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Aporia and Insight in Plato’s Parmenides

The hypotheses in Plato’s Parmenides, fascinating and seemingly obscure, are the subject to various interpretations: some argue that they present Plato’s late ontology, or emphasize a transition away from an earlier view of forms (e.g., Ryle, Rist, Kahn, Vlastos, Meinwald); some argue that the hypotheses are deeply ironic (Taylor, Rosen); and others, following the neoplatonic tradition, emphasize the eminence of the “one” of the first hypothesis (Proclus, Plotinus). I argue that the hypotheses should be seen aligned with the first part of the dialogue, namely, as an exercise program demonstrated for young Socrates. This view runs counter to those who would separate the first section from the second (Ryle) or who prioritize the third man argument over the structure of the whole (Vlastos). Such a demonstration is intended to help Socrates, and similarly, students of the dialogue, to overcome the aporiai that occur when trying to define forms in terms of participant individuals. This view is supported by Miller and more recently Sanday, but examines more specifically the under-appreciated explicitly educational aspect of the work. The hypotheses, I argue, are a propaedeutic for young philosophical learners, following from the example of Socrates, who, in the dialogue is himself a young learner, and is given a salutary exercise. The presentation of contradictory conclusions in juxtaposed hypotheses serve to provoke thought from the learner in such a way that the he or she can reconsider the nature of a form as radically different from that which a form articulates, namely, a participant example.
A clue to understanding the propaedeutic function of contradiction, I claim, can be seen in Socrates’ presentation to Glaucon concerning philosophical education in book VII of Plato’s Republic: Socrates here famously discusses with Glaucon an educational program of study that would guide a practitioner towards dialectic and the forms. During this illustration, Socrates has Glaucon consider three fingers [Rep. 523b]. With respect to largeness and smallness, the fingers appear to reveal a contradiction: the middle sized finger is large with respect to the smaller one, and small with respect to the larger one — seemingly both small and large. While the example is basic, such a contradiction or aporia, claims Socrates, summons insight (noesis) in order to disarm the contradiction [Rep. 523e]. I argue that this thought summoning in the Republic is also employed and moreover, explicated in the hypotheses demonstrated to young Socrates in the Parmenides. By examining the structure of the first two hypotheses in particular [Parm. 137c-157b], I show not only that the hypotheses demonstrate a crucial educational function of summoning thought and insight (noesis) for the young Socrates that is similar to the more basic one proposed to Glaucon, but also that they function as an educational propaedeutic for the figure of Socrates as a young learner, and for students of the Parmenides.