5 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. |
5845 | Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon] |
Full Idea: Niceratus said that his father, because he was concerned to make him a good man, made him learn the whole works of Homer, and he could still repeat by heart the entire 'Iliad' and 'Odyssey'. | |
From: Xenophon (Symposium [c.391 BCE], 3.5) | |
A reaction: This clearly shows the status which Homer had in the teaching of morality in the time of Socrates, and it is precisely this acceptance of authority which he was challenging, in his attempts to analyse the true basis of virtue |
7825 | The politics of Leibniz was the reunification of Christianity [Stewart,M] |
Full Idea: The politics of Leibniz may be summed up in one word: theocracy. The specific agenda motivating much of his work was to reunite the Protestant and Catholic churches | |
From: Matthew Stewart (The Courtier and the Heretic [2007], Ch. 5) | |
A reaction: This would be a typical project for a rationalist philosopher, who thinks that good reasoning will gradually converge on the one truth. |
5833 | Education is the greatest of human goods [Xenophon] |
Full Idea: Education is the greatest of human goods. | |
From: Xenophon (Apology of Socrates [c.392 BCE], 22) | |
A reaction: Of course, one might ask what education is for, and arrive at a greater good. If you ask what is the greatest good which a society can provide for you, or which you can give to your children, this seems to me a good answer. |