Beyond the hypothesis
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Plato has Socrates give a formulation of the Principle of Non-contradiction (PNC) in book IV of the Republic. The principle is used as a premise in an argument which divides the soul. Plato’s use of the principle has convinced most scholars that he endorses PNC. However, the endorsement in the text is qualified. Socrates refers to the principle as one that he and his interlocutors will hypothesize and he warns that if it be shown to be false all that follows from it will also be refuted. We view principles like PNC as belonging solely to logic. Plato does not. He does not have a realm for logic separate from those of being and becoming. This allows Plato to effectively reformulate the problem of the justification of PNC. The question for Plato has to do with scope: To what thing or things does PNC apply? In my dissertation I argue that Plato takes the principle to follow from and be grounded in the unity of form. The application of PNC presupposes the existence of some one thing to which to apply the principle and to which the principle in some sense belongs. As the oneness of things is in all cases a consequence of form, this would make PNC dependent on form. Yet, although PNC follows from form it cannot, I argue, be applied to form itself by itself. Rather, I will argue that PNC applies most properly to soul. This means that an investigation into PNC is also an investigation into the unity of the soul. That the soul in question belongs to the one capable of doing the hypothesizing is of no small relevance.