8 ideas
| 7557 | To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell] |
| Full Idea: Presumably Zeno appealed to the axiom that the whole has more terms than the parts; so if Achilles were to overtake the tortoise, he would have been in more places than the tortoise, which he can't be; but the conclusion is absurd, so reject the axiom. | |
| From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.89) | |
| A reaction: The point is that the axiom is normally acceptable (a statue contains more particles than the arm of the statue), but it breaks down when discussing infinity (Idea 7556). Modern theories of infinity are needed to solve Zeno's Paradoxes. |
| 10059 | In mathematic we are ignorant of both subject-matter and truth [Russell] |
| Full Idea: Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. | |
| From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.76) | |
| A reaction: A famous remark, though Musgrave is rather disparaging about Russell's underlying reasoning here. |
| 7556 | A collection is infinite if you can remove some terms without diminishing its number [Russell] |
| Full Idea: A collection of terms is infinite if it contains as parts other collections which have as many terms as it has; that is, you can take away some terms of the collection without diminishing its number; there are as many even numbers as numbers all together. | |
| From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.86) | |
| A reaction: He cites Dedekind and Cantor as source for these ideas. If it won't obey the rule that subtraction makes it smaller, then it clearly isn't a number, and really it should be banned from all mathematics. |
| 7554 | Self-evidence is often a mere will-o'-the-wisp [Russell] |
| Full Idea: Self-evidence is often a mere will-o'-the-wisp, which is sure to lead us astray if we take it as our guide. | |
| From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.78) | |
| A reaction: The sort of nice crisp remark you would expect from a good empiricist philosopher. Compare Idea 4948. However Russell qualifies it with the word 'often', and all philosophers eventually realise that you have to start somewhere. |
| 20759 | Feelings are prior to intelligence; we should be content to live with our simplest feelings [Rousseau] |
| Full Idea: To exist is to feel, our feeling is undoubtedly earlier than our intelligence, and we had feelings before we had ideas. …Let us be simpler and less pretentious; let us be content with the first feelings we experience in ourselves. | |
| From: Jean-Jacques Rousseau (Emile: treatise on education [1762], p.210), quoted by Kevin Aho - Existentialism: an introduction 6 'Moods' | |
| A reaction: Beginning of the sentimental movement, and precursor to romanticism, but here seen as the basis for the existentialist concept of authenticity. Wallowing in emotions doesn't appeal to me, but you have to make space for them. Rousseau loved walking. |
| 19854 | We all owe labour in return for our keep, and every idle citizen is a thief [Rousseau] |
| Full Idea: In a society where a man has to live at others' expense, he owes in labour the price of his keep; and that is without exception. Work, then, is an indispensable social obligation. Rich or poor, powerful or weak, every idle citizen is a thief. | |
| From: Jean-Jacques Rousseau (Emile: treatise on education [1762], Bk III) | |
| A reaction: Presumably rich landowners who live on rents can justify their position by good husbandry, at a higher level than tilling the soil. But Bertie Wooster won't last long in Rousseau's new world. This is a big challenge to the welfare state. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |