3 ideas
| 22304 | Truth is conceivability, or the systematic coherence of a significant whole [Joachim] |
| Full Idea: Truth is in its essence conceivability or systematic coherence. ...[p.78] It is the systematic coherence which characterises a significant whole. | |
| From: Harold Joachim (The Nature of Truth [1906], p.68), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 35 'coh' | |
| A reaction: We obviously need to know when a whole becomes 'significant'. Potter says mystical idealists liked this because it contributed to their teleological view of the whole of reality. Presumably its roots are in Hegel. |
| 18189 | ZFC could contain a contradiction, and it can never prove its own consistency [MacLane] |
| Full Idea: We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC. | |
| From: Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30). |
| 12709 | Motion is not absolute, but consists in relation [Leibniz] |
| Full Idea: In reality motion is not something absolute, but consists in relation. | |
| From: Gottfried Leibniz (On Motion [1677], A6.4.1968), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 3 | |
| A reaction: It is often thought that motion being relative was invented by Einstein, but Leibniz wholeheartedly embraced 'Galilean relativity', and refused to even consider any absolute concept of motion. Acceleration is a bit trickier than velocity. |