Massimiliano Carrara

University of Padua

Denial: a Logic, a Paradox and a Dilemma

10 November 2017, 16:00

Faculdade de Letras de Lisboa

Sala Mattos Romão (Departamento de Filosofia)

Abstract: How glut-theorists may express disagreement with the assertion of A if Boolean negation cannot be expressed in their language? A glut-theorist’s answer is by denying or rejecting A: To make up for the lack of exclusive negation, a glut-theorist like Priest introduces the notion of denial or rejection of a sentence, understood as a speech act, as clearly distinguished from the acceptance of the negation of A. I argue that the proposal meets some difficulties: the reason is that if the exclusivity of negation is the key to solving the semantic paradoxes, the exclusivity of denial/rejection land us back in paradox. I sketch a bilateral logic of exclusive denial for glut theorists – an extension of the Logic of Paradox (LP) and I observe that exclusive deniability – a key semantic notion of the logic – is not expressible in a dialetheist’s language. I conclude that glut theorists are faced with a dilemma: either denial can serve as means to express disagreement, but the notion of exclusive deniability is not expressible in the glut theorist’s language, or deniability is expressible, but denial may no longer serve as a means to express disagreement.