4 ideas
14235 | Saying 'they can become a set' is a tautology, because reference to 'they' implies a collection [Cargile] |
Full Idea: If the rule is asserted 'Given any well-determined objects, they can be collected into a set by an application of the 'set of' operation', then on the usual account of 'they' this is a tautology. Collection comes automatically with this form of reference. | |
From: James Cargile (Paradoxes: Form and Predication [1979], p.115), quoted by Oliver,A/Smiley,T - What are Sets and What are they For? Intro | |
A reaction: Is this a problem? Given they are well-determined (presumably implying countable) there just is a set of them. That's what set theory is, I thought. Of course, the iterative view talks of 'constructing' the sets, but the construction looks unstoppable. |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |
20645 | Heat is a state of vibration, not a substance [Joule] |
Full Idea: We consider heat not as a substance but as a state of vibration. | |
From: James Joule (works [1870]), quoted by Peter Watson - Convergence 01 'Nature's' | |
A reaction: The puzzle is that giving accurate accounts of vibrations, heat and movement require a quantitative substance, energy. But all we have here is movement, and the denial of a substance. Energy is 'nature's currency system'. |
20972 | Joule showed that energy converts to heat, and heat to energy [Joule, by Papineau] |
Full Idea: James Joule established the equivalence of heat and mechanical energy, in the sense of showing that a specific amount of heat will always be produced by the expenditure of a given amount of energy, and vice versa. | |
From: report of James Joule (works [1870]) by David Papineau - Thinking about Consciousness App 4.2 | |
A reaction: This was a major step towards the law of conservation of energy. |