Jacob, (forgive me if I've missed it in the thread - I did read it over late last night) from where in Oist literature does it state that the only source of knowledge is perception, and/or that A is A is validated perceptually? I'm just curious.
I would ask you to consider the following: how do you know that logical contradictions cannot exist, i.e. are impossible? More specifically, how did you form that idea? As I understand the Oist definition of logic to be "the art of non-contradictory identification" it would be begging the question to assert that you know that contradictions cannot exist because they're a logical impossibility - or perhaps that would be a tautology. Before making that claim or coming to that conclusion, we have to first grasp non-contradiction perceptually...
I think that on the perceptive level we grasp existence and consciousness, then after a lot of observation at the perceptual level, and utilizing consciousness we first grasp a "unit" or existent" as a visual (perceptual) differentiation from the rest of the (seeming) chaos. This, in my opinion, is on a perceptual level, prior to logic or perhaps it is our first instantiation of the process/art of logic: identification. At this point, that differentiation or recognition of the unit/existent is the identification; we then see that this unit/existent is itself, or A is A. If it wasn't the case, we would never have been able to identify it or anything else.
Now, please correct me if I'm misunderstanding your position to be the following: you're saying that there is a leap (induction) from this first identification to the principle A is A, and that logic must fill in that leap since no amount of perception alone can justify or provide the means to take this first identification and make it a general principle encompassing all existents. Is this what you're saying?
If so, I think it's important to note that A is A, or identity, comes and is grasped before non-contradiction: non-contradiction is Aristotle's law which rests on identity. Perhaps it could be looked at as a corollary of identity. In fact, Aristotle never formulated (algebraically) A is A, but he did state it as a general principle in book VII of his Metaphysics. Thus, identity, or A is A, must first be grasped on the perceptual level via consciousness, but only once existence is grasped. Since we can see that a thing exists and it is itself, we see that existence is identity, and identity is existence, thus A is A. This is the reason why there can be no contradictions. It is only after this implicit understanding (and well, much, much later) do we go onto formally understanding non-contradiction explicitly. Does this answer your question?
I hope that in the above I've been able to clarify how we grasp A is A as a universal axiom through perception. I look forward to your (and everyone else's) feedback.
One more thing to note, existence and consciousness are the primary axioms, qua axioms. Identity can be viewed as a corollary of them, but only AFTER the first two have been grasped. Identity is itself an axiom, but it is not, I repeat NOT the primary. Peikoff does touch on this stuff (and an error he made in OPAR regarding clarification of the axiom/corollary difference) this in his podcasts here:
http://www.peikoff.com/2009/08/03/are-you-contradicting-ayn-rand-when-you-state-that-the-validity-of-the-senses-is-an-axiom-and-it-is-a-corollary-of-consciousness-ayn-rand-states-that-identity-is-a-corollary-of-existence/#.T395YKZsbnc.link
http://www.peikoff.com/2009/09/07/you-validate-the-three-axioms-of-philosophy-in-the-following-order-existence-consciousness-identity-can-you-explain-why-you-chose-to-use-this-order/#.T395EchV5uo.link
