A History of Western Philosophy | Study Guide

Bertrand Russell

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A History of Western Philosophy | Book 1, Part 1, Chapters 3–6 : Ancient Philosophy (The Pre-Socratics) | Summary



Book 1, Part 1, Chapter 3: Pythagoras

According to Bertrand Russell, Pythagoras is one of the most important men who ever lived. "Mathematics, in the sense of demonstrative deductive argument, begins with him, and in him is intimately connected with a peculiar form of mysticism." Russell says Pythagoras was partially responsible for the unfortunate influence of mathematics on philosophy. Pythagoras founded a religion and taught that the soul is immortal and transmigrates from life to life. In his circle of discipleship, he admitted men and women equally, and they held property in common.

From Pythagoras came the idea that pure mathematics is the result of intuitive thought, and much that is "mistaken in metaphysics and theory of knowledge" began with Pythagoras, says Russell. Pythagoras's greatest discovery was that the square of the length of the longest side of a right triangle (the hypotenuse) is equal to the sum of the square of the other two sides of the triangle. The Pythagorean Theorem raised other problems, which led the Greeks to establish geometry as a study separate from arithmetic. Geometry, in its turn, had a profound influence on philosophy and the scientific method, since it begins with self-evident axioms and proceeds with deductive reasoning to arrive at theorems that are not self-evident. Russell claims mathematics is "the chief source of the belief in eternal and exact truth, as well as in a super-sensible intelligible world." This combination of mathematics and theology influenced philosophy down through the philosopher Immanuel Kant.

Book 1, Part 1, Chapter 4: Heraclitus

Bertrand Russell begins Chapter 4 by acknowledging the importance of geometry to modern science but also says the Greeks relied too heavily on deductive reasoning; only slowly did inductive reasoning based on observation take its rightful place in scientific thought. The philosopher Xenophanes, who came between Pythagoras and Heraclitus, believed all things are made of earth and water. He also believed in one God unlike human beings in form and thought. Russell calls him an early rationalist. Heraclitus is famous for his doctrine "everything is in a state of flux." Heraclitus believed in war and strife as inevitable and necessary, and Russell compares him to Friedrich Nietzsche. "Heraclitus values power obtained through self-mastery, and despises the passions that distract men from their central ambitions," says Russell. Heraclitus also believed in the importance of mingling opposites, prefiguring the German philosopher Georg Wilhelm Friedrich Hegel in this regard.

Book 1, Part 1, Chapter 5: Parmenides

While Heraclitus taught everything changes, Parmenides said nothing changes. Parmenides is known for inventing a metaphysics based on logic. According to this philosopher, sensible things are an illusion, and the only thing with true being is "the One," which is "material and extended," even though it cannot be divided. In Parmenides's metaphysics, anything that can be thought or spoken "must exist at all times." This is why he says nothing changes. In the case of imaginary objects, what is "real" is that something is imagined and named. What subsequent philosophers took from Parmenides is the idea that substance is indestructible, although the word substance does not enter philosophical vocabulary until much later. The idea of substance as a "persistent subject of varying predicates" became a ruling idea "for more than two thousand years," says Russell.

Book 1, Part 1, Chapter 6: Empedocles

Empedocles also lived in the 5th century BCE and is remembered for "his discovery of air as a separate substance," which he proves by showing that a bucket or similar vessel put upside down in water does not fill up with water. Empedocles claims that the four elements of earth, air, fire, and water are everlasting and "could be mixed in different proportions" to produce the myriad substances found in the world. Empedocles believes nature is "regulated by chance and necessity rather than by purpose," and in that respect he is more scientific than religious.


Early Greek philosophers are influenced by Asian sources, and most likely by the metaphysics of early Persian (Iranian) texts. Heraclitus and Pythagoras are influenced by Persian religious ideas. While monotheism is thought to be a new idea originating in Judeo-Christian religion, Parmenides is expressing a similar idea in his teaching of "the One." Monotheistic ideas also appear in Xenophanes, Plato, and Aristotle. Parmenides is expressing a similar idea in his teaching of "the One." Monotheistic ideas also appear in Xenophanes, Plato, and Aristotle. And while Russell credits Pythagoras for discovering the famous theorem, it is likely that the Babylonians had arrived at the same discovery a least 1,000 years prior. Moreover, proofs of the theorem appear in both Chinese and Indian texts. Nonetheless, it is Pythagoras who established the theorem in Western philosophy and opens the path for Euclid's geometry. Geometry is important for philosophy and the scientific method because the axioms and theorems "are held to be true of actual space, which is something given in experience," Russell explains. This taught philosophers that it was possible to notice something self-evident in the world and then use deduction to find out additional things about the physical world.

Russell claims that the belief in a perfect, intelligible world beyond the senses comes chiefly from mathematics because when things are actually measured, the measurement can never exactly correspond to a mathematical concept. Thus a perfect circle exists only as a concept in geometry. This suggests that "exact reasoning applies to ideal as opposed to sensible objects," further leading to the speculation that thought is higher than sensory data and "objects of thought [are] more real than those of sense-perception." Furthermore, numbers may be viewed as eternal and out of time. Thus, while Russell's view that mathematics inspires theology may at first seem overstated, upon closer inspection it appears valid in the context of how theology evolved in the West. Russell further states that Platonism is nothing but Pythagoreanism—meaning Plato's concept of a world of ideal forms follows from the same presuppositions derived from Pythagoras's view of mathematics.

Russell also lays at Pythagoras's door the addition of mysticism to philosophy, since he was a prophet as well as a mathematician. This assertion on Russell's part also seems reasonable, since many philosophers who follow Pythagoras, from Plato to Kant, do blend "religion and reasoning" as Russell claims, and their "intellectualized theology" is different from the "straightforward mysticism of Asia." It is important to keep in mind that for Russell, the mixing of mathematics and theology and mysticism and philosophy is a bad thing, in the sense that it results in untruths and faulty views of reality. While Russell admires the genius of Pythagoras and appreciates his mathematical discoveries, he finds unfortunate the turn that Western philosophy takes as a result of Pythagoras's views. This is because Russell stands firmly in the empiricist camp and is skeptical of anything that is said to exist outside of the world of sense experience.

Heraclitus said everything is in constant flux, while Parmenides said nothing changes. These opposing views are interesting and important, prefiguring later arguments about space and time that take place in both philosophy and science. Both philosophers are material monists: Heraclitus believed everything originated from fire while Parmenides believed everything originated from "the One." Parmenides is important for being the first to use logic to create a metaphysical system, reasoning that, since everything that exists must be eternal, it follows that nothing changes.

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