A History of Western Philosophy | Study Guide

Bertrand Russell

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A History of Western Philosophy | Book 1, Part 2, Chapter 24 : Ancient Philosophy (Socrates, Plato, and Aristotle) | Summary



Book 1, Part 2, Chapter 24: Early Greek Mathematics and Astronomy

Russell notes that the Greeks worked out early mathematical concepts and studied irrational numbers, which leads to a geometrical theory of proportion. Euclid (c. 300 BCE) wrote a textbook of geometry (Elements) that is still in use in the modern era. While most of Euclid's textbook is not original, the order of propositions and structure belongs to him. In Russell's view Elements is "one of the most perfect monuments of the Greek intellect."

Aristarchus of Samos first came up with the idea of a heliocentric (sun-centered) solar system and calculated Earth rotates on its axis every 24 hours. Copernicus knew something of Aristarchus's theory when he fashioned his own similar theory centuries later. The Greek picture of the solar system "was not so very far from the truth," says Russell. Nonetheless, the Greek astronomers imagined the planets were fixed together and moved together. The two great mathematicians, Archimedes (c. 287–12 BCE) and Apollonius (c. 240–190 BCE), were the last great men in a great age of philosophy, says Russell. After the Roman conquest the Greeks lost their self-confidence, which belongs to political liberty.


Russell notes that the Greeks were preeminent in mathematics and astronomy, but in fact the Indians and Chinese had uncovered some of the same principles as the Greeks in other parts of the world. The Hellenistic period is bookmarked by the death of Alexander the Great (323 BCE) and the ascendency of the first Roman emperor Octavian, soon to be called Augustus, who defeated his rivals and became sole ruler of the empire (27 BCE). The Greeks were conquered by the Romans in 146 BCE, and according to Russell, "the Roman soldier who killed Archimedes was a symbol of the death of original thought that Rome caused throughout the Hellenic world." Such a statement on Russell's part seems something of an exaggeration. The Romans rebuilt Greek cities after their conquest and preserved Greek culture. They patronized Greek intellectuals since they were enamored of the Greeks and appropriated much of their culture wholesale. Philosophy continued in the Greek world, although it was more eclectic and diverse than in earlier days.

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