Round squares are no contradictions (Tutorial on negation contradiction and opposition)

Abstract

We investigate the notion of contradiction taking as a central point the idea of a round square. After discussing the question of images of contradiction, related to the contest Picturing Contradiction, we explain why from the point of view of the theory of opposition, a round square is not a contradiction. We then draw a parallel between different kinds of oppositions and different kinds of negations. We explain why from this perspective, when we have a paraconsistent negation ￢, the formulas p and ￢p cannot be considered as forming a contradiction. We finally introduce the notions of paranormal negation and opposition which may catch the concept of a round square.