"The Practical Importance of Knowledge (Such As It Is)" is here. (Too lazy to put it into its own blog entry this year.) It's being given in session III-F (scroll down a while), 3:45 Friday, with very useful comments by Mylan Engel. (I'm still trying to figure out whether I can respond while preserving the point of the paper--I think and hope so.)
I'm not sure what room the session is in. That doesn't necessarily mean that the room isn't listed somewhere obvious on the APA program website, only that I didn't see it. Past experience indicates that the first doesn't follow from the second.
[FINAL UPDATE: OK, this post is lame. If the only occurrence of the obvious jumps-the-shark joke had been in a context where it wasn't obvious that the user was in on the joke, it might have been funny to point it out. But given that several other people were on it already, piling in on the jumps-the-shark joke was just lame. I'm leaving the post up as an example of the perils of failing to do a proper lit search.
This update is the promised post on the surprise inspection paradox, BTW.]
The other week I caught Damien Hirst's exhibition of new paintings at the Gagosian. Like most people, apparently, I thought it sucked. Coulda saved everyone a bunch of trouble by having his assistants paint a sign saying "I, Damien Hirst, am obsessed by pharmaceuticals, hospitals, and the marginalized of society."
I'm mentioning it now so I can link to this gallery roundup:
Most reviews say this is the show where Hirst jumps the shark, and I can see why as most of the subject matter has already been covered.
[UPDATE: Ah, you find the obvious pun by searching for "hirst 'jumped the shark'"; didn't really think I could be the first one on this.]
If the opposite of 'anonymous' is 'onymous', what's the opposite of 'pseudonymous'?
I mean the conditional seriously, in a way. That is: For most standards of usage the opposite of 'anonymous' isn't 'onymous', because 'onymous' isn't a word. But in silly uber-geeky online writing--yes, you, reading this right now--nonce words like 'onymous' are acceptable and in fact encouraged. So I want to set the standard of usage to the standard on which 'onymous' is the opposite of 'anonymous', and then find out what the opposite of 'pseudonymous' is for that standard.
Could it be that this is what's going on in the snowclones that Geoff Pullum is always complaining about, such as "If Eskimos have dozens of words for snow, Germans have as many words for bureaucracy." But probably not.
(Incidentally, I hope this warms Geoff's heart: "Although the claim that the Eskimos have hundreds of words for snow is an exaggeration, the Inupiat make distinctions among many different types of ice, including sikuliaq, 'young ice,' sarri, 'pack ice,' and tuvaq, 'landlocked ice.'" Please to forgive American-style punctuation.)
In comments here I wrote:
(1) If there were only one Pick'n'Save in that area I would have a better handle on where it was.
Does this make sense? It seems grammatical to me, but...
it also seems elliptical--I'm not sure whether this would be considered syntactic--in that "better" requires something that it's better than. So (1) means the same thing as
(2) If there were only one Pick'n'Save in that area I would have a better handle on where it was than the handle I actually have.
But the second occurrence of 'handle' requires explanation: handle on what? So:
(3) If there were only one Pick'n'Save in that area I would have a better handle on where it was than the handle I actually have on where it is.
And now the last 'it' is problematic. While the first 'it' can refer to the sole Pick'n'Save in the area in the counterfactual situation I describe, the last 'it' is to be evaluated in the actual world--in which there are two Pick'n'Saves in the area, and so there is no 'it' whose location I can have a handle on.
Maybe this fuzziness just comes from the basic problem raised by ontological confusion: It's hard to say exactly what I don't have a handle on. I think (well, not any more) that there is one Pick'n'Save, whose location I don't know well. But in fact when I'm trying to think about one Pick'n'Save, I'm actually thinking about two. And though there are some things that enables me to get right--if I go south and east I'll hit a Pick'n'Save--there are other things I get wrong about this.
The solution is to read up on ontological confusion, but I wonder if there's anything distinctive about the linguistic phenomenon in (1).
I'm making some changes to "Must We Know What We Say?" and I have a question. The question has two parts: What's going on here? and Should I put something about it in the paper?
This has to do with my account of the following case (from Williamson's "Knowing and Asserting," names supplied by me): Alice has a lottery ticket. The drawing has been held but the winner has not been publicly announced. Sarah, having no inside information, tells Alice
(1) Your ticket did not win
which turns out to be true. Nevertheless, when Alice finds out that Sarah's assertion of (1) was based entirely on the low probability of the ticket's winning, she's entitled to be annoyed. Why is that? Williamson says, "Because Sarah didn't know that (1) was true, and knowledge is the norm of assertion," but I don't think knowledge is the norm of assertion, so I need another account.
In the paper, after establishing that Alice is entitled to assume that Sarah has some warrant for asserting (1), I argue thus (last full paragraph on p. 15):
Why should Alice infer that Sarah's warrant is not merely probabilistic? The answer lies in Grice's maxim of Manner. If Sarah wants to make clear that her warrant is merely probabilistic, she has the option of saying(6) Your ticket is almost certain not to have won.Since Sarah did not say (6), Alice is entitled to assume that her warrant is not merely probabilistic. Since (1) is ambiguous between two kinds of warrant that Sarah may have, and (6) is appropriate if and only if Sarah has a probabilistic warrant (by the first maxim of Quantity), the assertion of (1) implicates that Sarah has a non-probabilistic warrant. [underlined words added due to referee's comment]
In response to a referee's comment, I've just added this footnote to the paragraph:
An anonymous referee suggests that a parallel argument would entitle Alice to conclude that Sarah has a probabilistic warrant. Sarah did not assert (6*):(6*) Your ticket is absolutely certain not to have wonwhich entails that the speaker has non-probabilistic warrant. So, the suggestion goes, if asserting (1) instead of (6) implicates that Sarah has non-probabilistic warrant for her assertion, asserting (1) rather than (6*) implicates that Sarah lacks non-probabilistic warrant for her assertion. I do not think that the argument is truly parallel. Though (6*) entails that Sarah has non-probabilistic warrant, (6*) cannot be felicitously asserted in every case in which she has non-probabilistic warrant. If Sarah has merely heard from a usually reliable source that Alice's ticket did not win, she cannot assert (6*), because she is not absolutely certain that the ticket did not win. So in asserting (1) rather than (6*), Sarah does not implicate that she has probabilistic warrant rather than a non-probabilistic warrant that falls short of absolute certainty. (I thank the referee for making me see that "if and only if" rather than "only if" was required in the text.)
But now I'm thinking about this problem: Why, if Sarah had a non-probabilistic warrant, couldn't she say (6')?
(6') I know your ticket didn't win.
If (6') were assertable whenever Sarah had a non-probabilistic warrant, then the referee's parallel argument would go through.
In one way it seems obvious to me that (6') is inappropriate even if Sarah has a non-probabilistic warrant. It's just an odd thing to say. Somehow it draws attention to Sarah rather than to the ticket, and so (by the maxim of Manner?) it suggests something more than merely that Sarah has a non-probabilistic warrant for believing that Alice's ticket didn't win. So the parallel argument doesn't go through--the fact that Sarah asserts (1) rather than (6') doesn't implicate that she lacks non-probabilistic warrant, and the fact that she asserts (1) rather than (6) still does implicate that she has probabilistic warrant.
But you'll notice that I don't exactly have a good account of why (6') is inappropriate even if Sarah has non-probabilistic warrant.
Another issue is this: It's not absolutely obvious that (6') is assertable whenever Sarah has a non-probabilistic warrant. It seems as though most of the non-probabilistic warrants she might plausibly have in this situation would be enough to give her knowledge, and I guess that's enough in this case. But it would take a little development to show that (6') is threatening in a way that (6*) isn't.
So: Should I extend the footnote to mention my worry about (6')? In posting about it here, have I fulfilled my duties of intellectual honesty? And do you have a theory about why (6') really would be inappropriate? I'm leaning toward "No," "Yes," and "Not as much as I'd like," respectively.
Click "Extended Entry" for an even more random post than usual. Unifying thought: People who write the columns that appear on page B-1 of the paper have been using this format for ages. Blogs just let you do it a bit at a time. Yet another reason against blogosphere triumphalism.
--From the allegedly factual Onion A.V. Club's review of the game NARC:
When it was announced that the new NARC would feature characters using street drugs, people naturally wondered whether the game would send the wrong message.
So people are worried about whether a game that basically appears to be a first-person shooter will send the wrong message because it depicts drug use? Whatevs.
--So, on the second night of Passover, Bill Frist is participating in a telecast about how opposition to Bush's most extreme judicial nominees is part of an attack on "people of faith." Well, it's nice to have it out there: "People of faith" doesn't include Jews, or most Christians. (And, for those of you keeping track, Orthodox Judaism is not the only brand of Jewish faith.)
But that's not what bugs me. What bugs me is that both Jon Langford's The Executioner's Last Songs and the John Scofield/Brad Mehldau concert are on the first night of Passover, when I will be otherwise engaged. Drat.
--Speaking of Passover--and to my surprise vaguely relevant to the post title--my official policy is that I follow some of the Passover rules, but none of the non-Passover rules of Kashrut that I don't follow the rest of the year. I think this makes perfect sense. So: bacon cheeseburgers are OK, so long as I don't eat the bun. This strikes me as perfectly consistent.
I used to be fairly strict about the Passover rules: no rice, no legumes, no grain-based booze. (But non-diet products involving corn syrup were always OK. Diet pop is an abomination that the Lord never intended us to drink. You could argue that the Lord intended us to have sugar rather than corn syrup in our pop, but in a country dominated by Big Corn that's not an option.) But since that rules out pretty much everything I ordinarily eat, I would wind up consuming ridiculous amounts of eggs, and one year I found myself pretty light-headed by the end of the week. So rice and legumes are back in, probably. But no blatant bread, pasta, or beer. Fortunately hard cider passes my tests.
So if you see me at the APA eating funny and drinking Woodchuck, there's a reason.
--One reader won't like this.
But this bit verges on online triumphalism:
Whatever its flaws, the writing you find online is authentic. It's not mystery meat cooked up out of scraps of pitch letters and press releases, and pressed into molds of zippy journalese. It's people writing what they think.
And sometimes it's undisclosed paid operatives of a Senate campaign engaging in pure hackery. If you don't know about the astroturf blogging in the 2004 South Dakota Senate race (Daschle v. Thune), read this, this, and this. (I'm unfamiliar with the writer and site in the last link, but it seems well sourced.)
[LATE ADDITION: In a book called The World Is Flat, Thomas Friedman says "We're not in Kansas anymore?" Sheesh.
There are two Pick 'n Saves a little bit south and a little bit west of my apartment. This explains some things. It may not explain others.
...is a day when you get to post a long excerpt from Joy in the Morning and be on-topic. And some nice person had already posted the passage in an easily Googlable place, so I could just cut and paste it! I am a ray of sunshine (in short supply in Milwaukee today).
From the Department of "Makes me so angry I have to post about it."
Army intelligence officials in Iraq developed and circulated "wish lists" of harsh interrogation techniques they hoped to use on detainees in August 2003, including tactics such as low-voltage electrocution, blows with phone books and using dogs and snakes -- suggestions that some soldiers believed spawned abuse and illegal interrogations.... Army investigative documents released yesterday, as well as court records and files, suggest that the tactics were used on two detainees: One died during an interrogation in November 2003 while stuffed into a sleeping bag, and another was badly beaten by inexperienced interrogators using a police baton in September 2003.
If no one is prosecuted for this--and if there are not investigations conducted to see exactly how high the culpability goes--then the International Criminal Court should step in. (Of course, Gen. Ricardo Sanchez should already be under investigation for lying under oath to Congress about torture, but that's not an ICC issue.)
Fitting in with the post title, via Professor B comes this form letter from Walmart about why they don't provide emergency contraception, and why they allow their pharmacists to deny you any sort of contraceptive drugs if the pharmacist feels you should not be having sex. Just another reason never to set foot in the store. I understand abortion as a controversial issue--I understand that some people will not want to use contraception themselves--but other people's use of contraception is their own business. Period. And if you don't want to dispense contraception, you shouldn't be a pharmacist.
As promised, but it's pretty weak. I'll have something else within ten days. But you won't know that it's up before you check the blog that day (where asking someone else counts as checking the blog).
Here's a nice explanation of the paradox by Lucian Wischik--attached to a paper that reviews all the literature up to 1970. I should read it, eh? Let's take it that the inspector says "There will be an inspection one day next week at 9:00, and before the inspection takes place you will not know what day it is."
Anyway, the paradox depends on the idea that the inspectee (examinee, whatever) in fact cannot know that there will be an inspection on day X. If the inspectee could know that, then there wouldn't be a paradox--the inspector's original statement is just false. The paradox is that we seem to be able to deduce that the statement is not true--and yet it is true.
This requires a serious sense of knowledge. Brian Weatherson argues off and on that knowledge is just true belief--here's perhaps the most relevant post. (And on and off he argues that knowledge is justified true belief, but leave that aside.)
In that post Brian argues that if you bet "S doesn't where x is" and S turns out to have a completely unjustified true belief concerning x's location, you've got to pay up or get beat up--which indicates that S did know where x is.
Applying the "pay up or get beat up" test, suppose the inspector says, "There'll be an inspection next week at 9:00, and I bet that before the inspection takes place you won't know when it is." (Let's assume the inspection is already scheduled.) The inspection is Wednesday. At 8:30 am on Wednesday, the inspectee says, "The inspection is today, isn't it?" The inspector has to pay up. Saying "Do you know that?" will earn a thumping.
--Note that this isn't quite true belief. The inspectee needn't even have a belief in any strong sense of the word that the inspection is Wednesday. The inspectee just needs to guess right. Note also that, if the inspection is in fact Thursday, when the inspectee says on Wednesday "The inspection is today, isn't it?" she has to pay up. The fact that she might be able to make the correct guess Thursday won't help. (This is possibly an idiosyncracy of the structure of the bet.)
OK, so this shows that if we take knowledge to be "true belief" or "ability to win a bet on whether you know" it is possible to know when the exam will take place before it does. It's just not possible (perhaps), well, to know reliably.
So--in order for the paradox to work, we need knowledge to mean something more than true belief or lucky guessing. I think we can intuitively understand how that works, but it's hard to formalize it exactly. Maybe when I write something else about the SIP I'll say more about this issue. Or maybe not.
(just down the road from Meadow)
Your Linguistic Profile:
|55% General American English|
|0% Upper Midwestern|
That 0% Upper Midwestern indicates that maybe it's time to leave town, eh? Yeah sure. I notice that "bubbler" wasn't one of the choices. And is "General American English" really a category?
[UPDATE: via the apostropher, here's one with "bubbler" and explanations for individual items. It still doesn't give the option of "route" rhyming with "put"; maybe it's only "root" that gets pronounced that way. It has me as "36% Yankee: You are definitely a Yankee." Unfortunately, since I don't know where they're from, I don't know whether that's unproblematically true (since I'm from the North) or unproblematically false (since I'm not from New England).]
[UPDATE 2: It says at the top that it's measuring your "southern blood." OK then.]
...but, if you check my blog every night, you won't know that I've posted about the SIP before you actually check and see the post. (Unless you ask someone else, and you wouldn't do that, would you?)
I'm reading Andrew Crumey's novel Mr Mee, having heard about it from Chris Bertram, and I quote this passage (pp. 182-3):
Tissot showed a similar misunderstanding of my teaching when, exasperated by his continuing moroseness and his near-permanent occupancy of my writing desk, I said to him, 'Next week I am going to bring your wife here so that you can speak to her in person and sort out your difficulties. I know you don't want to see her, and so I shall not tell you which day she will arrive; but you can be sure that you'll meet her before the week is out.'
Tissot knew his wife would not be brought to confront him next Friday, because in that case he could be certain by Thursday evening that she must be coming, and he could make himself absent. But equally, I would also have to avoid Thursday, since otherwise he would be forewarned when Wednesday passed without a scene. Dismissing every other day in a similar manner, Tissot concluded that his wife could never show up unexpectedly to harangue him; but on Thursday he answered the door to be greeted not only by her, but also by her mother, both of whom boxed him soundly about the ears while I made myself scarce, quietly judging that so poor a logician deserved everything he got.
I already know how the novel turns out, anyway: Mr Mee ends up really, really, really sadd.
A correspondent observes
It seems that saying "it's entirely likely" expresses less certainty than "it's likely," although semantically it should be the opposite. It doesn't seem to work that way with "possible," though - "it's entirely possible" seems to work as an intensifier. "It's completely likely" seems weaker than "it's likely," which makes me think that it's something about likely, but I can't figure out what. What do you think?
I think that I can't figure this out myself. Help me!
Ian Proops, University of Michigan
"Kant's Conception of Analytic Judgment."
Friday, April 15, 3:30 pm, Curtin Hall 118.
A reception will follow the talk.
Utah's income tax form instructs you to fill in "Your full name (first, middle, initial)" and then check a box for "Deceased in 2004 or 2005." I suppose the statement made by checking that box isn't analytically false, but it's metaphysically somewhat surprising.
(Yes, I'm leaving things late. Yes, it's after 11 pm. I don't care. I'm getting money back. Both how I'm living and my cat is large.)
Thanks to everyone who expressed good wishes in comments below and in e-mail. Sorry if I haven't been able to respond personally.
"Guns Up" is explained here. I find myself saying "Guns Up!" in exactly the same tone in which I say "L for love!" And the associated hand gestures have the same intrinsic properties, too, if "Guns Up" can be done with the right hand. Were I a partisan of one of Texas Tech's traditional enemies, I would say "Guns Up" while making the "L for love!" gesture. Luckily I'm not, and no one who is will ever have that idea or read about it anywhere.
I'm extremely pleased to announce that I've just unofficially accepted a tenure-track position at Texas Tech. Tech has a great group of people and a strong MA program--which, I've always argued, should be the wave of the future in philosophy. We're currently advertising another position as well--I hope this announcement will help rather than hurt recruiting!
[Post title almost was: "Hey, what's up, Knight?"]
"You never knew jumping off a bridge could be like that!"
See if you can guess what article I was teaching.
(If you didn't fall asleep during the post title, I'm taking that as license to be as technical as I wanna be.)
Gillian Russell considers the possibility that the truth predicate is like 'tonk' in that introducing it into the language makes it possible to derive contradictions. [tonkis the connective governed by the following rules: from P, you can deduce P tonk Q; from P tonk Q, you can infer Q.] Yet, given her intelim rules for the truth-predicate, 'true' has the local reduction property, so that any proof whose premises and conclusion don't contain 'true' can be normalized. (Background in these two posts of Gillian's; basically, local reduction means that if you use the result of the introduction rule as input to the elimination rule, you can get the same result without that introduction-elimination pair.)
I have a suggestion. Namely: When we introduce the truth-predicate, we have to do it in conjunction with an apparatus for naming propositions. Relatively intuitive intelim rules will then allow us to derive the liar paradox. But I'm not exactly clear on the relevance to the local reduction property.
First, a bit of handwaving about why we want different intelim rules than the ones Gillian has.
Gillian looks at "a truth predicate governed by simple disquotational rules like these ('T' is our truth predicate):
But at least on some views of quotation, this isn't actually disquotational, and our truth predicate shouldn't be a predicate of sentences. Take the view on which this expression, quotes included:
"Snow is white"
Snow is white
"Snow is white" is true
Snow is white
In very short: T(n) rather than T(A).
And we need to be able to express the fact that a proposition has a name, which I will do with the following notation:
which means that A occurs at this step, and A has name n.
The intelim rules for the naming convention are simple. If you have a premise, you can give it any name you like, so long as the name isn't already in use; if you have a named premise, you can stop calling it that. (You can assume A merely in order to name it, if you like that sort of thing.)
Aso long as n has not already been used in a previous step of the proof.
n: A [nI]
Now, I'm going to make the intelim rules for the truth predicate very strong. I could probably make them weaker, but the very strong rules will make it easy to derive the things I want.
n: Awhere--I'm not sure how to show this--the conclusion is under the scope of the same assumptions as φ(A), but not necessarily as n: A.
(Turns out I don't actually need the φ business, but I'm going to leave it in anyway.)
What this means, basically, is that if n names A, you can drop T(n) into a formula in place of A. If Fred is the name for "Snow is white," you can replace "Snow is white" with "Fred is true." "If snow is white then grass is green" becomes "If Fred is true then grass is green."
Elimination rule is the same in reverse:
n: Awith, again, the conclusion under the same assumptions as the second line, but not necessarily the first.
This will let you derive bits of the Liar Paradox like so (the assumption a line is under is in square brackets at the end of the line):
1 ~T(n) Assp [~T(n)]
2 n: ~T(n) nI 1 [~T(n)]
3 T(n) TI 2,2 [~T(n)]
4 ~T(n) Assp [~T(n)]
5 n: ~T(n) nI 4 [~T(n)]
6 T(n) Assp [T(n)]
7 ~T(n) TE 5, 6 [T(n)]
So we've derived ~T(n) from T(n) and vice versa. This is good enough for a paradox. And it should let us derive Q from P for any P, Q, by a process I don't have the nous to type up right now.
But these proofs don't show anything in particular about the local reduction property. For one thing, the premises and conclusions both involve T and n, so these proofs are in principle unnormalizable. For another thing, they don't involve any lines that are product of an I rule and input to an E rule for the same sign (or vice versa); 2 is the product of nI and the input to TI, whereas 5 is the product of nI and the input to TE. For a third thing, negation is involved here, and negation itself violates the local reduction property.
One thing is that these properties are sensitive to the way the intelim rules are formulated. And I probably formulated my rules in an eccentric fashion. But I offer these rules up as a contribution to the discussion, anywise.
In a 2002 Phil Review paper, discussed here at Certain Doubts, Jeremy Fantl and Matt McGrath argue that justification depends in part on pragmatic factors--Sally can be justified in believing p and Jane not justified in believing p, even though Sally and Jane have exactly the same evidence, because the stakes are higher for Jane than for Sally.
Brian is arguing that the difference doesn't come from pragmatic encroachment on justification; it comes from pragmatic encroachment on belief. To say that someone believes that p tout court is to say that her degree of belief in p passes a certain threshold, and that threshold is determined by pragmatics. So, if Sally and Jane believe that p to exactly the degree that is supported by their evidence, Sally will count as believing that p and Jane will not.
Brian suggests this definition (to a first approximation):
X believes that p iff for all actions A, B, X prefers A to B iff she prefers A & p to B & p
There are some complications to this, to deal with inconsistent agents and to deal with cases where p is of no practical importance, so it isnít perfect as it stands. But I think itís close enough to the truth to run with, at least properly understood
and going on to say that we must let the quantifier range over live practical options for X. (Look below the jump for an example of how this yields pragmatic encroachment on the degree of belief.)
I think Brian's proposed definition of belief leads to closure failures. Now, of course belief isn't closed under logical consequence; I may fail to believe all the logical consequences of my beliefs, because I haven't thought about them. But Brian's definition has (I think) the effect that I can have degrees of belief in p, q, and p & q that are in exact accord with the probability calculus--and yet I can believe p and q, and not believe p & q. That seems bad.
The failure of closure isn't exactly the one you might expect.
Here's the failure you might expect: On a view on which belief is belief to degree n or greater, closure will fail, because the property "having probability of n or greater" isn't closed under logical consequence (if n isn't 1 or 0). So you might say: Take a case in which p has probability 0.9, q has probability 0.9, and the threshold is between 0.9 and 0.81; then closure will fail.
That suggests a case in which there were three relevant pairs of actions, all of which require confidence of at least 0.833 in the relevant proposition for action; say, offering a bet at 5 to 1 odds.
(I'm just recapping my thought process, btw.)
So: assume you believe p and q to degree 0.9, and you believe they're independent, so you believe p & q to degree 0.81.
Action A = offering 5 to 1 odds against p (that is, if p is true you win 1, if p is false you lose 5); B = not doing so.
Action C = offering 5 to 1 odds against q; D = not doing so.
E = offering 5 to 1 odds against p & q; F = not doing so.
You prefer A to B, C to D, and F to E.
But, on Brian's definition, you don't believe either p or q. Because you have to consider whether you prefer E & p to F & p. And you believe that, given p, you'd have a 0.9 probability of winning that bet; which would make it worth offering. So you prefer E & p to F & p, even though you prefer F to E. Hence you don't count as believing p, on Brian's definittion. (q, the same.)
Here's the case where closure fails:
Action A = offering 5 to 1 odds against p; B = not doing so.
Action C = offering 5 to 1 odds against q; D = not doing so.
E = offering 99 to 1 odds against p & q; F = not doing so.
You prefer A to B, C to D, and F to E.
And you also prefer F & p to E & p, and F & q to E & q. You believe that, given p, you'd have a 0.9 probability of winning the bet that p & q. But you need a 0.99 probability in order to offer the bet. So, for all three pairs of actions, your preferences are unchanged by conjoining p to each option. Hence you believe p.
(I just noticed this: It seems as though you are indifferent between A and C, but you prefer A & p to C & p. Perhaps this shows that you don't believe p. But it seems to me that similar examples could be constructed to show that you don't believe just about anything. So I don't think this will rescue the argument.)
Similarly, you believe q.
However, you prefer E & p & q to F & p & q (since p & q guarantees that you win your bet), even though you prefer F to E; so you do not believe p & q. Hence your beliefs aren't and shouldn't be closed under logical consequence.
I was surprised at the way closure fails here--I don't have much more to say about the consequences, except that I have a funny feeling that this means that this way of defining belief isn't going to work at all.
But I should say that I'm extremely sympathetic with Brian's stated project, with the exception that I don't think that pure epistemology is going to turn out to be purely probabilistic:
there is no pragmatics in probabilistic epistemology, and hence no pragmatics in epistemology proper, but plenty of pragmatics in the relationship between probabilistic and non-probabilistic doxastic states, and hence pragmatics in non-probabilistic epistemology.
I think we can find a domain that's purely epistemic, with no pragmatic encroachment whatsoever. That's the domain circumscribed by question 5 here. But the way I want to go about this is not to try to rig things so that traditional epistemological terms such as "knowledge" or "justification" turn out to be free of pragmatic encroachment. Rather, we have to find or invent a concept that is free of pragmatic encroachment--I like "strength of evidence"--retreat within its walls, and throw the rest of the concepts to the pragmatic wolves.
I suppose I'm not allowed to link the paper in which I found the following disclaimer:
Draft (01 March 2005). Do Not Cite, Circulate, Read, or Otherwise Take Seriously.
However, I can nominate the author for a Nobel Peace Prize in Medicine, and have just done so.