Religious claims in the present framework
Now that this framework for the sources of knowledge has been discussed briefly it is instructive to see how to try and fit religious claims into it.
The central challenge then for the believers is to Prove the existence of God /Allah / Jehovah.
The concept of proof needs to be clarified.
In maths a proof of a theorem involves showing consistency with the axioms and definitions of the maths used. Such a proof cannot be of reality in the same way that maths cannot provide knowledge of reality as I just mentioned above.
In science a practical proof consists of testing hypotheses repeatedly. However, no scientific statement can claim to be proved true in an absolute and universal sense. We can only claim that in our experience the statement has not been disproved. A useful definition of a scientific claim is that it is in principle disprovable.
There are nevertheless attempts to prove Allahs existence like a maths theorem and they resort to several statements or definitions as stepping-stones. If I were to do this, I would have to assert that those statements and definitions are more universally true than the conclusion. I would then have to proceed to derive the lesser truth of the existence of something called Allah. This follows from the nature of syllogistic reasoning such as all a is b, some b is c implies some c is not a. This type of reasoning gives you always less information than what you started with. This approach can only show the existence of aspects of Allah. It cannot, by virtue of its limited understanding and questionable validity, demonstrate something claiming to be infinite and the ultimate in universality i.e. claiming to be The Truth. . It can only provide arguments in favour of the existence of Allah. It can never be a proof.
Any argument for the existence of Allah which uses the method Given that X, Y, Z is the case it can be inferred that Allah exists." can only amount to a neat way of conceptualising some aspect of Allah through a choice of definitions and concepts.
A practical proof may be possible of facts that confirm religious claims but the way to accept religious claims is not the same way that scientists now accept their theories. They do not assert the truth of their theories. They also do not assert the universal truth of their theories. The opposite may be the popular view but it is wrong. They used to, but no longer do so. For this reason the framework must change.
Various churches have historically set themselves up as being infallible and authoritative sources of knowledge. In the last century the theories of classical physics were proclaimed as the new truths. The religion of belief in science had begun. However the scientists foundations have now been shown to be quite wrong. The new physics has deflated the claims of scientists to know truths in the same way that the scientists previously deflated the claims of certain religious figures.