4 ideas
| 18203 | Avoid non-predicative classifications and definitions [Poincaré] |
| Full Idea: Never consider any objects but those capable of being defined in a finite number of word ...Avoid non-predicative classifications and definitions. | |
| From: Henri Poincaré (The Logic of Infinity [1909], p.63), quoted by Penelope Maddy - Naturalism in Mathematics II.4 |
| 13166 | Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu] |
| Full Idea: Essences and essential properties do not seem to be useful in mathematical contexts, since all mathematical truths are regarded as necessary (though Kit Fine distinguishes between essential and necessary properties). | |
| From: Paolo Mancosu (Explanation in Mathematics [2008], §6.1) | |
| A reaction: I take the proviso in brackets to be crucial. This represents a distortion of notion of an essence. There is a world of difference between the central facts about the nature of a square and the peripheral inferences derivable from it. |
| 541 | Virtue comes more from habit than character [Critias] |
| Full Idea: More men are good through habit than through character. | |
| From: Critias (fragments/reports [c.440 BCE], B09), quoted by John Stobaeus - Anthology 3.29.41 |
| 542 | Fear of the gods was invented to discourage secret sin [Critias] |
| Full Idea: When the laws forbade men to commit open crimes of violence, and they began to do them in secret, a wise and clever man invented fear of the gods for mortals, to frighten the wicked, even if they sin in secret. | |
| From: Critias (fragments/reports [c.440 BCE], B25), quoted by Sextus Empiricus - Against the Professors (six books) 9.54 |