Let's take the Law of Identity and change it to the Law of Identity with Overlapping Categories:
Would classical logic with the modified Law of Identity be completely different than classical logic. If so, how so? And is it something that has been explored before? I am wondering if there are ontological implications in using this as a basis for all physical models, or it won't have any difference whatsoever. My understanding is that because it is a model it won't have any effect.