Ideas from 'On the Cosmos (lost)' by Philolaus [435 BCE], by Theme Structure

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9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification

472	No things would be clear to us as entity or relationships unless there existed Number and its essence

			Full Idea: No existing things would be clear to anyone, either in themselves or in their relationship to one another, unless there existed Number and its essence.
			From: Philolaus (On the Cosmos (lost) [c.435 BCE], B11), quoted by John Stobaeus - Anthology 1.03.8

26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature

1518	Everything must involve numbers, or it couldn't be thought about or known

			Full Idea: Everything which is known has number, because otherwise it is impossible for anything to be the object of thought or knowledge.
			From: Philolaus (On the Cosmos (lost) [c.435 BCE], B04), quoted by John Stobaeus - Anthology 1.21.7b

473	There is no falsehood in harmony and number, only in irrational things

			Full Idea: The nature of number and harmony admits of no falsehood; for this is unrelated to them. Falsehood and envy belong to the nature of the Unlimited and the Unintelligent and the Irrational.
			From: Philolaus (On the Cosmos (lost) [c.435 BCE], B11), quoted by (who?) - where?

1519	Harmony must pre-exist the cosmos, to bring the dissimilar sources together

			Full Idea: It would have been impossible for the dissimilar and incompatible sources to have been made into an orderly universe unless harmony had been present in some form or other.
			From: Philolaus (On the Cosmos (lost) [c.435 BCE], B06), quoted by John Stobaeus - Anthology 1.21.7d

26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited

469	Existing things, and hence the Cosmos, are a mixture of the Limited and the Unlimited

			Full Idea: Since it is plain that existing things are neither wholly from the Limiting, nor wholly from the Unlimited, clearly the cosmos and its contents were fitted together from both the Limiting and the Unlimited.
			From: Philolaus (On the Cosmos (lost) [c.435 BCE], B02), quoted by John Stobaeus - Anthology 1.21.7a

26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical

476	Self-created numbers make the universe stable

			Full Idea: Number is the ruling and self-created bond which maintains the everlasting stability of the contents of the universe.
			From: Philolaus (On the Cosmos (lost) [c.435 BCE], B23), quoted by (who?) - where?

27. Natural Reality / E. Cosmology / 1. Cosmology

1787	Philolaus was the first person to say the earth moves in a circle

			Full Idea: Philolaus was the first person to affirm that the earth moves in a circle.
			From: report of Philolaus (On the Cosmos (lost) [c.435 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 08.Ph.3