7 ideas
| 8226 | A well-posed problem is a problem solved [Bergson, by Deleuze/Guattari] |
| Full Idea: Bergson said that a well-posed problem was a problem solved | |
| From: report of Henri Bergson (works [1910]) by G Deleuze / F Guattari - What is Philosophy? 1.3 | |
| A reaction: This is fairly well in tune with the logical positivist style of philosophising, which tends to ask "what exactly is the question?" rather more than it asks "what is the answer?". I thoroughly approve of both of them (e.g. on free will). |
| 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. |
| 23647 | Objects have an essential constitution, producing its qualities, which we are too ignorant to define [Reid] |
| Full Idea: Individuals and objects have a real essence, or constitution of nature, from which all their qualities flow: but this essence our faculties do not comprehend. They are therefore incapable of definition. | |
| From: Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1) | |
| A reaction: Aha - he's one of us! I prefer the phrase 'essential nature' of an object, which is understood, I think, by everyone. I especially like the last bit, directed at those who mistakenly think that Aristotle identified the essence with the definition. |
| 11958 | Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar] |
| Full Idea: Reid pointed out how easily conceivable mathematical and geometric impossibilities are. | |
| From: report of Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], IV.III) by George Molnar - Powers 11.3 | |
| A reaction: The defence would be that you have to really really conceive them, and the only way the impossible can be conceived is by blurring it at the crucial point, or by claiming to conceive more than you actually can |
| 23646 | Reference is by name, or a term-plus-circumstance, or ostensively, or by description [Reid] |
| Full Idea: An individual is expressed by a proper name, or by a general word joined to distinguishing circumstances; if unknown, it may be pointed out to the senses; when beyond the reach of the senses it may be picked out by an imperfect but true description. | |
| From: Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1) | |
| A reaction: [compressed] If Putnam, Kripke and Donnellan had read this paragraph they could have save themselves a lot of work! I take reference to be the activity of speakers and writers, and these are the main tools of the trade. |
| 23645 | A word's meaning is the thing conceived, as fixed by linguistic experts [Reid] |
| Full Idea: The meaning of a word (such as 'felony') is the thing conceived; and that meaning is the conception affixed to it by those who best understand the language. | |
| From: Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1) | |
| A reaction: He means legal experts. This is precisely that same as Putnam's account of the meaning of 'elm tree'. His discussion here of reference is the earliest I have encountered, and it is good common sense (for which Reid is famous). |