Logic and Argumentation

Abstract

At first glance, logic is paradigmatic. It provides us with the model for valid reasoning and, in its figures, proposes the exemplar which any procedure pretending to a rational foundation should try to approach. If it is such, it is undoubtedly because logic creates an ideal situation (ideal in the way one speaks in physics of an “ideal gas”), perhaps inspired by what effectively happens in the scientific pursuit, and — in a singular manner — what happens in mathematics, but free from any contingency. The notion of form expresses this well. Logic appears as soon as we discover that it is possible, in any proposition, to isolate an organizing diagram (which is available for an infinity of possible applications) and the terms organized by this diagram. The terms constituting a scientific language are generally divided into two classes: “purely logical” terms on the one hand, and, on the other, “descriptive” terms. This classification indeed corresponds to the presupposition of logic. It then appears that certain typical relationships between propositions are, in reality, relationships between their organizing diagrams, the “descriptive” terms being neutral, in a way, in these relationships. The usual procedures of modelling reflect this propositional behavior. If we take a language L and a universe U, in which we propose to construct an interpretation of language L, we will have to specify the interpretation of the individual and predicative constants of L by relating these elements of L respectively with well-defined individuals of U and with well-defined subsets of U.