Chapter

Around and Beyond the Square of Opposition

Part of the series Studies in Universal Logic pp 229-239

Privations, Negations and the Square: Basic Elements of a Logic of Privations

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Abstract

I try to explain the difference between three kinds of negation: external negation, negation of the predicate and privation. Further I use polygons of opposition as heuristic devices to show that a logic which contains all three mentioned kinds of negation must be a fragment of a Łukasiewicz-four-valued predicate logic. I show, further, that, this analysis can be elaborated so as to comprise additional kinds of privation. This would increase the truth-values in question and bring fragments of (more generally speaking) Łukasiewicz-n-valued predicate logics into the scene.

Keywords

Privation Negation Łukasiewicz-n-valued predicate logic

Mathematics Subject Classification

03B65 03B50