Bayes and unknown probabilites: is this reasoning from the failure of explanation a fallacy?

Question

Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief

Suppose I just don't know the probability of something, having considered everything else, and so would then place its likelihood at 50%. But also suppose I can nevertheless justify the claim that the best explanation for it is mistaken. Can I then conclude that the likelihood of either is less than 50% (and does anyone say that <50% mean it =0%: if I really have considered every other argument?)?

An explanation is a story about what caused an object to exist, or an event to occur.

I think perhaps Bayesian theory says yes, at least supposing we can talk about the probability of an explanation that does not really explain (because what it explains is likely not the case, or for some other reason). Quoting from the comments (emphasis added):

You have the prior p(G)=1/2, and you are asking, I think, about the posterior p(G|B'), where B' is that Bible is historically inaccurate? If you can justify that P(B' | G)

... i.e. that God's existence reduces the probability that the Bible is historically inaccurate, then your posterior does have to be less than your prior, since p(G|B')=P(B' | G)/P(B')p(G) by the Bayes's formula.

Does the answer change if I have to "make a bet", because whatever I decide has practical implications?

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A simple argument from analogy is that if my cheating at dice is the best explanation for my winning then my not cheating at dice implies I won't win, and my not winning implies I am not cheating at dice.

Here are two more convoluted examples of arguments on this basis: I'm only interested in the inference in bold. In the first the best explanation is not valid; in the second the best explanation is not sound.

A. The best explanation of my death is that everyone will eventually.

B. In fact, that explanation fails (Heidegger).

C. So the likelihood of my death decreases.

D. There can be no scientific argument for my death.

E. So I cannot die.

Or:

1. The best explanation of the bible's historical accuracy is that God exists

2. In fact, the bible is not historically accurate.

3. So the likelihood of God existing decreases.

4. The best explanation of the Bible being an argument against God is that all revelation and miracles are bunk.

5. So all revelation and miracles are bunk.

6. There are no sound a priori arguments.

7. So there is no God.

Answer 1

Probability is something that must be considered at a specific point in time, otherwise it would have no purpose.

Considering this Universe is based on duality, of balance of energy (because it otherwise could not maintain its integrity), it can be safely said that the default probability for something unknown is 50%.

Therefore, just not know the probability at all the probability of something could imply that it can be considered 50% (even considering some Universe-related observations that may alter the 50% a little).

Making a bet would have 2 separate ways: making it not trying to determine anything else (like in the case of tossing a coin) or making it after gathering sufficient information about the subject (like in the case with God). In the last case, any observation and determination can alter the probability one way or the other. For example, in the God situation you may consider the Bible as a way of shifting the probability towards its existence, while other evidence may shit it the other way. Unfortunately in such examples even the definition may alter your probability. In this case, we may consider God-creator-of-everything or God-creator-of-mankind-only. We already have 2 different situations with 2 different probabilities here.

Note that an explanation, accepted widely or not, is not at all sufficient to alter a probability significantly one way or the other. In the given example of God, there are dozens of alternate explanations, which vary in acceptance level over time (while at this very moment the theory of a simulated reality gains ground exponentially).

So basically, the probability of something will change and adapt over time when more and more things (that can be related to that thing of which we calculate a probability) are discovered and start to be considered, debated, proved and/or widely accepted.

As a conclusion, yes, you can definitely state that from your point of view a probability for something did change from 50% (and adapted over time given all gathered data), even if that something from an extreme perspective it cannot be completely proven or disproved at that time.

Answer 2

I am not sure that Bayesian probability can be applied to events that differ in nature.

If John Smith says, "it is going to rain tomorrow", and it rains, then the probability that he will succeed in previewing weather next time will raise, but I don't think it affects positively the probability of any other predictions by Mr. Smith not in the field of meteorology being fulfilled.

I am also not sure that we can safely assess the probability that "God" exists at 50%. There certainly isn't a 50% probability that there is a teapot in orbit around Saturn. There certainly isn't a 50% probability that unicorns actually exist. Why would there be a 50% chance that God exists? Come to think, it isn't even a yes/no question - there are many different gods out there, anyone of which could be the true God, if there is one.