The philosophy of dialectic has always been among the most controversial and least well understood aspects of Hegelian and Marxist thought. It is rejected by many writers who are otherwise sympathetic to Marxism. One such is Marquit. In a recent article (Marquit, 1990), he criticizes the dialectical concept of contradiction. Many of his arguments will be familiar to anyone acquainted with the r...

Contradiction is often seen as a defect of intelligent systems and a dangerous limitation on efficiency. In this paper we raise the question of whether, on the contrary, it could be considered a key tool in increasing intelligence in biological structures. A possible way of answering this question in a mathematical context is shown, formulating a proposition that suggests a link between intelli...

This paper presents an algorithm that redirects proofs by contradiction. The input is a refutation graph, as produced by an automatic theorem prover (e.g., E, SPASS, Vampire, Z3); the output is a direct proof expressed in natural deduction extendedwith case analyses and nested subproofs. The algorithm is implemented in Isabelle’s Sledgehammer, where it enhances the legibility of machine-generat...

This paper investigates the satisfaction of the Non-Contradiction Law (NC) within the domain of aggregation operators. It provides characterizations both for those aggregation operators that satisfy NC with respect to (w.r.t.) some given strong negation, as well as for those satisfying the law w.r.t. any strong negation. The results obtained are applied to some of the most important known class...

This paper intends to contribute to the debate about the uses of paraconsistent reasoning in the foundations of set theory, by means of employing the logics of formal inconsistency (LFIs) and by considering consistent and inconsistent sentences, as well as consistent and inconsistent sets. We establish the basis for new paraconsistent set-theories (such as ZFmbC and ZFCil) under this perspectiv...