Abstract
Not the least among the many puzzling features of the fourth book of Aristotle's Metaphysics is his discussion of the Principle of Non-Contradiction (hereafter ‘PNC’). Even leaving aside the obvious difficulty of determining what his arguments succeed in showing about PNC, we face the more fundamental problem of figuring out what he takes them to show. For he proceeds in such a way as to suggest that he is not always completely clear about what he is up to.Aristotle seems to be offering arguments in support of PNC. Yet to do so would be to try to demonstrate something he considers indemonstrable, to prove a first principle, to treat an ultimate explanans as also an explanandum – and to try to explain it. These maneuvers fly in the face of the teachings of the Organon, which allow no room for a demonstration, or proof (apodeixis), of PNC.
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