Quantum-logical propositions and philosophical implications

In this communication, after having mentioned the main formalisms and proposals called “quantum logics” (QL), the so-called QLs in the standard way will be introduced. This will be done from a philosophical perspective in order to underline the implications arising from the definition of “quantum propositions” (as a case study). For this purpose, the classical case of the logic-algebra-physics relation will be presented, explaining why it is less conflictive and what are the consequences of the above relation in the quantum one. In particular, two debates will be introduced. One considered settled, Putnam (1969), on the epistemological status of logic and another contemporary, Williamson (2018), on the relation between different non-classical logics and applied mathematics. It will be concluded that both debates are much closer than one might think at first and that the clarification of the meaning of quantum logics is still an open debate with great implications in the philosophy of logic and mathematics (and not only in philosophy of physics, of science, epistemology, metaphysics or applied logic).