I have a further question about this discussion and generally about any argument that we learn logical laws by experience, observation or induction or anything like that. Suppose it is argued that I learn that no x is white and not white by observing particular x's and noting of each one that it is either white, or not white. I then generalise this to 'no x is white and not white', and further generalise (by substituting other predicates like 'round', 'soft', 'large' etc) to 'no x is F and not F'.
I ask, how did I learn the meaning of the negation 'not'? Is this a sign whose meaning I understood correctly before all these observations? Or as part of the process of observation that led to the general conclusion? Surely not the first. Could anyone who thought it was possible that 'Socrates is white and Socrates is not white' was true, really understand the meaning of the word 'not'? It means negation, and negation means denial, and how could you assert and deny the same thing at the same time? So not the first.
But if the second, that means we learn the concept of negation by observation. Perhaps by your teachers pointing to different things and saying 'not white' when they were not white, and 'white' if the things were white. But that doesn't tell me whether the predicate 'not white' also applies to the white things. To do that, my teachers would have to say 'not not white' when pointing to the white things. And that still doesn't of itself tell me how to use the negation operator for I still haven't been taught that 'not not not white' applies to the not white things, and so on ad infinitum. To understand negation properly, I would have to understand its basic properties before all this took place. But if I understood that, the first point would apply, i.e. I would have to understand that 'x is white and x is not white' can never be true, on account of the meaning of the negation sign.
On the point attributed to Tim Crane, namely that one can perceive something 'as A and not-A' but rejects it through giving greater weight to the principle of contradiction, I'm not sure we can perceive something as A and not-A. Rather, it may seem that it is A and not A, but our understanding of the meaning of the word 'not' assures us that it is not the case that it is A and not A.