From determinism to quasideterminism in logic and beyond logic

##plugins.themes.bootstrap3.article.main##

V. Yu. Ivlev
Yu. V. Ivlev

Abstract

This article is concerned with transition from determinate causation in logic, social and natural sciences to indeterminate causation in these branches of scientific knowledge. Analysis of this transition results in formulation of the principle of quasi-functionality for logic and the principle of quasi-determinism for social, natural and technical sciences. In cognition, nature and society, there is not only the relation of definite conditionality between phenomena, but also the relation of indefinite conditionality, i.e. some definite cause can induce not only a single specific consequence, but also, under the same conditions, in one case, one distinct consequence of several possible consequences, and in another case – another. In logic the principle of functionality was implemented through the representation of logical terms as functions, and the principle of quasi-functionality was implemented through quasi-functions. Quasi-function is a correspondence by virtue of which an object from a certain subset of a certain domain is related with a certain object from a certain subset of some set (from the range of the quasi-function). Special cases of quasi-functions are a functional relation and complete uncertainty (randomness). An example of quasi-functional logic is the minimal modal logic $ S_{min} $. Other examples of such logics are quasi-matrix three-value $S_{r}$ logic; four-value quasi-matrix $ S_{a}^{-}, … S_{i}^{+} $ logics. Based on the principle of quasi-functionality, the idea of constructing abstract and real quasi-automata has been proposed. If there is a functional dependence between the signal at the input and the signal at the output of the automaton, then this dependence is quasi-functional in the quasi-automaton. The system of quasi-automatic machines can express functional dependence. Other actual problems are the application of the principle of quasi-determinism in biology to the description of contingency, the consideration from this point of view the functioning of neural networks, development in the social sphere and other areas of knowledge and objective reality. It is proposed to revise technical, natural sciences and social knowledge on the basis of the principle of quasi-functionality. DOI: 10.21146/2074-1472-2018-24-2-92-99

##plugins.generic.usageStats.downloads##

##plugins.generic.usageStats.noStats##

##plugins.themes.bootstrap3.article.details##

Section
Статьи

References

Ивлев В.Ю. Категории необходимости, случайности и возможности: их смысл и методологическая роль в научном познании // Философия и общество. 1997. № 3. С. 108–125.
Ивлев Ю.В. Логика норм: дис. ... канд. филос. наук. M., 1972.
Ивлев Ю.В. Табличное построение пропозициональной модальной логики // Вестн. Моск. ун-та. Сер. 7. «Философия». 1973. № 6. С. 51–61.
Ивлев Ю.В. Содержательная семантика модальной логики. М.: Изд-во Моск. ун-та, 1985. 170 с.
Ивлев Ю.В. Основы логической теории аргументации // Логические исследования. М., 2003. Вып. 10. С. 50–60.
Ивлев Ю.В. Методологическая функция квазиматричной (квазифункциональной) логики // Методология в науке и образовании. Материалы Всерос. конф. ун-тов и акад. ин-тов РАН. Москва, 30-31 марта 2017 г. М.: Изд-во МГТУ им. Н.Э. Баумана, 2017. С. 61–64.
Ивлев Ю.В., Ивлев В.Ю. Объективное содержание логических знаний // Александр Зиновьев и актуальные проблемы логики и методологии. М.: Канон+, 2017. C. 92–114.
Marcelo E. Coniglio, Luis Farinas del Cerro, Newton M. Peron Finite non-deterministic semantics for some model systems // Journal of nonClassical Logics. 2015. Vol. 25. No. 1. P. 20–45.
Omori H., Skurt D. More Modal Semantics Without Possible Worlds // IFColog Journal of Logics and their Applications. 2016. Vol. 3. P. 815–846.
Rescher N. Quasi-truth functional systems of propositional logic // The Journal of Symbolic Logic. 1962. No. 27. P. 1–10.