10 ideas
| 3035 | Dialectic involves conversations with short questions and brief answers [Diog. Laertius] |
| Full Idea: Dialectic is when men converse by putting short questions and giving brief answers to those who question them. | |
| From: Diogenes Laertius (Lives of Eminent Philosophers [c.250], 3.1.52) |
| 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? |
| 1816 | Sceptics say demonstration depends on self-demonstrating things, or indemonstrable things [Diog. Laertius] |
| Full Idea: Sceptics say that every demonstration depends on things which demonstrates themselves, or on things which can't be demonstrated. | |
| From: Diogenes Laertius (Lives of Eminent Philosophers [c.250], 9.Py.11) | |
| A reaction: This refers to two parts of Agrippa's Trilemma (the third being that demonstration could go on forever). He makes the first option sound very rationalist, rather than experiential. |
| 1819 | Scepticism has two dogmas: that nothing is definable, and every argument has an opposite argument [Diog. Laertius] |
| Full Idea: Sceptics actually assert two dogmas: that nothing should be defined, and that every argument has an opposite argument. | |
| From: Diogenes Laertius (Lives of Eminent Philosophers [c.250], 9.Py.11) |
| 3064 | When sceptics say that nothing is definable, or all arguments have an opposite, they are being dogmatic [Diog. Laertius] |
| Full Idea: When sceptics say that they define nothing, and that every argument has an opposite argument, they here give a positive definition, and assert a positive dogma. | |
| From: Diogenes Laertius (Lives of Eminent Philosophers [c.250], 9.11.11) |
| 3033 | Induction moves from some truths to similar ones, by contraries or consequents [Diog. Laertius] |
| Full Idea: Induction is an argument which by means of some admitted truths establishes naturally other truths which resemble them; there are two kinds, one proceeding from contraries, the other from consequents. | |
| From: Diogenes Laertius (Lives of Eminent Philosophers [c.250], 3.1.23) |
| 18555 | The beautiful is that from which nothing can be subtracted and to which nothing can be added [Alberti] |
| Full Idea: The beautiful is that from which nothing can be taken away and to which nothing can be added but for the worse. | |
| From: Leon Battista Alberti (De Re Aedificatoria [1485]), quoted by Roger Scruton - Beauty: a very short introduction 9 | |
| A reaction: Scruton rejects this Platonic tradition of beauty as organic wholeness, because you can't say how it would be 'worse' without invoking beauty, which makes it circular. Scruton appears to be correct. |
| 1838 | Cyrenaic pleasure is a motion, but Epicurean pleasure is a condition [Diog. Laertius] |
| Full Idea: Cyrenaics place pleasure wholly in motion, whereas Epicurus admits it as a condition. | |
| From: Diogenes Laertius (Lives of Eminent Philosophers [c.250], 10.28) | |
| A reaction: Not a distinction we meet in modern discussions. Do events within the mind count as 'motion'? If so, these two agree. If not, I'd vote for Epicurus. |
| 1769 | Cynics believe that when a man wishes for nothing he is like the gods [Diog. Laertius] |
| Full Idea: Cynics believe that when a man wishes for nothing he is like the gods. | |
| From: Diogenes Laertius (Lives of Eminent Philosophers [c.250], 6.Men.3) |