From determinism to quasideterminism in logic and beyond logic

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