You’re presupposing that trustworthiness is communicable, or that rationality demands trusting somebody absent evidence to do otherwise. There’s definitely incommunicable knowledge—what red looks like to me, for example. You’re stretching “rationality” to places it has no business being to defend a proposition, or else adding conditions (honesty) to make the proposition work.
The conditions are right there in the Aumann proofs, are they not? I’m not adding anything, I’m dividing up the possible outcomes: anthropics (questionable), communicable knowledge (contra you), or Aumann is inapplicable (honesty etc).
What I’m describing doesn’t depend on either SIA or SSA.
I’d be interested to see if you could prove that the result holds independently of them.
That’s not an argument. That’s begging the question.
That’s the point of the modus tollens vs modus ponens saying. You claim to derive a result, but using premises more questionable than the conclusion, in which case you may have merely disproven the premises via reductio ad absurdum. If this is begging the question (which it isn’t, since that’s when your premise contains the conclusion), then every proof by contradiction or reductio ad absurdum is question-begging.
Or, in short—the posteriors are different. The information is different. There is a piece of incommunicable evidence when something happens to me as opposed to somebody else.
Correct me if I am wrong, but in your example, M is not increased when O fails to happen—more concretely, you assume the number of spooked people you will hear of is constant—when it would be more appropriate to increase the number of observations of O by 1, since if you don’t go into the spooky house someone else does. Then you are merely deriving the uninteresting observation that if there are more events (by 1) consistent with Z, Z will be more likely. Well, yeah. But there is nothing special about one’s own observations in this case; if someone else went into the house and reported observations, you would update a little more, just like if you want into the house, and in both cases, more than if no one went into the house (or they went in and saw nothing).
Also, your equations are messed up. I think you need to escape some stuff.
Aha! I think the issue here is that you’re thinking of it in terms of two identical observers. The observers aren’t identical in my arguments—one is post-hoc. I have realized where the discrepancy between our arguments is coming from with your example, because of the way I keep framing problems as being about the observer. Suppose I and a friend, Bob, are arguing about who goes in the house. In this case, there’s not practical difference between our evidence. The difference isn’t between me and other, the difference is between me and (other who I wouldn’t have known about except for said experience).
Bob and I are identical (I did say this wasn’t necessarily anthropic!) for the purposes of calculation. Bob is included in p(M).
Steve, who wrote a post on a rationality forum describing his experiences, is -not- identical with me for the purposes of calculation. Steve is included in p(O).
Does my argument make more sense now? Bob’s information is fully transferable—in terms of flipping coins, he called heads before flipping ten heads in a row. Steve’s information is -not- - he’s the guy who flipped ten heads in a row without calling anything.
(ETA: I have no idea how to make them look right. How do you escape stuff?)
In certain contexts an asterisk is a magic character and you need to precede it with a backslash to keep it from turning into <em> or </em>. To get
p(X|M, M1) = p(M|X)*P(X|M1)/p(M|M1)
do
p(X|M, M1) = p(M|X)\*P(X|M1)/p(M|M1)
Or you can just put equations in their own paragraphs that are indented by four spaces, in which case no characters will have their magic meaning. (This is how I did the above paragraph where the backslash is visible.)
The conditions are right there in the Aumann proofs, are they not? I’m not adding anything, I’m dividing up the possible outcomes: anthropics (questionable), communicable knowledge (contra you), or Aumann is inapplicable (honesty etc).
I’d be interested to see if you could prove that the result holds independently of them.
That’s the point of the modus tollens vs modus ponens saying. You claim to derive a result, but using premises more questionable than the conclusion, in which case you may have merely disproven the premises via reductio ad absurdum. If this is begging the question (which it isn’t, since that’s when your premise contains the conclusion), then every proof by contradiction or reductio ad absurdum is question-begging.
Correct me if I am wrong, but in your example, M is not increased when O fails to happen—more concretely, you assume the number of spooked people you will hear of is constant—when it would be more appropriate to increase the number of observations of O by 1, since if you don’t go into the spooky house someone else does. Then you are merely deriving the uninteresting observation that if there are more events (by 1) consistent with Z, Z will be more likely. Well, yeah. But there is nothing special about one’s own observations in this case; if someone else went into the house and reported observations, you would update a little more, just like if you want into the house, and in both cases, more than if no one went into the house (or they went in and saw nothing).
Also, your equations are messed up. I think you need to escape some stuff.
Aha! I think the issue here is that you’re thinking of it in terms of two identical observers. The observers aren’t identical in my arguments—one is post-hoc. I have realized where the discrepancy between our arguments is coming from with your example, because of the way I keep framing problems as being about the observer. Suppose I and a friend, Bob, are arguing about who goes in the house. In this case, there’s not practical difference between our evidence. The difference isn’t between me and other, the difference is between me and (other who I wouldn’t have known about except for said experience).
Bob and I are identical (I did say this wasn’t necessarily anthropic!) for the purposes of calculation. Bob is included in p(M).
Steve, who wrote a post on a rationality forum describing his experiences, is -not- identical with me for the purposes of calculation. Steve is included in p(O).
Does my argument make more sense now? Bob’s information is fully transferable—in terms of flipping coins, he called heads before flipping ten heads in a row. Steve’s information is -not- - he’s the guy who flipped ten heads in a row without calling anything.
(ETA: I have no idea how to make them look right. How do you escape stuff?)
In certain contexts an asterisk is a magic character and you need to precede it with a backslash to keep it from turning into
<em>or</em>. To getp(X|M, M1) = p(M|X)*P(X|M1)/p(M|M1)
do
Or you can just put equations in their own paragraphs that are indented by four spaces, in which case no characters will have their magic meaning. (This is how I did the above paragraph where the backslash is visible.)
Is there a reference somewhere on LessWrong or the Wiki for the mark-up used in the comments?
There’s a “Show help” button on the right underneath comment fields. The quick reference it reveals includes a link to the wiki page.
The formatting language used is a (not totally bug-free) subset of Markdown.
Laughs I’m so used to useless help screens I ignored that button, looked for it manually on the wiki, couldn’t find it, and gave up. Thanks!