5 ideas
| 9987 | An aggregate in which order does not matter I call a 'set' [Bolzano] |
| Full Idea: An aggregate whose basic conception renders the arrangement of its members a matter of indifference, and whose permutation therefore produces no essential difference, I call a 'set'. | |
| From: Bernard Bolzano (Paradoxes of the Infinite [1846], §4), quoted by William W. Tait - Frege versus Cantor and Dedekind IX | |
| A reaction: The idea of 'sets' was emerging before Cantor formalised it, and clarified it by thinking about infinite sets. Nowadays we also have 'ordered' sets, which rather contradicts Bolzano, and we also expect the cardinality to be determinate. |
| 10856 | A truly infinite quantity does not need to be a variable [Bolzano] |
| Full Idea: A truly infinite quantity (for example, the length of a straight line, unbounded in either direction) does not by any means need to be a variable. | |
| From: Bernard Bolzano (Paradoxes of the Infinite [1846]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable §10 | |
| A reaction: This is an important idea, followed up by Cantor, which relegated to the sidelines the view of infinity as simply something that could increase without limit. Personally I like the old view, but there is something mathematically stable about infinity. |
| 16383 | Puzzled Pierre has two mental files about the same object [Recanati on Kripke] |
| Full Idea: In Kripke's puzzle about belief, the subject has two distinct mental files about one and the same object. | |
| From: comment on Saul A. Kripke (A Puzzle about Belief [1979]) by François Recanati - Mental Files 17.1 | |
| A reaction: [Pierre distinguishes 'London' from 'Londres'] The Kripkean puzzle is presented as very deep, but I have always felt there was a simple explanation, and I suspect that this is it (though I will leave the reader to think it through, as I'm very busy…). |
| 8416 | Reductionists can't explain accidents, uninstantiated laws, probabilities, or the existence of any laws [Tooley] |
| Full Idea: Reductionist accounts of causation cannot distinguish laws from accidental uniformities, cannot allow for basic uninstantiated laws, can't explain probabilistic laws, and cannot even demonstrate the existence of laws. | |
| From: Michael Tooley (Causality: Reductionism versus Realism [1990], 2) | |
| A reaction: I am tempted to say that this is so much the worse for the idea of laws. Extensive regularities only occur for a reason. Probabilities aren't laws. Hypothetical facts will cover uninstantiated laws. Laws are just patterns. |
| 8418 | Quantum physics suggests that the basic laws of nature are probabilistic [Tooley] |
| Full Idea: Quantum physics seems to lend strong support to the idea that the basic laws of nature may well be probabilistic. | |
| From: Michael Tooley (Causality: Reductionism versus Realism [1990], 3.2.1) | |
| A reaction: Groan. Quantum physics should be outlawed from all philosophical discussions. The scientists don't understand it themselves. I'm certainly not going to build my worldview on it. I don't accept that these probabilities could count as 'laws'. |