In Difesa del Principio di Non Contraddizione

The essential purpose of this thesis is to defend the law of non contradiction (LNC) from the threat of dialetheism, according to which there are true contradictions. The first chapter assesses the main terms involved in the matter, establishing what (LNC) is and what a contradiction is. Will be distinguished five fundamental versions of (LNC) and of contradiction, and will be underlined the importance in each one of them of the condition of the identity of parameters. The second chapter introduces what is traditionally considered the strongest argument against contradictions: the principle ex contraditione quodlibet (ECQ). An introduction to paraconsistent logic, dialetheism and their relationship follows. Then will be presented several systems of paraconsistent logic, to show that different attempts to model contradictions are all destined to fail, despite their peculiarities, because they all violate the condition of the identity of parameters. The beginning of chapter three examines Graham Priest’s paraconsistent logic, arguing that it’s superior to every one of those discussed in chapter two. Then will be introduced two arguments against paraconsistent logic developed by David Lewis and Hartley Slater, and the rejoinders given by Bryson Brown, Francesco Paoli and Greg Restall. I strengthen Restall’s defense of paraconsistency. My contribution leads to the general dilemma for the defender of (ECQ). The fourth chapter is preliminary to the real defense of LNC, which is the focus of chapter five. Here the purpose is to discuss if defending (LNC) is possible. After showing where the recurring charge of the impossibility to criticize dialetheism comes from, I will recall Graham Priest’s strategy to overcome it. Then the attention moves to some observations made by Dutilh Novaes, which raise the suspect that the debate between the dialetheist and the defender of LNC is a verbal dispute. I will show that her crucial assumption is wrong. In chapter fifth I present my two attacks against dialetheism. The first one shows that one is rationally justified to reject every contradiction in every circumstance, and this justifies the rejection of dialetheism. The second attack starts granting the existence of sentences of the form "alfa",¬"alfa" which are both true, and proceeds proving that if sentences of the form "alfa",¬"alfa" are both true, then they cannot be contradictory, hence there cannot be contradictions which are true.