Logic is being discussed as if it is a singularity. There are different logics, for different purposes, in some versions the law of the excluded middle operates, in others the law of the included middle. The laws of identity are different in dialectics, and ancient chinese logic,. 'Fuzzy logic' which allows smart machines to function has a different set of rules again. Bart Kosko has written a clear account of Fuzzy Logig, well worth a read