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. |
| 18431 | Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards] |
| Full Idea: Simons's 'nuclear' option blends features of the substratum and bundle theories. First we have tropes collected by virtue of their internal relations, forming the essential kernel or nucleus. This nucleus then bears the non-essential tropes. | |
| From: report of Peter Simons (Particulars in Particular Clothing [1994], p.567) by Douglas Edwards - Properties 3.5 | |
| A reaction: [compression of Edwards's summary] This strikes me as being a remarkably good theory. I am not sure of the ontological status of properties, such that they can (unaided) combine to make part of an object. What binds the non-essentials? |
| 21995 | Must production determine superstructure, or could it be the other way round? [Singer on Marx] |
| Full Idea: Once the 'interaction' between the superstructure and the productive forces is admitted, is it still possible to maintain that production determines the superstructure, rather than the other way round? | |
| From: comment on Karl Marx (Capital Vol. 1 [1867]) by Peter Singer - Marx 7 | |
| A reaction: It is much harder to defend historical determinism if Singer is right about this. Modern capitalism won't admit of the sort of simple distinctions that mark was looking for. |
| 20577 | Even decently paid workers still have their produce bought with money stolen from them [Marx] |
| Full Idea: Even if the workers are paid a fair wage, the whole thing still remains the age-old activity of the conqueror, who buys commodities from the conquered with the money has has stolen from them, | |
| From: Karl Marx (Capital Vol. 1 [1867], p.728), quoted by Johanna Oksala - Political Philosophy: all that matters Ch.8 | |
| A reaction: [Penguin edition cited] The word 'stolen' is obviously dubious here. 'Exploitation' is a much more accurate word. One might talk of 'blackmail' or 'extortion' rather than theft. |