I am not convinced enough to believe that the universe we inhabit is by nature completely rational and/or objective. I'm certainly not convinced it's even rational by a majority. This puts me squarely at odds with many other thinkers and quite a few professionals who have built their lives upon the notion that rationality is naturally ubiquitous. But we live in a universe naturally dominated by entropy, so I'm not sure where this notion comes from— centuries of politics clouding peoples' minds, perhaps? But in terms of logic, everyone is still insisting upon operating from the notions of Aristotle, who was alive 2300 years ago, and Plato, who was alive 2400 years ago. Since I do not feel compelled to adhere to traditions, I feel free to think for myself even if it enrages or upsets people outside of me, and my life-long scholarly journey includes reconsidering the axiomatic foundations of human thought itself. I am not paid to do this, it is a labor of passion compelled by a fiery curiosity coupled with religious trauma. I'll be damned if I'll let people who believe in bullshit (I'm looking at you, believers in the abrahamic cult religions! ADD: I'm also looking at you, antagonistic atheists!) influence my life through their religious politics with their faulty thought processes that aren't even remotely based in reality. I want to know the Truth that I know exists beyond all the politics and the religions and the secular cliques, and I'll find it by relying upon my own gnosis instead of someone else's chain of reasoning based on axioms I don't accept.
Regarding the traditional laws of thought...
Law of Identity says "Whatever is, is."
This one I completely agree with as a metaphysical truth, and like the "I think, therefore I am" argument, I consider this truth to be fundamentally essential. This is very rare and demonstrates how special I think this axiom truly is. If I had to make an amendment, it would be "and whatever isn't, isn't"— although maybe this is already implied? It may be splitting hairs, but if we're going to be insisting upon things being or not-being, I think it's best to remain consistent in our approach.
Law of Non-Contradiction says "Nothing can both be and not be."
This, I am extremely skeptical about. We humans cannot even conceive of Nothingness: how can we be so sure of what it is truly capable of? If "nothing can both be and not be" is taken as true, and we replace the word "nothing" with the identical equivalent notion denoted by the symbol X, we have "X can both be and not be." Something such as X must be truly powerful and indeed, could even be considered a supreme being, if it is capable of both being and non-being simultneously! X, then, could be considered God, or more accurately: Ain Soph. If X is nothing, well then what does this tell us about God? Does it mean there is nothing that can be considered superior to another, no favored viewpoint in the universe above all the rest, no perfect standards that can be applied universally— across all that Is and all that Isn't? I think it points to a familiar conclusion: that we live in a vast world within which contradictions abound ubiquitously, and there is no master(s) of the universe whose job is to tame them. It's just us and each other in this endless maelstrom of opposites coexisting for better or for worse. If anything this principle should be called "Law of Necessary Contradiction", rather than non-contradiction. Humans have learned much about the world since the times of Aristotle and Plato, and I believe we have an awful lot more to learn about the world around us and what it is capable of.
Law of Excluded Middle says "Everything must either be or not be."
This, I don't believe at all. There's no way for us to really know this is true since humans are not omniscient and there is plenty of the world around us that we have not ourselves observed— indeed, there is much that we are currently incapable of observing at all, like the edges of the cosmos or the insides of a quark. Hell, some of us haven't even observed anything outside of the country we were born into. How can we humans be so sure that beingness does not, cannot admit of degrees? It smacks of hubris to insist that everything we encounter in Nature must conform to our understanding of it, to believe that everything in the world must be sorted into only one of two piles— as if everything could be! The idea "everything must either be or not be" is a fascist statement & it's meant to make things easier for some by drawing a line in the sand and alotting everything in the universe to only one side or another. Unfortunately, things in this universe are meant to evolve and to change and to move around and to switch sides and to grow. Things just aren't meant to stay in one pile or on one side of the line forever. There is no way I can accept this principle as a natural law.
The Principle of Sufficient Reason says "everything must have a reason or a cause."
This I do agree with. Children come from their parents, baby birds come from their bird parents, plants come from their seeds, planets and stars come from nebulae, ideas come from either other people or from within— everything has to come from something that came before it. It should also be noted that I consider "because it makes me happy" or "because I wanted to" to be completely valid reasons, even if they are not themselves based in reason— meaning that if it is true that everything in the universe exists because everything in the universe wants to exist, I'll find this explanation completely satisfactory.