On the discrepancies between quantum logic and classical logic

In this chapter, by ‘logic’ we mean Logica Magna (Great Logic), involving higher-order systems and set theories. We revise some of the main reasons provided by quantum theory to question the standard connectives, quantifiers, identity, and the notion of set ascribed by classical logic. In the end, we discuss the interesting fact that even if these argumentations are feasible, quantum theories (as done by the physicists) continue to be developed within standard frameworks, and we ask for the reasons. We presuppose that the reader is more acquainted with logic than with quantum mechanics, so we deserve more space for explanations in this field.