EvSocja: from Aristotle's Topics to Fuzzy Logic

In this article, the author interprets Aristotle’s Topics as a kind of informal fuzzy logic. Since the time of Aristotle, there has been a distinction between real and apparent proofs. Galen of Pergamum noticed that some concepts have vague boundaries and fuzzy edges, and, consequently, as it was added by G. Lakoff, natural language sentences will very often be neither true nor false nor nonsensical, but rather true to a certain extent and false to a certain extent. As it is known, Topics contains the theory of dialectical discourse, which, as the author shows, is aimed at the study and use of fuzzy thinking and vague patterns of argumentation. After Topics, there has been a rich tradition of investigating reasoning and argumentation with approximate certainty. It is noteworthy that Alexander of Aphro-disias, the “chief imperial logician” and head of the Peripatetic school, treats Topics as a textbook for practising philosophers. This indicates that Topics was devised as a special philosophical tool designed both for communicative-dialectical counteraction between agents and for capturing vague content of ἔνδοξα. The key concepts of Topics are ἔνδοξα and πρότασις διαλεκτική. The latter can be represented as a fuzzy 6-valued truth-likelihood matrix (f), according to which the dialectical proposition accords with the opinion held by everyone (p1), or by the majority (p2), or by the wise (p3), or all of the wise (p4), or the majority (p5), or the most famous of them (p6), and which is not paradoxical. The likely or plausible here is ένδοξος. The epistemological guarantors of the likely truth (f) of some propositions (q) are elements of the disjunctive set E: {p1 ∨ p2 ∨ p3 ∨ p4 ∨ p5 ∨ p6}. All the disjuncts can be inter-preted as possible worlds. Obviously, (f) = fuzzy 1 if the disjunction E is true. Also, what is true for the wise (p3), or for the most famous (p6), may be false for the majority (p2). Thus, (f) is vague. Topics can be considered as a kind of informal fuzzy logic. When Lotfi A. Zadeh raised the question of approximate reasoning, he, in many ways, pursued Aristotle’s idea of construing a crisp discourse to deal with the fuzzy one. In fact, any concept of Topics within the framework of ἔνδοξα can be denoted as a fuzzy set because for each individual (X) there is a fuzzy membership function μX(y) from 0 to 1. Fuzzy membership function and fuzzy set jointly determine the lack of semantic precision described by Galen as the uncertainty of concepts.

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