2014/09/30 by Claudio Garola · 5 citations
Arts and Humanities · Computer Science · Mathematics · Physics and Astronomy · Psychology · #Algebra over a field #Categorical quantum mechanics #Classical logic #Consistent histories #Discrete mathematics #Epistemology #Mathematics #Philosophy #Philosophy and History of Science #Philosophy and Theoretical Science #Physics #Pure mathematics #Quantum #Quantum Mechanics and Applications #Quantum computer #Quantum dynamics #Quantum logic #Quantum mechanics #Quantum process #Relational quantum mechanics #Theoretical physics #cs.LO #msc:81P05 #quant-ph
paper · pdf · doi:10.1007/s10773-017-3309-7
published in International Journal of Theoretical Physics 56(12), 3770-3782 (Springer Science+Business Media) · Third version: 20 pages. Sects. 1, 2, and 4 rewritten and improved. Explanations added
arxiv created 2015/12/16 · openalex publication_date 2017/02/20 · openalex created_date 2017/03/03 · arxiv updated 2021/12/14 · openalex updated_date 2026/08/05
Scholars have wondered for a long time whether the language of quantum mechanics introduces a quantum notion of truth which is formalized by quantum logic (QL) and is incompatible with the classical (Tarskian) notion. We show that QL can be interpreted as a pragmatic language of assertive formulas which formalize statements about physical systems that are empirically justified or unjustified in the framework of quantum mechanics. According to this interpretation, QL formalizes properties of the metalinguistic notion of empirical justification within quantum mechanics rather than properties of a quantum notion of truth. This conclusion agrees with a general integrationist perspective that interprets nonstandard logics as theories of metalinguistic notions different from truth, thus avoiding incompatibility with classical notions and preserving the globality of logic. By the way, some elucidations of the standard notion of quantum truth are also obtained. Key words: pragmatics, quantum logic, quantum mechanics, justifiability, global pluralism.