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351.#.#.b: Crítica. Revista Hispanoamericana de Filosofía

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856.4.0.u: https://critica.filosoficas.unam.mx/index.php/critica/article/view/252/245

100.1.#.a: Lungarzo, Carlos

524.#.#.a: Lungarzo, Carlos (1977). The Role of Classical Logic in the So-Called Quantic Logic. Crítica. Revista Hispanoamericana de Filosofía; Vol. 9 Núm. 27, 1977; 49-66. Recuperado de https://repositorio.unam.mx/contenidos/4115680

245.1.0.a: The Role of Classical Logic in the So-Called Quantic Logic

502.#.#.c: Universidad Nacional Autónoma de México

561.1.#.a: Instituto de Investigaciones Filosóficas, UNAM

264.#.0.c: 1977

264.#.1.c: 2018-11-07

506.1.#.a: La titularidad de los derechos patrimoniales de esta obra pertenece a las instituciones editoras. Su uso se rige por una licencia Creative Commons BY-NC-ND 4.0 Internacional, https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode.es, para un uso diferente consultar al responsable jurídico del repositorio por medio del correo electrónico critica.ojs@filosoficas.unam.mx

884.#.#.k: https://critica.filosoficas.unam.mx/index.php/critica/article/view/252

001.#.#.#: 034.oai:ojs.pkp.sfu.ca:article/252

041.#.7.h: spa

520.3.#.a: The purpose of this paper is to prove that the construction of a quantum logic is a task of specific interest for non-classical logic, but that it is relevant neither to the methodology of quantum mechanics nor to the formalisation of the alternative yes-no process. The main argument is that quantum structures (for example, orthocomplemented partially ordered sets, orthomodular lattices and partial algebras) are not systems of logic proper, but rather are perfectly formalizable structures in classical logic. In § 1, the orthodox formulation of Jauch and Piron are analyzed. I affirm that the objections made by these authors against “quantum logic” are not eliminated by the introduction of a conditional in the lattice structures, since the true reason why quantum “logic” is not really logic lies in its formulation, which is not that of a propositional system, but rather that of a specific theory whose model is these lattices. It is argued that the collection of the properties satisfied by certain objects of a structure does not justify their presentation as purely logical properties, nor does the presence of certain operations of the least upper bound and greatest lower bound permit us to call symbols introduced by analogy in propositionaI logic “connectives”. In any case, if that formalization is indeed possible, it does not imply the adoption of a new logic as a formal instrument for quantum mechanics. In § 2, aspects of quantum theories which are especially semantic in nature are analyzed. I agree with van Fraassen’s statement in the sense that that semantic formulation makes specific concepts of the theory clearer, but it does not attempt to construct its own logic. I deduce that it is non-classical logic which can actually take advantage of quantum semantics, as a model which, eventually, could throw light on the metalogical properties of certain special propositional systems. Finally, by using Benioff’s profound set theory analysis, I advance the hypothesis that classical logic is possibly the only one that can account for the richness of the meanings that appear in quantum mechanics.[Summary by Carlos Lungarzo]

773.1.#.t: Crítica. Revista Hispanoamericana de Filosofía; Vol. 9 Núm. 27 (1977); 49-66

773.1.#.o: https://critica.filosoficas.unam.mx/index.php/critica

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310.#.#.a: Cuatrimestral

300.#.#.a: Páginas: 49-66

599.#.#.a: 34

264.#.1.b: Instituto de Investigaciones Filosóficas, UNAM

doi: https://doi.org/10.22201/iifs.18704905e.1977.252

harvesting_date: 2024-02-23 00:00:00.0

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Artículo

The Role of Classical Logic in the So-Called Quantic Logic

Lungarzo, Carlos

Instituto de Investigaciones Filosóficas, UNAM, publicado en Crítica. Revista Hispanoamericana de Filosofía, y cosechado de Revistas UNAM

Licencia de uso

Procedencia del contenido

Cita

Lungarzo, Carlos (1977). The Role of Classical Logic in the So-Called Quantic Logic. Crítica. Revista Hispanoamericana de Filosofía; Vol. 9 Núm. 27, 1977; 49-66. Recuperado de https://repositorio.unam.mx/contenidos/4115680

Descripción del recurso

Autor(es)
Lungarzo, Carlos
Tipo
Artículo de Investigación
Área del conocimiento
Artes y Humanidades
Título
The Role of Classical Logic in the So-Called Quantic Logic
Fecha
2018-11-07
Resumen
The purpose of this paper is to prove that the construction of a quantum logic is a task of specific interest for non-classical logic, but that it is relevant neither to the methodology of quantum mechanics nor to the formalisation of the alternative yes-no process. The main argument is that quantum structures (for example, orthocomplemented partially ordered sets, orthomodular lattices and partial algebras) are not systems of logic proper, but rather are perfectly formalizable structures in classical logic. In § 1, the orthodox formulation of Jauch and Piron are analyzed. I affirm that the objections made by these authors against “quantum logic” are not eliminated by the introduction of a conditional in the lattice structures, since the true reason why quantum “logic” is not really logic lies in its formulation, which is not that of a propositional system, but rather that of a specific theory whose model is these lattices. It is argued that the collection of the properties satisfied by certain objects of a structure does not justify their presentation as purely logical properties, nor does the presence of certain operations of the least upper bound and greatest lower bound permit us to call symbols introduced by analogy in propositionaI logic “connectives”. In any case, if that formalization is indeed possible, it does not imply the adoption of a new logic as a formal instrument for quantum mechanics. In § 2, aspects of quantum theories which are especially semantic in nature are analyzed. I agree with van Fraassen’s statement in the sense that that semantic formulation makes specific concepts of the theory clearer, but it does not attempt to construct its own logic. I deduce that it is non-classical logic which can actually take advantage of quantum semantics, as a model which, eventually, could throw light on the metalogical properties of certain special propositional systems. Finally, by using Benioff’s profound set theory analysis, I advance the hypothesis that classical logic is possibly the only one that can account for the richness of the meanings that appear in quantum mechanics.[Summary by Carlos Lungarzo]
Idioma
spa
ISSN
ISSN electrónico: 1870-4905; ISSN impreso: 0011-1503

Enlaces