The Pythagorean Plato And The Golden Section:
A Study In
Scott Anthony Olsen
Source: DAI, 45, no. 04A, (1983): 1132
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.