Sage Sri, Goudpada: ~ To establish the truth of Non-duality by sheer reasoning alone. He begins by defining "What is real?" "What is unreal?" etc, because that is the right way to discuss or teach. People must first know what they are talking about. (Mandukya Karika)
Logic is misunderstood. People cannot distinguish between reasoning and intellect as a Gnani does. Egocentric reason applied only to practical life within the practical world is called logic, intellect.
The Soulcentric reason is the Spiritualistic reason is necessary to unfold the truth of the whole.
A Gnani knows both egocentric reason (logic) and Soulcentric reason. He uses the egocentric reason (logic) in practical life within the practical world and uses the Soulcentric reason to know the truth beyond for, time and space. Logic is very much necessary for the practical purpose. But the logic cannot be applied to discover the truth because logic implies duality and the ultimate truth is based on Nondualistic perspective.
To say rise above logic, is generally confused with saying "Rise above Reason." It is wrong to give up reason. Life does not consist only of waking state. We must take all three states into account.
If one sticks to the old formal logic, he cannot get at the truth. People seeing this insufficiency of logic, therefore wrongly says: "Give up logic and go to intuition." Their error is “What is it that told them that logic was not enough?” It was Reason itself; not intuition. Thus, there is confusion between logic and reason.
Reasoning is interpretable in two ways. The defective interpretation is to apply it only to waking state. The correct interpretation is to apply it to the three states. The latter leads to a final settlement of the problems because it takes all data into consideration.
Logic, in short, is concerned with correct or valid thinking. Its main concern being non-contradiction, it can lay down the criterion of Truth as non-contradiction, but only with the assumed premises and not with facts. But when facts enter into consideration we have Reason but the same criterion of Truth remains, only the propositions with which we start must square with facts of experience, with observed data. Hence, the reason includes logic or correct thinking as well as strict fidelity to experience or facts. Bad logic or insufficiency of facts or wrong data may lead to untruth. The scientist with a plethora of data may reason illogically and reach false conclusions. Reason avoids both those mistakes. While reason searches for truth, logic insists on valid or correct thinking only.
Intellect is the power or faculty of thinking logically. The Reason is the power or faculty of thinking truly or towards truth. By reason, we go a step beyond anubhava or experience by making explicit in it. The Reason, I would, therefore, define as that which makes explicit what is implicit in an experience. This will I believe cover the reason of science as well as of Vedanta between which you have in some article of yours, made a distinction. When I read that definition of yours, I felt you have descended to mysticism.