3 ideas
| 10855 | Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss] |
| Full Idea: I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits ...which are permitted to increase without bound. | |
| From: Carl Friedrich Gauss (Letter to Shumacher [1831]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.7 |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles. | |
| From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro' | |
| A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture? |
| 22881 | Should we value environmental systems for human benefit, or for their own sake? [Hildebrand] |
| Full Idea: There is a long-running debate between anthropo-centrists and eco-centrists. The latter believe that humans must protect environmental systems because they have intrinsic value; the former argue that human interests are the root of all value. | |
| From: David Hildebrand (Dewey [2008], 8 'Environ') | |
| A reaction: How many tigers would you kill to save a human life? Would you allow a human to die in order to save a species from extinction? It is very hard to think that the Earth has great value if humans are removed from it! |