, there's the rub. Almost. I decline, he finally said. But you won't be sending me to hell will you?

—Much as I'd like to, I think someone might think I'm overstepping my role if I did. So I'll take Leopold and my leave now.

—Let's see, how long are you going to be in heaven for, said Daniele when they were safely out of earshot. It's heaven first you know, I hope you don't mind.

—I think I'd rather not know how long I'm there for, said Leopold, I'd rather it be a surprise.

—Suit yourself, said Daniele, but I have to book rooms for you upstairs and down, so let's see those envelopes.

He tore open the first, and took out a telephone.

—Central bookings? Yes, I'd like to reserve a place for Leopold for

Leopold tried to put his fingers in his ears, but found that he now lacked fingers, and ears.

—eighty days. That's pretty good isn't it, Daniele said turning to Leopold.

It was the worst moment of Leopold's life.

—Now let's see what you've got at the other end.

He tore open the other envelope.

—Zero, so no hell for you this time. A lucky break all in all I'd say. Do you want to know what Stephen turned down?

—Yes, said Leopold, only just having regained his composure.

—The green envelope says 20,480, this one goes to eleven, and, let me see what's in this yellow envelope, minus 10, so make that 20,490 days. Still, I think he made the right choice, don't you Leopold?

—20,490 days, that's practically a lifetime.

—Terrific thinking Leopold, said Daniele. Now try looking at the envelopes from Stephen's perspective.

—Oh I see, said Leopold after a pause. Yes, I think he did the right thing. And so did I I think. Well, all's well that ends well. When are you coming back to Purgatory?

Daniele didn't answer, and Leopold was rushed into his Heavenly rooms.


Who made the right decisions: Buck, Leopold or Stephen?


So here's a summary of the decisions the characters faced, for those who wanted to skip the story.

First, some stipulations. The default setting for the agents is that they will spend eternity in Purgatory. They can, from time to time, rise to Heaven or fall to Hell. The value of time spent in these places is, as Stephen puts it, equal, opposite and constant. So five days in Heaven and five days in Hell, in any order, is just as worthwhile for an agent as ten days spent at the default condition, being in Purgatory. The constant marginal utility of time out of Purgatory means that a 50% chance of ten days in Heaven plus a 100% chance of 5 days in Hell is worth literally nothing to our agents.

A rock is a special kind of unknown value object. It is an envelope with a number inside it. A green envelope means that the bearer gets to spend that many days in heaven. A yellow envelope means that the bearer must spend that many days in hell. The number is chosen by flipping a fair coin repeatedly until it turns up tails. (It's a St Petersburg process, for those who like thinking of things that way.) If it turns up tails the first time, 1 is written in the envelope, 2 if tails the second time, 4 if tails the third time, 8 the fourth time, and so on. A tenrock is a rock where all those numbers are multiplied by ten. A hundred rock is a rock where the numbers are multiplied by 100. A tenrock minus x is a rock where the numbers are multiplied by ten and then x is subtracted from the result. If this leads to a negative number then the bearer is sent to the opposite place. (So a green envelope saying minus fifteen means fifteen days in Hell, and a yellow envelope saying minus ten, as turns up towards the end of the story, means ten days in heaven.)

The first deal offered is that the angel 'Daniele' offers Buck a green hundredrock and a yellow hundredrock. Buck declines the offer. Daniele then changes the deal. Buck is now offered a green hundredrock in exchange also accepting a billion days in Hell. Buck declines this offer as well, and we are never told what is in his green hundredrock.

The second deal is that Daniele offers Leopold a green tenrock in exchange for also accepting a yellow tenrock minus ten. Leopold accepts the deal, and ends up spending eighty days in Heaven, and none in Hell.

The third deal is that Daniele offers Stephen a green tenrock in exchange for also accepting a yellow tenrock minus twenty. Before he can accept or decline, Stephen sees that his green envelope contains the number 20,480. This doesn't make Daniele withdraw the offer, but Stephen declines it. It turns out Stephen's yellow envelope says minus 10, so he turned down 20,490 days in Heaven.

So, which of the three characters do you think made the right choice? Click on that link to answer.


Occasional Footnotes.

This is the most bizarre theory of the afterlife I've ever read, said Stephen. Stephen is reading Frank Arntzenius and David McCarthy's "The Two Envelope Paradox and Infinite Expectations" (Analysis 1997) as theology.

I recall Jevons arguing finely. Stephen has been reading, or perhaps misreading, this paper, especially sections 8 and 9.

For you Leopold I'll make your yellow envelope a tenrock minus ten. I'm not sure where I learned of the decision problem Daniele sets Leopold here. I think I learned it during a course on infinity that Graham Oppy ran when I was at Monash. But I'm really not sure. So this is a disclaimer of originality.

posted by Brian Weatherson 1/18/2003 04:18:00 PM

The day's changes to the philosophy papers blog are up. There's no new free content, but there's some web publications of previously published documents, and David Deutsch has posted a Mac program for tracking web page changes, just in case you want to run your own philosophy papergs blog.

posted by Brian Weatherson 1/18/2003 10:10:00 AM

Friday

More on after all

Yesterday I noted this odd phenomena where after all is usually used to split up a verb phrase headed by a cognate of to be when the subject is a pronoun, rather than placing after all in front of the verb phrase, but when the subject is a quantified expression, this pattern is reversed. I thought this might indicate some difference between quantificational and referential phrases, so I was interested to see how the pattern transferred to definite descriptions. After a bit more digging around, I found that (a) it’s hard to find definite descriptions that are common enough to get any kind of usable data, but this is unimportant because (b) names behave like quantified phrases rather than pronouns, so whatever is going on here is not tracking a referential/quantificational split. Some more data.

 

Before

After

Bush

57

98

Clinton

36

33

Gore

22

35

Blair

19

6

Hussein

7

40*

Laden

46

21

The only one of these that behaves like a quantifier is Hussein. But even there the data is messy, hence the asterix, because from eyeballing the data it looks like 31 of the uses come from an advertisement that was placed in several newspapers. So I have now gone from being puzzled by yesterday’s data to having officially have no idea whatsoever about what could explain it. My tentative hypothesis is that it’s to do with the length of the noun, and maybe its stress patterns, but that doesn’t really explain why Bush and they are so different.

posted by Brian Weatherson 1/17/2003 05:40:00 PM

Today’s philosophy papers blog entry is up. There are three new papers and a book review. There’d be a fourth new paper, but I made a policy decision not to link to websites that insist on running music programs when loaded, especially if said music programs cause computers to crash. Unlike children, websites should be seen and not heard.

posted by Brian Weatherson 1/17/2003 06:38:00 AM

Thursday

As Bill Simmons used to say, these are my readers. UPDATE: This one is even odder. I don't want to know what lies behind such a search.

posted by Brian Weatherson 1/16/2003 05:24:00 PM

I somehow noticed that in my idiolect, (1a) is much more natural than (1b), but (2a) is much less natural than (2b).

(1a)    She is, after all, perfect.
(1b)    She, after all, is perfect.
(2a)    Nobody is, after all, perfect.
(2b)    Nobody, after all, is perfect.

I don’t know immediately why this is. Nor did I know, until about 20 minutes ago, whether this was an idiosyncrasy on my part, or a general feature of English speakers. Thanks to Google, I now know that it is a general pattern among English speakers. For a number of common pronouns and quantifiers, I checked how often phrases like “She is after all” and “She after all is” appeared in the Google search engine. The results appear below. (“Before” means “after all” before the verb, as in “She after all is”, after means “after all” after the verb, as in “She is after all”. Google ignores punctuation, so I didn’t have to worry about things like commas. But that does mean that there are some false reports in the ‘after’ section, things where the match is to “… she is. After all, …”. I don’t think this affects the conclusions I draw from the data.)

 

Before

After

Percentage Before

She is

199

5,950

3

He is

416

14,400

3

We are

424

15,400

3

They are

696

16,300

4

You are

445

6,550

6

It is

599

71,300

1

Nobody is

20

0

100

Everybody is

6

1

86

Somebody is

3

5

38

No one is

54

7

89

Everyone is

39

42

48

Someone is

10

25

29

Nothing is

77

31

71

Everything is

83

64

56

Something is

65

26

71

With the exception of ‘someone’, and to a lesser extent ‘somebody’ there’s a notable difference between the way referential phrases and quantificational phrases behave here. I don’t know what causes the reversed distribution there, it could just be noise.

UPDATE: I forgot to check for quantifiers involving ‘any’. Here are the numbers

 

Before

After

Percentage Before

Anyone is

6

10

38

Anybody is

0

0

n/a

Anything is

59

5

92

Not much there of note, except for the complete absence of sentences using anybody. Anybody, after all, is entitled to use ‘after all’.

posted by Brian Weatherson 1/16/2003 02:17:00 PM

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