6 ideas
| 14238 | A class is an aggregate of objects; if you destroy them, you destroy the class; there is no empty class [Frege] |
| Full Idea: A class consists of objects; it is an aggregate, a collective unity, of them; if so, it must vanish when these objects vanish. If we burn down all the trees of a wood, we thereby burn down the wood. Thus there can be no empty class. | |
| From: Gottlob Frege (Elucidation of some points in E.Schröder [1895], p.212), quoted by Oliver,A/Smiley,T - What are Sets and What are they For? | |
| A reaction: This rests on Cantor's view of a set as a collection, rather than on Dedekind, which allows null and singleton sets. |
| 5049 | Intelligent pleasure is the perception of beauty, order and perfection [Leibniz] |
| Full Idea: An intelligent being's pleasure is simply the perception of beauty, order and perfection. | |
| From: Gottfried Leibniz (A Résumé of Metaphysics [1697], §18) | |
| A reaction: Leibniz seems to have inherited this from the Greeks, especially Pythagoras and Plato. Buried in Leibniz's remark I see the Christian fear of physical pleasure. He should have got out more. Must an intelligent being always be intelligent? |
| 20646 | Helmholtz used 'energy' to mathematically link heat, light, electricity and magnetism [Helmholtz, by Watson] |
| Full Idea: Helmholtz provided the requisite mathematical formulation linking heat, light, electricity and magnetism, by treating these phenomena as different manifestations of 'energy'. | |
| From: report of Hermann von Helmholtz (On the Conservation of Force [1847]) by Peter Watson - Convergence 01 'Human' | |
| A reaction: I'm increasingly struck by the neglect by philosophers of nature of these amazing developments in 19th century physics, because they prefer the excitement of the latest nuclear physics. There is more philosophical interest in the earlier stages. |
| 20973 | All forces conserve the sum of kinetic and potential energy [Helmholtz, by Papineau] |
| Full Idea: Helmholtz crucially asserted that all forces conserve the sum of kinetic and potential energy; superficially non-conservative forces like friction are simply macroscopic manifestations of more fundamental forces conserving energy at the micro-level. | |
| From: report of Hermann von Helmholtz (On the Conservation of Force [1847]) by David Papineau - Thinking about Consciousness App 4.3 | |
| A reaction: Friction had been a problem case, because it appeared not to conserve energy when it slowed movement down. |
| 5048 | Perfection is simply quantity of reality [Leibniz] |
| Full Idea: Perfection is simply quantity of reality. | |
| From: Gottfried Leibniz (A Résumé of Metaphysics [1697], §11) | |
| A reaction: An interesting claim, but totally beyond my personal comprehension. I presume he inherited 'quantity of reality' from Plato, e.g. as you move up the Line from shadows to Forms you increase the degree of reality. I see 'real' as all-or-nothing. |
| 5050 | Evil serves a greater good, and pain is necessary for higher pleasure [Leibniz] |
| Full Idea: Evils themselves serve a greater good, and the fact that pains are found in minds is necessary if they are to reach greater pleasures. | |
| From: Gottfried Leibniz (A Résumé of Metaphysics [1697], §23) | |
| A reaction: How much pain is needed to qualify for the 'greater pleasures'? Some people receive an awful lot. I am not sure exactly how an evil can 'serve' a greater good. Is he recommending evil? |