Let's say when we measure the brainwaves of someone who is actually deluded and the brainwaves of someone who is fervently religious, they match up to an extraordinary degree. Are we justified to say that the religious person is deluded base on this observation of matching brainwaves alone?
Can we judge the propositional content of a belief as to its truth value by brain activity? Can scientific neurological experiments determine the truth and falsity of propositional content or are arguments the only way to determine the truth and falsity of propositional content? Can we appeal to brainwave activity to invalidate theism?
Interesting question(s)! I'm afraid that it will be very difficult to replace arguments and the different "tools" philosophers use with neurological data. First, I assume that in identifying a subject as "deluded" we would have to know the falsehood of her belief and perhaps identify which fallacies she has committed. We would also need to think through ideas of mental causation and the degree to which a person's beliefs may be linked to neurological events (are we going to assume a reductive account of the mental? or are we going to allow that propositions, mental acts such as 'believing' are irreducible to the physical, in particular, brain states and processes?. We also need more than neurology to identify and define what is a 'religion.' You seem particularly interested in theism, but some important religions are non-theistic (most forms of Buddhism), and some theists are not religious (Richard Taylor may have been a good case of this). Still, there are some common sense ways in which...