Great Ideas of Philosophy

4. Looking at geometry, we are told that a right-angle triangle has angles totaling 180° and that one of itsangles is 90°. No material rectilinear triangle, however, is perfect, but the relationship a 2 + b 2 = c 2 isperfect and eternal.5. There is a wonderful correspondence between the realm of matter and that of abstraction. Oftenmathematical abstractions predate physical discoveries which, however, they describe exactly. Ourwonder at this, and our sense that it is no coincidence, are Pythagorean.E. If we take the creative force behind all existing things to be a divine force, then we can only conclude thatnumber is a kind of divinity, that number, in its abstract, transcendental nature, is divine.F. Consider, however, numbers that do not match up with anything material, such as π or − 1 . Nonetheless,π is needed to calculate the circumference of a circle.1. For the Pythagoreans, coincidence cannot explain this. Further, the odds are long that a mathematicianwould come up with a complex equation that, 200 or 300 years later, would perfectly explain somebrute physical fact.2. Such occurrences, then, must express some plan. The ultimate plan must be abstract but capable ofgenerating the physical reality. The abstract plan must also be a plan of relationships.III. What kind of governor was Pythagoras? The answer is: “not successful.”A. The people of Crotona ultimately staged riots in reaction to Pythagoras’s “old-time religion.”B. How could Pythagoras be a man of affairs at all? Is politics the sort of activity in which a philosopherengages?1. As Aristotle teaches, we seek precision only insofar as the subject allows it. There could be noPythagorean theorem for political life.2. A philosophically guided state is unlikely to survive the reality in which it finds itself.C. What can we say about Pythagoras as “first philosopher,” a title that he arrogated to himself?1. The word philosophy means “love of wisdom.”2. The Greeks had several words for intelligence or knowledge, some denoting scientific knowledge andsome, practical knowledge.3. Sophia, however, was what the wise person possessed, the person who delves into core questionsabout the meaning of life.4. Pythagoras appropriately called himself a philosopher because he devoted himself to an inquiryserving the purposes of knowledge. He sought to discover what it is that makes anything possible andreal and, as in chemistry and particle physics today, found the answer in number.Recommended Reading:Fideler, D. ed. The Pythagorean Sourcebook and Library. Phanes Press, 1987.Questions to Consider:1. Summarize in what ways Pythagorean “numerology” is like and unlike modern mathematical models of reality.2. Explain the striking agreement found between abstract mathematics and actually occurring natural items.8©2004 The Teaching Company Limited Partnership