In G. R. F. Ferrari (ed.), The Cambridge Companion to Plato's Republic. Cambridge University Press. pp. 310--344 (2007)

Mitchell Miller
Vassar College
At 435c-d and 504b ff., Socrates indicates that there is a "longer and fuller way" that one must take in order to get "the best possible view" of the soul and its virtues. But Plato does not have him take this "longer way." Instead Socrates restricts himself to an indirect indication of its goals by his images of sun, line, and cave and to a programmatic outline of its first phase, the five mathematical studies. Doesn't this pointed restraint function as a provocation, moving us to want to begin the "longer way" and to make use of its conceptual resources to rethink Socrates' images? I begin by finding a double movement in the complex trajectory of the five studies: they both guide the soul in the "turn away from what is coming to be ... [to] what is" (518c) and, at the same time, lead the soul back, albeit in the medium of pure intelligibility, to the sensible world; for the pure figures and ratios that they disclose constitute the core structures of sensible things. I then draw on what Socrates says about geometry and harmonics to address three fundamental questions that he leaves open: the nature of the Good in its responsibility for truth and for the being of the forms; the relations of forms, mathematicals, and sensibles as these are disclosed by dialectic; and the bearing of the philosopher's discovery of the Good on his disposition towards his community and the task of ruling. I close by marking six sets of further questions that these reflections bequeath for dialogues to come.
Keywords longer way  Plato  Republic  mathematics  the Good
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References found in this work BETA

The Third Man Argument in the Parmenides.Gregory Vlastos - 1954 - Philosophical Review 63 (3):319-349.
Greek Mathematical Thought and the Origin of Algebra.Jacob Klein, Eva Brann & J. Winfree Smith - 1969 - British Journal for the Philosophy of Science 20 (4):374-375.
A Commentary on Plato's Meno.Jacob Klein - 1965 - University of Chicago Press.

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Citations of this work BETA

Mathematics, Mental Imagery, and Ontology: A New Interpretation of the Divided Line.Miriam Byrd - 2018 - International Journal of the Platonic Tradition 12 (2):111-131.
The Supremacy of Dialectic in Plato’s Philebus.George Harvey - 2012 - Ancient Philosophy 32 (2):279-301.
The Unorthodox Theory of Forms in Plato's Philebus.James Wood - 2017 - Journal of Ancient Philosophy 11 (2):45.

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