Different meanings of logical definition. About Ajdukiewicz criticism against classifi-cation of Łukasiewicz considerations, some comments

Abstract

Background: The article analyzes the rarely raised issue of Kazimierz Ajdukiewicz, Polish lo­gician, supporter of two-valued logic, and critic of the classification of reasoning by Jan Łu­kasiewicz, creator of trivalent logical calculus.

Research purpose: The purpose of the article is an attempt to elucidate how Ajdukiewicz’s cri-ticism of Łukasiewicz’s reasoning system concerns the issue of the role and place of definition in logic. Ajudkiwicz was a student of Łukasiewicz, who was a world-renowned genius of logic, and did not get into a scientific dispute with his master. While using the cover of criticizing a frag­ment of Łukasiewicz’s research, he expresses a contradictory stance towards, in his opinion, the erroneous ways of defining by the terms used by Łukasiewicz in his classification of reasoning.

Ajdukiewicz considered the issues related to the definition important. In his work, he emphasizes, as contemporary researchers of Ajdukiewicz’s thinking point out, that certain aspects of defini­tion theory go beyond formalized definition procedures. An analysis of his views shows that he himself aspired to create a new science of definitions in logic. In the criticism he makes about Jan Łukasiewicz’s classification of reasoning, he emphasizes that it concerns the definition, not the process of reasoning.

According to Ajdukiewicz, the definitions of alogical system must be meaningful and expressed in the sentence of the given logic language L, while to Łukasiewicz definitions presented in the classification are meaningless and contain an equivocation error. Fragmentary criticism of the problem of defining by Łukasiewicz is the beginning of in-depth research on understanding and the role of definition in logic.

Methods: In the article, analytical methods demonstrate different approaches of logicians to the role of definitions in logic. The juxtaposition of Kazimierz Ajdukiewicz’s views on the classi­fication of reasoning, with the views of the author of the classification – Jan Łukasiewicz, re­veal differences in logic’s positions within the methodology of logical systems. In this way, Ajdukiewicz’s opinion, rarely raised in science and didactics, is presented about how Łu­kasiewicz’s methodology is incorrect, as it was created based on definitions bearing the equivo­cation error. According to Ajdukiewicz, Łukasiewicz, contrary to the principles of classical logic methodo- logy, gave existing definitions a new meaning, thus creating an incorrect logic system.

Conclusions: The issue of how to define is often taken up, both in science and in the teaching pro­cess. The classification of reasoning by Jan Łukasiewicz in didactics is given today. It is different than the criticism by Kazimierz Ajdukiewicz, which is rarely undertaken in literature. The analy­sis of the views of the leading Polish logicians presented in the article regarding the classification of reasoning is a valuable contribution to the development of the subject of reasoning in logic. The analysis of Ajdukiewicz’s criticism presented in the article indicates a new face of his views regarding the dispute over definitions in logic. This new perspective may result in the extension of research on the meaning of definitions in two- and three-valued logic.