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? |
| 4867 | Whether nature is beautiful or orderly is entirely in relation to human imagination [Spinoza] |
| Full Idea: I do not attribute to nature either beauty or deformity, order or confusion. Only in relation to our imagination can things be called beautiful or deformed, ordered or confused. | |
| From: Baruch de Spinoza (Letters to Oldenburg [1665], 1665?) | |
| A reaction: This is clearly a statement of Hume's famous later opinion that there are no values ('ought') in nature ('is'). It is a rejection of Aristotelian and Greek teleology. It is hard to argue with, but I have strong sales resistance, rooted in virtue theory. |
| 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'). |
| 4866 | God is a being with infinite attributes, each of them infinite or perfect [Spinoza] |
| Full Idea: I define God as a being consisting in infinite attributes, whereof each is infinite or supremely perfect. | |
| From: Baruch de Spinoza (Letters to Oldenburg [1665], 1661) | |
| A reaction: This seems to me the glorious culmination of the hyperbolic conception of God that expands steadily from wood spirits through Zeus, to eventually mop up everything in nature, and then everything that can be imagined beyond nature. All very silly. |
| 4868 | Trying to prove God's existence through miracles is proving the obscure by the more obscure [Spinoza] |
| Full Idea: Those who endeavour to establish God's existence and the truth of religion by means of miracles seek to prove the obscure by what is more obscure. | |
| From: Baruch de Spinoza (Letters to Oldenburg [1665], 1675?) | |
| A reaction: Nicely put. On the whole this has to be right, but one must leave open a possibility. If there is a God, and He seeks to prove Himself by a deed, are we saying this is impossible? Divine intervention might be the best explanation of something. |