It is important to note that systems of logic have no particular relationship to "truth" in an ontological sense. They are simply systems of formulating propositions that have internal consistency - such as mathematics. In math, propositions are called "true" or "false" when they fall within the parameters defined by the basic assumptions of the system.
I find that the most eye-opening and mind-expanding insights into what might or might not be "logical," is to encounter n-value logic systems:
Many-Valued Logic (Stanford Encyclopedia of Philosophy)
I find more relationship to what might be called "reality" or "the real world" in statements that allow propositions to be both true and false at the same time, for example.
To be bound by "either/or" logic systems is to be truly limited in one's ability to conceive of what is possible in this or other potential universes and universes of discourse.