The existence of that low prior is the proof that it's very likely false
I think you're trying to double-dip :-) The prior itself is a probability (or a set of probabilities). A "low prior" means that something is unlikely -- directly. It does not offer proof that it's unlikely, it just straight out states it is unlikely.
And there doesn't seem to be any reason to talk about priors, anyway. It's not like at any moment we expect a new chunk of information and will have to update our beliefs. I think it's simpler to just talk about available evidence.
As a preface let me say that I basically agree with the thrust of your arguments. I am not a Christian, afer all. However I don't consider them as anything close to a "proof" -- they look weaker to me than to you.
makes supernatural claims; that is, claims which are by definition counter to all previous observations
That is not so. Supernatural claims do not run "counter" to previous observations, they just say that certain beings/things/actions are not constrainted by laws of nature. Wright brothers' airplane was not "counter" to all previous observations of transportation devices with an engine. Recall Clarke's Third Law.
Not to mention that "all previous observations" include a lot of claims of miracles :-)
its core claims (and future predictions) are similar to many sets of (mutually contradictory) claims made by many other religions
Yep. But there is a conventional explanation for that (I do not imply that I believe it): different traditions take different views of the same underlying divinity, but find themselves in the position of the nine blind men and the elephant.
This point will also need to explain why large civilizations (e.g. China) did NOT develop anything which looks like monotheism.
the average probability of any specific branch of Christianity would still be low
That's a wrong way to look at it. Imagine that you have an underlying phenomenon which you cannot observe directly. You can only take indirect, noisy measurements. Different people take different sets of measurements, they are not the same and none of them are "true". However this does not mean that the underlying phenomenon does not exist. It only means that information available to you is indirect and noisy.
it's likely that all sects' beliefs had human causes
See above -- different people might well have human reasons to prefer this particular set of measurements or that particular set of measurements. Still does NOT mean there's nothing underlying them.
it's because many people are Christians
Well, and why is that? Why is Christianity a huge world religion? It started with a small band of persecuted Jews, why did it spread so?
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Worst case is IMHO that a new person will be created in an old and damaged body.
How would you tell, what would this "new person" theory predict differently then the old person theory.