### Logic may be simple. Logic, congruence and algebra

Jean-Yves Béziau

DOI: http://dx.doi.org/10.12775/LLP.1997.009

#### Abstract

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).

#### Keywords

algebraic logic; paraconsistent logic; universal logic

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