The book presents an original, new system of logic intended to possess the characteristics of our everyday reasoning and to avoid properties alien to human thought. A dominant role is played by the subordination of the system to the Universal Principle of Consistency, newly formulated by the author. Naturally, this principle refers to Aristotle’s Principle of Non-Contradiction. Both the system as a whole and the Universal Principle of Consistency are tested in several selected but highly diverse contexts: everyday reasoning, including implicatures, presuppositions, and default thinking; the context of legal norms; as well as formal mathematical and metalogical contexts. In each case, the tests yield very positive results. It turns out that—apart from metalogic—in all the contexts mentioned we reason in terms of the contents of propositions, rather than their truth values. In none of these contexts do we infer from falsehood, and thus from contradiction. Consequently, our reasoning is not subject to the principle of explosion. On the contrary, it is governed by a principle of implosion: from falsehood, nothing follows. The book shows that classical implication finds no application anywhere, not even in mathematics or metalogic. In the latter case, the well-known characterization of material implication is not fully applied. Metalogic is not a classical logic, but rather an algorithm for assigning truth values to sentences on the basis of their connectives, and it has nothing to do with implication as a form of inference. The book constitutes an argument in favor of logical monism, understood here not as the denial of the existence of different logical systems—since such systems undeniably exist—but as the claim that there is a single method of logical reasoning that we apply independently of the subject matter of thought.
LanguagePolish
Title in Englishmplication, entailment and universal principle of consistency