9 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? |
| 20416 | By 1790 aestheticians were mainly trying to explain individual artistic genius [Kemp] |
| Full Idea: By 1790 the idea that a central task for the aesthetician was to explain or at least adequately to describe the phenomenon of the individual artistic genius had definitely taken hold. | |
| From: Gary Kemp (Croce and Collingwood [2012], Intro) | |
| A reaction: Hence when Kant and Hegel write about art, though are only really thinking of the greatest art (which might be in touch with the sublime or Spirit etc.). Nowadays I think we expect accounts of art to cover modest amateur efforts as well. |
| 20417 | Expression can be either necessary for art, or sufficient for art (or even both) [Kemp] |
| Full Idea: Seeing art as expression has two components: 1) if something is a work of art, then it is expressive, 2) if something is expressive, then it is a work of art. So expression can be necessary or sufficient for art. (or both, for Croce and Collingwood). | |
| From: Gary Kemp (Croce and Collingwood [2012], 1) | |
| A reaction: I take the idea that art 'expresses' the feelings of an artist to be false. Artists are more like actors. Nearly all art has some emotional impact, which is of major importance, but I don't think 'expression' is a very good word for that. |
| 20419 | We don't already know what to express, and then seek means of expressing it [Kemp] |
| Full Idea: One cannot really know, or be conscious of, what it is that one is going to express, and then set about expressing it; indeed if one is genuinely conscious of it then one has already expressed it. | |
| From: Gary Kemp (Croce and Collingwood [2012], 1) | |
| A reaction: That pretty conclusively demolishes the idea that art is expression. I picture Schubert composing at the piano: he doesn't feel an emotion, and then hunt for its expression on the keyboard; he seeks out expressive phrases by playing. |
| 20418 | The horror expressed in some works of art could equallly be expressed by other means [Kemp] |
| Full Idea: The horror or terror of Edvard Much's 'The Scream' could in principle be expressed by different paintings, or even by works of music. | |
| From: Gary Kemp (Croce and Collingwood [2012], 1) | |
| A reaction: A very good simple point against the idea that the point of art is expression. It leaves out the very specific nature of each work of art! |
| 7346 | Jeremiah implied a link between weakness and goodness, and the evil of the state [Jeremiah, by Johnson,P] |
| Full Idea: Jeremiah was the first to perceive the possibility that powerlessness and goodness were somehow linked; ...he comes close to the notion that the state itself was inherently evil. | |
| From: report of Jeremiah (24: Book of Jeremiah [c.570 BCE]) by Paul Johnson - The History of the Jews Pt II | |
| A reaction: This looks like the first seeds of the anarchist idea. You abandon the state for something 'higher'. 'Perceive' rather begs the question of whether he is right. This is the full 'inversion of values' of Nietzsche. |
| 22920 | Do I not fill heaven and earth? saith the Lord [Jeremiah] |
| Full Idea: Can any hide himself in secret places that I shall not see him? saith the Lord. Do I not fill heaven and earth? | |
| From: Jeremiah (24: Book of Jeremiah [c.570 BCE], 23:24), quoted by Robin Le Poidevin - Travels in Four Dimensions 03 'Where' | |
| A reaction: If the Lord is omnipresent, then He must be present in each one of us. But does the Lord interact with each of us? |
| 22089 | Am I a God afar off, and not a God close at hand? [Jeremiah] |
| Full Idea: Am I a God afar off, and not a God close at hand? Do I not fill heaven and earth? | |
| From: Jeremiah (24: Book of Jeremiah [c.570 BCE], 23:23), quoted by Clare Carlisle - Kierkegaard: a guide for the perplexed 3 | |
| A reaction: I assume this was often quoted by eighteenth century divines, against the rise of deism. |