If I’m talking with someone about something that they’re likely to disbelieve at first, is it correct to say that the longer the conversation goes on, the more likely they are to believe me? The reasoning goes that after each pause or opportunity to interrupt they can either interrupt and disagree, or don’t do anything (perhaps nod their head but it’s not required). If they interrupt and disagree then that obviously that’s evidence in favor of them disbelieving. However, if they don’t, then is that evidence in favor of them believing?
If they interrupt and disagree then that obviously that’s evidence in favor of them disbelieving. However, if they don’t, then is that evidence in favor of them believing?
If X is evidence of A, then ~X (not-X) is evidence of ~A. They are two ways of looking at the same thing—it’s the same evidence. This is called conservation of expected evidence.
So if your premise is true, then your conclusion is necessarily also true.
Please note that this says nothing about whether your premise is indeed true. If you have doubts that “not disagreeing indicates belief”, that is exactly the same as having doubts that “disagreeing indicates disbelief”. The two propositions may sound different, one may sound more correct than the other, but that is an accident of phrasing: from a Bayesian point of view the two are strictly equivalent.
I have a question:
If I’m talking with someone about something that they’re likely to disbelieve at first, is it correct to say that the longer the conversation goes on, the more likely they are to believe me? The reasoning goes that after each pause or opportunity to interrupt they can either interrupt and disagree, or don’t do anything (perhaps nod their head but it’s not required). If they interrupt and disagree then that obviously that’s evidence in favor of them disbelieving. However, if they don’t, then is that evidence in favor of them believing?
If X is evidence of A, then ~X (not-X) is evidence of ~A. They are two ways of looking at the same thing—it’s the same evidence. This is called conservation of expected evidence.
So if your premise is true, then your conclusion is necessarily also true.
Please note that this says nothing about whether your premise is indeed true. If you have doubts that “not disagreeing indicates belief”, that is exactly the same as having doubts that “disagreeing indicates disbelief”. The two propositions may sound different, one may sound more correct than the other, but that is an accident of phrasing: from a Bayesian point of view the two are strictly equivalent.
Thanks—I knew that this was conservation of expected evidence, I just wasn’t sure if I was using it correctly.