5 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? |
2614 | Modern phenomenalism holds that objects are logical constructions out of sense-data [Ayer] |
Full Idea: Nowadays phenomenalism is held to be a theory of perception which says that physical objects are logical constructions out of sense-data. | |
From: A.J. Ayer (Phenomenalism [1947], §1) |
2615 | The concept of sense-data allows us to discuss appearances without worrying about reality [Ayer] |
Full Idea: The introduction of the term 'sense-datum' is a means of referring to appearances without prejudging the question of what it is, if anything, that they are appearances of. | |
From: A.J. Ayer (Phenomenalism [1947], §1) |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |