ARISTOTLE'S PROGRAM Aristotle says outright that the law of non-contradiction cannot be demonstrated: you can't prove everything, and among the things you ...

Aristotle Categoriae et Liber de Interpretatione.

The so called “elenctic” defense of the principle of non-contradiction in Metaphysics Γ4 will succed if only the opponent will say something. The strategy consists in showing that, in speaking, the opponent has al- ready accepted the principle. Given the structure of the argument, the only way to avoid begging the question is not to ask from the opponent any commitment exceeding the conditions of mere meanigfullness of speech. In particular, it is specially important to avoid any reliance on Aristotelian (...) essentialism. A reading which is in accordance with these requirements will hold that the core of the proof consists in showing that meaning something amounts to singling out a meaning. The mere aim of telling what is within from what is without the bounds imposed on speech of any complexity is enough to show that the speaker accepts the principle of non-contradiction. One is thereby not required to commit oneself to any particular description of reality. Nonetheless, the extention of this result to the conditions of predication will pave the way for the develop- ment of the science of being as being. (shrink)

My object is Aristotle's discussion of principle of non-contradiction in the first stretch of Metaphysics IV.4. My main focus rests on the connections between Aristotle's discussion of the principle and some key notions of his (explicit or implied) semantics.

One crucial part of the Aristotle´s discussion of the principle of non-contradiction in Metaphysics IV 4 is his notion of semainein hen, which must be carefully distinguished from the closely connected notion of semainein kath´ henos. The Aristotelian proof is located at 1006b28-34 and it is argued that it does not suppose any bit of essentialism nor does it contain any petitio principii; some improvements are further proposed to the current translations.