4 ideas
| 18085 | Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy] |
| Full Idea: When the successive absolute values of a variable decrease indefinitely in such a way as to become less than any given quantity, that variable becomes what is called an 'infinitesimal'. Such a variable has zero as its limit. | |
| From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
| A reaction: The creator of the important idea of the limit still talked in terms of infinitesimals. In the next generation the limit took over completely. |
| 18084 | When successive variable values approach a fixed value, that is its 'limit' [Cauchy] |
| Full Idea: When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others. | |
| From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
| A reaction: This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction? |
| 16712 | Atheism is an atrocious and intolerable crime in any country [Descartes] |
| Full Idea: Atheism is the most atrocious crime, and should be tolerated in no republic, however free. | |
| From: René Descartes (Letters to Voetius [1640], VIIIB:174), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 16711 | Heretics should be eradicated like wolves [Aquinas] |
| Full Idea: Heretics are wolves …and therefore ought to be eradicated. | |
| From: Thomas Aquinas (Sentences [1264], IV.13.2.3sc), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |