The Dissolution of Bar-Hillel-Carnap Paradox by Semantic Information Theory Based on a Paraconsistent Logic

Abstract

Several logical puzzles, riddles and problems are defined based on the notion of games in informative contexts. Hintikka argues that epistemology or the theory of knowledge must be considered from the notion of information. So, knowledge cannot just be based on the notions of belief and justification. The present proposal will focus on the logical structure of information, and not only on the quantification of information as suggested by Claude A. Shannon (1916-2001) (Shannon 1948). In many cases, the information bits, although seemingly or factually contradictory, are quite relevant. The paraconsistent systems of logic offer a formalization of reasoning that can support certain contradictions. The well-known “Bar-Hillel–Carnap Paradox” (Bar-Hillel, 1964) causes embarrassment when it concludes that the informational content of a contradiction would be maximum, opposing the traditional notion that the semantic information must be true, and that contradictions are necessarily false.