Some Remarks on the Subject Matter of Formal Logic

Abstract

K.Ajdukiewicz wrote that each correct scheme of inference is based on the logical theorem which asserts an objective relation between facts. Accordingly, while we study logic we train ourselves in the art of logical thinking, and learn some relations between facts. For instance, we learn the law of excluded middle, that is that a given state of affairs, a given situation occurs or does not occur. In this paper Ajdukiewicz's pronouncements have been completed, e.g. by way of turning our attention on this point that the relations asserted by the laws of classical calculus, especially by the laws of classical propositional calculus, are those relations whose existence they assume and of which speak − by means of appropriate logical constants − all scientific disciplines with an ontological bias. Of such relations one speaks also in everyday language. The paper seeks to show that Z. Zawirski, T. Kotarbiński, S. Kamiński and G. Küng, although each of them uses different words, expressed in principle the above thesis of Ajdukiewicz. Some attention has been devoted to outline the differences which occur between the laws of classical propositional calculus, the laws of non-classical logics, in which there occur nonextensional functors, and the laws of the natural sciences.