display all the ideas for this combination of philosophers
2 ideas
| 18690 | Induction is said to just compare properties of categories, but the type of property also matters [Murphy] |
| Full Idea: Most theories of induction claim that it should depend primarily on the similarity of the categories involved, but then the type of property should not matter, yet research shows that it does. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 6) | |
| A reaction: I take this to be good empirical support for Gilbert Harman's view that induction is really inference to the best explanation. The thought (which strikes me as obviously correct) is that we bring nested domains of knowledge to bear in induction. |
| 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. |