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THE DUNS SCOTUS LAW: A CLASSICAL SOLUTION TO THE PARADOX OF MATERIAL IMPLICATION

A. S. Zamorev, V. V. Khlystenko

Abstract

The paper focuses on the paradox of material implication with the special reference to the Duns Scotus Law associated therewith. The article contains two different proofs of this law. The paper also seeks to evaluate the role of this law in the proof theory and the damage caused to the latter by the multitude of non-classical approaches in logic which call this law into question. The paper also addresses the conditions upon which the statements about empty sets are possible and evaluates the relevance of material implication, in particular, implication based on inconsistent premises. The paper deals with defining the boundaries for applicability of three basic laws of AristotleВ’s logic, according to the works of Aristotle himself. The basic paradoxes, connected to the violation of these boundaries, are also considered in the article. The conclusions are as following: 1) there is no need in distinguishing between material, strict or relevant implication, since the truth of any implication is determined only by the validity of the propositions it consists of, according to the classical truth table. 2) neither two-valued logic nor three-valued logic is able to escape the paradox of implication, since the first one allows making absurd conclusions based on inconsistent premises, while the second does not allow making true conclusions at all. 3) for solving the problem at least four-valued logic is required which was the classical AristotleВ’s logic; according to the latter, the Duns Scotus Law is true, however, only as a principle of proof by contradiction.

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DOI resolver: doi.org/10.5593/sgemsocial2018H/21/S06.045

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