Hi Speusippus, just ask if there is anything you want to have clarified.
But I am wondering what you think about this: Does Carrier's argument strike you as one that has been _poorly formalized_ using BT but nevertheless has (or might have) some plausibility in itself?
I am asking myself that question! The truth is that I am not even a well-read amateur on history, so I am really the worst person to evaluate the historical case. I know Neil (on Vridar) is working on a review and I am sure there must be threads on this forum that discuss Carriers hypothesis. I hope to have time to read these reviews later:
http://www.raphaellataster.com/Articles ... r,OHOJ.htm
https://www.reddit.com/r/AcademicBiblic ... e_read_to/?
http://www.strangenotions.com/an-atheis ... rt-1-of-2/
But since you ask: I do think that many of the points Carrier brings up are interesting and relevant. I think it shows how fluid the evidence can be when one factor in different interpretations and the possibility of interpolation. Sometimes, I think Carrier is a to optimistic when it comes to interpreting the evidence, for instance when discussing Paul where I think the most natural reading would be that Paul is talking about a human.
If I can bring up one point of the review which I would most like a historians opinion on it is that Carriers hypothesis would imply that at around the time of Paul (ca. 55CE?) Jesus is thought to have been a celestial being who lived and died in the supernatural realm and than a few decades later we have the Gospels where Jesus is clearly on earth and (presumably?) this is believed by many Christians. I think it would be very interesting to search for similar historical cases to evaluate how plausible this type of scenario is, especially considering how rapid the transition was and how little evidence it left behind.
When I try to talk about this purely in terms of "confidence levels" like I just did, I run into discussions I don't understand about frequentism and Bayesianism. It's not so much that I don't understand what those are--I basically do, or anyway, always am able to catch myself up on it when it comes up--but rather, I don't understand _why that dispute matters._
I don't think it should matter at all and this is one of the most frustrating aspects of the discussion. Just to fix the terminology, "Baysianism" is essentially a set of assumptions which implies that we are allowed to talk about the probability of one-off events like "Does Jesus exist" and then if we do, these probabilities will obey the rules of probability theory (the sum and product rule). There is nothing more to it. You don't get anything "more" than the rules of probability by "being Baysian".
Frequentism is another interpretation of probability theory where probabilities are thought to be either finite frequencies, i.e. (#times an event happened)/(#trials), or a limit of such frequencies. Assigning probabilities to one-off events with that type of interpretation is much more problematic. But that's an aside: If we agree we can talk about the probability of such an event we just end up with the rules of probability theory no matter what.
And I don't quite understand why the question of whether rational credences should be based more on frequencies or on bayesian somethingerothers should really affect whether we can use the theorem--provable from the K axioms after all--to decide how confident we should be in certain propositions giving other propositions.
The only snag is that if you use a frequency-based interpretation, a philosopher will have a field day asking you questions like "the frequency of what?" with regards to the probability of Jesus existence. Asides that, you are absolutely right: Just start with the Kolmogorov axioms and go from there.
I suppose I'm saying I think of this as kind of a "shut up and calculate" kind of thing, and I am not really sure why the frequentism stuff keeps coming up, or why anyone thinks it's important to the validity of his arguments.
Here is where it becomes complicated. Carrier believes that he has invented a new interpretation of probability theory which is neither Baysian (i.e. degree-of-belief or degree-of-rational-credence based) or frequentistic in the ordinary sense. The interpretation is based on a frequentistic concept. From PH:
"When Bayesians talk about probability as a degree of certainty that h is true, they are just talking about the frequency of a different thing than days of rain or number of smokers. They are talking about the frequency with which beliefs of a given type are true"
Long story short, I think the definition suffers from well-known problems and Carrier disagrees. Obviously this does not answer why we should care: as a discussion on the philosophy of probability that might be interesting, but it should not bother us as long as we agree that we will subscribe to the rules of probability because the rules of probability are what they are and we can just "shut up and calculate"?
The problem here is that in other discussions with Carrier he has referred to (or at the very least hinted at) certain rules that prohibit or allows an operation which I don't think can be justified from any foundation of probability theory I am aware of. For instance, when I discussed his fine-tuning argument, Carrier invoked a rule that certain pieces of information must be treated as "background information" (thereby implying they are not subject to the product rule), see for instance section 5.2 here:
https://www.scribd.com/doc/296697791/Ri ... g-argument
A similar type of intuition also underlies some of Zbykows responses this Vridar thread. The annotated version:
"Zbykow: You also seem to have problems[which?] with the concept of background knowledge[how does this concept differ from other propositions?] for some strange reason. If you understood what it is[what is it?] and where it kicks in[when does it kick in?], you’d know[what book should I read to know this?] it’s not subject to calculations like yours.[according to what rule, formula or law?]"
http://vridar.org/2016/04/15/what-does- ... /#comments
I think what Carrier or Zbykow is getting at is that I am violating something which is true on Carriers account of probabilities. I also think that if Carrier believes all probabilities are frequencies then it is more natural to make frequentistic approximations (like the RR hero class) but I am not sure.. everything is very vague and whenever Carrier says that someone don't know how probabilities work or that you can't do this or that he never says how probabilities do work and what rules (i.e. textbook rules) I or other who are accused of this are actually violating. It also appears impossible to get a straight answer to these questions.
tl;dr: The bottom line is that I would be *really* glad if the discussion of philosophy of probability was kept isolated from the application of probabilities because to me it is irrelevant, and it would be really good for the discussion if accusations of "violating" a rule of probability would be followed up with the exact rule which was violated.