I hear what you are saying and I agree with the fact, though you didn't explicitly state it this way, that each side cannot actually grasp what the other is saying due to their perspectives. So, the word "Impasse" is quite apropos in this situation.
At this point, maybe it would help if I injected a question: Have you ever experienced a nothingness beyond thought and what thought has constructed? Philosophy and science are predicated on thought. The so-called enlightened perspective is devoid of thought, or prior to thought. When the mind completely shuts off — no thought at all — it is at first a baffling, stunning experience. In the least it gives one a clarity that cannot be had with thought.
And there's one more idea I would like to add to this conversation to try to explain my perspective: There are two environments, to use a crude word: They are often explained as the "inner" and "outer" experience, although these words are misused and are in nearly all cases no different from one another because the sense of self and thought are active in both.
One perspective of which I speak is all that exists, including forms, expressions, thought, reason, ideas, memories, phenomena, the body, the brain, and the sense of self, which is the "me." This is a changeable, fluid existence bound by consciousness. And the other one is that which is the void out of which all that exists emanates. When one can have a full realization of the latter then one has realized the ineffable as oneself. No amount of discussion, philosophy, science, religion, belief, or anything else can bear upon the void, nothingness, or capacity — whatever word you want to use. The idea is not to prove this to anyone, but rather to understand oneself, the whole of consciousness, the basis for suffering, and so on. Debating about it is folly.
The ineffable cannot be figured out at all, simply because thought is the wrong tool for perception of that which exists prior to thought. Reason can never be used to explain or understand or realize the mystical experience if that experience is permanent and not simply an experience that comes and goes. The experience that comes and goes falls into the category of that which has emanated out of the void. The true mystic seeks that which is permanent, and to find this means to negate all that it is not, including reason, words, descriptions, and so on.
Finally, one who comes to the mystic to uncover what he has cannot do so merely by understanding the mystic's words. The mystic cannot observe or have an Aha! realization on behalf of anyone. Words and logic may encourage a person but will not awaken him.
