3 ideas
| 9226 | If mathematical theories conflict, it may just be that they have different subject matter [Field,H] |
| Full Idea: Unlike logic, in the case of mathematics there may be no genuine conflict between alternative theories: it is natural to think that different theories, if both consistent, are simply about different subjects. | |
| From: Hartry Field (Recent Debates on the A Priori [2005], 7) | |
| A reaction: For this reason Field places logic at the heart of questions about a priori knowledge, rather than mathematics. My intuitions make me doubt his proposal. Given the very simple basis of, say, arithmetic, I would expect all departments to connect. |
| 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? |
| 13097 | Force in substance makes state follow state, and ensures the very existence of substance [Leibniz] |
| Full Idea: By the force I give to substances, I understand a state from which another state follows, if nothing prevents it. ...I dare say that without force, there would be no substance. | |
| From: Gottfried Leibniz (Letters to Lelong [1712], 1712), quoted by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 7.1 | |
| A reaction: [the whole quote is interesting] This remark, more than any other I have found, places force at the centre of Leibniz's metaphysics. He is using it to resist Spinoza's one-substance view. |