4 ideas
| 18086 | Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher] |
| Full Idea: Weierstrass effectively eliminated the infinitesimalist language of his predecessors. | |
| From: report of Karl Weierstrass (works [1855]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.6 |
| 18092 | Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock] |
| Full Idea: After Weierstrass had stressed the importance of limits, one now needed to be able to prove the existence of such limits. | |
| From: report of Karl Weierstrass (works [1855]) by David Bostock - Philosophy of Mathematics 4.4 | |
| A reaction: The solution to this is found in work on series (going back to Cauchy), and on Dedekind's cuts. |
| 22307 | Propositions don't name facts, because two opposed propositions can match one fact [Russell] |
| Full Idea: It is perfectly evident that a proposition is not the name for a fact, from the mere circumstance that there are two propositions corresponding to each fact. 'Socrates is dead' and 'Socrates is not dead' correspond to the same fact. | |
| From: Bertrand Russell (Papers of 1918 [1918], VIII.136), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 42 'Prop' | |
| A reaction: He finally reaches in 1918 what now looks fairly obvious. The idea that a proposition is part of the world is absurd. We should call the parts of the world 'facts' (despite vagueness and linguistic dependence in such things). Propositions are thoughts. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |