Once again William Connolley has set me on a path I hadn't really intended to take, in this case reading Bertrand Russell's History of Western Philosophy. Well, it seems that it is a really good book, not only entertainingly written but full of fresh insights. Not long ago I took a course in Ancient Greek Philosophy, and while Pythagoras got some ink, he was definitely consigned to the minor leagues by my prof and the author of my textbook.
Russell puts him and his mathematical and mystical notions at or near the center of all subsequent thought, especially Plato, the Christian philosophers, and even Newton. Russell, unlike my teachers, was a mathematician, and this allows him to see threads of thought hidden from the enumerate.
The influence of geometry upon philosophy and scientific method has been profound. Geometry, as established by the Greeks, starts with axioms which are (or are deemed to be) self-evident, and proceeds, by deductive reasoning, to arrive at theorems that are very far from self-evident. The axioms and theorems are held to be true of actual space, which is something given in experience. It thus appeared to be possible to discover things about the actual world by first noticing what is self-evident and then using deduction. This view influenced Plato and Kant, and most of the intermediate philosophers. When the Declaration of Independence says “we hold these truths to be self-evident,” it is modelling itself on Euclid. The eighteenth-century doctrine of natural rights is a search for Euclidean axioms in politics.VIII The form of Newton’s Principia, in spite of its admittedly empirical material, is entirely dominated by Euclid. Theology, in its exact scholastic forms, takes its style from the same source. Personal religion is derived from ecstasy, theology from mathematics; and both are to be found in Pythagoras.
Russell, Bertrand. History of Western Philosophy: And Its Connection with Political and Social Circumstances from the Earliest Times to the Present Day (p. 44). Touchstone. Kindle Edition.