Philosophy, Sophistry and Mathematics: A Meditation on Theodorus, the Geometer in Plato's "Theaetetus"
Dissertation, University of California, San Diego (
1996)
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Abstract
The striking fact that Plato's philosophic works consist solely of dialogues--that is, of dramatic representations of philosophic matters--necessarily raises the issue of the importance of such dramatic elements to an understanding of Plato's thought. This study focuses on the Theaetetus, a dialogue predominately concerned with an investigation of the question, "what is knowledge?" and the strange and wonderful presence of the elder mathematician/geometer, Theodorus. Plato portrays Theodorus as being both technically capable and eminent as a mathematician/geometer and as being profoundly mistrustful and disdainful of, and terrifically resistant to, philosophic discussion. However, in the portion of the Theaetetus that has been dubbed the "digression," Socrates seems to accomplish the remarkable feat of a wholesale and wildly enthusiastic conversion of Theaetetus to philosophy. ;This study argues that the conversion of Theodorus is a dramatic representation of, on the one hand, the dangers attendant to the abandonment of philosophic inquiry in favor of the seemingly more productive and useful allure of technical discourse and, on the other, the deeply false and pernicious nature of Protagorean wisdom. The doctrine of radical perspectivism, as attributed to the sophist Protagoras by Socrates in the Theaetetus, permeates the dialogue, represented most blatantly by Socrates equating Theaetetus' first definition of knowledge with Protagoras' doctrine of homo mensura and by the three defenses of Protagorean doctrine that Socrates presents. Developing the similarities between such Protagorean doctrine and Frederick Nietzsche's doctrine of the will to power, this study explores the claim of radical perspectivism to appropriate discourse by reducing speech to the mere generation of opinions, none of which can be certified as more excellent than the other. This study concludes that the dramatic dynamics brought together by Plato in the digression--in which Socrates, Theodorus and Socrates in the guise of a Protagorean wise man are arrayed--permit Plato to exhibit the psychic deficiencies of a thinker whose embrace of technicism has rendered him vulnerable to sophistic manipulation and the false and deleterious effects of a doctrine that cannot account for the difference between mere opinion and actuality