10 ideas
| 10152 | Set theory and logic are fairy tales, but still worth studying [Tarski] |
| Full Idea: People have asked me, 'How can you, a nominalist, do work in set theory and in logic, which are theories about things you do not believe in?' ...I believe that there is a value even in fairy tales and the study of fairy tales. | |
| From: Alfred Tarski (talk [1965]), quoted by Feferman / Feferman - Alfred Tarski: life and logic | |
| A reaction: This is obviously an oversimplification. I don't think for a moment that Tarski literally believed that the study of fairy tales had as much value as the study of logic. Why do we have this particular logic, and not some other? |
| 10151 | I am a deeply convinced nominalist [Tarski] |
| Full Idea: I am a nominalist. This is a very deep conviction of mine. ...I am a tortured nominalist. | |
| From: Alfred Tarski (talk [1965]), quoted by Feferman / Feferman - Alfred Tarski: life and logic Int I | |
| A reaction: I too am of the nominalist persuasion, but I don't feel justified in such a strong commitment. |
| 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 |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 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 |