One of the philosophy classes I teach at our county community college is Logic. Logic seems to be hard-wired into persons. For example, if one were to deny that logic is hard-wired into persons one would have to use logic to do so. That is, the argument against logic would itself have to have a conclusion supported by one or more premises, the conclusion must follow logically from the premises (i.e., the argument must be formally valid), and the premises must be true.
One cannot meaningfully argue non-logically against the universality of logic. When one tries to do so, or does so without hardly trying, the result often is that informal logical fallacies are committed.
I have heard some say that postmoderns are not interested in logic but value experience above logic. But even if this is true, an experiential postmodern person would have to use logic to make a case that experience is to be preferred above logic.
