Is (quantum) logic empirical?

Nicolas Alzetta

David J. Foulis, Charles H. Randall

David J. Foulis, Charles H. Randall

Guido Bacciagaluppi

Claudio Garola

Scholars have wondered for a long time whether quantum mechanics (QM) subtends a quantum concept of truth which originates quantum logic (QL) and is radically different from the classical (Tarskian) concept of truth. We show in this paper that QL can be interpreted as a pragmatic language of pragmatically decidable assertive formulas, which formalize statements about physical systems that are empirically justified or unjustified in the framework of QM. According to this interpretation, QL formalizes properties of the metalinguistic concept of empirical justification within QM rather than properties of a quantum concept of truth. This conclusion agrees with a general integrationist perspective, according to which nonstandard logics can be interpreted as theories of metalinguistic concepts different from truth, avoiding competition with classical notions and preserving the globality of logic. By the way, some elucidations of the standard concept of quantum truth are also obtained.

Giovanni Battista Rossi, Francesco Crenna

Measurement can be defined on the basis of the notion of empirical relation, which appears as a primitive term in the representational theory. Here a language is introduced for dealing with empirical relations and a probabilistic logic is applied to statements concerning them.