4 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? |
7073 | I am a creative nothing, out of which I myself create everything [Stirner] |
Full Idea: I am not nothing in the sense of emptiness, but I am the creative nothing, the nothing out of which I myself as creator create everything. | |
From: Max Stirner (The Ego and Its Own [1844]), quoted by Simon Critchley - Continental Philosophy - V. Short Intro Ch.2 | |
A reaction: This appears to be the germ of the entire existentialist view, which gives a helpful gloss on the concept of 'nothing' - as the motivation for human creation, the vacuum in the mind that has to be filled. Call it 'creative boredom'. |
6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
Full Idea: Hermarchus said that animal killing is justified by considerations of human safety and nourishment and by animals' inability to form contractual relations of justice with us. | |
From: report of Hermarchus (fragments/reports [c.270 BCE]) by David A. Sedley - Hermarchus | |
A reaction: Could the last argument be used to justify torturing animals? Or could we eat a human who was too brain-damaged to form contracts? |