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Working paper

Questions and Answers about Oppositions

The Square of Opposition (A General Framework for Cognition). ISBN 978-3-0343-0537. Peter Lang - Editions Scientifiques Internationales, 2012
A general characterization of logical opposition is given in the present paper, where oppositions are defined by specific answers in an algebraic question-answer game. It is shown that opposition is essentially a semantic relation of truth-values between syntactic opposites, before generalizing the theory of opposition from the initial Apuleian square to a variety of alternative geometrical representation. In the light of this generalization, the famous problem of existential import is traced back to an ambiguous interpretation of assertoric sentences in Aristotle's traditional logic. Following Abelard's distinction between two alternative readings of the O-vertex: Non omnis and Quidam non, a logical difference is made between negation and denial by means of a more fine-grained analysis. A consistent treatment of assertoric oppositions is thus made possible by an underlying abstract theory of logical opposition, where the central concept is negation. A parallel is finally drawn between opposition and consequence, laying the ground for future works on an abstract operator of opposition that would charcterize logical negation just as does Tarski's operator of consequence for logical truth.