I have a request for those bayesianly inclined among the LW crowd.
I had mentioned in an article that I had become addicted to watching theist/atheist debates. Unfortunately I have not weaned myself off this addiction as of yet. In one I watched recently, it is William Lane Craig (the theist that Eliezer wanted to debate) arguing for the provability of the resurrection of Jesus, and New Testament scholar Dr. Bart Ehrman arguing for its historical improvability.
At some point in this debate, Dr. Ehrman argues that miracles are fundamentally unprovable by historical analysis as they are by definition ‘the least probable event’. So history cannot find them as ‘the most probable event’. Craig then responds by bringing up Bayes’ theorem, to prove show that (if I understand correctly) Dr. Ehrman is ignoring the evidence.
To hear the arguments for yourselves, the video of the debate is here, Dr. Ehrman’s argument is stated from 34:59 to 36:02, and Dr. Craig’s counter is from 42:03 to 46:24. (do not go past 46:24, as Dr. Craig derails and starts talking supernatural again)
Against my prior bias, I strongly suspect that Dr. Craig is in fact correct. The irony is that while Dr. Craig usually wins his debates by sophistry and pure rhetorical ability, this time he gets bogged down by the details of actually trying to debunk a bad argument. In a turn of poetic justice, the argument goes over the head of the audience, and this debate is one of the few that Dr. Craig can be said to have lost.
The problem I see in this argument is that if you define a miracle as the least expected event (low prior), you can still prove a miracle if it leaves behind strong enough evidence (multiple, unbiased, independent, consistent sources), which would give you a high posterior.
So, to those of you who care to look into this, do I have it right? Have I lost the plot somewhere?
I didn’t bother listening to Craig’s rebuttal, because I agree with you that what Ehrman’s saying from 34:58 to 36:02 is poorly argued, and I don’t even need Bayes’ theorem to see it. My transcription of Ehrman:
Historians can only establish what probably happened in the past, and by definition, the miracle is the least probable occurrence. And so by the very nature of the canons of historical research, we can’t claim, historically, that a miracle probably happened. By definition, it probably didn’t. And history can only establish what probably did. I wish we could establish miracles, but we can’t. It’s no one’s fault; it’s simply that the canons of historical research do not allow for the possibility of establishing the probable, uh as probable, the least probable of all occurrences. For that reason, uh, Bill’s four pieces of evidence are completely irrelevant. There cannot be historical probability for an event that defies probability, even if the event did happen. The resurrection has to be taken on faith, not on the basis of proof.
But this is silly. If a historian, or anyone, can establish that X probably happened, they can establish that X’s complement probably didn’t happen (because P(X) + P(¬X) = 1). So how can Ehrman argue that history can establish what probably happened but not what probably didn’t? I suspect there are other issues (like playing definitional games with the word ‘miracle’ and suggesting an event ‘defies probability’ - what would that even mean?) but his claims about what historians can and can’t do is the most obvious issue to me.
I think we have a problem. While the default at LW is to not want to believe in possible miracles done by God, there’s considerable interest in knowing whether we live in a simulation.
Aside from logic or from careful examination of physics which find indicators of another level, the other category of evidence for this world being a simulation is transient anomalies. How do you evaluate reports of anomalies?
I think my main rule of thumb is to think about how anomalous the anomaly is, and the strength of the evidence for it. More anomalous and less well substantiated anomalies get taken less seriously.
I have a request for those bayesianly inclined among the LW crowd.
I had mentioned in an article that I had become addicted to watching theist/atheist debates. Unfortunately I have not weaned myself off this addiction as of yet. In one I watched recently, it is William Lane Craig (the theist that Eliezer wanted to debate) arguing for the provability of the resurrection of Jesus, and New Testament scholar Dr. Bart Ehrman arguing for its historical improvability.
At some point in this debate, Dr. Ehrman argues that miracles are fundamentally unprovable by historical analysis as they are by definition ‘the least probable event’. So history cannot find them as ‘the most probable event’. Craig then responds by bringing up Bayes’ theorem, to prove show that (if I understand correctly) Dr. Ehrman is ignoring the evidence.
To hear the arguments for yourselves, the video of the debate is here, Dr. Ehrman’s argument is stated from 34:59 to 36:02, and Dr. Craig’s counter is from 42:03 to 46:24. (do not go past 46:24, as Dr. Craig derails and starts talking supernatural again)
Against my prior bias, I strongly suspect that Dr. Craig is in fact correct. The irony is that while Dr. Craig usually wins his debates by sophistry and pure rhetorical ability, this time he gets bogged down by the details of actually trying to debunk a bad argument. In a turn of poetic justice, the argument goes over the head of the audience, and this debate is one of the few that Dr. Craig can be said to have lost.
The problem I see in this argument is that if you define a miracle as the least expected event (low prior), you can still prove a miracle if it leaves behind strong enough evidence (multiple, unbiased, independent, consistent sources), which would give you a high posterior.
So, to those of you who care to look into this, do I have it right? Have I lost the plot somewhere?
I didn’t bother listening to Craig’s rebuttal, because I agree with you that what Ehrman’s saying from 34:58 to 36:02 is poorly argued, and I don’t even need Bayes’ theorem to see it. My transcription of Ehrman:
But this is silly. If a historian, or anyone, can establish that X probably happened, they can establish that X’s complement probably didn’t happen (because P(X) + P(¬X) = 1). So how can Ehrman argue that history can establish what probably happened but not what probably didn’t? I suspect there are other issues (like playing definitional games with the word ‘miracle’ and suggesting an event ‘defies probability’ - what would that even mean?) but his claims about what historians can and can’t do is the most obvious issue to me.
I think we have a problem. While the default at LW is to not want to believe in possible miracles done by God, there’s considerable interest in knowing whether we live in a simulation.
Aside from logic or from careful examination of physics which find indicators of another level, the other category of evidence for this world being a simulation is transient anomalies. How do you evaluate reports of anomalies?
I think my main rule of thumb is to think about how anomalous the anomaly is, and the strength of the evidence for it. More anomalous and less well substantiated anomalies get taken less seriously.