Publishing House SB RAS:

Publishing House SB RAS:

Address of the Publishing House SB RAS:
Morskoy pr. 2, 630090 Novosibirsk, Russia



Advanced Search

Philosophy of Sciences

2020 year, number 4

MATHEMATICAL PROOF: DEDUCTIVE NORMATIVITY AND DIVERSITY OFPRACTICE

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

Abstract

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.