Concluding Remarks: Classical Logic and Quantum Logic

Abstract

The considerations of Chapters 3–5 have led to the result that the most general propositional logic which is equally applicable to propositions about classical and quantum mechanical systems is given by the calculus Q eff of effective quantum logic. In addition, in Chapter 6 we have shown that, by a weak assumption concerning the confirmation of commensurability propositions, this calculus can be extended to the calculus Q of full quantum logic. Hence, one arrives at the conclusion that the ‘true’ logic is given by the calculus of full quantum logic, whereas ordinary effective logic and classical propositional logic are formal systems, the validity of which is restricted to the special case of unrestrictedly available (commensurable) propositions. In particular, propositions about physical systems have this property to the extent that the system in question can be considered as a classical one. Consequently, from this point of view classical propositional logic turns out to be an idealisation, which has only approximate validity and, thus, no fundamental meaning.