4 ideas
| 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. |
| 14303 | Truth-functional conditionals have a simple falsification, when A is true and B is false [Peirce] |
| Full Idea: The utility of [truth-functional conditionals] is that it puts us in possession of a rule...[namely] The hypothetical proposition may be ...falsified by a single state of things, but only by one in which A [antecedent] is true and B [consequent] is false. | |
| From: Charles Sanders Peirce (On the Algebra of Logic [1895], p.218), quoted by Stephen Mumford - Dispositions | |
| A reaction: Personally I am rather more interested in verifying conditionals than in falsifying them. I certainly don't accept them until they are falsified, unless they have massive support from surrounding facts. |
| 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 |