11 ideas
10121 | Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal] |
Full Idea: Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth. | |
From: Blaise Pascal (works [1660]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
A reaction: [Quoted in Auden and Kronenberger's Book of Aphorisms] Presumably we would now say that contradiction is a purely formal, syntactic notion, and not a semantic one. If you hit a contradiction, something has certainly gone wrong. |
16608 | Ockham was an anti-realist about the categories [William of Ockham, by Pasnau] |
Full Idea: Ockham is the scholastic paradigm of anti-realism with respect to the categories. | |
From: report of William of Ockham (Summula philosophiae naturalis [1320]) by Robert Pasnau - Metaphysical Themes 1274-1671 05.3 | |
A reaction: These are the ten categories mentioned in Aristotle's book 'Categories'. |
472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
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 |
16599 | Ockham says matter must be extended, so we don't need Quantity [William of Ockham, by Pasnau] |
Full Idea: Ockham regards Quantity as an entirely superfluous ontological category, …because matter is intrinsically extended. | |
From: report of William of Ockham (Summula philosophiae naturalis [1320]) by Robert Pasnau - Metaphysical Themes 1274-1671 04.4 |
16681 | Matter gets its quantity from condensation and rarefaction, which is just local motion [William of Ockham] |
Full Idea: Matter is made to have a greater or lesser quantity not through its receiving any absolute accident, but through condensation and rarefaction alone. Parts come more or less close together, which can happen with local motion. | |
From: William of Ockham (Summula philosophiae naturalis [1320], I.13), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 15.1 | |
A reaction: This is Ockham at his most modern, rejecting the odd idea of Quantity in favour of a modern corpuscular view of the mere motions of matter. |
1518 | Everything must involve numbers, or it couldn't be thought about or known [Philolaus] |
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 |
1519 | Harmony must pre-exist the cosmos, to bring the dissimilar sources together [Philolaus] |
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 |
473 | There is no falsehood in harmony and number, only in irrational things [Philolaus] |
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? |
469 | Existing things, and hence the Cosmos, are a mixture of the Limited and the Unlimited [Philolaus] |
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 |
476 | Self-created numbers make the universe stable [Philolaus] |
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? |
1787 | Philolaus was the first person to say the earth moves in a circle [Philolaus, by Diog. Laertius] |
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 |