On the Plural Conceptions of Logic: A Dialogical Framework for the Teaching and Study of Logical Systems

About 40 years ago, or perhaps even earlier, logical systems started to emerge at a breath-taking pace almost every day. At the same time several unifying approaches have been proposed, that are also plural. Let me focus on two main families of unifying approaches based on two different ways to conceive Logic: 1. One approach takes up the traditional conception of logic, according to which a logical systems is determined by the set of inferential rules. 2. The other main approach that appeared around the 60ties, conceives logical systems as the set of valid formulae they determine. Thus, according to the first approach, let us call it the inferentialist conception, we can unify different logical systems by changing some rules or properties of the inference relation. A common example is to distinguish classical logic from intuitionistic logic by distinguishing between a logical systems that allows more than one conclusion (classical logic) and one that do not (intuitionistic logic). In relation to the second approach, let me call it the formal semantics conception, proposes to unify logical systems by studying them under the background of the kind of truth-functional semantics presupposed by the determination of their valid formulae. For example, some early attempts to distinguish classical logic from intuitionistic logic, was to compare these logics by comparing them under the background of a truth-functional semantics. According to these perspective while classical logic is the set of valid formulae determined by Boolean-truth functions, the valid formulae of intuitionistic logic are determined by some specific form of a three-valued truth-function: so while the third excluded is valid under the Boolean background it is not valid under the three-valued one. Moreover, while the formal semantics approach is built on the traditional strict differentiation between semantics, syntax and pragmatics inherited from Charles Morris (1938, p.3) – that I may recall was published in the first volume of the International Encylcopedia of Unified Science, inferentialism grew up out of a background that avoids keeping form and meaning apart (see Martin-Löf (1984, p. 2)), and the dialogical form of inferentialism, main subject of 1 The paper has been developed in the context of the researches for transversal research axis Argumentation (UMR 8163: STL), the research project ADA at the MESHS-Nord-pas-de-Calais and the research projects: ANR-SÊMAINÔ (UMR 8163: STL)