I'm not entirely sure if I understand exactly what it is you've said here... But let me see if I can address it anyhow:
A newborn humanbeing experiences almost immediately the world via the senses. There are different, contrasting things discovered by the senses. Light and nonlight. Round and not round. Moving and not moving. Differences in smell, in touch, in taste. Being assaulted with all this sensory data we eventually notice that there are two kinds of stuff: A and not A, B and not B, and so on. If a baby sees motion, it can contrast it with nonmotion. If it hears a loud sound, it can contrast it with silence. By taking sensory data we can see that if A were to mean, for instance, the loud sound, there must be not A perceived to make that call. In other words, you would not take notice of a loud sound if you did not know the absence of it or something other than it. Also, you could not detect movement if you had nothing to contrast it to. This is pretty evident.
Now, an axiom is self evident because it can be verified by our senses with relatively little internalization. We don't really have moments where A and not A aren't apparent except in cases of extreme rarity. But we experience it young as sensing beings an through this we learn the most basic of knowledge foundations: axioms. And building on axioms we have logic. Now, anyone who can read this thread understands logic to some degree or another. Perhaps their use of it isn't perfect, or perhaps they aren't even aware of their actual level of reason (Which is why intuition CAN be argued as a post-reason idea; I can intuit that there's something wrong with a picture, but consciously I may not be able to make the distinction right off the bat.) But each person must use reason to do anything else involving thought. To recognize my words, you must realize that the letters are unique and have identity. You cannot intuit this in your definition; that is, you cannot derive the knowledge of this letter being unique without first having contrasted it with say, blank space or another symbol. You must apply logic to the data in order to come up with knowledge. There is no other way. To say otherwise would be tantamount to saying we can acquire knowledge of the world via insanity or irrationality.
And keep in mind, the definition of knowledge is that one must believe A, know A, and provide the logos for A.