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As the science of rational thought, logic has set itself the task of identifying the major theoretical principles that enable us to distinguish between correct and fallacious reasoning. Over the course of its history, it has forged increasingly precise and rigorous analytical tools. These developments have led to the various formal systems of contemporary symbolic logic. It is now possible to treat many lines of reasoning as calculations, the validity of which is ensured simply by compliance with previously established rules of inference. However, the question of whether or not our reasoning is correct presupposes that we also consider other criteria of relevance and legitimacy, which the study of sophisms and paradoxes makes it possible to identify a contrario. In addition, it is important to take into account the dialectical and rhetorical dimensions of argumentation, i.e. the way in which reasoning is used in everyday debates. This will be the subject of our next publication.