display all the ideas for this combination of philosophers
4 ideas
| 23186 | Numbers enable us to manage the world - to the limits of counting [Nietzsche] |
| Full Idea: Numbers are our major means of making the world manageable. We comprehend as far as we can count, i.e. as far as a constancy can be perceived. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1885-86 [1886], 34[058]) | |
| A reaction: I don't agree with 'major', but it is a nice thought. The intermediate concept is a 'unit', which means identifying something as a 'thing', which is how we seem to grasp the world. So to what extent do we comprehend the infinite. Enter Cantor… |
| 20361 | We need 'unities' for reckoning, but that does not mean they exist [Nietzsche] |
| Full Idea: We need 'unities' in order to be able to reckon: that does not mean we must suppose that such unities exist. | |
| From: Friedrich Nietzsche (The Will to Power (notebooks) [1888], §635) | |
| A reaction: True. I takes this thought to be important in the Psychology of Metaphysics (an unfashionable branch). |
| 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? |