3 ideas
| 10180 | Mathematicians do not study objects, but relations between objects [Poincaré] |
| Full Idea: Mathematicians do not study objects, but relations between objects; it is a matter of indifference if the objects are replaced by others, provided the relations do not change. They are interested in form alone, not matter. | |
| From: Henri Poincaré (Science and Hypothesis [1902], p.20), quoted by E Reck / M Price - Structures and Structuralism in Phil of Maths §6 | |
| A reaction: This connects modern structuralism with Aritotle's interest in the 'form' of things. Contrary to the views of the likes of Frege, it is hard to see that the number '7' has any properties at all, apart from its relations. A daffodil would do just as well. |
| 13128 | 'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins] |
| Full Idea: 'Ultimate sortals' are said to be non-subordinated, disjoint from one another, and uniquely paired with each object. Because of this, the ultimate sortal cannot be a satisfactory explication of the notion of an ontological category. | |
| From: comment on David Wiggins (Identity and Spatio-Temporal Continuity [1971], p.75) by Jan Westerhoff - Ontological Categories §26 | |
| A reaction: My strong intuitions are that Wiggins is plain wrong, and Westerhoff gives the most promising reasons for my intuition. The simplest point is that objects can obviously belong to more than one category. |
| 6570 | Imagine millions made happy on condition that one person suffers endless lonely torture [James] |
| Full Idea: Consider a case in which millions could be made permanently happy on the one simple condition that a certain lost soul on the far-off edge of things should lead a life of lonely torture. | |
| From: William James (The Will to Believe [1896], p.188), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.2 | |
| A reaction: This seems to be one of the earliest pinpointings of a key problem with utilitiarianism, which is that other values than happiness (in this case, fairness) seem to be utterly overruled. If we ignore fairness, why shouldn't we ignore happiness? |