7 ideas
| 10053 | Geometrical axioms imply the propositions, but the former may not be true [Russell] |
| Full Idea: We must only assert of various geometries that the axioms imply the propositions, not that the axioms are true and therefore that the propositions are true. | |
| From: Bertrand Russell (Foundations of Geometry [1897], Intro vii), quoted by Alan Musgrave - Logicism Revisited §4 | |
| A reaction: Clearly the truth of the axioms can remain a separate issue from whether they actually imply the theorems. The truth of the axioms might be as much a metaphysical as an empirical question. Musgrave sees this as the birth of if-thenism. |
| 10052 | Geometry is united by the intuitive axioms of projective geometry [Russell, by Musgrave] |
| Full Idea: Russell sought what was common to Euclidean and non-Euclidean systems, found it in the axioms of projective geometry, and took a Kantian view of them. | |
| From: report of Bertrand Russell (Foundations of Geometry [1897]) by Alan Musgrave - Logicism Revisited §4 | |
| A reaction: Russell's work just preceded Hilbert's famous book. Tarski later produced some logical axioms for geometry. |
| 17527 | Causation seems to be an innate concept (or acquired very early) [Bird] |
| Full Idea: There is evidence that the concept of causation is innate, or that we are primed to acquire it very early in life, within months at most. | |
| From: Alexander Bird (Causation and the Manifestation of Powers [2010], p.167) | |
| A reaction: Bird doesn't give any references. This is important for our understanding of induction. Creatures seem to learn from a single instance, rather than waiting for habit to be ingrained by many instances. They must infer a cause. |
| 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 |
| 17528 | The dispositional account explains causation, as stimulation and manifestation of dispositions [Bird] |
| Full Idea: The analysis of causation in terms of dispositions provides no conceptual reduction, but it does provide insight into the metaphysics of causation. We then know what causation is - it is the stimulation and manifestation of a disposition. | |
| From: Alexander Bird (Causation and the Manifestation of Powers [2010], p.167) | |
| A reaction: I would say that it offers the essence of causation, by giving a basic explanation of it. See Mumford/Lill Anjum on this. |
| 17526 | The counterfactual approach makes no distinction between cause and pre-condition [Bird] |
| Full Idea: The counterfactual approach makes no distinction between cause and condition, ...but when the smoke sets off the fire alarm, the smoke is the cause, whereas the presence of the alarm is just the condition. | |
| From: Alexander Bird (Causation and the Manifestation of Powers [2010], p.162) | |
| A reaction: Bird defends the idea that causes are what stimulate dispositions to act. |
| 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 |