A = A
This simple declaration is the foundation of all logic. Whether her politics inspire cheers or chills, Ms. Ayn Rand was correct in asserting that the Law of Identity ("if it's true, it's true," "if it's false, it's false," "if it is, it is," "if it's not, it's not," "a thing is what it is") is the Law of logic. All other elements of the study of logic are implied by that law.
This objective standard may cause some to howl that this is the source of bigotry, or narrowmindness, or what have you. But it is no such thing.
It is simply the foundation of consistency. It does not posit that A cannot change, but even if it changes, it is still itself.
Aksapada Gautama and the Indian logicians noted the difference between being and perceived being. So did the Greek logicians, but the idea often is lost from introductory logic texts.
There is "A as it is," and "A as it is perceived." I may see a puddle and assume it's water. It may actually be poison. My faulty perception does not change what it is, but my interaction is guided only by my perception. Its impact on me involves its actual being, however.
Hence, the need for abductive logic, where perception is tested. A is still A, but to know what A is, I must form and test a hypothesis. My collection of theories of the world, my web of belief, is simply my process of understanding what A is.
Because I cannot have total knowledge of any object (perhaps I should back that claim up in a coming post), I can never truly know A. A is always, to me, my perception of A. But this does not change the fact that A is A.
Of course, this presumes an external reality, which I do.
For now, let us note that the fundamental law of rationality was almost given what it does not need: legal precedence.