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? |
| 21226 | Husserl sees the ego as a monad, unifying presence, sense and intentional acts [Husserl, by Velarde-Mayol] |
| Full Idea: Husserl's notion of monad expresses a complete inegration of every intentional presence into its sense, and every sense into the intentional acts, ....and finally every intentional act is integrated into the ego. | |
| From: report of Edmund Husserl (Cartesian Meditations [1931]) by Victor Velarde-Mayol - On Husserl 4.6.2 | |
| A reaction: No, I don't understand that either, but it makes good sense to employ the concept of a 'monad' into the concept of the ego, if you think it embodies perfect unity. That was a main motivation for Leibniz to employ the word. |
| 1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
| Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature. | |
| From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8 |
| 21228 | Husserl's monads (egos) communicate, through acts of empathy. [Husserl, by Velarde-Mayol] |
| Full Idea: For Husserl monads have windows because they communicate with each other. The windows of the monads are the acts of empathy. | |
| From: report of Edmund Husserl (Cartesian Meditations [1931]) by Victor Velarde-Mayol - On Husserl 4.7.5 | |
| A reaction: Leibniz said his monads (which include minds) have 'no windows'. The mere existence of empathy (or mirror neurons, as we would say) is hardly sufficient to defeat solipsism. |
| 21225 | The psychological ego is worldly, and the pure ego follows transcendental reduction [Husserl, by Velarde-Mayol] |
| Full Idea: Husserl distinguishes two sorts of egos or subjects of experience, the psychological ego and the pure ego. The psychological ego is a reality of the world, and the pure ego is a result of transcendental reduction. | |
| From: report of Edmund Husserl (Cartesian Meditations [1931]) by Victor Velarde-Mayol - On Husserl 4.6.1 | |
| A reaction: The sounds like embracing both the Cartesian and the Kantian egos. This is obviously the source of Sartre's interesting early book on the self. 'Transcendental reduction' is his bracketing or epoché. |