Christopher Watkin in his section, “Proving the Principle of Logic”, of the book Other Logics, says,
Since the birth of philosophy itself, thinkers have been searching for the principle of all logic: not a logical proof but the proof of the validity of logic itself. The search is for a justification of logic that is not waiting for us at the end of a chain of reasoning but that validates all reasoning in the first place. Both Plato and Aristotle call this principle of logic the “anhypothetical principle”: the principle that does not need to be hypotheized. (17)
For Plato, the anhypothetical principle is “apprehended with νους, a direct intellectual intuition of the truth” (Watkin 17). Following Kant, we can reject Plato right here: intellectual intuition is non-sensible intuition, which, for us humans, is a contradiction in terms. For Plato, the anhypothetical principle is the Good beyond being. Aristotle, contrary to Plato, does not take such a “mystical” perspective, so to speak. Rather, Aristotle sees the anhypothetical as “the assumption behind all reasoning, an assumption which neither is nor can be directly established by any hypothesis” (Watkin 18). For Aristotle, the anhypothetical principle doesn’t take the form of something beyond being, as it does with Plato, rather, it takes the form of the principle of non-contradiction. Obviously, though, Aristotle’s transcendental argument for the principle of non-contradiction is weak. As Greg Bahnsen points out in Presuppositional Apologetics,
What justification has the autonomous man for assuming the law of non-contradiction to be a reliable principle? The independent thinker is quick to respond that the critic himself must assume the law of non-contradiciton in order to argue against him; of course this true since all discourse require logical distinctions (or else every utterance would mean anything and everything else). But it does not follow from this fact that the function of logic is its own foundation! … Strictly speaking, this is only an indication that we are bound to think in certain patterns; this does not tell us anything about the truthfulness or appropriateness of those patterns! Perhaps we are locked into a distorted mind-set. (103)
Though Bahnsen’s presuppositionalism too supposes certain patterns of thinking (Bahnsen is good at raising objections but not solving them for himself as David Pallmann said), Bahnsen here still makes an important point: the transcendental argument does not necessarily confer a truth value upon the necessary conditions for the making of a proposition. Erik and I have called this the particularist view in that the bindingness of particular behaviors is not indicative of their truth.