3 ideas
| 18801 | Classical negation is circular, if it relies on knowing negation-conditions from truth-conditions [Dummett] |
| Full Idea: Explanations of classical negation assume that knowing what it is for the truth-condition of some statement to obtain, independently of recognising it to obtain, we thereby know what it is for it NOT to obtain; but this presupposes classical negation. | |
| From: Michael Dummett (The Logical Basis of Metaphysics [1991], p.299), quoted by Ian Rumfitt - The Boundary Stones of Thought 1.1 | |
| A reaction: [compressed wording] This is Dummett explaining why he prefers intuitionistic logic, with its doubts about double negation. |
| 10245 | One geometry cannot be more true than another [Poincaré] |
| Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
| From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
| A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
| 21097 | Modern monarchies are (like republics) rule by law, rather than by men [Hume] |
| Full Idea: In modern times monarchical government seems to have made the greatest advances towards perfection. It may now be affirmed of civilized monarchies, what was formerly said in praise of republics alone, that they are a government of laws, not of men. | |
| From: David Hume (Of Civil Liberty [1750], p.54) | |
| A reaction: Dreams of simple 'government by law' disappeared with the rise of modern media, which can be controlled by wealth. |