Although there are no extant fragments of the writings of Pythagoras, his views were influential in the ancient world and have been referred to by a number of philosophical writers, among them Plato, Aristotle, Porphyry, and Diogenes Laërtius. As one might expect, the accounts are not entirely consistent, and it is often difficult to determine precisely or even approximately what view Pythagoras held on a question under discussion, but there is a body of beliefs that critics generally attribute to Pythagoras or to his followers. The followers are generally assumed either to have inherited the master’s views or to have been inspired by his philosophy and practice to develop their ideas along lines that have a distinctive inherited character.

Pythagoras (like many ancient Greek philosophers) did not distinguish his metaphysical convictions from his beliefs about the physical world: His ontology (theory of being), cosmology (theory of cosmic origin and development), epistemology (theory of knowledge), theology, and ethics appear to be grounded in certain abstract mathematical ideas and beliefs and to be interrelated.

Number as a Basis

According to Aristotle, the Pythagoreans believed that all things are numbers in the sense that the principles of numbers are the principles of all things. “There is but one number, the mathematical,” is a view attributed to Pythagoras by Aristotle, together with the related propositions that all objects of sense are numbers and that numbers are prior, both in power and existence, as well as logically, to physical objects. Accordingly, the Pythagoreans differed from the Milesian philosophers, who found in water, fire, or earth the fundamental substance and cause of things; for the Pythagoreans, the primary cause and substance of all things is number. Not only physical things but also justice and the other virtues, as well as the soul and reason, are in principle and composition numbers. The early writers attributed this philosophical tendency of Pythagoras and his followers—the tendency to take number as primary, creative essence and substance—to the Pythagoreans’ having noticed similarities between numbers and objects of sense (although it is not clear what sorts of relationships counted as similarities). Thus, Aristotle writes, “They see many qualities of numbers in bodies perceived by sense” and “in numbers, . . . they thought they saw many likenesses to things that are and that are coming to be.”

No doubt part of the belief in the creative power of numbers stemmed from the discovery of the numerical ratios involved in musical harmony. If numbers...

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The Origin of the Universe

The Pythagorean account of the origin of the universe as an ordered system consistently accords to numbers the power of generation and the essential determination of the direction and quality of world order. According to Aristotle in Physica (second Athenian period, 335-323 b.c.e.; Physics, 1812), the Pythagoreans argued that void entered into heaven, which breathed it in from the Unlimited. Somehow “void defines the nature of things,” and first of all defined numbers. Void is described as “a kind of separating and distinguishing factor between terms in a series.” (It is not clear from Aristotle’s account—and perhaps it was not clear to Aristotle—whether the Pythagoreans believed that number was somehow in void and then drawn out of void by a movement, like breathing, stemming from a resolution of tension between the limited and the unlimited, or that void somehow actually gave rise to number. In any case, the universe results from the forming power of number, according to the Pythagoreans.)

Aristotle remarks that although the common belief is that the earth is at the center of the universe, the Pythagoreans (who were dedicated astronomers) believed that a central fire is the center and that the earth creates day and night by circling about this fire. Fire as the center of space, matter, and nature also was regarded as the authoritative guard of all being, “the guard of Zeus.”


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Hippolytus’s View

Hippolytus speaks of the Pythagoreans as combining astromony, geometry, and music in their study of nature. He reports that Pythagoras claimed that God is a monad, and he mentions the Pythagorean belief that the universe is melodic and that the stars move rhythmically and hence melodiously. For the Pythagoreans, Hippolytus continues, number is the first principle, and this first principle is a male monad in substance, “begetting as a father all other numbers.” The dyad is female, the triad male; that is, even is female; odd is male. All numbers are fours, and four generates ten, the perfect number. (If one adds the numbers 1, 2, 3, and 4, the total is 10.) The four parts of the decad—number, monad, power, and cube—by combining, account for all growth.

Hippolytus also calls attention to the Pythagorean belief in the immortality of the soul and in the soul’s moving from one body to another. (He mentions the Pythagorean prohibition against the eating of beans because “at the beginning and composition of all things when the earth was still a whole, the bean arose.”)

Others on Pythagoras

The Neoplatonic philosopher Proclus alludes to the Pythagorean discovery that the square of the hypotenuse of a right-angle triangle is equal to the sum of the squares of the other two sides. (The Pythagorean practice of arranging units or “dots” in squares may have contributed to some of their mathematical discoveries as well as to their metaphysical conviction that all things are numbers. As the Greek philosopher Speusippus points out, for the Pythagoreans 1 is the point, 2 is the line, 3 is the triangle, and 4 is the pyramid. The tetraktys, a triangle with a four dot base, then a line of three, then two, then one dot—making ten in all—was a key figure.)

Religious Beliefs and Practices

The Pythagoreans were subject to a number of rules of considerable moral and religious importance but hardly of philosophical significance (such as “Stir not the fire with iron,” “Speak not of Pythagorean matters without light,” and “Let not a swallow nest under your roof”). These rules, together with others—such as the prohibitions against the eating of flesh and beans and against the sacrifice of animals—stem from certain beliefs involved in the religion of the Pythagoreans as influenced by Orphism (the cult of Orpheus). The strictures against the eating of flesh and the sacrifice of animals, for example, are required by the belief in the transmigration of souls.

The moral emphasis in religious beliefs...

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(Student Guide to World Philosophy)

Additional Reading

Bamford, Christopher, ed. Homage to Pythagoras: Rediscovering Sacred Science. Hudson, N.Y.: Lindisfarne Press, 1994. This collection of essays touches on Pythagoras’s ideas as they affect architecture and religion, among other topics. Includes bibliography.

Boudouris, K. I., ed. Pythagorean Philosophy. Athens: International Center for Greek Philosophy and Culture, 1992. This volume examines Pythagoras and the Pythagorean school. Includes bibliography.

Burkert, Walter. Lore and Science in Ancient Pythagoreanism. Translated by Edwin L. Minar, Jr. Cambridge,...

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