3 ideas
| 8972 | What in the real world could ground the distinction between the sets {A,{A,B}} and {B,{A,B}}? [Inwagen] |
| Full Idea: Nothing in the world of nominalistically acceptable things could ground or explain the non-identity of the set {A,{A,B}} with the set {B,{A,B}}. | |
| From: Peter van Inwagen (Existence,Ontological Commitment and Fictions [2003], p.154) | |
| A reaction: [He cites Goodman for this thought] Van Inwagen is offering this to show that the existence of sets is abstract, whereas Goodman was denying the existence of sets altogether. I'm with Goodman. Nice example. |
| 10247 | We have no adequate logic at the moment, so mathematicians must create one [Veblen] |
| Full Idea: Formal logic has to be taken over by mathematicians. The fact is that there does not exist an adequate logic at the present time, and unless the mathematicians create one, no one else is likely to do so. | |
| From: Oswald Veblen (Presidential Address of Am. Math. Soc [1924], 141), quoted by Stewart Shapiro - Philosophy of Mathematics | |
| A reaction: This remark was made well after Frege, but before the advent of Gödel and Tarski. That implies that he was really thinking of meta-logic. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |