According to M. Wedin, R. M. Dancy and C. Kirwan, Aristotle does not restrict the range of the Principle of Non-Contradiction to essential sentences about substances. The reason for this is that the Principle lies on the universal character of per se-being and on each thing’s essence. Contrary to this opinion, I will argue that the PNC is bound to the semantic of substantial predicates. I will analyse two main arguments from Metaphysics Γ 4, and will make explicit some ontological and semantical consequences arising from these arguments.