Abstract
Humans have used arguments for defending or refuting statements long before the creation of logic as a specialized discipline. This can be interpreted as the fact that an intuitive notion of or a psychic disposition to articulate reasoning according to this pattern is present in common sense, and logic simply aims at describing and codifying the features of this spontaneous capacity of human reason. It is well known, however, that several arguments easily accepted by common sense are actually fallacies, and this indicates that logic is not just a descriptive, but also a prescriptive or normative enterprise, in which the notion of logical consequence is defined in a precise way and then certain rules are established in order to maintain the discourse in keeping with this notion. Yet in the justification of the correctness and adequacy of these rules commonsense reasoning must necessarily be used, and in such a way its foundational role is recognized. Moreover, it remains also true that several branches and forms of logic have been elaborated precisely in order to reflect the structural features of correct argument used in different fields of human reasoning and yet insufficiently mirrored by the most familiar logical formalisms.
Highlights
A preliminary clarification, when one wants to investigate the issue of the plurality of logics, consists in distinguishing at least two meanings of this plurality
Let us add that, not being interested in historical reconstructions, we ignore several facts: for example, that what we consider the content of logic was called “dialectic” during several centuries, that according to other traditions logic contained two parts, “analytic” and “dialectic”, that in the Scholastic tradition it was customary to speak of a logica maior which encompassed a variety of issues that we include today rather in epistemology and philosophy of language, and a logica minor that was much similar to the formal logic as we conceive it
This answer is interesting, since it surfaces in it that term “logical” that supports our choice of defining logic as the study of the correct reasoning; still it is not very informative, for it is by no means obvious what “logical consequence” means
Summary
The question of the plurality of logics has been lively discussed, especially in the first decades of the twentieth century, mainly as a consequence of the construction of several logical calculi. The lack of sufficient analysis we have mentioned consists in the fact that no preliminary clarification was carefully proposed as to the very meaning of logic. If such a clarification had been provided, the debated issue could have been seen not as an “aut-aut” question (one logic, or many logics), but as a question admitting a double answer: there is a sense according to which logic is unique, and another sense according to which several logics are legitimate. The best known part of this programme consists in the group-theoretic treatment of the different geometries (elementary, metric, projective, affine, etc.) that permits to uncover a strict and almost genetic relationship among these theories, which puts them on an equal footing as to their mathematical legitimacy.
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