On Certain Kinds of Implications

Abstract

In the article the main kinds of implications that are known in contemporary logic are characterized. The material implication and the problems connected with it are discussed. Among others, insufficiency of this implication is stressed for expressing unreal conditionals. The strict implication is comprehensively analyzed. Its connections with Philo’s, Diodoros Kronos’ and Chrysippus’ implication are discussed. The strong implication and other ones connected with the relevant logics are briefly characterized. In the article reason are insistently looked for for the appearance of several kinds of implications in logic.

The second part of the article discusses implications connected with causal clauses. It briefly presents the results obtained in this field by, among others, S. Jaśkowski, G. H. von Wright and A. W. Burks and gives a critical discussion of them. In the article the author also looks for the conditions that must be met by the implication functor which may be used to adequately formalize conditional causal clauses used in physics and expressed in the notional language. The axioms which characterize such a functor must be true in the physical model of causality.