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Book I Chapter 10

12 ⟨Aëtius, Opinions⟩: Archelaus and the Ionian succession

Archelaus posits unlimited air and its density and rarefaction: one of these is fire, the other water.³³⁹

These men, following one another in succession, make up Ionian philosophy, so called because its founder was a man of Miletus: Thales, from the Ionians’ mother-city.

12 ⟨Aëtius, Opinions⟩: Philolaus

Philolaus the Pythagorean posits limit and the unlimited.³⁴⁰

12 ⟨Aëtius, Opinions⟩: Strato

Strato makes ⟨the hot⟩ and the cold the elements.

12 ⟨Aëtius, Opinions⟩: Pythagoras: principles

Pythagoras of Samos, son of Mnesarchus, who first called philosophy by that name, makes numbers and the proportions among them, which he calls harmonies, the principles; ⟨and⟩ the compounds formed from both, the elements. Again, he places the monad and the indefinite dyad among the principles. In his account, one principle tends toward the productive and formal cause, which is mind, or god; the other toward what is receptive and material, which is the visible world.³⁴¹

12 ⟨Aëtius, Opinions⟩: Pythagoras: the tetractys

The nature ⟨of number⟩ is the decad: everyone counts up to ten and, having reached it, returns again to the unit. The power of ten, he says, is in four, since ten is completed from four and its parts; if ⟨someone⟩ goes beyond the number four, he will also overshoot ten. Hence the Pythagoreans would declare, treating the tetrad as the greatest ⟨oath⟩:³⁴²

No, by him who handed down to our mind the tetractys, which holds the source and root of ever-flowing nature!³⁴³

13 Theano, On Piety

I have learned that many Greeks have supposed Pythagoras to have said that everything grows out of number. But this assertion involves a difficulty: how can things that do not even exist be conceived as generating things as well? He said that everything comes to be not out of number but according to number, because order is first present in number; by participation in that order, things that are counted are likewise arranged as first, second, and the rest in succession.³⁴⁴

14 ⟨Aëtius, Opinions⟩: Heraclitus and Hippasus

Heraclitus and Hippasus make fire the principle of everything. First, its coarser part contracts into itself and becomes ⟨earth⟩; then earth, loosened by fire, melts to form water, and water, exhaled as vapor, becomes air. In turn, the world and all bodies are dissolved by fire in the conflagration.³⁴⁵

14 ⟨Aëtius, Opinions⟩: Further accounts of the principles

Metrodorus of Chios, son of Theocritus, posits the indivisibles and the void.

Diogenes of Apollonia, unlimited air.

Zeno of Citium, son of Mnaseas, makes god and matter the principles, and the elements four.

Leucippus of Miletus makes the full and the void the principles and elements.

Democritus posits compact bodies and void.³⁴⁶

14 ⟨Aëtius, Opinions⟩: Epicurus

Epicurus holds that the principles of existing things are bodies discernible by reason, containing no void, ungenerated and indestructible, incapable of being broken or altered. A body is called an atom not because it is the smallest, but because it cannot be cut, being unaffected and containing no void.³⁴⁷

15 Hermes

For the monad, being the principle and root of everything, is present in everything as its root and principle; without a principle there is nothing. A principle comes from nothing else, but from itself, if indeed it is the principle of other things. Being a principle, then, [the monad] contains every number, while being contained by none; and it generates every number, while being generated by no other number. Everything generated is incomplete, divisible, capable of increase and decrease; none of these things happens to what is complete. Such, then, Tat, is the image of god sketched for you as far as is possible.³⁴⁸

16a ⟨Aëtius, Opinions⟩: Ecphantus

Ecphantus of Syracuse, one of the Pythagoreans, makes indivisible bodies and the void the principles of everything. For he was the first to declare the Pythagorean units to be corporeal.³⁴⁹

16a ⟨Aëtius, Opinions⟩: Plato

Plato, son of Ariston, posits three principles: god, matter, and form; that by which, that out of which, and that with reference to which. God is the mind of the world; matter is what underlies coming-to-be and passing-away; form is an incorporeal being in the thoughts and representations of god.³⁵⁰

16a ⟨Aëtius, Opinions⟩: Aristotle

Aristotle of Stagira, son of Nicomachus, makes form, matter, and privation the principles. There are four elements, and a certain fifth body, the aetherial, which is unchanging. The elements of generated things, considered in their powers, are the hot, the cold, the moist, and the dry; considered as the substances in which and about which these powers are found, they are the four elements.³⁵¹

16a ⟨Aëtius, Opinions⟩: Diodorus Cronus

Diodorus, surnamed Cronus, posits infinitely many partless bodies, also called smallest bodies: infinite in number, but bounded in magnitude.³⁵²

16b ⟨Aëtius, Opinions⟩: principles and elements

The followers of Aristotle and Plato, then, consider principle and elements to differ.

Thales of Miletus considers principle and elements to be the same. ⟨But they differ from one another very greatly. For the elements⟩ are composite, whereas we say that principles are neither composite nor products. For example, we call earth, water, air, and fire elements; but we speak of principles because they have nothing prior to them from which they arise. Otherwise it will not be a principle; what it arises from will be the principle. Yet earth and water do have something prior to them from which they have arisen: matter without shape or form.³⁵³

16b ⟨Aëtius, Opinions⟩: quotation from Plato

Accordingly, he says in the Timaeus: “For god wished everything to be good and nothing bad, so far as was possible. He therefore took over everything visible, which was not at rest but moving discordantly and without order, and brought it from disorder into order.”³⁵⁴

339.The report leaves the last pair as “one ... the other” rather than explicitly matching each condition with its product. The succession that follows is the ancient account’s classification of the thinkers.

340.The verb and the reference to principles are understood from the sequence. The opposition of limit and unlimited also appears in the surviving On Arithmetic at the beginning of this volume.

341.The monad is unity; the indefinite dyad is an indeterminate twofold principle. The report aligns them with acting, form-giving cause and receptive matter. This is a transmitted account under Pythagoras’s name, not his own surviving exposition.

342.The decad is ten, the tetrad four. The explanation sums 1 + 2 + 3 + 4 = 10; continuing with five would pass ten. It does not mean multiplying four by itself.

343.The tetractys is the arrangement of the first four numbers whose sum is ten. The oath invokes the person who transmitted it. “Our mind” renders the printed kephalāi, literally “our head”; the apparatus records psychāi, “soul,” in the parallel text.

344.The distinction is between number as a supposed material source and number as the order according to which things arise. The phrase about what does not exist is compressed and textually repaired in the base edition; the translation does not add a theory of numbers’ existence to resolve it. Theano is the transmitted author-name.

345.Ekpyrōsis, “conflagration,” is the burning up of the world in this reported account. The passage describes transformations among the ancient elements.

346.“The full” and “compact bodies” describe bodies without internal void. The terse catalogue supplies no account here of their shapes or combinations. Zeno’s distinction between principles and elements is developed further in excerpt 16c.

347.Atomos means “uncuttable” or “indivisible.” The passage explains that name through the body’s resistance to division, rather than through a claim that it is the smallest conceivable magnitude. “Containing no void” concerns the atom’s interior.

348.The unit or monad serves as an image of a first principle: it gives rise to number without itself arising from another number. The conclusion identifies this as an image of god, not merely an arithmetic claim. Square brackets retain the editor’s rejection of the repeated word “monad.”

349.The report treats the units themselves as bodies. This differs from Theano’s insistence in excerpt 13 on things arising “according to number.”

350.The three compressed phrases distinguish the maker, the material, and the pattern. The placement of form in divine thought belongs to this ancient report’s interpretation of Plato; this is not a direct quotation from a Platonic dialogue.

351.Privation is the absence of a form; the list distinguishes it from both the form and the underlying matter. The final distinction separates elemental qualities from the bodies that possess them. The aetherial fifth body is set apart as unchanging.

352.Amerē means “without parts.” The qualification distinguishes an unlimited number of bodies from their limited individual size.

353.A principle, archē, is treated here as something prior to a composite or generated element. This account explains why the chapter’s different lists cannot all be read as lists of the same sort of thing. Angle brackets reproduce the passage supplied by the base editor.

354.The speaker cited is Plato, Timaeus 30a. The quotation presents the ordering of what is already moving; the preceding explanation of principles and elements is the reporter’s discussion.