CRITICISM OF THE GROUNDS FOR ADOPTING INDEPENDENT EXPERIMENT MODELS BASEDON INTUITIVE ARGUMENTS
Vladimir Moiseevich Reznikov1,2
1Institute of Philosophy and Law, SB RAS, 8, Nikolaev st., Novosibirsk, 630090
2Novosibirsk National Research State University, 2, Pirogov st., Novosibirsk, 630090, Russia
Keywords: philosophy, category, cause, mathematics, non-Euclidean geometry, probability theory, verification of independence, common cause principle, maximum entropy principle
Abstract
The article analyses the value of the concept of independence for philosophy, pure mathematics and applied mathematics. Thus, examples from geometry and set theory demonstrate that the study of mathematical statements independent of axiomatics provided an impetus for the development both of these sciences and mathematical logic. The main attention is paid to the analysis of the use of independence in applications. As we know, the most popular applications of mathematical disciplines such as elementary probability theory and mathematical statistics often use models of independent experiments. Since formal verification of the relation of independence is labor-intensive, independence is often introduced on the basis of intuitive reasoning. The article shows the inconsistency of arguments in favor of adopting independent experiment models based on intuitive considerations, such as control of experimental conditions and a negligible correlation of random values. The author outlines the prospects for accepting independence out of pure mathematical approaches, but on the basis of philosophical principles and those of natural sciences, namely the common cause principle and the maximum entropy principle.
|
