I’m teaching an upper level decision theory course at Rutgers this semester, and I thought I’d try and write detailed notes for each of the classes I’m teaching. I’m not sure it’s been a great success so far – largely because I haven’t really had time to carefully edit the notes. But still I thought there might be some interest in these beyond just my class, so I’ll post them here.
These notes take us through the first 14 of 28 planned classes.
My university (Rutgers) is fairly actively encouraging students to register to vote. And I’ve occasionally done a bit to help, hosting students who do a spiel on voter registration and personally encouraging students to vote.
Now I think this is all a good thing. Voting is a good thing, and a healthy democracy requires a decent turnout of voters, so doing our little bit to help democracy is being on the side of the good. It’s not exactly related to the courses we’re teaching, but spending 45 seconds before class is officially scheduled to start encouraging voter registration, or putting voter registration ads on course management software as Rutgers has done, seems far from an abuse of official positions.
Still, voting isn’t the only good thing in the world. It seems to me that voting in the upcoming election for Obama/Biden over McCain/Palin is pretty close to a moral requirement. (For those who are eligible to so vote. I of course won’t be voting for Obama, because that would be illegal, and undemocratic.) But it seems it would be seriously wrong for either Rutgers, or for me, to use our positions of authority to promote voting for Obama. And I think this isn’t a particularly controversial position.
But it’s a little hard to say just exactly why it’s OK for Rutgers (and me) to do what we’re doing, and not do what we’re not doing. (Mike and Ross in the comments to the previous post were pushing just this question, which led to me trying to think about it a little.) Below the fold I have a few thoughts on this question.
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On the non-partisan side, I’ve posted a link above to a U.S. vote registration site. I imagine most readers of this site who are eligible to vote in the U.S. are registered. But many of you probably teach students who are eligible and are not registered. And voter registration closes in a couple of weeks in most states. At Rutgers there is a large push on by the university to register as many students as possible. And I think it would be very good to encourage students to register to vote. While I think it would be irresponsible to use one’s position in a class to promote one particular candidate, I think promoting vote registration is a perfectly good thing to do, even in an official capacity.
But this blog isn’t a classroom, so I don’t have to be non-partisan. And I think that it’s pretty overdetermined who the better candidate is this election.
The last 8 years in America have been considerably worse than the previous 8. The country has been involved in unnecessary wars, wages have stagnated, the markets have been in a mess, and the legal foundations of the country, from the separation of powers to the prohibition on torture, have been undermined. There’s no reason to think that things will get better under McCain, and some reasons (his cavalier attitude towards getting involved in wars in Iran and Georgia, his Hooveresque insistence that the economy is fundamentally sound) that things will get worse.
Barack Obama’s plans, on the other hand, are, in my opinion, the most promising set of policies and priorities we’ve ever seen from a major American Presidential candidate. On “the environment”:http://my.barackobama.com/page/content/newenergy, on “healthcare”:http://www.barackobama.com/issues/healthcare/ and (dear to my heart) on “immigration”:http://www.barackobama.com/issues/immigration/, he’s pushed for sensible positions that, until recently, most Democrats would have been too scared to touch. So there’s a pretty stark difference between the candidates.
In any election campaign there’s a lot you can do. Due to the odd nature of the American electoral system, for many people there is no close campaign within 100, or even 500, miles. So it’s often hard to work on the ground. But you can donate money! There’s an interesting collective action problem here of course. But I think if everyone who wants Obama to win, especially everyone who has a decent income and can spare a few dollars, donates what they can spare, there’s a much better chance we’ll have a much better America in the next few years.
Note that while only citizens can vote in U.S. elections, permanent residents are allowed to donate money to the campaign. Indeed it’s one of the few ways that (non-naturalised) immigrants can be involved in the politics of the country they live in. So I’d certainly encourage all green card holders out there to help out.
I’ve posted a small donation link on the sidebar, and donations through TAR will be counted up there. Happy donating everyone, and even if you don’t want to donate, encouraging as many students as possible to register to vote will be helping democracy grow one student at a time!
I’ve been spending most of the last few weeks getting ready for term and fretting over elections, so blogging has been somewhat lighter than expected. There’s some possibility I’ll start using this blog as an outlet for fretting about the election over the next 7 weeks, so posting might get a little more frequent but less philosophical.
Anyway, today I just wanted to put in a brief plug for Manuel García-Carpintero and Max Kölbel’s edited collection “Relative Truth”:http://www.oup.com/uk/catalogue/?ci=9780199234950. The OUP site says this is “The hottest topic in philosophy”, which sounds like slight hyperbole to me. But it is an important topic, and this is an excellent collection. The papers are largely from the Barcelona workshop on relative truth, which I thought was a great success. And anyone who is interested in the subject should pick up this collection.
(This post is a collection of some ideas I had in a conversation with Dan Korman about six months ago, at the APA Pacific in Pasadena.)
Are there such things as constellations? I’ll presume that there are such things, which then of course raises the question of what they are. The natural thought is that a constellation is a collection of stars, which means that it’s a bunch of balls of hydrogen and such, each glowing from the heat of its fusion, scattered across large expanses of space.
But this seems to give the wrong persistence conditions. Consider the constellation of <A href=http://en.wikipedia.org/wiki/Orion_(constellation)>Orion</a>, which is probably the most easily recognizable and visible constellation in the northern hemisphere (unfortunately, at this time of year in the southern hemisphere it doesn’t rise until about 1 am, and whenever it does appear it’s upside-down). If <A href=http://en.wikipedia.org/wiki/Epsilon_Orionis>the middle star in his belt</a> were to suddently cease to exist, it seems that we wouldn’t say that Orion has ceased to exist (as would be the case if Orion were just a set of stars), but rather that Orion’s belt is now missing a buckle. Similarly, if a new, extremely bright star were to appear in the vicinity of <A href=http://en.wikipedia.org/wiki/Lambda_Orionis>Orion’s head</a>, we would say that Orion’s head is now brighter, and not that we’re looking at a new constellation. So we might suggest that a constellation is not a set of stars, but is rather an object composed of them.
Now, when I say “in the vicinity of”, it doesn’t actually matter how close this new star is to the star that already exists there – the star that currently serves as Orion’s head is about 1000 light years away, while <A href=http://en.wikipedia.org/wiki/Gamma_Orionis>Orion’s right shoulder</a> (the less bright one) is only about 240 light years away. A new bright star could count as an addition to Orion if it was over 1000 light years away (like the head and middle of the belt), or if it was closer to the shoulder, or if it was only 1 or 2 light years away, in which case it would be much closer to the stars in <A href=http://en.wikipedia.org/wiki/Crux>the Southern Cross</a> than it would be to most of the other stars in Orion. The important thing is just what angle you’d have to look at to see it from Earth.
Thus, I suggest that rather than being composed of stars (as in the actual glowing balls of gas), a constellation is composed of beams of light reaching Earth. [UPDATE: see comments for a modification of the “beam of light” view.] To be part of Orion, it doesn’t matter where the ball of gas is in relation to the other balls of gas (after all, a few of those balls of gas are closer to stars in constellations that can’t even be seen from most of the northern hemisphere than they are to most of the other balls of gas in Orion), but it does matter what angle the beam of light reaches Earth. As further confirmation of this view, note that if the middle star in Orion’s belt were to explode right this instant and stop shining, we wouldn’t actually say that Orion has lost his belt buckle yet – that wouldn’t happen for another 1300 years. Although the ball of gas would no longer exist, the beam of light reaching the Earth still would for quite a while.
This suggestion then raises another question – if constellations are composed of beams of light rather than of balls of gas, then are constellations really made of stars? I think the natural answer here is that the word “star” is actually ambiguous between a glowing ball of gas and a beam of light reaching the Earth, and that constellations are composed of the latter but not the former. As it turns out, a few “stars” aren’t really beams of light from individual glowing balls of gas at all. Some of them are <A href=http://en.wikipedia.org/wiki/Binary_star>binary star systems</a> (for instance, <A href=http://en.wikipedia.org/wiki/Sirius>Sirius</a>, which is the brightest “star” in the sky, and which you can find conveniently by following the line of Orion’s belt down and to the left (reverse the directions in the Southern hemisphere of course). And the bright middle “star” in Orion’s belt [sword] is actually <A href=http://en.wikipedia.org/wiki/Orion_Nebula>the Orion Nebula</a>, which is a cloud of gas that is giving birth to many stars in the other sense.
Of course, not just any beam of light coming down to Earth counts as a star – some are planets, some faint ones are asteroids or moons of planets, and some are man-made satellites. (For instance, a few weeks ago I was able to spot the International Space Station using a guide <A href=http://heavens-above.com/PassSummary.aspx?satid=25544&lat=0&lng=0&loc=Unspecified&alt=0&tz=CET>here</a> – you’ll need to input your own location and time zone for that to be helpful.) Presumably, for a beam of light to count as a star in this sense, it must be bright enough to be visible to the naked eye, but also stable enough that it doesn’t noticeably move from year to year, and must come from far enough away that it doesn’t noticeably move as the observer moves from point to point on Earth. But constellations in the ordinary sense I would say are composed of these sorts of stars, and not of balls of gas in space.
Thus, I think it’s incorrect to say (as we standardly do) that stars are glowing balls of gas in space, and that constellations are made of stars. This involves an equivocation on the word “star”. Stars in one sense tend to be created by stars in the other sense, but the examples pointed out above show that one can exist without the other.
(Astronomers do have terms for certain natural collections of balls of gas, like <A href=http://en.wikipedia.org/wiki/Star_cluster>star clusters</a>, which are balls of gas of the relevant type that are gravitationally bound to one another. They also have a<A href=http://en.wikipedia.org/wiki/Constellation>technical use</a> of the term “constellation” to refer to one of 88 specific regions of the sky and all the stars in them – thus for instance, the astronomical constellation of <A href=http://en.wikipedia.org/wiki/Crux>Crux</a> consists not just of the five stars of the Southern Cross seen on <A href=http://en.wikipedia.org/wiki/Flag_of_Australia>the Australian flag</a> (for some reason the <A href=http://en.wikipedia.org/wiki/Flag_of_New_Zealand>New Zealand flag</a> has only four stars) but actually has <A href=http://en.wikipedia.org/wiki/List_of_stars_in_Crux>at least a dozen</a> stars. However, they use the technical term <A href=http://en.wikipedia.org/wiki/Asterism_(astronomy)>”asterism”</a> for something very much like the ordinary term “constellation”.)
I’ve been in Australia for a while, and therefore have fallen behind in my reading of the New Yorker (I only just last week read the one with the controversial cover). But I just read <A href=http://www.newyorker.com/reporting/2008/07/28/080728fa_fact_osnos>an article</a> from the July 28 issue about growing nationalistic sentiment among educated Chinese youth, and was struck by the fact that the main person the article was discussing is a student at a university in China writing his dissertation on Husserl. There’s also some discussion of the influence of Leo Strauss among the relevant group. It made me wonder what sorts of connections there are between the relevant academic communities in China and the rest of the world.
The Australasian Association of Philosophy has compiled a new set of journal rankings for submission to the Australian Research Council. Without knowing exactly what the ARC wants them for, I would nevertheless imagine these are worth knowing about if you ever plan to work in Australia. Some of the rankings look very odd to me. Several flaws with the whole procedure are noted in the AAP’s covering letter.
I’m mostly just writing lecture notes for the upcoming term and paying more attention to vice-presidential rumours than baseball rumours. So some links to keep the blog moving.
At least since Robert Cummins’s paper “Reflections on Reflective Equilibrium”:http://books.google.com/books?id=kOjtQwQ0XmkC&pg=PA113&source=gbs_toc_r&cad=0_0&sig=ACfU3U3tRJ9Pv34k2FDeD3emET6VzxcK2g in “Rethinking Intuition”:http://books.google.com/books?id=kOjtQwQ0XmkC, a lot of people have worried that intuition, that old staple of philosophical argument, is unreliable. This is fairly important to the epistemology of philosophy, especially to intuition-based epistemologies of philosophy, so I think it’s worth considering.
(Worries about intuition obviously don’t start 10 years ago, but the particular worry about reliability does become pronounced in Cummins. I suspect, though I don’t have the relevant papers in front of me, that there are related worries in earlier work by Stich. Note that this post is strictly about reliability, not a general defence of intuition in philosophy.)
The happy new is that there’s a simple argument that intuition isn’t unreliable. I think it isn’t clear whether intuition simply is reliable, or whether there’s no fact of the matter about how reliable it is. (Or, perhaps, that there is no such thing as intuition.) But we can be sure that it is not unreliable.
Start with a fact that may point towards the unreliability of intuitions. Some truths are counter-intuitive. That’s to say, intuition suggests the opposite of the truth. I’m told it’s true that eating celery takes more calories than there is in the celery, so you can’t gain weight by eating it. If true, that’s pretty counterintuitive. And just about everything about “counter-steering”:http://en.wikipedia.org/wiki/Countersteering strikes me as counterintuitive. So those are some poor marks against intuition.
But now think of all the falsehoods that would be even more counterintuitive if true. If you couldn’t gain weight by eating steak, that would be really counterintuitive. Intuitively, steak eating is bad for your waistline. And that’s true! Intuitively, you have less control of a motorbike at very high speeds than at moderate speeds. And that’s true too! It would be really counterintuitive if remains from older civilisations were generally closer to the surface and easier to find than remains from more recent civilisations. And that’s false – the counterintuitive claim is false here.
In fact almost everywhere you look, from archeology to zoology, you can find falsehoods that would be very counterintuitive if true. That’s to say, intuition strongly supports the falsehood of these actual falsehood. That’s to say, intuition gets these right.
To be sure, most of these cases are boring. That’s because, to repeat a familiar point, we’re less interested in cases where common sense is correct. And here intuition overlaps common sense. But that doesn’t mean intuition is unreliable; it’s just that we don’t care about it’s great successes.
There are so many of these successes, so many falsehoods that would be extremely counterintuitive if true, that intuition can hardly be unreliable. But maybe it’s not actually reliable either. I can think of two reasons why we might think that.
First, there may be no fact of the matter about how reliable intuition is.
It’s counterintuitive that there can be proper subsets of a set that are equinumerous with that set. And that’s true, so bad news for intuition. It would be really counterintuitive if there could be proper subsets of a set of cardinality 7 that are also of cardinality 7. But there can’t be, so good news for intuition. And the same for cardinality 8, 9, etc. So there are infinitely many successes for intuition! A similar trick can probably be used to find infinitely many failures. So there’s no such thing as the ratio of successes to failure, so no such thing as how reliable intuition is.
On the other hand, perhaps we’re counting wrongly. Perhaps there is one intuition that covers all of these cases. Perhaps, though it isn’t clear. It isn’t clear, that is, how to individuate intuitions. Arguably our concept of an intuition isn’t that precise to give clean rules about individuation. But if that’s right, there again won’t be any fact of the matter about how reliable intuition is.
This isn’t, I think, bad news for using intuition in philosophy. Similar arguments can be used to suggest there is no fact of the matter in how reliable vision is, or memory is. But it would be absurd on this ground to say that vision, or memory, is epistemologically suspect. So this doesn’t make intuition epistemologically suspect.
Second, there might be no single such thing as intuition. (I’m indebted here to conversations with Jonathan Schaffer, though I’m not sure he’d endorse anything as simple-minded as any of the sides presented below.)
It would be counterintuitive if steak eating didn’t lead to weight gain. It would be counterintuitive if Gettiered subjects have knowledge. In both cases intuition seems to be correct. But perhaps this is just a play on words. Perhaps there is no psychologically or epistemologically interesting state that is common to this view about steak and this view about knowledge.
If that’s so, then perhaps, just perhaps, one of the states in question will be unreliable.
I doubt that will turn out to be the case though. Even if there are distinct states, it will still turn out that each of them gets a lot of easy successes. Let’s just restrict our attention to philosophical intuition. We’ll still get the same results as above.
It would be counterintuitive if torturing babies for fun and profit was morally required. And, as it turns out, torturing babies for fun and profit is not morally required. Score one for intution! It would be counterintuitive if I knew a lot about civilisations on causally isolated planets. And I don’t know a lot about civilisations on causally isolated planets. Score two for intuition! It would be counterintuitive if it were metaphysically impossible for me to put off serious work by writing blog posts. And it is metaphysically possible for me to put off serious work by writing blog posts. 3-0, intuition! I think we can keep running up the score this way quite easily, even if we restrict our attention to philosophy.
The real worry, and this might be a worry for the epistemological significance of intuition, is that the individuation of state types here is too fuzzy to ground any epistemological theory. For once any kind of intuition (philosophical, epistemological, moral, etc) is isolated, it should be clear that it has too many successes to possibly be unreliable.
The following puzzle is a cross between the “Newcomb puzzle”:http://en.wikipedia.org/wiki/Newcomb’s_paradox and the “centipede game”:http://en.wikipedia.org/wiki/Centipede_game.
You have to pick a number between 1 and 50, call that number _u_. A demon, who is exceptionally good at predictions, will try to predict what you pick and will pick a number _d_, between 1 and 50, that is 1 less than _u_. If she predicts _u_ is 1, then she can’t do this, so she’ll pick 1 as well. The demon’s choice is made before your choice is made, but only revealed after your choice is made. (If the demon predicts that you’ll use a mixed strategy to choose _u_, she’ll set _d_ equal to 1 less than the lowest number that you have some probability of choosing.)
Depending on what numbers the two of you pick, you’ll get a reward by the formula below.
If _u_ is less than or equal to _d_, your reward will be 2u.
If _u_ is greater than _d_, your reward will be 2d – 1.
For an evidential decision theorist, it’s clear enough what you should do. Almost certainly, your payout will be 2u – 3, so you should maximise _u_, so you should pick 50, and get a payout of 97.
For a causal decision theorist, it’s clear enough what you should not do. We know that the demon won’t pick 50. If the demon won’t pick 50, then picking 49 has a return that’s better than picking 50 if _d_ = 49, and as good as picking 50 in all other circumstances. So picking 49 dominates picking 50, so 50 shouldn’t be picked.
Now the interesting question. What *should* you pick if you’re a causal decision theorist. I know of three arguments that you should pick 1, but none of them sound completely convincing.
_Backwards Induction_
The demon knows you’re a causal decision theorist. So the demon knows that you won’t pick 50. So the demon won’t pick 49; she’ll pick at most 48. If it is given that the demon will pick at most 48, then picking 48 dominates picking 49. So you should pick at most 48. But the demon knows this, so she’ll pick at most 47, and given that, picking 47 dominates picking 48. Repeating this pattern several times gives us an argument for picking 1.
I’m suspicious of this because it’s similar to the bad backwards induction arguments that have been criticised effectively by Stalnaker, and by Pettit & Sugden. But it’s not quite the same as the arguments that they criticised, and perhaps it is successful.
_Two Kinds of Conditionals_
In his very interesting “The Ethics of Morphing”:http://web.mit.edu/~casparh/www/Papers/CJHareMorphing.pdf, Caspar Hare appears to suggest that causal decision theorists should be sympathetic to something like the following principle. (Caspar stays neutral between evidential and causal decision theory, so it isn’t his principle. And the principle might be slightly stronger than even what he attributes to the causal decision theorist, since I’m not sure the translation from his lingo to mine is entirely accurate. Be that as it may, this idea was inspired by what he said, so I wanted to note the credit.)
Say an option is unhappy if, supposing you’ll take it, there is another option that would have been better to take, and an option is happy if, supposing you take it, it would have been worse to have taken other options. Then if one option is happy, and the others all unhappy, you should take the happy option.
Every option but picking 1 is unhappy. Supposing you pick n, greater than 1, the demon will pick n-1, and given that you would have been better off picking n-1. But picking 1 is happy. Supposing that, the demon will pick 1, and you would have been worse off picking anything else.
There’s something to the _pick happy options_ principle, so this argument is somewhat attractive. But this does seem like a bad consequence of the principle.
_Stable Probability_
In Lewis’s version of causal decision theory, we have to look at the probability of various counterfactuals of the form _If I were to pick n, I would get k dollars_. But we aren’t really told where those probabilities come from. In the Newcomb problem that doesn’t matter; whatever probabilities we assign, two boxing comes out best. But the probabilities matter a lot here.
Now it isn’t clear what constrains the probabilities in question, but I think the following sounds like a sensible constraint. If you pick n, the probability the demon picks n-1 (or n if n=1) should be very high. That’s relevant, because the counterfactuals in question (what would I have got had I picked something else) are determined by what the demon picks.
Here’s a constraint that seems plausible. Say an option is Lewis-stable if, conditional on your picking it, it has the highest “causally expected utility”. (“Causally expected utility” is my term for the value that Lewis thinks we should try to maximise.) Then the constraint is that if there’s exactly one Lewis-stable option, you should pick it.
Again, it isn’t too hard to see that only 1 is Lewis-stable. So you should pick it.
_Summary_
It seems intuitively wrong to me to pick 1. It doesn’t dominate the other options. Indeed, unless the demon picks 1, it is the worst option of all. And I like causal decision theory. So I’d like a good argument that the causal decision theorist should pick something other than 1. But I’m worried (a) that causal decision theory recommends taking 1, and (b) that if that isn’t true, it makes no recommendation at all. I’m not sure either is a particularly happy result.