display all the ideas for this combination of philosophers
2 ideas
| 22193 | Consilience makes the component sciences more likely [Gorham] |
| Full Idea: The more unification and integration is found among the modern sciences, the less likely it seems it will have all been a dream. | |
| From: Geoffrey Gorham (Philosophy of Science [2009], 4) | |
| A reaction: I believe this strongly. Ancient theories which were complex, wide ranging and false do not impress me. This is part of my coherence view of justification. |
| 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. |