Abstract

The thesis of this dissertation is an interweaving relation of three factors. First is the contention that Plato employed and taught a method of logical discovery, or analysis, long before Charles Sanders Peirce rediscovered the fundamental mechanics of the procedure, the latter naming it abduction. Second, Plato was in essential respects a follower of the Pythagorean mathematical tradition of philosophy. As such, he mirrored the secrecy of his predecessors by avoiding the use of explicit doctrinal writings. Rather, his manner was obstetric, expecting the readers of his dialogues to abduct the proper solutions to the problems and puzzles presented therein. Third, as a Pythagorean, he saw number, ratio, and proportion as the essential underlying nature of things. In particular he saw the role of the golden section as fundamental in the structure and aesthetics of the Cosmos. ;Plato was much more strongly influenced by the Pythagoreans than is generally acknowledged by modern scholars. The evidence of the mathematical nature of his unwritten lectures, his disparagement of written doctrine, the mathematical nature of the work in the Academy, the mathematical hints embedded in the "divided line" and the Timaeus, and Aristotle's references to a doctrine of mathematicals intermediate between the Forms and sensible things, tend to bear this out. In his method of analysis, Plato would reason backwards to a hypothesis which would explain an anomalous phenomenon or theoretical dilemma. In many ways Plato penetrated deeper into the mystery of numbers than anyone since his time. This dissertation is intended to direct attention to Plato's unwritten doctrines, which centered around the use of analysis to divine the mathematical nature of the Cosmos