Foundations of Classical Logic and Its Applications to Informatics

Foundations of Classical Logic and Its Applications to Informatics

Copyright: © 2018 |Pages: 16
DOI: 10.4018/978-1-5225-4128-8.ch005

Abstract

This is a brief chapter recalling the essential elements of classical Boolean logic, its foundations and the first possible relationships with certain basic notions of psychoanalysis, in view of the wider discussions of the next chapters. We have also basically recalled, in a very sketchily fashion, the usual applications of Boolean logic in informatics, which are well-known. This, because the truly important aim of this chapter is simply to prepare the logic ground for a possible psychoanalytic interpretation of the basic elements of Aristotelian logics, to be identified in the unconscious realm, as we shall see better in the next chapters.
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5.2. A Brief Historical Account Of Logic And Its Applications

Since the beginnings, logic is inseparable from philosophy, and vice versa. Aristotle is however unanimously recognized as the founder of logic as an autonomous discipline, giving it a systematic framework and a formal outlook. Around the first century BC, he exposes the doctrine of logic in the Organon, the canonical text of Aristotelian corpus just devoted to logic. Differently from the Euclid’s Elements, it seems that Aristotle’s work on logic does not have antecedents. He is therefore the founder of classical logic, also said to be Aristotelian logic, to be meant as a symbolic way to conduct formal reasoning.

Aristotelian logical theories analyse the discourse, that is to say, they spring out from the formal analysis of language, distinguishing, into a sentence or proposition, terms or concepts (i.e., noun and verb) in dependence on subject and predicate, and their relative internal position. Furthermore, in dependence on their quality and quantity, the propositions are classified according to their possible logical interrelationships, so giving rise to the known Aristotelian square of opposition, and identifying certain conversion laws ruling the derivation of propositions from others.

Aristotle’s main contribution is on the theory of proof, in which he discusses inferences. In particular, it is in the Prior Analytics that Aristotle discusses the theory of inferences, giving pre-eminence to the syllogistic inference, deemed to be the logical mechanism par excellence. Then, he discusses the logical argumentations, distinguishing between dialectic and proof argumentations in dependence on the degree of certainty of the premises; both these two types of argumentation are however carried on according to a common logical mechanism, that of syllogistic inference.

The Megarian-Stoical school then privileges the analysis of the persuasive discourse from a logical standpoint, distinguishing between rhetoric and dialectics, and giving pre-eminence to sentences rather than to argumentations, so developing a refined analysis of logical connectives. This school privileges the study of the possible relationships amongst sentences related to each other through logical connectives, makes a distinction between validity and truth, as well as between argument and sentence, and points out the existence of many logical paradoxes.

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