But this position, that it is impossible for God to give us evidential reasons, is completely anti-intuitive.
Yes well a lot of true things go against our “intuition”. If I test positive for a rare disease where the false positive rate is 0.001 I would “intuitively” think I have the disease “almost certainly”, yet if the prevalence of the disease were only 1:100,000 there is still only about a 1 in a hundred chance I actually have the disease! And if there were an actually infinite number of people alive my positive test has no value at all, for false positive rates, prevalences, etc., anything having to do with fractions is undefined for infinite numbers.
If the “Heavens opened” and angels descended and shouted praises ceaselessly for months, you’re saying this wouldn’t be evidence?
Yes. It wouldn’t be evidence.
If we apply Bayes’ theorem, then we have a) something that was clearly extraordinarily improbable prior to happening, and b) something that clearly happened. It sounds like evidence to me.
You’re not applying Bayes’ theorem properly. If this is supposed to be evidence for God’s existence, then the relevant prior is that of God’s existence. So if A = angels descending and G = God’s existence, then what we want is
P(G|A) = P(G)*P(A|G)/P(A) = P(G)*P(A|G)/(P(G)*P(A|G)+P(~G)*P(A|~G))
So the problem here is what is the
likelihood? Given God’s existence, what is the likelihood P(A|G) of heavens opening and angels descending? And this is impossible to define because there are an infinity of possibility of angels and ways to descend, etc., which God could have done.
If your position, however, is that past evidence yields no justification, then – although a witness of the above event would be justified in belief (if they had their Bayes’ spreadsheets filled in beforehand
) – no one told about the event afterward could ever be justified in believing. Not even if they were told by hundreds of people.
(Or, wait, maybe they could. For consider: the prior likelihood of a hundred people telling them about such an event was extremely low. Does Bayes’ allow for secondhand induction?)
I’m not claiming past evidence yields no justification just because it is in the past, so this isn’t relevant.
At any rate, we clearly inductively infer all kinds of things, justifiably, without having any sense of their prior likelihood, which means that Bayesianism is incomplete.
No, we don’t. We need to have at least a back-of-the-envelope sense of the order of magnitude of the likelihood and/or the prior. If we don’t, then we don’t infer it justifiably. I gave an example above (the test for disease) where we intuitively induct the wrong thing. It’s been shown that if you give this question to people unschooled in statistics and Bayesian inference, the majority get it wrong.
If, on returning from a business trip, I discover that my lawn is filled with snow, though the neighbors’ lawn haven’t a flake on them, I can infer that a highly localized and highly unusual storm happened. I could be wrong, but it is a valid inference.
Only because you have a sense of the likelihood and priors of alternative hypotheses. If your neighbors had told you beforehand instead they were going to load a dump truck with snow from the ski slopes and dump it on your lawn you’d make a different inference. If you had absolutely no idea of the likelihood of your neighbors doing such a thing then you would not be justified in making any inductive inference.
Perhaps. But how does one inductively justify the belief in other minds, for example? Here we have a case similar to the God case.
You can’t. Belief in other minds is a metaphysical assumption.
Problem: Two people subjectively estimate different likeihoods before the fact. Who is right? Whose calculus wins? Isn’t subjectivity a problem here?
If it is not possible to objectively estimate the likelihoods and priors then it is impossible to make an objective inference.
It’s just another level of causation, though, in the end – the idea of God influencing reality should not be more scientifically controversially than the idea that the laws of physics are realized at the subatomic level.
I’m not quite sure what you mean here. You seem to be begging the question - assuming there can be empirical evidence for God - when that is just the point under discussion.
Yes, of course, the God hypothesis is not scientifically falsifiable, but no rational person can take that as an indication of His nonexistence.
But a rational person will and should take that as an indication that empirical evidence for or against the God hypothesis is
impossible, which is what I am saying.
The existence of God does have explanatory power, which makes sense of one standard of inference.
The existence of God does
not have explanatory power since there is nothing which can falsify it; it is consistent with
any dataset which means inductive evidence in favor or against is
impossible. If you have 20 datapoints, any set of 20 functions will fit the data perfectly. Thus, this model has no explanatory power whatsoever. If you can fit the data was one or two basis functions, then you have much more explanatory power.
