SETON HALL UNIVERSITY

IMMACULATE CONCEPTION SCHOOL OF THEOLOGY

Fall Semester, 2009

History of Philosophy

PLTL 1111 AA

THE DIVINITY OF NUMBER:

The Importance of Number in the Philosophy of Pythagoras

by

Br. Paul Phuoc Trong Chu, SDB

Pythagoras and his followers, the Pythagoreans, were profoundly fascinated with numbers. In this paper, I will show that the heart of Pythagoras’ philosophy centers on numbers. As true to the spirit of Pythagoras, I will demonstrate this in seven ways. One, the principle of reality is mathematics and its essence is numbers. Two, odd and even numbers signify the finite and infinite. Three, perfect numbers correspond with virtues. Four, the generation of numbers leads to an understanding of the One, the Divinity. Five, the tetractys is important for understanding reality. Six, the ratio of numbers in the tetractys governs musical harmony. Seven, the laws of harmony explain workings of the material world.

The Pythagoreans “believed that [the principles of mathematics] are the principles of all things that are”. Further, “number is the first of these principles”.[1] “’The numerals of Pythagoras,’ says Porphyry, who lived about 300 A. D., ‘were hieroglyphic symbols, by means whereof he explained all ideas concerning the nature of things…’”[2] In modern time, we can see clearly the application of mathematical principles in our daily lives. For example, the computer that I am using now to type this paper operates on number. Each letter and symbol on this page has a corresponding numerical value inside the computer. The image I see on the computer screen consists of millions of tiny pixels each displaying a specific color generated by its corresponding numerical value. Because letters, symbols, and images can be “enumerated” in a computer, one can manipulate these numerical values to simulate reality via mathematical principles. Thus, we can see reality based on its numerical representation.

Pythagoras saw that “the elements of numbers are the Even and the Odd, and of these the latter is limited and the former is unlimited.”[3] Odd numbers are limited because an odd number of pebbles in a gnomon make up a square; there is exactly one square for a given side length since the length and width are equal. In contrast, an even number of pebbles in a gnomon makes up a rectangle; there can be an infinite number of possible rectangles if we know the length of only one side.

The Pythagoreans classified even numbers into three categories: Perfect, Deficient, and Superabundant. Perfect numbers like 6 and 28 are numbers whose factors add up to the number itself. For example, the factors of 6 are (1, 2, 3) and 6 = 1 + 2 + 3; the factors of 28 are (1, 2, 4, 7, 14) and 28 = 1 + 2 + 4 + 7 + 14. Deficient numbers are numbers whose factors add up to less than the number itself. For example, the deficient number 14 has factors (1, 2, 7) which add up only to 12. Superabundant numbers are numbers whose factors add up to more than the number itself. For example, the superabundant number 12 has factors (1, 2, 3, 4, 6) which add up to 16. Perfect numbers are considered rare because “there is but one perfect number between 1 and 10, that is 6; only one between 10 and 100, that is 28; only one between 100 and 1000, that is 496; and between 1000 and 10,000 only one, that is 8128…”[4] The superabundant and deficient numbers are much more abundant than perfect numbers. “[Superabundant] numbers …looked … similar to Briareus, the hundred-handed giant: his parts were too numerous; the deficient numbers resembled Cyclops, who had but one eye; whilst the perfect numbers have the temperament of a middle limit, and are the emulators of Virtue, a medium between excess and defect…”[5] Thus, perfect numbers are “like the virtues, few in number; whilst the other two classes [superabundant and deficient] are like the vices—numerous,...