Is the principle of contradiction a consequence of x^2 = x?

Is the principle of contradiction a consequence of x^2 = x

Logic may be simple. Logic, congruence and algebra

This paper is an attempt to clear some philosophical questions about the nature of logic by setting up a mathematical framework. The notion of congruence in logic is defined. A logical structure in which there is no non-trivial congruence relation, like some paraconsistent logics, is called simple. The relations between simplicity, the replacement theorem and algebraization of logic are studied (including MacLane-Curry’s theorem and a discussion about Curry’s algebras). We also examine how these concepts are related to such notions as semantics, truth-functionality and bivalence. We argue that a logic, which is simple, can deserve the name logic and that the opposite view is connected with a reductionist perspective (reduction of logic to algebra)

The paraconsistent logic Z. A possible solution to Jaśkowski’s problem

We present a paraconsistent logic, called Z, based on an intuitive possible worlds semantics, in which the replacement theorem holds. We show how to axiomatize this logic and prove the completeness theorem

Multifocal Ectopic Purkinje-Related Premature Contractions: A New SCN5A-Related Cardiac Channelopathy.: MEPPC: a new SCN5A-related cardiac channelopathy

International audienceOBJECTIVES: The aim of this study was to describe a new familial cardiac phenotype and to elucidate the electrophysiological mechanism responsible for the disease. BACKGROUND: Mutations in several genes encoding ion channels, especially SCN5A, have emerged as the basis for a variety of inherited cardiac arrhythmias. METHODS: Three unrelated families comprising 21 individuals affected by multifocal ectopic Purkinje-related premature contractions (MEPPC) characterized by narrow junctional and rare sinus beats competing with numerous premature ventricular contractions with right and/or left bundle branch block patterns were identified. RESULTS: Dilated cardiomyopathy was identified in 6 patients, atrial arrhythmias were detected in 9 patients, and sudden death was reported in 5 individuals. Invasive electrophysiological studies demonstrated that premature ventricular complexes originated from the Purkinje tissue. Hydroquinidine treatment dramatically decreased the number of premature ventricular complexes. It normalized the contractile function in 2 patients. All the affected subjects carried the c.665G>A transition in the SCN5A gene. Patch-clamp studies of resulting p.Arg222Gln (R222Q) Nav1.5 revealed a net gain of function of the sodium channel, leading, in silico, to incomplete repolarization in Purkinje cells responsible for premature ventricular action potentials. In vitro and in silico studies recapitulated the normalization of the ventricular action potentials in the presence of quinidine. CONCLUSIONS: A new SCN5A-related cardiac syndrome, MEPPC, was identified. The SCN5A mutation leads to a gain of function of the sodium channel responsible for hyperexcitability of the fascicular-Purkinje system. The MEPPC syndrome is responsive to hydroquinidine

Possibilidade, imaginação e concepção

In this paper we investigate the relations between possibility, imagination and conception. We develop a theory according to which these three notions are compatible but independent. This means in particular that none of these notions reduces to another one and that there are things which are:  (1) imaginable but neither possible nor conceivable; (2) conceivable but neither possible nor imaginable; (3) possible but neither imaginable nor conceivable. We first explain our methodology: structuralism, equilibrium between norm and description, prototypical examples. And then we proceed. 

The Contingency of Possibility

In this paper we criticize the way possibility is characterized in contemporary modal logic through the diamond operator. We explain that it does not match with the usual notion of possibility and that this notion is better described by the vertex Y of the hexagon of opposition usually called contingency