4 ideas
| 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. |
| 3291 | Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel] |
| Full Idea: The supposition that a diamond or organism should truly have emergent properties is that they appear at certain complex levels of organisation, but are not explainable (even in principle) in terms of any more fundamental properties of the system. | |
| From: Thomas Nagel (Panpsychism [1979], p.186) |
| 490 | Everything happens by reason and necessity [Leucippus] |
| Full Idea: Nothing happens at random; everything happens out of reason and by necessity. | |
| From: Leucippus (fragments/reports [c.435 BCE], B002), quoted by (who?) - where? |
| 3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |
| Full Idea: Given what heat is and what water is, it is literally impossible for water to be heated beyond a certain point at normal atmospheric pressure without boiling. | |
| From: Thomas Nagel (Panpsychism [1979], p.186) |