That is not the sense of “crazy” that Eliezer is using. Maybe you could say that crazy is when you think that you have a solution but you don’t (ETA: and you ought to be able to see that). But that seems like a special case of stupid.
Are you sure? It seems to me that having an intellectual problem that you are capable of solving but are unwilling to update on due to ideological reasons or otherwise (eg Aumann) is the sense in which Eliezer is using the word “crazy”. Of course, I could just be stupid.
What does it mean to say that you are “capable of solving [a problem] but are unwilling to update on [it] due to ideological reasons”? You obviously don’t mean something like the sense in which I’m capable of opening the window but I’m unwilling to because I don’t want the cold air to get in. Aumann isn’t thinking to himself, “Yeah, I could update, but doing so would conflict with my ideology.” So, tabooing “capable” and “unwilling”, can you explain what it means to be “capable but unwilling”?
What leads you to suggest Aumann isn’t thinking that? Are you saying he is unaware that his ideological beliefs conflict with evidence to the contrary? Of course he is aware he could update on rational evidence and chooses not to, that’s what smart religious people do. That’s what faith is. The meaning of “capable but unwilling” should be clear: it is the ability to maintain belief in something in the face of convincing evidence opposing it. The ability to say, “Your evidence supporting y is compelling, but it doesn’t matter, because I have faith in x.” And that’s what I think crazy is.
What leads you to suggest Aumann isn’t thinking that?
That I’ve met smart religious people who don’t think that way, and I expect that Aumann is at least as smart as they are.
There are intellectual religious people who believe that they’ve updated on all the evidence, taken it all into account, ignored none of it, and concluded that, say, Young Earth Creationism is the best account of the evidence.
You and I can see that they are ignoring evidence, or failing to weigh it properly, and that their ideology is blinding them. But that is not their own account of what’s going on in their heads. They are not aware of any conscious decision on their part to ignore evidence. So it’s subtle and tricky to unpack what it means for them to be “capable but unwilling” to update.
ETA: Your unpacking of “capable but unwilling” uses the word “ability”, which does not illuminate the meaning of “capable”. And you’ve used the phrase “convincing evidence” in a sense that clearly does not mean that the evidence did in fact convince them. So, additionally tabooing “ability” and “convincing”, what does “capable but unwilling” mean?
The behavior eirenicon complained of amounts to denying modus ponens. “I accept X, and I accept X->Y, but I deny Y.”
Defying the data, otoh, is a correct application of a contrapositive. “You claim X, and I accept X->Y, but I deny Y, and therefore I deny X. I have updated on your claim, but that wasn’t nearly enough to reverse the total weight of evidence about Y.” The difference is that this doesn’t involve saying that logical contradictions are ok, so if you ever see enough evidence for X that you can’t deny it all, you know something’s wrong.
Wouldn’t defying the data more mean “I deny that X, on it’s own, is sufficient to justify Y. I’ve updated based on X, but there was plenty of reason to have really low prior belief in Y and X, on it’s own, isn’t sufficient to overcome that, although it definitely is something we should look into, replicate the experiment, see what’s going on, etc...”?
Yes, but there’s also the part about “~Y predicts ~X, so I predict a decent chance that X will turn out to not be what you thought it was.” Which is why replication is one of the proposed next steps; and is also, I think, the part that RichardKennaway pointed to as a parallel.
That is not the sense of “crazy” that Eliezer is using. Maybe you could say that crazy is when you think that you have a solution but you don’t (ETA: and you ought to be able to see that). But that seems like a special case of stupid.
Are you sure? It seems to me that having an intellectual problem that you are capable of solving but are unwilling to update on due to ideological reasons or otherwise (eg Aumann) is the sense in which Eliezer is using the word “crazy”. Of course, I could just be stupid.
What does it mean to say that you are “capable of solving [a problem] but are unwilling to update on [it] due to ideological reasons”? You obviously don’t mean something like the sense in which I’m capable of opening the window but I’m unwilling to because I don’t want the cold air to get in. Aumann isn’t thinking to himself, “Yeah, I could update, but doing so would conflict with my ideology.” So, tabooing “capable” and “unwilling”, can you explain what it means to be “capable but unwilling”?
What leads you to suggest Aumann isn’t thinking that? Are you saying he is unaware that his ideological beliefs conflict with evidence to the contrary? Of course he is aware he could update on rational evidence and chooses not to, that’s what smart religious people do. That’s what faith is. The meaning of “capable but unwilling” should be clear: it is the ability to maintain belief in something in the face of convincing evidence opposing it. The ability to say, “Your evidence supporting y is compelling, but it doesn’t matter, because I have faith in x.” And that’s what I think crazy is.
That I’ve met smart religious people who don’t think that way, and I expect that Aumann is at least as smart as they are.
There are intellectual religious people who believe that they’ve updated on all the evidence, taken it all into account, ignored none of it, and concluded that, say, Young Earth Creationism is the best account of the evidence.
You and I can see that they are ignoring evidence, or failing to weigh it properly, and that their ideology is blinding them. But that is not their own account of what’s going on in their heads. They are not aware of any conscious decision on their part to ignore evidence. So it’s subtle and tricky to unpack what it means for them to be “capable but unwilling” to update.
ETA: Your unpacking of “capable but unwilling” uses the word “ability”, which does not illuminate the meaning of “capable”. And you’ve used the phrase “convincing evidence” in a sense that clearly does not mean that the evidence did in fact convince them. So, additionally tabooing “ability” and “convincing”, what does “capable but unwilling” mean?
This crazy?
Not the same thing.
The behavior eirenicon complained of amounts to denying modus ponens. “I accept X, and I accept X->Y, but I deny Y.”
Defying the data, otoh, is a correct application of a contrapositive. “You claim X, and I accept X->Y, but I deny Y, and therefore I deny X. I have updated on your claim, but that wasn’t nearly enough to reverse the total weight of evidence about Y.” The difference is that this doesn’t involve saying that logical contradictions are ok, so if you ever see enough evidence for X that you can’t deny it all, you know something’s wrong.
Wouldn’t defying the data more mean “I deny that X, on it’s own, is sufficient to justify Y. I’ve updated based on X, but there was plenty of reason to have really low prior belief in Y and X, on it’s own, isn’t sufficient to overcome that, although it definitely is something we should look into, replicate the experiment, see what’s going on, etc...”?
Yes, but there’s also the part about “~Y predicts ~X, so I predict a decent chance that X will turn out to not be what you thought it was.” Which is why replication is one of the proposed next steps; and is also, I think, the part that RichardKennaway pointed to as a parallel.