https://plato.stanford.edu/entries/aristotle-noncontradiction/

 

Stanford Encyclopedia of Philosophy

 

Aristotle on Non-contradiction

First published Fri Feb 2, 2007

According to Aristotle, first philosophy, or metaphysics, deals with ontology and first principles, of which the principle (or law) of non-contradiction is the firmest. Aristotle says that without the principle of non-contradiction we could not know anything that we do know. Presumably, we could not demarcate the subject matter of any of the special sciences, for example, biology or mathematics, and we would not be able to distinguish between what something is, for example a human being or a rabbit, and what it is like, for example pale or white. Aristotle's own distinction between essence and accident would be impossible to draw, and the inability to draw distinctions in general would make rational discussion impossible. According to Aristotle, the principle of non-contradiction is a principle of scientific inquiry, reasoning and communication that we cannot do without.

Aristotle's main and most famous discussion of the principle of non-contradiction occurs in Metaphysics IV (Gamma) 36, especially 4. There are also snippets of discussion about the principle of non-contradiction early in the corpus, for example in De Interpretatione, and there is the obscure chapter 11 of Posterior Analytics I, but none of these rival Aristotle's treatment of the principle of non-contradiction in Metaphysics IV. The discussion below mostly concerns the main interpretative and philosophical issues that arise from reading Metaphysics IV 36.

Aristotle's discussion of the principle of non-contradiction also raises thorny issues in many areas of modern philosophy, for example, questions about what we are committed to by our beliefs, the relationship between language, thought and the world, and the status of transcendental arguments. Arguments from conflicting appearances have proved remarkably long-lived, and debates about skepticism, realism and anti-realism continue to this day.