This is an interview I just found of Anthony Kenny, a former Catholic priest turned agnostic and a very fine philosopher. What caught my eye in the interview is Kenny's claim that the experience of God is "impossible." I tend to agree with Anthony Kenny that the experience of God is impossible.
But it seems like every traditional theist would, or the very least should, agree. Of course no one can directly experience an essentially spaceless,timeless, and immaterial entity who is the ground of all being, much less one whose essence just is to exist. It seems that when believers say they have this or that experience of God, what they really mean is that they had an indirect and unnatural experience of God -- i.e., they experience His effects in time. So when someone says they had a (typical) mystical experience of God, Kenny and I would just translate that to "I experienced certain unnatural sensations of love, peace, etc., which are the indirect effects of God. " Somewhat tangentially, I suppose this line of reasoning makes sense of St. John's claim that "no one has ever seen God, but the one and only Son, who is Himself God and is at the Father’s side, has made Him known (John 1:18)". The experience of God is impossible, and natural reason alone can only bequeath to us a (mostly) apophatic knowledge of God, i.e., of what He is not. We can infer, for example, that there exists a cause of the universe that is not material, not timeless, not caused, not limited in knowledge, not this or that, but we can not arrive at positive knowledge of what He is unless he chooses to reveal himself (e.g., through Jesus of Nazareth). And even if and when he does, even if God reveals to us positive information about what he is (e.g., a Trinity of love), this positive knowledge would be extremely limited and we still wouldn't experience God per se. In summary, the agnostic philosopher Kenny is right that it is in principle impossible to experience God, but that doesn't appear to be a problem for traditional theists. Believers just use the word "experience" in a more permissive or semantically fluid way than Kenny does.
I quote the relevant excerpt from the interview below:
Experience of God is impossible. From a philosophical point of view, if God is a transcendent spirit, he can’t be the object of experience in the way other things can be the objects of experience. We experience things by the activity of discriminating — colour changes, the table ends, a sound gets louder, and so on — but, in God, there’s nothing to discriminate: all is everlastingly the same. That doesn’t mean that nothing can be said about God. People are saying things all the time — but not on the basis of experience. People who see visions are not really seeing God, in my view. A revelation by God is not the same as an experience of God. The Sermon on the Mount was a kind of revelation to the people who heard it, but they experienced Jesus, not the divine Spirit.