I can imagine a rock existing without there being any conscious observer of it — Janus

Really? You can imagine a rock without imagining yourself observing it?

I would like the halfer to explain why ruling out the Tuesday scenario doesn't affect their credence in the coin toss outcome at all. — Pierre-Normand

For Lewis, if I recall correctly, it raises her credence for heads from 1/2 to 2/3, which he finds curious, but that's it.

What should SB's credence be that this is her first (or second) interview?

Any thoughts?

But given the set {10,20}, E(z)=15=(5/4)12, and 12 isn't the value of the chosen envelope. — Michael

That's true. It's not in the set. Neither is 15. But 15 is, for all that, the expected value of both envelopes.

The total value of any pair of envelopes is 3x, where x is the smaller of the two. I choose one, and call it y; if I got the smaller then y is x, if the larger then y is 2x; so x is either y or y/2. The total value of the envelopes is then either 3y or 3y/2, so the average total value is 9y/4. Alternatively, you could just say that since x is y or it's y/2, the average value of x is 3y/4, again making a total of 9y/4, on average. By definition, my envelope is y, so the other envelope must be worth 5y/4, on average.

Where have I gone wrong?

Given a set {10, 20}, the expected value of a number selected from that set is 15. There's nothing wrong with your first set of equations, and it gives the right answer. You don't have to go through all that; you just need the average.

The second set of equations is different.

Are the situations described in the following questions the same? If not, what's the difference?

(1) What are the chances that y = x and the chances that y = 2x if y is chosen randomly from a set {x, 2x}? (You may, if you like, write it backwards as x = y and x = y/2.)

(2) What are the chances that a y chosen randomly from a set {x, 2x} was chosen from a set {y, 2y} and the chances it was chosen from a set {y/2, y}?

Consider what the halfer says next with my marble analogy: which marble-holding-self this is was selected by a coin toss. That's the same as saying whether the marble I have is white or black was determined by a coin toss.

But that's not good enough, because there's more than one black-marble-holding momentary self. There's just no way to select from more than two moments this might be with a single coin toss.

Here's a halfer analogy I found convincing before:

Two urns, one with a single white marble, one with many black marbles; you flip a coin to decide which urn to draw from; even though there are more black marbles than white, the chances of getting the white marble are equal to the chances of getting one of the many blacks.

The argument I've been making lately seems to be roughly this: if you close your eyes and someone selects a marble and places it in your hand, and if you know there are more black marbles than white, then you can figure it's more likely to be black. Fair enough.

But if you know they selected the marble in your hand by flipping a coin to select which urn to draw from, you should figure it's just as likely to be the one white as any of the blacks.

That looks like trouble for the thirder position, but it's missing the repetition, and missing SB's uncertainty about her own state. It's not just that she knows someone's put a marble in her hand, she knows they'll do it more than once for tails. So SB is justified in wondering, who is this person with a marble in her hand? Who is she more likely to be?

I think.

This relies on the intuition of repeating the experiment over and over. If so, then there are unconditionally more tail slices. But the coin is flipped exactly once. Therefore, even though there are more tail slices, they both exist only upon a tails flip. — hypericin

I think it's hard.

If you wake up and ask yourself "Which of the selves I could have become while I was asleep am I?" there are two ways to take that.

You could think of the self you're seeking as a continuous self (a sort of world-line, if I have the parlance right) accumulating experiences, in which case it's reasonable to describe that self from any point along the line: in the past you're the self who's going to end up having exactly one or exactly two interviews; in the future, you're the self that had exactly one or exactly two interviews.

But you could also think of your self as this momentary self, even if it is part of a larger stream of momentary selves. Your question then is, which stream is this self-moment likely to be part of? If any such moment is more likely to be part of one stream than another, then you are more likely to be the self living out that stream than the other.

What are we supposed to learn here?

I mainly take it as a logic puzzle: there's a bit of fallacious reasoning, you have to spot it, explain why it's fallacious, and why it's attractive, easy to fall into.

On the other hand there is a way of taking it as an interesting probability problem, where you have to model several different sorts of issues, and under some additional conditions there are interesting switching systems available. (I don't have the background for that stuff anyway, as you know.)

So there's kinda an old school and a new school response possible.

The old school take is just another case study in faulty reasoning, but might have some interest in how people elide different sorts of uncertainty and chance. And last time I recall speculating about some use for the new school approach. (Something about improving performance without feedback -- it was pretty half-baked.)

Besides an opportunity to play with our respective toys, do you get anything out of this?

I don't see any disagreement.

I see this has been gone over quite a bit — Mikie

Going back five years.

The "puzzle" is not figuring out what the right way to analyze this is -- although @Michael did argue, at length, in the old thread, for switching, and there are some interesting practical aspects to switching in the real world where the probability distributions need to be possible -- but why a seemingly natural way to analyze the game is wrong. There's not even agreement among analysts about whether this is a probability problem. (I don't think it is.)

As always, GOP cuts will worsen the deficit and benefit the wealthy while the GOP are bleating about 'cutting wasteful spending'. — Wayfarer

You may be right -- and surely this is true for many Republicans, but also Democrats -- that this is intended as a deliberate move to benefit the owner class, but don't underestimate how much the Freedom Caucus is motivated not by money but ideology. Some are against the IRS not because they are shills for donors far, far wealthier than they will ever be, but because "Muh liberty!" It's a, so to speak, principle.

I don't know case by case which explanation is best. Someone like Matt Gaetz is apparently just a piece of shit who plays a populist on TV but has always had his hand out to every lobbyist and donor he came anywhere near, and presumably has been more or less peddling influence since he entered politics. But some of these folks just aren't bright enough to be that corrupt. MTG probably only manages to be corrupt when someone explains to her in small words exactly what she needs to do for the money. In the meantime she's just a dangerous narcissist. But then there are those who are so dumb they really believe, you know, God hates the Fed and loves AR-15s. Not kidding. Not kidding at all. Most who make it to the national legislature have learned which of their true beliefs it's cool to say on a hot mic, but if you drop down to the Congressional minor leagues, state legislatures, it is shocking how absolutely stupid a lot of these tea-party-maga-evangelical-libertarian bozos are. Just plain stupid.

So gutting the IRS even though it will cost more, that's just a bit too subtle for some of these yahoos. The IRS are jackbooted thugs who hate our liberty, period. They want to take our money and use it to pay for abortions.

Crashing the world economy? That's just something some eggheads say will happen, I don't believe it. And even if the world economy crashes, what's that got to do with America? Fuck em. Let em take care of their economy and we'll take care of ours. -- No, seriously, this is the level of thought of the people who vote in Republican primaries and too many of those who end up getting elected.

Never attribute to malice what can be explained by greed or stupidity, the saying goes. You're right about the greed, but don't forget about the stupidity.

There are two reasonable ways to assign variables to the set from which you will select your envelope: {x, 2x} and {x, x/2}. Either works so long as you stick with it, but if you backtrack over your variable assignment, you have to completely switch to the other assignment scheme.

Thus you can say, if I have the smaller, I have x and the other is 2x, or you can say, I have x/2 and the other is x. The main thing is that you have to use the same scheme for the other case, where you have the larger.

If you choose to label the envelope you've chosen "A", it's true that the other envelope contains either 2A or A/2, but that's because there are two consistent ways to assign actual variables, and the "or" there is capturing the alternative variable schemes available, not the values that might be in the other envelope. "A" is an alias for one of the members of {x, 2x} or for one of the members of {x, x/2}, but you still have to choose which before you can think about expected values.

The key is that "or" up there ("2A or A/2") is not a matter of probability at all; once you've chosen a set, which member of the chosen set A is, is a matter of probability. But we won't be summing over the possible choices of variable scheme.

For an analogy: it's 11 am, and you're asleep in bed; how old are you? Odds are you're one of the ages where you were more often asleep in bed at 11 am, even if every year of your life has had at least one such day.

This is a quote from Descartes posted by @Fooloso4 next door in that thread:

For a life-span can be divided into countless parts, each completely independent of the others, so that from my existing at one time it doesn’t follow that I exist at later times, unless some cause keeps me in existence – one might say that it creates me afresh at each moment.

We can say of the sleeping beauty problem, just as a way of beginning, that there are three possible future SB slices which the SB being interviewed could be.

The halfer camp seems to take the view that two of those belong to one person, and one to another, and that the correct analysis is that the coin flip partitions SB's future slices into a heads set and a tails set, just two, equal chances of being in each set.

The thirder view is that only the current slice that you might be is relevant, and there are more being-interviewed slices in the tails partition, so you're more likely one of those.

It may not be true that I am more likely to be a person who is interviewed more than once, and yet be true that this slice of me being interviewed is more likely to be a somewhat common tails slice, considering the entire pool of possible slices of me, than to be a comparatively rarer heads slice.

What does the cut correspond to?
— Srap Tasmaner

Answering that gives you the origin of the paradox, right? — fdrake

In a sense yes. The cut is a "committed choice" thing, and you could take that as representing the dealer's not monkeying with the envelopes once he's offered them to you.

But we know how the game works objectively; the problem is why some ways of modeling your own epistemic situation as the player work and others, though quite natural, don't. It's clear that including the cut in your model works; but it's not as clear why you must include it.

It's not even perfectly clear to me what sort of epistemic move the cut is; what have I done when I've done that? I'm not considering certain options for backtracking; okay, but why shouldn't I consider those options? The dealer may not monkey with the envelopes after he presents them, but I still don't know which branch (perhaps of many) he went down, so why shouldn't I consider those?

It is, after all, simply true that the other envelope must contain half the value of mine or twice. (And the problem here doesn't seem to be spurious or-introduction, because {mine/2, mine*2} is the minimal set for which that claim is always true.)

But it's also just as clear that this not equivalent to the {x, 2x} framing. Both envelopes, mine included, are members of that set, but mine is of course never a member of {mine/2, mine*2}. Given a set that includes both, you get a proper disjunctive syllogism: whichever one I have, the other one can't be, so it's the only other one in the set. Reasoning from the "mine" framing isn't nearly so clean.

Feels like the explanation is right here, but I'm not quite seeing it.

Since we've all been throwing code around, here's a curiosity in Prolog:


Here's a swish link so you can try it out.

The idea is that if you run a query like this


you'll be able to backtrack all the way up the tree and back down, like this:


(There's a duplicate 10, but oh well. It shouldn't really be a tree but just a graph, since there's two routes from root to 10. Might redo it, but this was quick.)

This (nearly -- ignoring the dupe issue) represents @Michael's view of the problem construction.

BUT, the design of the actual problem is more like this:


If you insert a cut between the two predicates, backtracking all the way up to the selection of the envelope pair is blocked. When you ask for more solutions, you get just the one, not three.



Asking for another solution -- backtracking -- corresponds cleanly to swapping. (It's why the predicates are written a little odd, to be both randomized and backtrackable.)

What does the cut correspond to?

There is a difference between these two claims:

1. I have a 1 in 2 chance of picking the larger of two envelopes.

2. The envelope I have chosen has a 1 in 2 chance of being the larger of the two envelopes.

Suppose the pair is (5, 10). I have a 1 in 2 chance of picking 10. But 10 does not have a 1 in 2 chance of being greater than 5; it _is_ greater than 5.

just because I can plead, cajole, call in a favor, etc. and call them all “asking” doesn’t make the conditions allowing for a request to be any less specific nor the criteria for judging the line where it becomes pressuring any less clear. — Antony Nickles

Is that line particularly clear? Isn't this exactly the sort of thing people very often disagree about?

("Allowing"???)

And sure we can use language lazily if we like, but beating a nail in with a screwdriver doesn’t make it a hammer. — Antony Nickles

But this is odd. It takes considerable effort for Descartes to achieve the degree of abstraction he does in his reasoning, to extract himself from everyday ways of thinking. Doesn't look like laziness.

Now, f I don't understand the difference between a hammer and a screwdriver, I might select one or the other indifferently, much like a lazy person who does understand the difference but doesn't care. But that doesn't make me lazy. For that I would have to have deliberately shunned opportunities to learn the difference, and so on.

Besides, maybe you pound with the screwdriver because there's no hammer to hand. Recognizing that the screwdriver will do is not laziness, here, but insight, achieved by abstracting, and by flouting the rules about how tools ought to be used.

Affirming or doubting are acts with very specific criteria done in particular situations, just like asking, or thanking. — Antony Nickles

How specific?

Is there not more than one way of asking? Of thanking? Of affirming or doubting?

Are there not specific sorts of specificity?

How finely must we chop experience before the spectre of generality has been sufficiently warded off?

What you want is the odds that this interview is a heads-type interview. — Srap Tasmaner


Yes, that's the left hand side of the theorem: P(Heads|Questioned). — Michael

No, that's the probability that the coin was heads given that I'm being interviewed. The trouble is on the RHS, the probability that I am being interviewed given that my coin was heads.

Take a space and partition it evenly into a heads half and a tails half. Now, in the heads half put one point, an interview; in the tails half, put many interviews.

If you choose a half space, in each you will find at least one interview. You're interviewed either way.

But if you randomly select an interview among all the interviews, is it more likely to have come from the heads half, with its one interview, or the tails, where there are more?

That's what we want to capture with the base rate of heads interviews among all interviews, not the non-emptiness of the heads half of the space.

The probability that I will be questioned if the coin lands heads is 1. The probability that I will be questioned is 1. — Michael

But these are useless, uninformative, ambiguous categories. What you want is the odds that this interview is a heads-type interview. If Beauty could determine her current state in the world, what type of interview she is being given, she could answer with certainty. She cannot, but she can determine the likelihood of her being in each of the two possible states, states that she cannot otherwise distinguish. And she knows that it is more likely that she is being interviewed because it was tails.

I don't think your numbers are accurate there. — Michael

Meaning?

But in this case we're not asking about an outsider's analysis of frequency, but Sleeping Beauty's when it is known that just a single experiment is being run. — Michael

And how do you expect to apply Bayes's rule without any base rate information? SB can reason as I have described to determine what those base rates would be were the experiment repeated a number of times, and set her subjective probabilities accordingly.

How do you condition on such a thing? What values do you place into Bayes' theorem? — Michael

Just scroll back up. I went through all that.

The point of the variation is that she is told something will happen only at the second heads interview. Fill in whatever you like, it will be missing from the others and from all of the interviews in stock SB. The absence of that thing is informative, it amounts to "it was tails or this is your first interview," and this is true as well for stock SB. Being asked is itself information you can condition on.

So you've switched back to being a thirder? — Michael

I switched back shortly after that post; it's right there in the thread. The argument that convinced me was this: consider a variation, "Informative SB", in which Beauty is told she will be awakened twice either way, but if it was heads she will be told at the second interview that it was heads and that this is her second interview; at none of the others will she be given such information.

Beauty cannot distinguish between this variation and the actual experiment. This just makes it clear that being interviewed is itself informative and she should condition on it; it amounts to being told "either it was tails or this is your first interview." The likelihood that the coin came up heads is of course 1/2; the likelihood that it came up heads, given that you're asking, the conditional probability, is 1/3.

Let's say that I wanted to bet on a coin toss. I bet £100 that it will be tails. To increase the odds that it's tails, I ask you to put me to sleep, wake me up, put me back to sleep, wake me up, put me back to sleep, wake me up, and so on. Does that make any sense? — Michael

In our version, the base rate of heads interviews is 1 in 3. Make it 1 in 1000. (That is, 999 awakenings on tails, not 2.) Isn't it obvious that if I'm a subject in such an experiment, I know it's far more likely I'm being asked for my credence because my coin came up tails? If I'm one of 1200 subjects, I know there are 600,000 interviews, only 600 of which were for heads, while 599,400 were for tails. Equally likely that this interview is for heads as for tails? Not by a long shot.

Suppose you actually did this, as an experiment, just looking for each subject's response.

Let's say you have 1200 subjects; one coin toss each, and let's say you get 600 heads and 600 tails. So 600 subjects get a single interview, and 600 get two. Total of 1800 interviews.

How many interviews are conducted, the toss having come up heads? 600.

Then for any given interview, the chances that it's one of the heads interviews are 1 in 3. I think that's all the reasoning you need.

****

If you're inclined to double-check, you might try something like this:

$\small pr(\mathsf{heads | interview}) = \cfrac{pr(\mathsf{heads}) \times pr(\mathsf{interview | heads})}{pr(\mathsf{interview})}$

Not perfectly clear what that means though, so let's explicitly take subjects one at a time, something like this:

$\small pr(\mathsf{hds}(x) | \mathsf{intv}(x)) = \cfrac{pr(\mathsf{hds}(x)) \times pr(\mathsf{intv}(x) | \mathsf{hds}(x))}{pr(\mathsf{intv}(x))}$

That looks a little more tractable. Certainly pr(heads(x)) is 1/2 for everyone. If in fact x gets heads, then x is one of the 1800 interviews, so pr(interview(x)) would be 1/1800, and for tails 2/1800. For an "average" subject x, then, the value should be their average (because halves), which is 1.5/1800, or 1/1200. Hey, that looks right! Maybe we needn't have bothered about the heads and tails...

(Is 1/1200 really the right value for pr(interview(x)) -- doesn't it make a difference whether their coin came up heads or tails? Yes and no: what we want here is an absolute probability, not a conditional one, so we deliberately average out the cases to get a baseline, and the result is just what you'd expect. Pick an interview at random, and the chances of it being an interview of a specific subject are, on average, 1 in 1200. Just as we leave pr(heads(x)) at the baseline of 1/2 for everyone.)

What about pr(interview(x) | heads(x))? What does this mean, and how do we assign a value to it? It's the chances that a given interview is of subject x, given that x's toss came up heads. That's the 1/1800 we just looked at.

Now we have values for everything on the right:

$\small \begin{align}pr(\mathsf{heads}(x) | \mathsf{interview}(x)) &= \cfrac{1/2 \times 1/1800}{1/1200}\\ &= 1/3 \end{align}$

That is, given any interview, the chances of the subject of that interview's toss having come up heads are 1 in 3. Exactly the same as above.

SB ought to reason that it's more likely the interview she's currently engaged in is one of the tails interviews, so her credence for heads should be 1/3.

This is a basic problem with Hume's approach. His proposed separation appears to between the senses, and reason. But "reason" in its proper definition is only the rational and logical activity of the mind. This leaves a vast amount of mental, or brain, activity which is obviously not reasoning, and obviously not activity of the senses, as unassailable, in an uncategorized grey area. — Metaphysician Undercover

So close, but isn't it the case that Hume is precisely discovering that a lot of mental activity cannot be attributed to the senses or to reason? Isn't that what we've been talking about for pages now? How on earth can you end up claiming that Hume overlooked this, when he's the one that drew our attention to it in the first place?

If we adhere to the principles then, we sense continuity, but the brain wants to break up the continuity into discrete, or distinct parts for the purpose of understanding. Therefore, individual, fixed and distinct objects is a creation of the brain, hence mind (even reason?) rather than senses. Now Hume says that this is an unjustified creation, an erroneous fiction. — Metaphysician Undercover

Obviously there's a problem with saying "brain, hence mind (even reason?)," and Hume is very clear that we cannot attribute the theory of external objects to reason. As for mind — well, perceiving (in the modern sense) sure looks like a mental activity, in addition to being a physical activity, but you'll have to look carefully to figure out what in your perceiving is down to the peripheral nervous system and what the central. No reason at all to think it's only one or the other. Hume doesn't talk about the brain much, so I don't think it's helpful to read his claims about the mind as just being 18th-century speak for 'brain'.

So the problem here is with the sense/reason division. As described above, there is vast area of activity which fits neither category, it lies between these two. We can find other ways of dividing, sense/brain, or body/mind, but each has its own problems of not being able to properly account for everything, sp we get aspects, parts of reality which have no category. This indicates that this sort of division is not the best way to go. — Metaphysician Undercover

And again it's Hume who takes enormous pains to insist that there is centrally important mental activity clearly not attributable either to the senses or to reason. Somehow you've talked yourself into accusing him of doing what he, quite remarkably for his time, did not do.

if someone represents our observations of change as seeing the way things are at one moment (a perception), then seeing them in a different way at the next moment (the next perception), and we conclude with the use of reason, that change has occurred between these two perceptions, this is really not the way that we actually sense change. Through the senses we are actually perceiving change directly. — Metaphysician Undercover

This is just assertion.

I'm not taking a position on whether you're right, but on what grounds will anyone agree or disagree?

Honestly, the only thing I can see here worth doing, is try to determine what our powers of discrimination are scientifically, to treat this as an empirical question.

No doubt the terms in which we investigate the question will change, but I think we'll have to allow that based on what the investigation shows. "Senses" will turn out to be far too coarse, as will "perception". We'll want to know which neurons are activated, what level of input it takes to do so, how long that takes, when they're ready to be activated again, at what point information is passed up to the central nervous system, how much information is enough to act on, all with or without conscious awareness, and then there are additional questions about what we become aware of, how, and when.

The problem though is that reason works best with static descriptions, predications with laws of logic, like non-contradiction, so it does not properly apprehend what the senses give to it, change. — Metaphysician Undercover

If the story you're telling is that reason distorts the true nature of the senses, or of their testimony, then that seems to me not a story worth telling. Better actually to go and look at how our nervous system works. That would include what the senses actually do and how, but also how our brains organize the information we have about the world. Reason comes in elsewhere, I suspect, and I think so far as all this goes, Hume's general approach is the right one, regardless of what particulars he may have gotten wrong.

In this case, it's the cow that he saw that establishes his conclusion that there's a cow in the field. He is mistaken about which cow he saw, but that doesn't undermine his conclusion. — Andrew M

One point about the analysis I was offering is that it is deductively more palatable. Whenever we've talked about Gettier on the forum, or introduction is a real sticking point, and thus existential generalization is. People accept it in math class, but they balk at someone in real life inferring something of the form A v B v C v ... from A. I went around that by treating the name as a description. Now, instead of or introduction, we have and elimination, which doesn't seem to bother anyone.

Or introduction is not a crucial element of Gettier cases; it's just the easiest way to construct them. All we need is a situation in which your reasons for believing some proposition are not the reasons it's true. Stated abstractly, I think it's obvious this happens, and that when it does we think of this exactly as being lucky, a little like this:



"It's Disembodied Reggae Space Voice, but that's just a coincidence, you didn't know that!" (If you let the clip play on, you'll also be treated to Phineas asking Baljeet to quit arguing with the soundtrack. That show ...)

Descriptivism as a theory of names is controversial, of course, but there are a couple of specifics here in its favor: first, we're not looking at reference in general, but at recognition of a particular we are familiar with (to continue RussellFest, a particular we know by acquaintance); the other point is that the part of the description we keep is the sortal.

I think it is plausible to think of recognition as inherently a descriptive enterprise, involving a list of criteria. And sortals always play a special role. That post looks a little odd:

(1) I believe that's Daisy out there.
(2) I know Daisy to be a cow. — Srap Tasmaner

It's like that because what I thought I was going to do was have the farmer form a belief regarding the particular, Daisy, non-descriptively, and then infer further beliefs from his beliefs about Daisy; doing that would jam an and in between the recognition and the other inferences, creating two new scopes and allowing us to screw around with the reasons they're true. (I had a sort of Twin-Earthy idea that Daisy might turn out to have been a schmow all along, but with all the other things the farmer knew about Daisy still true.)

But non-descriptive recognition is so implausible, and implausible in particular if you give up the sortal. I think our beliefs are in almost every case centered on sortals; Daisy, for instance, is not just a particular, she is a particular cow. Certainly for the task of recognition, the list of Daisy's properties is going to begin with cow, and then include features (the nick in her ear, her weight, etc.) that distinguish her not from the farmhouse or the farmer's wife or the Milky Way or the tractor or democracy, but from other cows.

So all of that is to bolster the sense that you do have knowledge if you infer that you've seen a cow from your belief that you've seen Daisy the cow, even if you actually saw Clarabelle the cow.

Back to Gettier. Must there always be a false lemma when your reasons for believing a proposition are not the reasons it's true? No, obviously. It was an act of the Kansas state legislature (I'm guessing) that made Topeka the capital; you believe it because you learned it in school. There is, doubtless, a causal chain between that session of the Kansas state legislature and what your teacher told you or you read in a textbook, but it's a causal chain you cannot possibly be familiar with from beginning to end.

Now suppose you're in grade school and your teacher — because he's a bit of a prankster, or because he wants to make some point about remembering, or whatever — writes a list of cities on the board and a list of states. His intention is that he'll catch out some of the students wanting to match up Wichita to Kansas, even though Wichita is not the capital, and both Wichita and Kansas should remain unmatched. But, because he's also vulnerable to accessibility bias, he actually writes Topeka on the board. When he asks the payoff question, "What about Kansas?" a bunch of kids say "Topeka!" and he responds, "Oh-ho! But Topeka" — here he looks at the board — "is right there. Shoot." He intended there to be a conflict between the list the students had memorized and the list in front of them, to see if they could be tricked into taking what's in front of them instead of relying on what they remember, but he inadvertently made the lists the same. Now he has no experiment, because some of the students may have done exactly what he hoped, chosen Topeka remembering only that it's in Kansas. That's necessary but not sufficient for being the capital of Kansas, so it's not wrong, but it's still a mistake. But because of his mistake, it's a mistake that's undetectable. Of course, little kids tend to be pretty candid, so if he just asks, "How many of you remembered that Topeka is the capital of Kansas?" and "How many of you chose it because it's only city in Kansas on the board?" he'll probably get some hands up for each, and some embarrassed giggles.

And there's the other part of the Gettier case. Our epistemic agent always has explicit knowledge of what reasons they're relying on, what they're inferring from. To defeat no-false-lemmas, we have to construct a case in which those reasons are true and do provide strong enough support for the conclusion, but we can't do that counterfactually — that is, with reasons that the conclusion might have been true but isn't — so what we need are independent reasons, as "I learned it in school" is, epistemically if not causally, independent of "The Kansas state legislature said so."

My classroom wasn't intended to be a Gettier case, only a neighbor that illustrates the issues. But it's close, because it has elements of getting the right answer for the wrong reasons, only it adds a twist that the wrong reasons are coincidentally the right reasons. That's a funny thing, because it's almost as if "Wichita" is misspelled "Topeka" on the board, but in the teacher's mind is still the word "Wichita". So there's a false lemma here, but pushed back from the kids to the teacher. Never even realized on the board, but it's there in the teacher's beliefs. It's similar to my thing about Russell's clock, having the worker set the clock correctly from a watch that only happened to be right. Pushing the false lemma out over the agent's epistemic horizon leaves us in an uncertain position I think: depending on how the details are presented, the agent might strike us genuinely lucky to acquire knowledge, or too lucky for his belief to count as knowledge. It's like the conflicting intuitions among philosophers about the fake barn cases. What's interesting here is that most of the kids can probably report whether they had knowledge because they know whether they remembered, and it's the remembering that would be factive, but even some of them might not be sure they would have stuck with Topeka had Wichita been written on the board. And some might not know whether they would have remembered without being prompted. "I know it when I see it" is a real thing.

I'm going to take a break, but I really think we should be able to construct a clear case, roughly along the lines above, of Gettier case without a false lemma.

Charles Mingus, Blues and Roots

Story behind this one, I believe, is that one of the Ertegun brothers suggested he do a whole record in the vein of Haitian Fight Song, from The Clown.

So here's that:

Duke Ellington — Jamal

As a pianist, Ellington is thought of as having a percussive style, as opposed to say the fluidity of Art Tatum, the great pianist of the swing era. So there's a tradition that runs from this



through Monk to Cecil. Watch Monk play, oh my god:

possible worlds — Banno

I have very strong doubts that stories count as possible worlds.

semantics — Banno

I don't see how to avoid semantic issues: the truth conditions of "Frodo carried the ring to Mordor" look nothing like the truth conditions for "Washington crossed the Delaware." That ought to be obvious.

But the problem with my position is apparently that 'within the story', or from an 'in-world perspective', Frodo going to Mordor has exactly the same sort of truth conditions as Washington crossing the Delaware has (in our world, if that needs to be said). We can carry out such an analysis by pretending that Frodo is a person, Mordor is a place, the one ring is a thing, and so on.

But we are also aware of the book as a textual artifact and must analyze it as such. Whatever happens in the story happens because the author says it did. So one way to frame the issue here is to ask how these two frames of analysis are related. Is one dependent on the other? Are they dependent on each other? Independent of each other?

(Incidentally, I wanted to refresh my memory so I checked the wiki for "willing suspension of disbelief" — it's nearly Coleridge's phrase, as I thought, but he didn't mean what I learned in school. The wiki article is interesting and notes a sort of response from one J. R. R. Tolkien!)

I'm initially inclined to think that the 'in-world' analysis is parasitic on the textual analysis, precisely because whether something counts, within the story, as having happened, depends entirely on whether the storyteller says it did. Arguments about what did or didn't happen in Tolkien's story are settled — or at least, attempted to be settled — by reference to the text. Thus to ask whether Pippin accompanied Frodo and Sam to Mount Doom is elliptical for asking what it says in the book.

But now 'what it says in the book' is going to be from the in-world perspective, so indeed we have to understand the sentences in the story by taking them as pretend. If we could not carry out such an in-world analysis much as we would analyze sentences like "Washington crossed the Delaware," then we could not answer any question of the form, "What does the book say?"

So it appears the two sorts of analysis are interdependent. There is an extensional layer, what the book does or doesn't say; and an intensional layer, what what it says means within the story.

Having at least scratched the surface of the sort of work I imagine is necessary, has it become any clearer whether Frodo is real? If by Frodo we mean a hobbit person, then in-world, of course he is; in our world certainly not. In our world, Frodo is a fictional character, which is a real thing just as stories are a real thing. We seem to need a definition for "fictional character" and the obvious one is that a character is whatever counts as a person within the story, from that in-world perspective. Especially in fantasy literature, this may present some problems, because the characters in the story may not all share a perspective on what is a person, and the storyteller has a perspective on this too, again perhaps shared and perhaps not. Ghost stories are the obvious example.

But in our example it's clear enough that within The Lord of the Rings Frodo is a real person and a hobbit, and so for us he would count as a fictional character.

Can we spell this out as truth conditions for "X is a fictional character"? Can we just say "X is a fictional character if and only if there is a fictional story within which X is considered a person"? What sort of X do imagine filling in here? I mean, there's a temptation just to plug in a name there and call it a day. But it's the semantic value of that name that is exactly our problem.

On the right-hand side, we want to take the in-world perspective, and leverage that to define a term in our world, on the left-hand side. In Middle Earth, we want to say, Frodo is a person; in our world, he's a fictional character. Is this the same 'entity' we're talking about? Has it a dual existence, in one 'world' as one sort of thing and in ours as another? Is this no different from saying that chocolate can exist as something yummy for one person and something repulsive for another?

The pretending that matters here is done in our world, and I think this might provide a start on a solution. I don't think we really want to say that Tolkien pretends — and we pretend with him as readers — Frodo is real and a hobbit. That sounds right, but there is no Frodo for him to pretend is real, as there is real chocolate for one person to like and another dislike. (It's no good to say that Tolkien pretends his fictional character is a real person because (a) there is no such character until he does the pretending, and (b) we were trying to rely on the pretended reality in order to define the character, not the other way around.) Instead, I think we say that Tolkien pretends to be telling a true story — at least in some sense. (We still don't have an account of pretending to hand.) Among other things, Tolkien pretends to be telling a story about Frodo. He isn't actually, because there is no Frodo, but he can tell a story about the Frodo who doesn't exist as if he did. But he's never actually talking about Frodo, only pretending to.

You can tell a story about a real person, and within that story the semantic value of that person's name is the person. You can also pretend to tell a story about a person who doesn't exist, and the name of the person you pretend to be talking about has no semantic value, but you pretend it does. (Deja vu. I think I've written that on this forum before, but I had forgotten until just now.) The important thing is to see that the pretending is precisely that the story is about someone; it's not.

That's still not quite right because I think we need to make an even stronger claim to make sense of this. What is telling a story, telling a story about something that really happened, the sorts of stories we tell all the time? It's a recounting of events you know to have happened.

Fictional storytelling is pretending you're doing that, when you're not, and your audience knows you're not. It's next-door to lying but without the intent to deceive. When you lie, you maintain a pretense that you're telling the truth, but when telling a fictional story that's not it exactly. You pretend to be recounting. In the course of recounting, you pretend to narrate events that happened, as you would real events; you pretend to talk about people and places, as you would talk about people and places when recounting. But you're not doing any of those things, you're pretending to. The pretense sweeps in everything, beginning with the idea that you're in a position to tell the story because you know what happened, when and where and who did it and to whom. You don't. You don't know any of those things, but you pretend you do. (It is not true, for instance, that you're the only person who knows, since you're the storyteller; you don't know things you're making up.) You might even pretend you translated the story you're telling from an old manuscript bound in red leather. But that's not true either.

I think that does still leave 'fictional character' as someone you pretended to be talking about but weren't really — it's just that we want to read that holistically. It's the whole story that carries the pretense of being a recounting of events, not atomistically a matter of an entity in the story not being real. If I thought it would fly, I'd just say that fictional storytelling is pretending to tell a story, that it's a flow of speech meant to sound like a story but isn't really. But I doubt anyone will plump for that.

That's the best I can do tonight. Some of the analysis near the beginning of this post might still be okay, but the whole in-world/our-world analysis might be kind of a blind alley. Worth exploring though, and maybe it's salvageable. But it does seem to me now that the right starting point is where I've ended up: fictional storytelling is parasitic on the sort of true narratives we trade in all the time, and the primary pretense is that it is this sort of speech one is engaged in. (Not for nothing, but early novels overwhelmingly presented themselves as diaries or letters to establish this pretense of being a recounting of actual events, a tradition Tolkien keeps to.)

This does not seem like a good way of describing reasoning, the act of passing from one perception to another. — Metaphysician Undercover

The insight which captivated and shook him, is that those laws don't look much like reason. — Srap Tasmaner

If the cow that he doesn’t know about is the one that establishes the truth, then he didn’t know there was a cow in the field. — Ludwig V

Not sure I agree. I already worried over this a bit too, so I get the concern here.

I think the essence of this objection is to deny that the existential generalization actually takes place. If we leave aside justification for a moment, the idea is something like this:

(1) I believe that's Daisy out there.
(2) I know Daisy to be a cow.

In fact, I know a number of things about Daisy, so the presence of Daisy in the field entails the presence of a creature with any such feature. That is, the inference I'm prepared to make is that wherever Daisy is, an instance of Daisy's features is, including something being a cow. -- That is, I also accept that sometimes Daisy features are present without her, singly or in bunches, because other things are cows, other things are placid, other things ruminate, etc. (If our farmer prefers tropes to properties, all bets are off.)

I'm not immediately going to claim this is enough to justify the EG. I think first we take a detour through some obvious counterfactuals. We're trying to give due weight to the idea that the farmer only believes there's a cow in the field because he believes Daisy is, and he knows Daisy is a cow. That's to say, if he did not believe Daisy was in the field, he would not believe a cow was in the field.

But that sounds far too strong, at least because if it turns out to have been Clarabelle, the farmer will retreat to: I knew it was a cow and I thought it was Daisy. He might even be genuinely surprised and wonder how such a mistake happened: I could have sworn it was Daisy.

What I want to note here is that on discovering his mistake, the farmer will quite naturally itemize the Daisy features he correctly identified in search of the one he was mistaken about. All of which suggests his Daisy belief was -- contra my sympathies for a casual account of names -- in fact a sort of compound belief regarding those many descriptive features of Daisy. Maybe this is specific to cases of recognition, but the farmer's ready recasting of his belief as a compound suggests there's a list of criteria for recognizing Daisy and he was right about some of them, but not all. (Such lists look easy to Gettier-ize.)

And if all of that is right, then the EG was compound to begin with, even with only Daisy criteria in mind: there is something in the field that is a cow, and is placid, and ruminates, and has a nick on her left ear, and is pretty fat for this time of year, etc. And if that's right -- and even if that list is somehow taken as open-ended -- it can be split: there's something in the field that's a cow; there's something in the field that's placid; and so on.

Which, again, is why the farmer won't feel nearly such a fool if it turns out to be Clarabelle, even if he's very surprised, because he will still have gotten a lot right.

(I was going to head in a completely different direction, so I'll wait to see what people think of this before trotting out alternative analyses.)

Well if a valid deduction is enough to be deductively justified — neomac

I think the general view is that inference confers justification no more than it confers truth; rather, valid deduction is often expected to conserve justification and to conserve knowledge, just as it conserves truth. Since people may not make inferences they're entitled to, you have to add some clause, such as Gettier does, that the agent makes the valid inference. (Similarly, you don't automatically know everything entailed by what you know, but if you made all the inferences you're entitled to, you would.)

Some nice points in this thread, which I'll reread.

I'm only surprised no one has yet used the phrase "instrumental rationality," which could be defined something like, the rational selection of a course of action to achieve a given goal -- the kicker being that this means any goal, however arbitrary. Sometimes "reasonableness" is contrasted specifically with instrumental rationality in submitting to judgment also the worthwhileness of the goal and the acceptability of the means of achieving it, so a broader decision-making process.

He and George Adams (ts) were in Mingus's last quartet, and then carried on as a band.

Pullen had a unique technique that involved rolling his hand over the keys to get clusters of notes (and some otherworldly effects). There's a cute video on YouTube of his band appearing on a show Ramsey Lewis hosted, and Ramsey tells him, I tried it, tried to play like you do, and I ended up with bandaids all over my hands.

Here's a good place to start:

My starting point was maybe his first record as a leader. He does a killer version of Bemsha Swing. Gets how Monk had already broken into, let's say, tactical atonality. Monk understands what can be done with a piano as a physical thing, not just as a manifestation of music theory.

For a sort of point between Monk and where Cecil ends up, don't miss the incredible Don Pullen.

If you've listened to some other earlyish Ornette but not to Free Jazz, just spin it. There's just more players, but it's very listenable. I only finally got around to it in the past year, and it's nothing to be afraid of. (It used to be said there were two routes into free jazz (my music theory is almost non-existent, so grain of salt here): Ornette just passes right by the theory of harmony and frees melody from it; Cecil layers in more, augmenting traditional harmony, broadening it. Free Jazz the record is definitely still on Ornette's end of the spectrum.)

I'll certainly revisit late Coltrane, so thanks for your impressions.