On the concept of proof

Abstract

The term “proof” is used to refer to the whole spectrum of intellectual procedures aimed at establishing the objective truth or at proving the truth of a certain sentence, the acceptability of the imperative, the fairness of evaluation, as well at convincing other people of its adequacy. In mathematics, a proof plays a central role, but at the same time, there is not a general concept of mathematical proof. There are some very different perspectives on the nature of mathematical proof, its objectives, criteria and ideals, and over time these criteria and ideals change.

Proof in other sciences is seen as a process of research, verification and confirmation of certain provisions for the search and justification of truth – objective or conventionally accepted. Here proof consists essentially in searching for supporting evidence, assessing it and establishing that it proves the hypothesis best. Demonstrating reasoning, which is considered proof in deductive sciences, does not need to be built in many other areas.

In different areas of knowledge, the criteria of viability and acceptability of evidence are different. In some it is formal-deductive rigor, in others it is evidence of arguments and the intuitive clarity of reasoning, in a third it is the reliability and adequacy of supporting evidence.

The main criterion for the admissibility of evidence is its credibility – the ability to cause the recipient to accept the proof of the statement so that he/she is willing to convince others. The proof is always immersed in the socio-historical context, therefore, common to all sciences and all times, the concept of proof not only does not exist but cannot exist. DOI: 10.21146/2074-1472-2018-24-2-100-107