The Theology of Arithmetic

...[counsel] and impulse. The text begins mid-word, likely completing "boule" (counsel), a name the Pythagoreans gave to the Dyad because it represents the first movement toward a decision or direction. They also used to call it Opinion, because truth and falsehood reside in opinion In Platonic and Pythagorean thought, "Opinion" (doxa) is the realm of the changing and the double-minded, unlike "Knowledge" (episteme), which is fixed and singular.. They named it motion, generation, change, division, length, increase, composition, communion, the "relative," and the ratio in proportion; for the relationship between two numbers encompasses every possible form.

10It remains the only number without a share in shape This refers to the idea that two points can only form a line (length), but not a two-dimensional geometric shape or "plane," which requires at least three points.. Both in three-term sequences and in the definition of proportion, the Dyad original: dyas; the principle of "two" or "twoness" exists as something contrary and most opposite to the Monad The principle of "one" or "unity." compared to all other terms in number—just as Matter original: hyle is to God, and as the body is to the incorporeal. It is the principle and the "root" (as it were) of the diversity original: heteroeideias; literally "other-form-ness" of number, fashioned after the image of matter. It stands in contrast to the nature of God, in that the Dyad is thought to be the cause of transition and change for existing things, while God is the cause of identity and unchanging permanence.

Therefore, each thing in the cosmos is "one" according to the natural and systematic Monad within it, but each is also divisible insofar as it participates in the necessary and material Dyad. Hence, their first coming-together produced the first defined plurality—the element of existing things—which would be the triangle of magnitudes and of numbers, both corporeal and incorporeal.

For just as rennet original: opos; the curdling agent in cheesemaking curdles liquid milk through its creative and active quality, so the unifying power of the Monad, advancing upon the Dyad (which is the source of abundance and dissolution), produced a "limit"—and a form, which is Number—in the Triad The principle of the number three.. For the Triad is the beginning of number in actualization, defined by collections of units.

In a certain way, the Dyad is also a "monad" due to its status as a primary principle. The word "Dyad" is said to be derived from "passing through" original: dieienai and "traveling through" original: diaporeuesthai. For the Dyad was the first to separate itself from the Monad, which is why it is also called Audacity original: tolma; a famous Pythagorean term for the "boldness" of the number two in breaking away from the unity of the One.. Since the Monad signifies union, the Dyad, having intervened, signifies separation. It also initiates the "relative" relationship, either in its ratio to the Monad, which...