display all the ideas for this combination of texts
2 ideas
| 9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
| Full Idea: A set is any collection into a whole M of definite, distinct objects m ... of our intuition or thought. | |
| From: George Cantor (The Theory of Transfinite Numbers [1897], p.85), quoted by James Robert Brown - Philosophy of Mathematics Ch.2 | |
| A reaction: This is the original conception of a set, which hit trouble with Russell's Paradox. Cantor's original definition immediately invites thoughts about the status of vague objects. |
| 7035 | God does not create the world, and then add the classes [Heil] |
| Full Idea: It is hard to see classes as an 'addition of being'; God does not create the world, and then add the classes. | |
| From: John Heil (From an Ontological Point of View [2003], 13.4 n6) | |
| A reaction: This seems right. We may be tempted into believing in the reality of classes when considering maths, but it seems utterly implausible when considering trees or cows. |