6 ideas
| 13165 | Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus] |
| Full Idea: Geometry does not ask 'why?' ..When from the exterior angle equalling two opposite interior angles it is shown that the interior angles make two right angles, this is not a causal demonstration. With no exterior angle they still equal two right angles. | |
| From: Proclus (Commentary on Euclid's 'Elements' [c.452], p.161-2), quoted by Paolo Mancosu - Explanation in Mathematics §5 | |
| A reaction: A very nice example. It is hard to imagine how one might demonstrate the cause of the angles making two right angles. If you walk, turn left x°, then turn left y°, then turn left z°, and x+y+z=180°, you end up going in the original direction. |
| 9569 | The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus] |
| Full Idea: It is unsurprising that geometry was discovered in the necessity of Nile land measurement, since everything in the world of generation goes from imperfection to perfection. They would naturally pass from sense-perception to calculation, and so to reason. | |
| From: Proclus (Commentary on Euclid's 'Elements' [c.452]), quoted by Charles Chihara - A Structural Account of Mathematics 9.12 n55 | |
| A reaction: The last sentence is the core of my view on abstraction, that it proceeds by moving through levels of abstraction, approaching more and more general truths. |
| 22405 | Negative utilitarianism implies that the world should be destroyed, to avoid future misery [Smart] |
| Full Idea: The doctrine of negative utilitarianism (that we should concern ourselves with the minimisation of suffering, rather than the maximisation of happiness) ...means we should support a tyrant who explodes the world, to prevent infinite future misery. | |
| From: J.J.C. Smart (Outline of a System of Utilitarianism [1973], 5) | |
| A reaction: That only seems to imply that the negative utilitarian rule needs supplementary rules. We are too fond of looking for one single moral rule that guides everything. |
| 22404 | Any group interested in ethics must surely have a sentiment of generalised benevolence [Smart] |
| Full Idea: A utilitarian can appeal to the sentiment of generalised benevolence, which is surely present in any group with whom it is profitable to discuss ethical questions. | |
| From: J.J.C. Smart (Outline of a System of Utilitarianism [1973], I) | |
| A reaction: But ethics is not intended only for those who are interested in ethics. If this is the basics of ethics, then we must leave the mafia to pursue its sordid activities without criticism. Their lack of sympathy seems to be their good fortune. |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |