Pythagoras: His Life and Teaching, a Compendium of Classical Sources (31 page)

P
HYSIC

T
he general heads of Physic are these: of the world, and of all things in the world, of Heaven, and of Earth, and of the natures between them.
⁷⁹⁰
The defect of the fragments concerning these, we shall endeavor to supply by adding the Treatise of Timaeus the Locrian upon the same subject. [See
page 301
]

The brass tripod of Apollo appears on the reverse of this silver stater of Croton, struck c.420
B.C.
The obverse shows young Heracles seated before an altar, and among his accouterments. The reverse shows Apollo's tripod decorated with hanging fillets, amidst a scene of Apollo preparing to discharge an arrow into the serpent Python.

Photo courtesy of Numismatica Ars Classica

CHAPTER
1

P
RINCIPLES

T
he most learned of the Naturalists (says Sextus Empericus) attributed so great power to numbers, that they thought them to be the principles and elements of all things.
⁷⁹¹
These were the disciples of Pythagoras. For, say they, such as treat of philosophy aright imitate those who study a language. They first examine words, because language consists of words; then, because words consist of syllables, they next consider syllables; and because syllables consist of letters, they next examine letters. In like manner, say the Pythagoreans, natural philosophers, when they make enquiry into the universe, must first examine into what the universe is resolved.

Now to affirm that something apparent to sense is the principle of all things is repugnant to Physic. For whatsoever is apparent to sense must be compounded of things not apparent. Whereas a principle is not that which consists of any thing, but that of which the thing consists. Therefore things apparent cannot be said to be principles of the universe, but those of which things apparent consist, themselves not being apparent.

They who maintain atoms, or
Homoeomeries
, or bulks, or intelligible bodies, to be the principles of all things were partly in the right, partly not. As conceiving the principles to be unapparent, they are in the right; as holding them to be corporeal, they err. For as intelligible unapparent bodies precede the sensible, so must incorporeals precede intelligible bodies. The elements of words are not words; nor of bodies, bodies. But they must either be bodies or incorporeal; therefore they are wholly incorporeal.

Neither can we say that Atoms are eternal, and therefore though corporeal, the principles of all things. For first they who assert Homoeomeries, and bulks, and leasts, and indivisibles, to be elements, conceive their substance eternal; so as in that respect, Atoms are no more elements than they. Again, though it were granted that atoms were eternal, yet they who conceive the world to be unbegotten and eternal, enquire by an imaginary way the principles whereof it first consists. So we (say the Pythagoreans), treating of Physic,
consider in an imaginary way of what things these eternal bodies, comprehensible only by reason, consist.

Thus the Universe consists either of bodies or incorporeals. We cannot say bodies, for then we must assign other bodies whereof they consist; and so proceeding to infinite, we shall remain without a principle. It rests therefore to affirm that intelligible bodies consist of incorporeals, which Epicurus confesses, saying, “By collection of figure, and magnitude, and resistance, and gravity, is understood a body.”

Yet it is not necessary that all corporeals preexistent to bodies be the elements and first principles of beings. Ideas (according to Plato) are incorporeals, pre-existent to bodies, and all generated beings have reference to them; yet they are not the principles of being. For every Idea, singly taken, is said to be one; when we comprehend others with it, they are two, or three, or four. Number therefore is transcendent to their substance, by participation whereof, one, two, or more, are predicated of them. Again, solid figures are conceived in the mind before bodies, as having an incorporeal nature; yet they are not the principles. Superficies precede them in our imagination, for solids consist of superficies. But neither are superficies the elements of beings, for they consist of lines; lines precede them; numbers precede lines. That which consists of three lines, is called a Triangle; that which of four, a Quadrangle. Even line itself, simply taken, is not conceived without number—but being carried on from one point to another, is conceived in two. As to Numbers, they all fall under the Monad. For the Duad is one Duad, the Triad one Triad, and the Decad one summary of number.

This moved Pythagoras to say, that the principle of all things is the Monad, by participation hereof, every being is termed One. And when we reflect on a being in its identity, we consider a Monad. But when it receives addition by the other, it produces indeterminate Duad, so called in distinction from the Arithmetical determinate Duads, by participation whereof all Duads are understood as Monads by the Monad. Thus there are two principles of beings, the first Monad, and the indeterminate Duad.

That these are indeed the principles of all things, the Pythagoreans reach variously. Of beings (say they), some are understood by
Difference
, others by
Contrariety
, others by
Relation.
By difference are those which are considered by themselves subjected by their proper circumscription: as, a man, a horse, a plant, earth, water, air, fire; each of these is considered absolutely without any comparison. By contrariety are those which are considered by one to the other: as good and ill, just and unjust, profitable and unprofitable, sacred and profane, pious and impious, moving and fixed, and the like. By relation are those which are considered by relation to others: as right to left, upwards to downwards, double to half. For right is understood by a relative habit to left, and left by a relative habit to right; upwards to downwards, and downward to upwards; and so on of the rest.

Those which are understood by contrariety differ from those that are understood by relation. In contraries, the corruption of the one is the generation of another: as of health, sickness, motion, rest. The induction of sickness is the expulsion of health, and the induction of health is the expulsion of sickness; the same in grief and joy, good and ill, and all things of contrary natures. But the relative exist together, and perish together. For right is nothing unless there be left; double is nothing unless we understand the half whereof it is the double. Moreover, in contraries there is no mean, as between health and sickness, life and death, motion and rest. But between relatives there is a mean—as between greater and lesser, the mean is equal; between too much and too little, sufficient; between too flat and too sharp, concord.

Above these three kinds—absolute, contrary, relative—there must necessarily be some Supreme Genus; every genus is before the species which are under it. For if the Genus be taken away, the species are taken away also; but the removal of the species takes not away the genus; the species depending on the genus, not the genus on the species. The transcending genus of those things which are understood by themselves (according to the Pythagoreans) is the One. That exists and is considered absolutely, so they say. Of contraries, equal and unequal, holds the place of a genus; for in them is considered the nature of all contrarieties. By example, of rest in equality, it admits not intension and remission; of motion or inequality, it admits intension and remission. In like manner, natural inequality is the instable extremity; preternatural inequality admits
intension and remission. The same of health and sickness, straightness and crookedness. The relative consists of excess and defect as their genus; great and greater, much and more, high and higher, are understood by excess: little and less, low and lower, by defect.

Now forasmuch as absolutes, contraries, and relatives appear to be subordinate to other genera (that is, to one, to equality and inequality, to excess and defect), let us examine whether those genera may be reduced to others. Equality is reducible to one, for one is equal in itself; inequality is either in excess or defect; of unequals, one exceeds, the other is deficient. Excess and defect are reducible to the indeterminate Duad; for the first excess and defect is in two, in the
excedent
and the deficient. Thus the principles of all things appear above all the rest in the first Monad and the indeterminate Duad.

Of these are generated the Arithmetical Monad and Duad. From the first Monad, one; from the Monad and the indeterminate Duad, two. The Duad, being not yet constituted amongst Numbers, neither was there two before it was taken out of the indeterminate Duad. From the indeterminate Duad, together with the Monad, was produced the Duad which is in Numbers. Out of these, in the same manner proceeded the rest of the Numbers: one continually stepping forward, the indeterminate Duad generating two, and extending Numbers to an infinite multitude.

Hereupon they affirm that, in principles, Monad has the nature of the efficient cause, Duad of passive matter. And after the same manner as they produced Numbers, which consists of them, they composed the world also and all things in it.

A Point is correspondent to the Monad. The Monad is indivisible, so is the Point; the Monad is the principle of Numbers, so is the Point of Lines. A Line is correspondent to the Duad; both are considered by transition. A line is length without breath, extended between two points. A Superficies corresponds to the Triad. Besides length, whereby it was a Duad, it receives a third distance, breadth. Again, settling down three points: two opposite, the third at the juncture of the lines made by the two, we represent a superficies. The solid figure and the body (as a pyramid) answer the Tetrad. If we lay down, as before, three points, and set over them another point—
behold the pyramidical form of a solid body, which has three dimensions, length, breadth, thickness.

Some there are who affirm that a body consists of one point; the point by fluxion makes a line; the line by fluxion makes a superficies; the superficies moved to thickness makes a body in three dimensions. This sect of the Pythagoreans differs from the former. They held that of two principles—the Monad and the Duad—were made Numbers; of Numbers were made Points, Lines, Superficies, and Solids. These hold that all things come from one point—for of it is made a line, of the line a superficies, of the superficies a body.

Thus are solid bodies produced of numbers precedent to them. Moreover, of them consist Solids, Fire, Water, Air, Earth, and in a word, the whole World; which is governed according to Harmony—as they affirm again—recurring to Numbers which comprise the proportions that constitute perfect Harmony.
⁷⁹²
Harmony is a system consisting of three concords: the Diatessaron, the Diapente, the Diapason; the proportions of these three concords are found in the first four numbers: one, two, three, four. The Diatessaron consists in a sesquitertia proportion. The Diapason is in sesquialtera. The Diapente is in duple. Four being sesquitertius to three (as consisting of three and one third) has a Diatessaron proportion; three being sesquialter to two (as containing two and its half), a Diapente; four being the double of the Monad of two, a Diapason. The Tetractys affording the analogy of these concords, which make perfect harmony, according to which all things are governed, they styled it:

The root and fountain of eternal nature.

Moreover, whatsoever is comprehended by man (say they) either is a body or incorporeal; but neither of these is comprehended without the notion of numbers. A body, having a triple dimension, denotes the number three. Besides of bodies, some are by connection: as ships, chains, buildings; others by union comprised under one habit: as plants and animals; others by aggregation: as armies and herds. All these have numbers, as consisting of plurality. Moreover of bodies: some have simple qualities, others multiplex. Examples include an apple, various colors to the sight, juice to the taste, odor
to the smell; these also are of the nature of numbers. It is the same of incorporeals. Time, an incorporeal, is comprehended by number: years, months, days, and hours. The like of a Point, a Line, a Superficies, as we said already.

Likewise to numbers are correspondent both naturals and artificials. We judge everything by criteria, which are the measures of numbers. If we take away number, we take away the cubit, which consists of two half-cubits, six palms, twenty four digits. We take away the bushel, the balance, and all other criteria, which, consisting of plurality, are kinds of number. In a word, there is nothing in life without it. All art is a collection of comprehensions. Collection implies number; it is therefore rightly said:

To number all things reference have.

That is to determinative reason, which is of the same kind with numbers, whereof all consists. Hitherto Sextus.

The sum of all (as said by Alexander in his Successions, extracted out of the Pythagorean commentaries) is this: the Monad is the principle of all things.
⁷⁹³
From the Monad came the indeterminate Duad. As matter subjected to the cause, Monad; from the Monad and the indeterminate Duad came Numbers. From Numbers came Points. From Points came Lines; from Lines, Superficies; from Superficies, Solids; from these, solid bodies. Solid bodies are composed of four elements: Fire, Water, Air, Earth; of all which, transmutated and totally changed, the world consists.