No, I have not. The problem is that you have to be very careful about the application of this law. For example, it is NOT a contradiction to say that an electron has a probability of being in two different places at the same time. But many people seem to think it is. it is not a contradiction for something to be both hair and black even though hair and black are not the same thing.<quoted text>
How can you argue using logic?
You have just denied the first law of logic.
The law of non-contradiction...
I probably know more about logic and its foundations than you will ever know. Yes, we *assume* certain things, like propositional logic and the quantifier calculus. We can then *assume* certain statements about mathematic. From those assumptions, we can derive a great deal in a formal way. BUT, there is no a priori reason to *assume* that logic and mathematics apply to the real world or exactly how they apply. We *use* the formal system to help us understand the real world, but that understanding is a process involving hypothesis making, testing, and model building.