Logic and Metalogic

This article is the first in a series of three, the second of which will deal with "propositional and predicate logics" [AF 89] and the third with "non-classical logics" [AF 91] .

The word logic comes from the ancient Greek lógos, meaning both "language" and "reasoning", and is said to have been first used by Xenocrates of Chalcedon (396-314 BC). At first glance, it refers to the study of the formal rules that all rigorous reasoning (and therefore all rigorous argumentation) must respect. In a more modern sense, logic is the study of inference, which designates an elementary process of reasoning, concerned with the form, not the content, of a rational argument (leaving aside any underlying psychological or biological processes).

Situation (teaching logic). In France, logic is rarely taught, even though it is fundamental to many scientific and engineering fields (biology, chemistry, law, computer science, artificial intelligence, linguistics, mathematics, medicine, philosophy, psychology...) and to everyday life in general.

Logic is considered the most general of the exact sciences, dealing with the container and not the content, since it does not deal with any particular "matter". It is not a closed and finished science, and will probably never cease to develop.

Concepts of logic. The history of logic is marked by different philosophical approaches, and even by what its subject was (Aristotle, Abelard, Kant, Hegel, Frege).