What I’m trying to figure out is if this community thinks that any SREoE must necessarily reject G1 (based largely on the inconsistency of E1). I’m not claiming that a SREoE must accept G1 upon being exposed to E1.
I get that you’re trying to be polite and all, and that’s nice of you.
Politeness is important, and the social constraints of politeness are a big reason I steered this discussion away from emotionally loaded terms like “rational,” “irrational,” “God,” “faith,” etc.in the first place; it’s a lot easier to discuss what confidence a SREoE resides in G1 given E1 without getting offended or apologetic or defensive than to discuss whether belief in God is rational or irrational, because the latter formulation carries so much additional cultural and psychological weight.
But politeness aside, I don’t see how what you’re saying can possibly be the case given what you’ve already agreed to. If E1 entails high confidence in G1, then an SREoE given E1 concludes that G1 is much more likely than NOT(G1), and an agent that does not conclude this is not an SREoE. That’s just what it means for evidence to entail a given level of confidence in a conclusion, be it a low level or a high level.
Which means that if you’re right that I have evidence that entails reasonably high confidence in the existence of God, then my vanishingly low confidence in the existence of God means I’m not being rational on the subject. Maybe that’s rude to say, but rude or not that’s just what it means for me to have evidence that entails reasonably high confidence in the existence of God.
And I get that you’re looking for the same kind of politeness in return… that we can believe or not believe whatever we want, but as long as we don’t insist it’s irrational to conclude from available evidence that God exists, we can all get along.
And in general, we’re willing to be polite in that way… most of us have stuff in our lives we don’t choose to be SREoEs about, and going around harassing each other about it is a silly way to spend our time. There are theists of various stripes on LW, but we don’t spend much time arguing about it.
But if you insist on framing the discussion in terms of epistemic rationality then, again, politeness aside, that doesn’t really work. If E1 entails low confidence in G1, then an SREoE given E1 concludes that G1 is much less likely than NOT(G1), and an agent that does not conclude this is not an SREoE. That’s just what it means for evidence to entail a given level of confidence in a conclusion, be it a low level or a high level.
Or, expressed in the more weighted way: either we have shared evidence that entails high confidence in the existence of God and I’m not evaluating that evidence as reliably as you are, or we have shared evidence that entails low confidence in the existence of God and you’re not evaluating that evidence as reliably as I am.
All the politeness in the world doesn’t change that.
All of that said, there’s no obligation here to be an SREoE in any particular domain, which is why I started this whole conversation by talking about pragmatic reasons to continue practicing your religion in the first place. If you insist on placing the discussion in the sphere of epistemic rationality, I don’t see how you avoid the conclusion, but there’s no obligation to do that.
I’m not trying to be nice. Do not interpret the fact that I’m won’t admit to attacking you to mean that I’m trying to be nice—perhaps I’m really not attacking you. I honestly believe that your position is fully self-justified, and I respect it.
Neither am I asking for politeness. I didn’t get come on here expecting you to be nice, only rational and reasonable, which most people have been. I’d be happy for you all to tell me that it’s irrational to conclude that God exists. One of my biggest questions was whether you all thought this was the case. Some of you don’t, but you all did, and undiplomatically told me so, I wouldn’t be offended. I might come away disappointed that this community wasn’t as open-minded as I had hoped (no accusations intended), but I wouldn’t be offended. If you think it’s the case, please tell me so, and I will respectfully disagree.
If E1 entails high confidence in G1, then an SREoE given E1 concludes that G1 is much more likely than NOT(G1), and an agent that does not conclude this is not an SREoE. That’s just what it means for evidence to entail a given level of confidence in a conclusion, be it a low level or a high level.
I think the biggest problem here is that, as I wrote in the other post, I don’t believe there’s only one conclusion a rational person (SREoE) can draw from the evidence. I don’t believe that there is only one correct “methodology,” and so I don’t believe that evidence necessarily entails one thing or the other.
I don’t believe that there is only one correct “methodology,” and so I don’t believe that evidence necessarily entails one thing or the other.
I see. I apologize; I missed this the first time you said it.
So, on your view, what does it mean to evaluate evidence reliably, if not that sufficiently reliable evaluations of given evidence will converge on the same confidence in given propositions? What does it mean for a methodology to be correct, if not that it leads a system that implements it to a given confidence in given propositions given evidence?
Or, to put it differently… well, let’s back up a step. Why should anyone care about evaluating evidence reliably? Why not evaluate it unreliably instead, or not bother evaluating it at all?
Yeah, I don’t really know. It just depends on your paradigm—according to rationalists like yourself, it seems, a cold rational analysis is most “correct” and reliable. For some others, the process involves fasting and prayer. I’m not going to say either is infallible. Certainly logic is a wonderful thing which has its place in our lives. But taken too far it’s not always helpful or accurate, especially in us subjective humans.
Well, I certainly agree about fallibility. Humans don’t have access to infallible epistemologies.
That said, if fasting and prayer reliably gets me the most useful confidence levels in propositions for achieving my goals, then I should engage in fasting and prayer because that’s part of the most reliable process for evaluating evidence.
If it doesn’t, then that’s not a reason for me to engage in fasting and prayer, though I may choose to do so for other reasons.
Either one of those things is true, or the other is. And I may not know enough about the world to decide with confidence which it is (though I sure do seem to), but even if I don’t my ignorance doesn’t somehow make it the case that they are both true.
These words seem subjective or at the very least unmeasurable. There is no way of determining absolutely whether something is “reliable” or “useful” without ridiculously technical definitions, which ruin the point anyway.
(sorry if I don’t respond right away. I’ve been retributively downvoted to −15 and so LW is giving me a hassle about commenting. The forum programming meant well...)
sorry if I don’t respond right away. I’ve been [...] downvoted to −15
That’s OK. If we no longer have any way of agreeing on whether propositions are useful, reliable, or true, or agreeing on what it means for propositions to be any of these things, then I don’t anticipate the discussion going anywhere from here that’s worth my time. We can let it drop here.
(sorry if I don’t respond right away. I’ve been retributively downvoted to −15 and so LW is giving me a hassle about commenting. The forum programming meant well...)
Working as intended. Evangelism of terrible thinking is not welcome here. For most intents and purposes you are a troll. It’s time for you to go and time for me to start downvoting anyone who feeds you. Farewell Ibidem (if you the user behind the handle ever happen to gain an actual sincere interest in rationality I recommend creating a new account and making a fresh start.)
I don’t believe there’s only one conclusion a rational person (SREoE) can draw from the evidence.
There is one direction a SREoE updates on evidence—towards the evidence.
If I have strong reasons (high prior probability) of thinking that a coin has heads on both sides, I’m making a mistake by becoming more confident after I flip the coin and it comes up tails.
Likewise, if I have strong reasons of thinking that another coin is biased towards heads, so it turns up heads 60% instead of 50%, I’m committing the same error if I become more confident after seeing the coinflip turn up tails.
So learning E1 should make any SREoE become more confident of G1 unless that person’s priors are already very heavily weighed towards G1. In the real world, there just aren’t that many SREoE’s with high priors on G1 before being exposed to E1.
In the real world, there just aren’t that many SREoE’s with high priors on G1 before being exposed to E1.
First of all, note that you effectively just said that nearly all religious people are irrational. I won’t hold it against you, just realize that that’s the position you’re expressing.
If I have strong reasons (high prior probability) of thinking that a coin has heads on both sides, I’m making a mistake by becoming more confident after I flip the coin and it comes up tails.
Obviously. If there is clear evidence against your beliefs, you should decrease your confidence in your beliefs. But the problem is that this situation is not so simple as heads and tails.
What I’m trying to say is that two SREoEs can properly examine E1 and come up with different conclusions. I’m sorry if I agreed too fully to Dave’s first set of propositions—the devil’s in the details, as we irrational people who believe in a Devil say sometimes.
So on your account, if I’ve understood it, I have sufficient evidence to justify a high confidence in a conscious higher Power consistent with the accounts of all believers in Abrahamic religions, though not necessarily identical to that described in any of those accounts, and the fact that I lack such confidence is merely because I haven’t properly evaluated the evidence available to me.
Yes?
The key is “if I haven’t properly evaluated the evidence.” I took “properly” to mean “in a certain way,” while Dave intended it as “in the one correct way.” When this became clear, I tried to clarify my position.
I’m going to reiterate it again, because you don’t seem to be getting it: I believe that it’s possible for two equally R Es oE to evaluate the same evidence and come up with different conclusions. Thus exposure to E1 does not necessarily entail any confidence-shifting at all, even in a SREoE.
First of all, note that you effectively just said that nearly all religious people are irrational. I won’t hold it against you, just realize that that’s the position you’re expressing.
I’ll pop in here and note that the general point of view here is that everyone is irrational, and even the best of us frequently err. That’s why we tend to use the term “aspiring rationalist,” since nobody has reached the point of being able to claim to be an ideal rationalist.
The highest standard we can realistically hold people to is to make a genuine effort to be rational, to the best of their abilities, using the information available to them.
That’s true. It’s not actually “rational” vs. “irrational,” even if that would make the situation so much easier to understand.
I hope you’d agree, though, that there are many people in this world (think: evangelicals) who don’t make any sort of effort to be rational in the sense you mean it, and even some who honestly think logical inference is a tool of the devil. How sad...but probably no need to worry about them in this thread.
I believe that it’s possible for two [SREoEs] to evaluate the same evidence and come up with different conclusions.
That is possible if and only if the two SREoEs started with different beliefs (priors) before receiving the same evidence. Aumann’s Agreement Theorem says that SREoEs who start with the same beliefs and see the same evidence cannot disagree without doing something wrong.
In the real world, there just aren’t that many SREoE’s with high priors on G1 before being exposed to E1.
I didn’t write this clearly. I meant that most human SREoEs who haven’t been exposed to E1 don’t assign high probability to G1. Theoretically, an SREoE who hadn’t been exposed to E1 could have such high confidence in G1 that expose to E1 should reduce confidence in G1. In practice, I’m not sure any adult human hasn’t been exposed to E1 already, and I’m doubtful that most children are SREoEs—thus, I’m not sure whether the set (human&non-E1&SREoE) has any elements in existence.
First of all, note that you effectively just said that nearly all religious people are irrational. I won’t hold it against you, just realize that that’s the position you’re expressing.
I’m saying that people who assign high probability to G1 after exposure to E1 either (a) had very different priors about G1 than I before exposure to E1, or (b) are not SREoEs. Alternatively, I either (a) am not an SREoE, or (b) have not been exposed to the evidence we have referred to as E1.
To put it slightly differently, I can identify evidence that would make me increase the probability I assign to G1. Can you identify evidence that would make you decrease the probability you assign G1?
Aumann’s Agreement Theorem says that SREoEs who start with the same beliefs and see the same evidence cannot disagree without doing something wrong.
Perhaps, then, I don’t fully agree with Aumann’s Agreement Theorem. I’ll leave it to you to decide whether that means I’m not a “genuine” Bayesian. I wouldn’t have a problem with being unable to fully adopt a single method of thinking about the universe.
In practice, I’m not sure any adult human hasn’t been exposed to E1 already, and I’m doubtful that most children are SREoEs
Is it fair to say that most current SREoEs became that way during a sort of rationalist awakening? (I know it’s not as simple as being a SREoE or not, and so this process actually takes years. but let’s pretend for a moment.) Imagine a child who grows up being fed very high priors about G1. This child (not a SREoE) is exposed to E1 and has a high confidence in G1. When he (/she) grows up and eventually becomes a SREoE, he first of all consciously throws out all his priors (rebellion against parents), then re-evaluates E1 (re-exposure?) and decides that in fact it entails ~G1.
Whether or not this describes you, does it make sense?
I’m saying that people who assign high probability to G1 after exposure to E1 either (a) had very different priors about G1 than I before exposure to E1, or (b) are not SREoEs. Alternatively, I either (a) am not an SREoE, or (b) have not been exposed to the evidence we have referred to as E1.
How about this: since both of you have been exposed to the same evidence and don’t agree, then either (a) you had very different priors (which is likely), or (b) you evaluate evidence differently. I’m going to avoid saying either of you is “better” or “more rational” at evaluating evidence.
Perhaps, then, I don’t fully agree with Aumann’s Agreement Theorem.
Whoa there. Aumann’s agreement theorem is a theorem. It is true, full stop. Whatever that term “SREoE” means (I keep going up and keep not seeing an explanation), either it doesn’t map onto the hypotheses of Aumann’s agreement theorem or you are attempting to disagree with a mathematical fact.
I believe it was “Sufficiently reasonable evaluator of evidence”—which I was using roughly equivalently to Bayesian empiricist. I’m beginning to doubt that is what ibidem means by it.
TheOtherDave defined it way back in the thread to try to taboo “rationalist,” since that word has such a multitude of denotations and connotations (including the LW intended meanings). Edit: terminology mostly defined here and here.
Sufficiently reliable, but otherwise yes. That said, we’ve since established that ibidem and I don’t have a shared understanding of “reliable” or “evidence,” either, so I’d have to call it a failed/incomplete attempt at tabooing.
For it to be a mathematical fact, it needs a mathematical proof. Go ahead...!
Like it or not, rationality is not mathematics—it is full of estimations, assumptions, objective decisions, and wishful thinking. Thus, a “theorem” in evidence evaluation is not a mathematical theorem, obtained using unambiguous formal logic.
If what you mean to say is that Aumann’s Agreement “Theorem” is a fundamental building block of your particular flavor of rational thinking, then what this means is simply that I don’t fully subscribe to your particular flavor of rational thinking. Nothing (mathematics nearly excepted) is “true, full stop.” Remember? 1 is not a probability. That one’s even more “true, full stop” than Aumann’s ideas about rational disagreement.
When did I claim that rationality was mathematics?
Right here:
you are attempting to disagree with a mathematical fact.
it needs a mathematical proof.
Here you go.
Maybe not “rationality” exactly but Aumann’s work, whatever it is you call what we’re doing here. Rational decision-making.
So yes, Aumann’s theorem can be proven using a certain system of formalization, taking a certain set of definitions and assumptions. What I’m saying is not that I disagree with the derivation I gave, but that I don’t fully agree with its premises.
If what you mean to say is that Aumann’s Agreement “Theorem” is a fundamental building block of your particular flavor of rational thinking
When did I say this?
You didn’t yet, I didn’t say you did. I’m guessing that that’s what you actually mean though, because very, very few things if any are “true, full stop.” Something like this theorem can be fully true according to Bayesian statistics or some other system of thought, full stop. If this is the case, then in means I don’t fully accept that system of thought. Is disagreement not allowed?
Maybe not “rationality” exactly but Aumann’s work, whatever it is you call what we’re doing here. Rational decision-making.
How does what I said there mean “rationality is mathematics”? All I’m saying is that Aumann’s agreement theorem is mathematics, and if you’re attempting to disagree with it, then you’re attempting to disagree with mathematics.
What I’m saying is not that I disagree with the derivation I gave, but that I don’t fully agree with its premises.
I agree that this is what you should’ve said, but that isn’t what you said. Disagreeing with an implication “if P, then Q” doesn’t mean disagreeing with P.
I’m guessing that that’s what you actually mean though
No, it’s not. I just mean that mathematical facts are mathematical facts and questioning their relevance to real life is not the same as questioning their truth.
Now this just depends on what we mean by “disagree.” Of course I can’t dispute a formal logical derivation. The math, of course, is sound.
Disagreeing with an implication “if P, then Q” doesn’t mean disagreeing with P.
All I disagree with X, which means either that I don’t agree that Q implies X, or I don’t accept P.
I’m not questioning mathematical truth. All I’m questioning is what TimS said.
But if we agree it was just a misunderstanding, can we move on? Or not. This also doesn’t seem to be going anywhere, especially if we’ve decided we fundamentally disagree. (Which in and of itself is not grounds for a downvote, may I remind you all.)
I didn’t downvote you because we disagree, I downvoted you because you conflated disagreeing with the applicability of a mathematical fact to a situation with disagreeing with a mathematical fact. Previously I downvoted you because you tried to argue against two positions I never claimed to hold.
Glad we’ve got that cleared up, then. I wasn’t only talking to you; there are a few people who have taken it upon themselves to make my views feel unwelcome here. Sorry if we’ve had some misunderstandings.
Imagine a child who grows up being fed very high priors about G1. This child (not a SREoE) is exposed to E1 and has a high confidence in G1. When he (/she) grows up and eventually becomes a SREoE, he first of all consciously throws out all his priors (rebellion against parents), then re-evaluates E1 (re-exposure?) and decides that in fact it entails ~G1.
This was not my experience. I was raised in a practicing religious family, and the existence of the holy texts, the well-being of the members of the religious community, and the existence of the religious community were all strong evidence for G1.
I reduced the probability I assigned to G1 because I realized I was underweighing other evidence. Things I would expect to be true if G1 were true turned out to be false. I think I knew those facts were false, but did not consider the implications, and so didn’t adjust my belief in G1.
Once I considered the implications, it became clear to me that E1 was outweighed by the falsification of other implications of G1. Given that balance, I assign G1 very very low probability of being accurate. But I still don’t deny that E1 is evidence of G1. If I didn’t know E1, learning it would adjust upward my belief in G1.
In practice, what people seem to mean is best described technically as changing what sorts of things count as evidence. I changed my beliefs about G1 because I started taking the state of the world and the prevalence of human suffering as a fact about G1
Also, if we are going to talk coherently about priors, we can’t really describe anything humans do as “throwing out their priors.” If we really assign probability zero to any proposition, we have no way of changing our minds again.. And if we assign some other probability, justifying that is weird.
Certainly you can’t simply will your aliefs to change, but it does seem to be a conscious and deliberate effort around here. The belief in G1 usually happens without any knowledge about Bayesian statistics, technical rationality, or priors, so this “awakening” may be the first time a person ever thought of E1 as “evidence” in this technical sense.
the prevalence of human suffering
By the way, I think the best response to this argument is that yes, there is evil, but God allows it because it is better for us in the long run—in other words, if there is an afterlife which is partly defined by our existence here, than our temporary comfort isn’t the only thing to consider. If we all lived in the Garden of Eden, we would never learn or progress. But I don’t want a whole new argument on my hands.
I get that you’re trying to be polite and all, and that’s nice of you.
Politeness is important, and the social constraints of politeness are a big reason I steered this discussion away from emotionally loaded terms like “rational,” “irrational,” “God,” “faith,” etc.in the first place; it’s a lot easier to discuss what confidence a SREoE resides in G1 given E1 without getting offended or apologetic or defensive than to discuss whether belief in God is rational or irrational, because the latter formulation carries so much additional cultural and psychological weight.
But politeness aside, I don’t see how what you’re saying can possibly be the case given what you’ve already agreed to. If E1 entails high confidence in G1, then an SREoE given E1 concludes that G1 is much more likely than NOT(G1), and an agent that does not conclude this is not an SREoE. That’s just what it means for evidence to entail a given level of confidence in a conclusion, be it a low level or a high level.
Which means that if you’re right that I have evidence that entails reasonably high confidence in the existence of God, then my vanishingly low confidence in the existence of God means I’m not being rational on the subject. Maybe that’s rude to say, but rude or not that’s just what it means for me to have evidence that entails reasonably high confidence in the existence of God.
And I get that you’re looking for the same kind of politeness in return… that we can believe or not believe whatever we want, but as long as we don’t insist it’s irrational to conclude from available evidence that God exists, we can all get along.
And in general, we’re willing to be polite in that way… most of us have stuff in our lives we don’t choose to be SREoEs about, and going around harassing each other about it is a silly way to spend our time. There are theists of various stripes on LW, but we don’t spend much time arguing about it.
But if you insist on framing the discussion in terms of epistemic rationality then, again, politeness aside, that doesn’t really work. If E1 entails low confidence in G1, then an SREoE given E1 concludes that G1 is much less likely than NOT(G1), and an agent that does not conclude this is not an SREoE. That’s just what it means for evidence to entail a given level of confidence in a conclusion, be it a low level or a high level.
Or, expressed in the more weighted way: either we have shared evidence that entails high confidence in the existence of God and I’m not evaluating that evidence as reliably as you are, or we have shared evidence that entails low confidence in the existence of God and you’re not evaluating that evidence as reliably as I am.
All the politeness in the world doesn’t change that.
All of that said, there’s no obligation here to be an SREoE in any particular domain, which is why I started this whole conversation by talking about pragmatic reasons to continue practicing your religion in the first place. If you insist on placing the discussion in the sphere of epistemic rationality, I don’t see how you avoid the conclusion, but there’s no obligation to do that.
I’m not trying to be nice. Do not interpret the fact that I’m won’t admit to attacking you to mean that I’m trying to be nice—perhaps I’m really not attacking you. I honestly believe that your position is fully self-justified, and I respect it.
Neither am I asking for politeness. I didn’t get come on here expecting you to be nice, only rational and reasonable, which most people have been. I’d be happy for you all to tell me that it’s irrational to conclude that God exists. One of my biggest questions was whether you all thought this was the case. Some of you don’t, but you all did, and undiplomatically told me so, I wouldn’t be offended. I might come away disappointed that this community wasn’t as open-minded as I had hoped (no accusations intended), but I wouldn’t be offended. If you think it’s the case, please tell me so, and I will respectfully disagree.
I think the biggest problem here is that, as I wrote in the other post, I don’t believe there’s only one conclusion a rational person (SREoE) can draw from the evidence. I don’t believe that there is only one correct “methodology,” and so I don’t believe that evidence necessarily entails one thing or the other.
I see. I apologize; I missed this the first time you said it.
So, on your view, what does it mean to evaluate evidence reliably, if not that sufficiently reliable evaluations of given evidence will converge on the same confidence in given propositions? What does it mean for a methodology to be correct, if not that it leads a system that implements it to a given confidence in given propositions given evidence?
Or, to put it differently… well, let’s back up a step. Why should anyone care about evaluating evidence reliably? Why not evaluate it unreliably instead, or not bother evaluating it at all?
Yeah, I don’t really know. It just depends on your paradigm—according to rationalists like yourself, it seems, a cold rational analysis is most “correct” and reliable. For some others, the process involves fasting and prayer. I’m not going to say either is infallible. Certainly logic is a wonderful thing which has its place in our lives. But taken too far it’s not always helpful or accurate, especially in us subjective humans.
Well, I certainly agree about fallibility. Humans don’t have access to infallible epistemologies.
That said, if fasting and prayer reliably gets me the most useful confidence levels in propositions for achieving my goals, then I should engage in fasting and prayer because that’s part of the most reliable process for evaluating evidence.
If it doesn’t, then that’s not a reason for me to engage in fasting and prayer, though I may choose to do so for other reasons.
Either one of those things is true, or the other is. And I may not know enough about the world to decide with confidence which it is (though I sure do seem to), but even if I don’t my ignorance doesn’t somehow make it the case that they are both true.
Is there no possibility of partly true?
These words seem subjective or at the very least unmeasurable. There is no way of determining absolutely whether something is “reliable” or “useful” without ridiculously technical definitions, which ruin the point anyway.
(sorry if I don’t respond right away. I’ve been retributively downvoted to −15 and so LW is giving me a hassle about commenting. The forum programming meant well...)
That’s OK. If we no longer have any way of agreeing on whether propositions are useful, reliable, or true, or agreeing on what it means for propositions to be any of these things, then I don’t anticipate the discussion going anywhere from here that’s worth my time. We can let it drop here.
Working as intended. Evangelism of terrible thinking is not welcome here. For most intents and purposes you are a troll. It’s time for you to go and time for me to start downvoting anyone who feeds you. Farewell Ibidem (if you the user behind the handle ever happen to gain an actual sincere interest in rationality I recommend creating a new account and making a fresh start.)
There is one direction a SREoE updates on evidence—towards the evidence.
If I have strong reasons (high prior probability) of thinking that a coin has heads on both sides, I’m making a mistake by becoming more confident after I flip the coin and it comes up tails.
Likewise, if I have strong reasons of thinking that another coin is biased towards heads, so it turns up heads 60% instead of 50%, I’m committing the same error if I become more confident after seeing the coinflip turn up tails.
So learning E1 should make any SREoE become more confident of G1 unless that person’s priors are already very heavily weighed towards G1. In the real world, there just aren’t that many SREoE’s with high priors on G1 before being exposed to E1.
First of all, note that you effectively just said that nearly all religious people are irrational. I won’t hold it against you, just realize that that’s the position you’re expressing.
Obviously. If there is clear evidence against your beliefs, you should decrease your confidence in your beliefs. But the problem is that this situation is not so simple as heads and tails.
What I’m trying to say is that two SREoEs can properly examine E1 and come up with different conclusions. I’m sorry if I agreed too fully to Dave’s first set of propositions—the devil’s in the details, as we irrational people who believe in a Devil say sometimes.
The key is “if I haven’t properly evaluated the evidence.” I took “properly” to mean “in a certain way,” while Dave intended it as “in the one correct way.” When this became clear, I tried to clarify my position.
I’m going to reiterate it again, because you don’t seem to be getting it: I believe that it’s possible for two equally R Es oE to evaluate the same evidence and come up with different conclusions. Thus exposure to E1 does not necessarily entail any confidence-shifting at all, even in a SREoE.
I’ll pop in here and note that the general point of view here is that everyone is irrational, and even the best of us frequently err. That’s why we tend to use the term “aspiring rationalist,” since nobody has reached the point of being able to claim to be an ideal rationalist.
The highest standard we can realistically hold people to is to make a genuine effort to be rational, to the best of their abilities, using the information available to them.
That’s true. It’s not actually “rational” vs. “irrational,” even if that would make the situation so much easier to understand.
I hope you’d agree, though, that there are many people in this world (think: evangelicals) who don’t make any sort of effort to be rational in the sense you mean it, and even some who honestly think logical inference is a tool of the devil. How sad...but probably no need to worry about them in this thread.
That is possible if and only if the two SREoEs started with different beliefs (priors) before receiving the same evidence. Aumann’s Agreement Theorem says that SREoEs who start with the same beliefs and see the same evidence cannot disagree without doing something wrong.
I didn’t write this clearly. I meant that most human SREoEs who haven’t been exposed to E1 don’t assign high probability to G1. Theoretically, an SREoE who hadn’t been exposed to E1 could have such high confidence in G1 that expose to E1 should reduce confidence in G1. In practice, I’m not sure any adult human hasn’t been exposed to E1 already, and I’m doubtful that most children are SREoEs—thus, I’m not sure whether the set (human&non-E1&SREoE) has any elements in existence.
I’m saying that people who assign high probability to G1 after exposure to E1 either (a) had very different priors about G1 than I before exposure to E1, or (b) are not SREoEs. Alternatively, I either (a) am not an SREoE, or (b) have not been exposed to the evidence we have referred to as E1.
To put it slightly differently, I can identify evidence that would make me increase the probability I assign to G1. Can you identify evidence that would make you decrease the probability you assign G1?
Perhaps, then, I don’t fully agree with Aumann’s Agreement Theorem. I’ll leave it to you to decide whether that means I’m not a “genuine” Bayesian. I wouldn’t have a problem with being unable to fully adopt a single method of thinking about the universe.
Is it fair to say that most current SREoEs became that way during a sort of rationalist awakening? (I know it’s not as simple as being a SREoE or not, and so this process actually takes years. but let’s pretend for a moment.) Imagine a child who grows up being fed very high priors about G1. This child (not a SREoE) is exposed to E1 and has a high confidence in G1. When he (/she) grows up and eventually becomes a SREoE, he first of all consciously throws out all his priors (rebellion against parents), then re-evaluates E1 (re-exposure?) and decides that in fact it entails ~G1.
Whether or not this describes you, does it make sense?
How about this: since both of you have been exposed to the same evidence and don’t agree, then either (a) you had very different priors (which is likely), or (b) you evaluate evidence differently. I’m going to avoid saying either of you is “better” or “more rational” at evaluating evidence.
Whoa there. Aumann’s agreement theorem is a theorem. It is true, full stop. Whatever that term “SREoE” means (I keep going up and keep not seeing an explanation), either it doesn’t map onto the hypotheses of Aumann’s agreement theorem or you are attempting to disagree with a mathematical fact.
I believe it was “Sufficiently reasonable evaluator of evidence”—which I was using roughly equivalently to Bayesian empiricist. I’m beginning to doubt that is what ibidem means by it.
TheOtherDave defined it way back in the thread to try to taboo “rationalist,” since that word has such a multitude of denotations and connotations (including the LW intended meanings). Edit: terminology mostly defined here and here.
Sufficiently reliable, but otherwise yes.
That said, we’ve since established that ibidem and I don’t have a shared understanding of “reliable” or “evidence,” either, so I’d have to call it a failed/incomplete attempt at tabooing.
They’re using it to mean “sufficiently reliable evaluator of evidence”.
For it to be a mathematical fact, it needs a mathematical proof. Go ahead...!
Like it or not, rationality is not mathematics—it is full of estimations, assumptions, objective decisions, and wishful thinking. Thus, a “theorem” in evidence evaluation is not a mathematical theorem, obtained using unambiguous formal logic.
If what you mean to say is that Aumann’s Agreement “Theorem” is a fundamental building block of your particular flavor of rational thinking, then what this means is simply that I don’t fully subscribe to your particular flavor of rational thinking. Nothing (mathematics nearly excepted) is “true, full stop.” Remember? 1 is not a probability. That one’s even more “true, full stop” than Aumann’s ideas about rational disagreement.
Here you go.
When did I claim that rationality was mathematics?
When did I say this?
Right here:
Maybe not “rationality” exactly but Aumann’s work, whatever it is you call what we’re doing here. Rational decision-making.
So yes, Aumann’s theorem can be proven using a certain system of formalization, taking a certain set of definitions and assumptions. What I’m saying is not that I disagree with the derivation I gave, but that I don’t fully agree with its premises.
You didn’t yet, I didn’t say you did. I’m guessing that that’s what you actually mean though, because very, very few things if any are “true, full stop.” Something like this theorem can be fully true according to Bayesian statistics or some other system of thought, full stop. If this is the case, then in means I don’t fully accept that system of thought. Is disagreement not allowed?
How does what I said there mean “rationality is mathematics”? All I’m saying is that Aumann’s agreement theorem is mathematics, and if you’re attempting to disagree with it, then you’re attempting to disagree with mathematics.
I agree that this is what you should’ve said, but that isn’t what you said. Disagreeing with an implication “if P, then Q” doesn’t mean disagreeing with P.
No, it’s not. I just mean that mathematical facts are mathematical facts and questioning their relevance to real life is not the same as questioning their truth.
Now this just depends on what we mean by “disagree.” Of course I can’t dispute a formal logical derivation. The math, of course, is sound.
All I disagree with X, which means either that I don’t agree that Q implies X, or I don’t accept P.
I’m not questioning mathematical truth. All I’m questioning is what TimS said. But if we agree it was just a misunderstanding, can we move on? Or not. This also doesn’t seem to be going anywhere, especially if we’ve decided we fundamentally disagree. (Which in and of itself is not grounds for a downvote, may I remind you all.)
I didn’t downvote you because we disagree, I downvoted you because you conflated disagreeing with the applicability of a mathematical fact to a situation with disagreeing with a mathematical fact. Previously I downvoted you because you tried to argue against two positions I never claimed to hold.
Glad we’ve got that cleared up, then. I wasn’t only talking to you; there are a few people who have taken it upon themselves to make my views feel unwelcome here. Sorry if we’ve had some misunderstandings.
This was not my experience. I was raised in a practicing religious family, and the existence of the holy texts, the well-being of the members of the religious community, and the existence of the religious community were all strong evidence for G1.
I reduced the probability I assigned to G1 because I realized I was underweighing other evidence. Things I would expect to be true if G1 were true turned out to be false. I think I knew those facts were false, but did not consider the implications, and so didn’t adjust my belief in G1.
Once I considered the implications, it became clear to me that E1 was outweighed by the falsification of other implications of G1. Given that balance, I assign G1 very very low probability of being accurate. But I still don’t deny that E1 is evidence of G1. If I didn’t know E1, learning it would adjust upward my belief in G1.
Also, if we are going to talk coherently about priors, we can’t really describe anything humans do as “throwing out their priors.” If we really assign probability zero to any proposition, we have no way of changing our minds again.. And if we assign some other probability, justifying that is weird.
In practice, what people seem to mean is best described technically as changing what sorts of things count as evidence. I changed my beliefs about G1 because I started taking the state of the world and the prevalence of human suffering as a fact about G1
Certainly you can’t simply will your aliefs to change, but it does seem to be a conscious and deliberate effort around here. The belief in G1 usually happens without any knowledge about Bayesian statistics, technical rationality, or priors, so this “awakening” may be the first time a person ever thought of E1 as “evidence” in this technical sense.
By the way, I think the best response to this argument is that yes, there is evil, but God allows it because it is better for us in the long run—in other words, if there is an afterlife which is partly defined by our existence here, than our temporary comfort isn’t the only thing to consider. If we all lived in the Garden of Eden, we would never learn or progress. But I don’t want a whole new argument on my hands.