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Philosophy of Sciences

2020 year, number 4


Aleksandr Valerievich Khlebalin
Institute of Philosophy and Law, Siberian Branch of the Russian Academy of Sciences, 8 Nikolaeva str., Novosibirsk, 630090, Russia
Keywords: deductive proof, induction, experiment, thought experiment


The article discusses the opposition of the normative function of the ideal of deductive proof and the diversity of the practice of mathematical research, which includes inactive elements. On the example of the analysis of the explanatory function of proof, it is shown that its implementation requires the conceptual content of the proof, which is not provided only by the deductive inference. The example of research in the field of foundations of mathematics shows that the implementation of the explanatory function is provided by the coexistence and interaction of inductive and deductive elements in mathematical research.