Occam, I didn’t see this before… it looks like a more mathematical version of Howard Bloom’s stuff. I think Gödel, Escher, Bach explains in about six places why things like the XOR/NXOR distinctions don’t make sense (essentially, XOR is an operator within propositional logic, while the idea of proving theorems in steps, or that exactly one of a proposition and its negation is true, is external to the system).
Are you sure that you understand my work?
If you look at it from a XOR-only point of view, then it does not make sence.
Maybe this dialog can help:
[quote author=“DoronShadmi”][quote author=“DrMatt”]Heh. It cited Wikipedia instead of learning mathematics.
It wants to have its cake and eat it too, and so it is attacking the definition of logical consistency instead of learning some mathematics.
It is a fool.
A dialog that I have found in another forum:
What exactly did you mean by “the two need not be exclusive”. Please be specific with an example of it not needing to be exclusive and then, for contrast, an example of it needing to be exclusive. I think it’ll be become clear to me as soon as you do it.
In the strictly logical sense, “OR” is not exclusive. So, if I ask, what kind of clothing do you want to buy, and you answer, “a shirt OR a pant,” then you would find it acceptable if we bought just a shirt, just a pant, or both. “XOR” means “exclusive-OR”. If you were to say, “a shirt XOR a pant,” then that means you would want just a shirt, just a pant, but not both. I believe, in most situations, we use “or” as logic uses “XOR.” When someone asks you what you want to eat, and you say, “italian or chinese” you mean either italian, or chinese, but not both. “XOR” is like saying EITHER option 1 OR option 2, BUT not both.
When I say that LEM says that they need not be exclusive, then that means that the case could be that P, ~P, or both. Now you would ask, “both P and ~P? That’s weird.” Indeed, it is, and that’s what LNC is for. LEM says P, ~P, or both, and LNC says, no, not both. Putting them together, we get either P or ~P, just one or the other, not both. Now, I don’t think I can give an example where we have P and ~P. LEM allows it, but LNC does not, so to give an example, I would have to deny LNC. I don’t think I could make a rational English sentence using the word “not” if I were to deny LNC. Technically, such an example is possible, but I don’t think you would buy it as a reasonable example because it would sound so unnatural.
LNC of Classical Logic (the Law of Non-Contradiction) is based on XOR connective of a bivalence framework , and the ability to compare between at least two states is based on a hidden assumption, if we ignore NXOR as the logical basis of the concept of Framework (or Context, if you wish).
Classical Logic is the particular case of NXOR\XOR logic where the middle is excluded.
DrMat does not understand NXOR\XOR Logic because he looks at it from a XOR-only point of view and then he concludes that:
It wants to have its cake and eat it too
In NXOR\XOR two opposites define their middle domain, and as a result each product of this domain is a consistent “off spring” of both NXOR and XOR connectives, which complement their middle domain (a domin which is equivalent to the “content” of the Empty-Set from a XOR-only point of view).
In a NXOR\XOR logic the concept of Cake exists in any part of it, and as a result the concept of Cake exists as long as there is some part of it.
In other words Alon, please ask some questions before you conclude something about my work.
The part about entropy is a New Agened version of existing results about partitions, but even it looks at the most trivial and least interesting portion of it.
Do not be so sure. Please read http://www.geocities.com/complementarytheory/TOUM.pdf to learn more about it.