Aksjomatyczne ujęcia genidentyczności według Zdzisława Augustynka. Część II. Definicje warunkowe
The Axiomatic Approach to Genidentity according to Zdzisław Augustynek. Part II. Conditional Definitions

Summary/Abstract: The results obtained by Zdzisław Augustynek and Mariusz Grygianiec can be supplemented or even corrected in some places. This fact motivated me to analyze systems AS1, AS2, and AS3 once again. The results are presented in two articles. The aim of Part I (Porwolik 2017) was to present the set-theoretic approach to the analysis of Augustynek’s systems and to use the presented method to compare the three systems. Part II (this paper) is devoted to conditional definitions describing relations present in the systems. In one of his works, Augustynek posed a number of questions regarding the possibility of formulating conditional definitions of a certain type, which might refer to the notions included in his axioms. He did not answer all of these questions, and my aim is to complete this task. Apart from that, I analyze the problem of reducing Augustynek’s systems to conditional definitions containing the necessary condition and the sufficient conditio of a selected notion from these systems. At the same time, I prove that Augustynek’s systems can be reduced to certain conditional definitions (that they are equivalent to them), including the ones containing two conditions of genidentity: the sufficient condition and the necessary condition. I also argue that in AS2 it is possible, with the use of normal (equivalence) definitions, to define two relations: logical identity (I) and logical difference (I*). For the other relations a definitione of this type does not exist in the analyzed systems.

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