Semantics of Physical Theories

Milan M. Ćirković

Claudio Garola, Sandro Sozzo

The old Bohr–Einstein debate about the completeness of quantum mechanics (QM) was held on an ontological ground. The completeness problem becomes more tractable, however, if it is preliminarily discussed from a semantic viewpoint. 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 of the physical theory can be introduced and inquired. In particular, standard QM adopts a verificationist theory of truth that implies its semantic nonobjectivity; moreover, we show in this paper that standard QM is semantically complete, which matches Bohr’s thesis. On the other hand, one of the authors has provided a Semantic Realism (or SR) interpretation of QM 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, which matches EPR’s thesis. Thus, standard QM and the SR interpretation of QM come to opposite conclusions. These can be reconciled within an integrationist perspective that interpretes non–Tarskian theories of truth as theories of metalinguistic concepts different from truth.

Alejandro Ascarate

Based on a clear ontology of material individuals, we analyze in detail the factual semantics of quantum theory, and argue that the basic mathematical formalism of quantum theory is just okay with (a certain form of ) realism and that it is perfectly applicable to quantum gravity. This is basically a process about 'cleansing' the formalism from semantic assumptions and physical referents that it doesn't really need (we use the term 'semantics' in the sense of the factual semantics of a physical theory, and not in the sense of model theory of abstract mathematics or logic). We base our study on the usual non-Boolean lattice of projectors in a Hilbert space and probability measures on it, to which we give a careful physical interpretation using the mentioned tools in order to avoid the usual problems posed by this task. At the end, we study a possible connection with the theory of quantum duration and time proposed in [arXiv:2012.03994, arXiv:2107.06693], for which this paper serves as a philosophical basis, and argue for our view that quantum gravity may show that what we perceive as change in the classical world was just (an ontologically fundamental) quantum collapse all along.

Peter Bongaarts

Hans Primas