A Philosophical Treatise on the Connection of Scientific Reasoning with Fuzzy Logic

Mathematics

卷:8

MichaelGr. Voskoglou¹  Evangelos Athanassopoulos² 

[1] Department of Applied Mathematics, Graduate Technological Educational Institute of Western Greece, 22334 Patras, Greece;

[2] Independent Researcher, Giannakopoulou 39, 27300 Gastouni, Greece;

关键词: inductive and deductive reasoning;    fuzzy logic (FL);    scientific method;    probability and statistics;    Bayesian probabilities;   

DOI  :  10.3390/math8060875

来源: DOAJ

【 摘 要 】

The present article studies the connection of scientific reasoning with fuzzy logic. Induction and deduction are the two main types of human reasoning. Although deduction is the basis of the scientific method, almost all the scientific progress (with pure mathematics being probably the unique exception) has its roots to inductive reasoning. Fuzzy logic gives to the disdainful by the classical/bivalent logic induction its proper place and importance as a fundamental component of the scientific reasoning. The error of induction is transferred to deductive reasoning through its premises. Consequently, although deduction is always a valid process, it is not an infallible method. Thus, there is a need of quantifying the degree of truth not only of the inductive, but also of the deductive arguments. In the former case, probability and statistics and of course fuzzy logic in cases of imprecision are the tools available for this purpose. In the latter case, the Bayesian probabilities play a dominant role. As many specialists argue nowadays, the whole science could be viewed as a Bayesian process. A timely example, concerning the validity of the viruses’ tests, is presented, illustrating the importance of the Bayesian processes for scientific reasoning.

【 授权许可】

Unknown