He following work is a delivered by one of the authors “Mathematical modeling of biological processes” lection course adapted to the format of a journal article. It criticizes holistic conceptions of some of pseudoscientific philosophic thoughts (e.g. vitalism, dialectical materialism, neovitalism, organicism, holism, emergintism) and points out the significance of reductionism as the philosophic basis for modern Natural science thoughts on the whole and biological processes mathematical modeling in particular. However, it is emphasized that holistic conceptions should not be considered to be totally pseudoscientific. As a rule, they correspond to either the empirical level of scientific cognition, or the next cognition level “phenomenological theories” (i.e. theoretical) stage, when empirical factual material accumulation, systematization and generalization take place. Moving to the higher stage (The stage of explanatory theories), holistic thoughts naturally disappear and give way to reductionism. In the article scientific thoughts evolution stages, from holism to reductionism, are consistently examined and analyzed. The existence of motion of matter forms accentuated by Engels is thoroughly questioned . Higher to lower motion of matter forms irreducibility is proved ambiguous, in this way, failure of dialectical materialism theory is proved. By using Korzukhin theorem and enzyme kinetics as the examples, apparent biological to chemical processes reducibility is showed. At the same time, in contrast, some arguments in favor of holistic views as a necessary stage in the development of scientific thoughts are offered. And, of course, it was hardly possible to avoid science development in Russia issue, where during a long period of time under oppression of the Soviet regime pseudoscientific thoughts had been cruelly enforced. Perhaps some of these thoughts remain in the minds of the younger generation even nowadays?