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. |
| 17593 | Always be ready to give reasons for your beliefs [Peter] |
| Full Idea: Be ready to give an answer to every man that asketh you a reason of the hope that is in you with meekness and fear. | |
| From: St Peter (21: First Epistle of Peter [c.50], 3:15) | |
| A reaction: This quotation is the rational theologian's standard response to pure fideism. |