Lately, I have found myself in contentious discussions--generally with theists of one stripe or another--about what the fundamental laws of the universe actually are. It is pretty much unanimously held that there are fundamental laws of Aristotlean logic which are taken to be applied at all levels of this world, and beyond. These laws are assumed to be so sacred that God, Himself could not disobey them, even given that He was omnipotent! In some sense, it is held, these laws are so fundamental that the world cannot be sensibly conceived of or thought about without using and assuming them. Without them, our brains simply cannot operate--and neither could the universe. Or so it is assumed, at any rate.
For reference, by way of the normal definitions, here are some links to standard discussions of these laws:
http://en.wikipedia.org/wiki/Law_of_identity
http://en.wikipedia.org/wiki/Law_of_noncontradiction
http://en.wikipedia.org/wiki/Law_of_excluded_middle
When I encounter a belief system so seemingly incontrovertible, so widely accepted, so ingrained... Well, I can't help but wonder if this might not be a paradigm in need of shifting! Perhaps these laws need to be re-examined. Perhaps they are the proverbial "albatross around our neck" that is somehow in the way of further progress in the fields of ontology, logic, and other areas that seem to me to be kind of stuck in the muck. I ask myself, how fundamental are these laws, really? Is it really true that the universe would "blow up" into utter chaos if we were to stop jealously guarding these rules with such fervor?
In any event, I have recently been reading Feynman's book "Quantum Mechanics and Path Integrals". In the course of this study, it occurred to me that maybe, just maybe, there might be a little wiggle room in at least one of these sacred cows, these so-called "Laws of Thought". Maybe, just maybe, the Law of Noncontradiction is not quite as basic as it might appear: Perhaps it can be derived from a set of looser assumptions. Anyway, that is the position I intend to take in this thread. I want to see how it might be possible to use elements of quantum logic, calculational methods from the Path Integral approach, and a few other considerations to derive this law from even simpler assumptions, or even from its polar opposite--a "Law of Contradiction," so to speak!
This agenda is not an easy row to hoe, I'm afraid. Virtually everyone I have engaged on the topic has deep-seated, intense feelings about the inherent truth of this rule, almost to the point of declaring me a heretic--both scientifically and religiously--for even suggesting such a thing, in the first place. I imagine that I will get a lot of opposition to my program here, as well, assuming anyone pays any attention to this thread at all. All I ask of anyone who wants to participate is this: If you can bring yourself to do so, at least hear me out. I make no claims of expertise in matters of logic, quantum theory, or anything, really. I'm just a guy with a crazy idea that's been nagging me, and I'd like to explore it just to see where it might lead. I just want to be permitted to present the idea. Nobody needs to believe it, or change their belief system. All you need to do is engage in a bit of a hypothetical, for the sake of argument.
Before I get to the meat of the matter, I'd like to set the stage with a few quotes on the topic of open-mindedness from one of its most ardent practitioners. After that, after some sleep, I'll take on the task of explaining my thoughts as best as I can.
(On that note, I am going home to bed. More tomorrow, time permitting.)“No, no, you're not thinking; you're just being logical.” ~Niels Bohr
“We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that it is not crazy enough.” ~Niels Bohr
“How wonderful that we have met with a paradox. Now we have some hope of making progress.” ~Niels Bohr
“The opposite of a fact is falsehood, but the opposite of one profound truth may very well be another profound truth.” ~Niels Bohr
“Prediction is very difficult, especially if it's about the future.” ~Niels Bohr