6 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? |
| 21227 | The Cogito demands a bridge to the world, and ends in isolating the ego [Velarde-Mayol] |
| Full Idea: All philosophies inspired in the Cogito have the problem of building a bridge from the starting point of consciousness to the external world. The result of this is the isolation and solitude of the very ego. | |
| From: Victor Velarde-Mayol (On Husserl [2000], 4.7.2) | |
| A reaction: This strikes me as a pretty good reason not to develop a philosophy which is inspired by the Cogito. |
| 21215 | The representation may not be a likeness [Velarde-Mayol] |
| Full Idea: Representationalism is the doctrine that maintains that the object is represented in consciousness by means of an image. ...One should not confuse an image with a likeness. | |
| From: Victor Velarde-Mayol (On Husserl [2000], 2.4.3) | |
| A reaction: Helpful reminder that sense-data or whatever may not be a likeness. But then how do they represent? Symbolic representation needs massive interpretation. |
| 21219 | Find the essence by varying an object, to see what remains invariable [Velarde-Mayol] |
| Full Idea: Eidetic Reduction consists of producing variations in the individual object until we see what is invariable in it. What is invariable is its essence or Eidos. | |
| From: Victor Velarde-Mayol (On Husserl [2000], 3.2.2) | |
| A reaction: This strikes me as an excellent idea. It more or less describes the method of science. Chemical atoms were thought to be unsplittable, until someone tried a new variation for dealing with them. |
| 5470 | The idea of laws of nature arose in the Middle Ages [Hall,AR, by Ellis] |
| Full Idea: According to A.R. Hall, the idea that nature is governed by laws does not appear to have existed in the ancient Greek, Roman or Far Eastern traditions of science, but arose from religious, philosophical and legal ideas in medieval Europe. | |
| From: report of A.R. Hall (The Scientific Revolution 1500-1800 [1954]) by Brian Ellis - The Philosophy of Nature: new essentialism Ch.5 | |
| A reaction: This is a very illuminating point, which gives good circumstantial support for questioning the existence of external laws which are imposed on a passive nature. Modern essentialism suggest the 'laws' are the intrinsic results of properties. |