Objectivity versus Completeness in Quantum Mechanics

The old Bohr--Einstein debate about the completeness of quantum mechanics (QM) was held on an ontological ground but can be transferred at a semantic level. Indeed every physical theory adopts, explicitly or not, a truth theory for its observative language, in terms of which the notions of semantic objectivity and semantic completeness can be introduced and inquired. In particular, standard QM adopts a verificationist theory of truth (empirical verificationism) that implies its semantic nonobjectivity; moreover, we show in this paper that standard QM is semantically complete, which accords with Bohr's thesis. On the other hand, one of the authors has provided an interpretation of QM (Semantic Realism, or SR, interpretation) that adopts a Tarskian theory of truth as correspondence for the observative language of QM (which was previously mantained to be impossible): according to this interpretation QM is semantically objective, yet incomplete. Thus, standard QM and the SR interpretation of QM come to opposite conclusions. These conclusions can be reconciled within an integrationist perspective, which interpretes non classical theories of truth in a classical framework, looking at them as theories of metalinguistic concepts different from truth