When examined more closely, Rand appears to have confused "classification" with "identification." Rand seems to have believed that A is A, which is a short-hand expression for logical identity, is equivalent to deciding which category a specific entity is to be placed. The integration Rand has in mind is (at least partly) conceptual. In any case, Rand's view of concepts is heavily saturated with her theory of concept-formation, which she places at or near the center of her epistemology. So having unravelled these tangles as best we can, we may safely assume that (1) reason involves creating a logically consistent body of knowledge, and (2) reason involves concept-formation. Rand's reason, for ought we know, may involve much more than what's listed here. I am merely trying to isolate two elements that can be subjected to empirical testing.
Reason, Rand claims, is man's only means of both grasping reality and acquiring knowledge. What evidence did she present for this view? Unfortunately, none at all. Worse, it would not be a very plausible assertion even on a priori grounds. Let us say (as Rand seems to say) that reason involves creating a logically consistent body of knowledge. Is having such logical consistenty necessary for grasping reality? In its absence, is knowledge impossible? No, of course not. Just imagine a man whose knowledge is divided in two parts, A and B, which contradict each other. Is this man incapable of having knowledge or grasping reality? No, not at all. All that the contradiction between A and B entails is that only one of the two parts of his knowledge can be in accord with reality. But if one part does accord with reality, that part grasps reality and can be considered as knowledge of the real world. Rand and her disciples, if they wish to be taken seriously on this point, really need explain in more detail what they mean by "reason" and provide evidence for why Randian "reason" is the "only" method that can grasp reality.
If we identify "reason" with concept-formation, we are in no better shape than before. Rand presented hardly any evidence for her theory of concept-formation; yet there exists a large body of evidence that can be placed against it, some of which I introduced in my "The Cognitive Revolution and Objectivism" series, others of which will be introduced in a future series on Rand's epistemology. Let me just note that, in the light of evidence brought to light by exponents of Wittgenstien's Family Resemblance theory of concepts and discoveries about the large role played in concept-formation by the cognitive unconscious, Rand's theory appears rather implausible. If "reason" involves forming concepts in accordance to Rand's theory, then we can safely assume that "reason" is entirely mythical faculty that has nothing to do with real cognition.
“Logic is man’s method of cognition.” (Peikoff, ITOE) If by "logic," Peikoff means Rand's bizarre mixture of logical identity with categorization, this is almost certainly wrong. If, on the other hand, Peikoff means only the ordinary logic of Aristotle and philosophy textbooks, this is almost certainly wrong as well. As Morton Hunt put it:
[F]ormal logic is not a good description of how our minds usually work. Logic tells us how we should reason when we are trying to reason logically, but it does not tell us how to think about reality as we encounter it most of the time....
Logic enables us to judge the validity of our own deductive reasoning, but much of the time we need to reason non-deductively — either inductively, or in terms of likelihoods, or of causes and effects, none of which fits within the rules of formal logic. The archetype of everyday realistic reasoning might be something like this: This object (or situation) reminds me a lot of another that I experienced before, so probably I can expect much to be true of this one that was true of that one. Such reasoning is natural and utilitarian — but logically invalid....
Our natural reasoning is thus a kind of puttering around — the intellectual equivalent of what a child does when it messes around with some new toy or unfamiliar object. After a spell of mental messing around, we may put our reasoning into logical terms, but the explanation comes after the fact, the actual process took place according to some other method... [The Universe Within, p. 132-136]
“The alternative to reason is some form of mysticism or skepticism.” (Peikoff, OP) Since when?
The only way to make this true is to define mysticism and skepticism analytically -- i.e., as the only alternatives to "reason." But if defined this way, these words become trivial and lose their sting. Suddenly, Morton Hunt's "natural reasoning" becomes merely another form of mysticism and/or skepticism. But since this natural reasoning is precisely the method which has allowed the species to reproduce and survive for hundreds of thousands of years, then to describe it as mysticism or skepticism is to give those words a far more benign meaning than Rand originally intended.
If, however, we assume that Peikoff is not using the words analytically, but using mysticism and skepticism in the usual disparaging, Objectivist sense of the terms, then his statement is most probably false (which would explain why he provides no evidence for it). There is all kinds of evidence from cognitive science (popularized, for example, by Malcolm Gladwell in Blink ) that demonstrate the empirical paucity of Peikoff's assertion.