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Book I Chapter 21

5 ⟨Arius Didymus⟩: The planets in order

Of the wandering stars, the highest sphere, following that ⟨of⟩ the fixed stars, is Saturn’s; after it comes Jupiter’s, then Mars’s, next Mercury’s, then Venus’s, then the sun’s, and last of all the moon’s, adjoining the air. Hence the moon also appears more airlike, and its power reaches the regions about earth most strongly.⁶³³

5 ⟨Arius Didymus⟩: The center and “down”

Below the moon lies the sphere of the air carried beneath it, then that of water, and last that of earth, which lies about the central point of the world. This is the “down” of the universe; “up” is the direction from it toward the circumference on every side.⁶³⁴

6a ⟨Aëtius⟩: Ecphantus

Ecphantus held that the world is constituted from atoms, but is governed by providence.⁶³⁵

6b ⟨Aëtius⟩: Aristotle

Aristotle held that the world is not throughout its whole extent endowed with soul, reason, or intelligence, or governed by providence. For the heavenly regions share in all these things, containing ensouled and living spheres, while the regions about earth share in none of them; they participate in good order incidentally, not primarily. If the world is nourished, it will also perish; but it needs no nourishment, and for that reason is eternal.⁶³⁶

6c ⟨Aëtius⟩: Pythagoras and cosmic order

Pythagoras says that the world is generated in conception, not in time. He was also the first to call the enclosure of all things a kosmos, from the order within it. The generation of the world began from fire and the fifth element.⁶³⁷

6c ⟨Aëtius⟩: Five solid figures

There are five solid figures, also called mathematical figures. He says that earth came from the cube, fire from the pyramid, air from the octahedron, ⟨water⟩ from the icosahedron, ⟨and⟩ the sphere of the universe ⟨from the dodecahedron⟩.⁶³⁸

6d ⟨Aëtius⟩: Philolaus

Philolaus said that the exhalations, arising partly from fire flowing from heaven and partly from lunar water poured out through the revolution of the air, are the world’s nourishment. Its ruling part is in the fire at the very center, which the craftsman God laid down first, like a keel, beneath the ⟨sphere⟩ of the universe.⁶³⁹

6e ⟨Aëtius⟩: Where the ruling part lies

Cleanthes the Stoic said that the ruling part of the world is in the sun.

Archedemus declared that the ruling part of the world is in earth.⁶⁴⁰

6f ⟨Aëtius⟩: Accounts of formation

Heraclitus held that the world is generated not in time but in conception.

Epidicus held that the world came into being through nature.

Archelaus held that the world was constituted through heat and cooling.⁶⁴¹

7a Philolaus, On the World: Limiters

All things that are must be either limiting or unlimited, or both limiting and unlimited; they could not be unlimited alone. Since, then, they plainly consist neither wholly of limiters nor wholly of unlimiteds, it is clear that both the world and the things within it were fitted together from limiters and unlimiteds. Things in actual experience show this too. Those made from limiters appear limiting, those from limiters and unlimiteds both limiting and not limiting, and those from unlimiteds unlimited.⁶⁴²

7b ⟨The same author⟩: Number and knowledge

Indeed, all things that are known have number. For without it nothing can be either conceived or known.⁶⁴³

7c ⟨The same author⟩: Kinds of number

Number has two kinds of its own, odd and even, and a third formed from the mixture of both, even-odd. Each of the two kinds has many forms, as each thing itself indicates.⁶⁴⁴

7d ⟨The same author⟩: Nature and knowing

Concerning nature and harmony, the situation is this. The being of things, which is eternal, and indeed nature itself, is divine and admits of no human knowledge, except that none of the things that are and are known by us could have come into being unless the being of the things from which the world was constituted, both the limiters and the unlimiteds, already existed.⁶⁴⁵

7d ⟨The same author⟩: Why harmony is needed

Since the principles that already existed were neither alike nor of the same kind, they could not have been brought into order unless harmony had arisen in addition, however it arose. Things alike and of the same kind had no need of harmony; but things unlike, of different kinds, and unequally allotted must be bound together by such a harmony if they are to be held within an ordered world.⁶⁴⁶

7d ⟨The same author⟩: The musical intervals

The extent of the octave is a fourth and a fifth; the fifth exceeds the fourth by a tone of nine to eight. For from hypatē to mesē is a fourth, from mesē to neatē a fifth, from neatē to tritē a fourth, and from tritē to hypatē a fifth. The interval between mesē and tritē is nine to eight. The fourth is four to three, the fifth three to two, and the octave two to one.⁶⁴⁷

7d ⟨The same author⟩: Tones and remainders

Thus the octave comprises five tones of nine to eight and ⟨two⟩ dieses; the fifth comprises three tones of nine to eight and one diesis.⁶⁴⁸

8 ⟨The same author⟩: The hearth

The first thing fitted together, the one at the center of the sphere, is called the hearth.⁶⁴⁹

633.The order is the one printed in this report: Saturn, Jupiter, Mars, Mercury, Venus, sun, moon. It has not been rearranged to match another ancient scheme. The Greek planetary names are Cronus, Zeus, Ares, Hermes, and Aphrodite; conventional English names are used.

634.The phrase hyp’ autou pheromenou is difficult: the masculine pronoun does not agree with “moon.” “Carried beneath it” gives the apparent spatial sense, without establishing the pronoun’s reference. Wachsmuth records several proposed repairs. The supplied Greek article before “water” has no separate natural English equivalent.

635.This report combines atomic constituents with providential government, unlike the atomist account in excerpt 3c. It illustrates why the chapter’s reports should not be forced into a single division between atomism and divine governance.

636.This is a doxographical summary attributed to Aristotle, not a quotation from a named Aristotelian work. Its contrast concerns the cosmic regions and their governance; the statement about the earthly region should not be expanded into a denial that individual terrestrial animals have souls.

637.“In conception” distinguishes an explanatory account of how the world is constituted from an event at a first moment in time. The report assembles several claims under Pythagoras’s name. Kosmos can mean “order”; the claim of first naming is the ancient compiler’s, not an independently established priority. The fifth element is not defined here.

638.The five are the regular solids: the “pyramid” is the tetrahedron. The supplement restoring water and the dodecahedron comes from the parallel doxographical tradition. The scheme resembles Plato’s Timaeus 53c-55c; here it is transmitted under Pythagoras’s name.

639.The obscure fire and lunar-water wording also appears in I.20.1g, there in a report about destruction. Here it concerns nourishment. The central fire is likened to a ship’s keel, the structural foundation laid first; “sphere” is supplied by the editor. The imagery is transmitted as a report about Philolaus.

640.The reports give distinct locations for the directing center. Archedemus is the name retained by Wachsmuth; his apparatus rejects an earlier alteration to Archidamus.

641.The printed names are retained. Wachsmuth notes a tentative conjecture “Heraclides” for “Heraclitus” and a variant of “Epidicus.” “Heat and cooling” follows the editor’s repairs of corrupt readings. A stray repetition from I.10.12, noted in the apparatus but omitted from the base text, is not inserted here.

642.This is Philolaus fragment 2 in modern numbering. Excerpts 7a-d and 8 belong to the generally accepted core of his fragments, unlike the On the Soul extract in I.20.2; see C. A. Huffman, “Philolaus,” Stanford Encyclopedia of Philosophy, §§1.3-1.4. Perainonta is active, “things that limit,” rather than simply things already bounded. The Doric forms are retained on the Greek side.

643.Philolaus fragment 4. “Have number” is the wording of this fragment; it has not been replaced by the different proposition “are numbers.” Wachsmuth supplies “the same author” for 7b-d and 8; these headings refer back to Philolaus.

644.Philolaus fragment 5. The fragment names but does not define the “even-odd.” Its last clause is textually difficult; “as each thing itself indicates” follows Wachsmuth’s printed wording without supplying a particular example or theory of the third kind.

645.Philolaus fragment 6. Estō is the Doric term rendered “being.” The opening is substantially repaired in the base edition; the English takes “nature itself” as a restatement of “the being of things.” The restriction on knowledge still permits the inference that the constituents of the world must already have existed.

646.Harmonia means a fitting or joining together; the next passage gives it the specific musical sense of an octave. “Unequally allotted” renders isolachē with the preceding negative, following a conjecture retained by Wachsmuth. The phrase “however it arose” leaves the origin of harmony unspecified.

647.The traditional terms syllaba and di’ oxeian mean the fourth and fifth here; harmonia and dia pasān both designate the octave. Hypatē and neatē are its lower and upper notes, with mesē and tritē between them. The ratios combine by multiplication: (4/3) × (3/2) = 2. The supplied Greek article before dia pasān has no separate English equivalent.

648.Here a diesis is the small remainder needed to complete these intervals, with ratio 256:243, not half of an equal-tempered modern tone. “Two” is supplied from the parallel in Nicomachus. Wachsmuth does not add the further sentence about the fourth that some editions include. Compare Huffman, “Philolaus,” §2.2, on fragment 6a.

649.Philolaus fragment 7. The hearth is the central fire, not the earth or sun. The wording links its formation with the fitting together discussed above. “The one” is retained without turning it into an explicitly named abstract first principle.