11 ideas
| 10245 | One geometry cannot be more true than another [Poincaré] |
| Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
| From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
| A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
| 17818 | How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau] |
| Full Idea: We want to know How many what? You must first partition an aggregate into parts relevant to the question, where no partition is privileged. How the partitioned set is to be numbered is bound up with its unique members, and follows from logic alone. | |
| From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'New Problem') | |
| A reaction: [Compressed wording of Yourgrau's summary of Frege's 'relativity argument'] Concepts do the partitioning. Yourgau says this fails, because the same argument applies to the sets themselves, as well as to the original aggregates. |
| 17822 | Nothing is 'intrinsically' numbered [Yourgrau] |
| Full Idea: Nothing at all is 'intrinsically' numbered. | |
| From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'What the') | |
| A reaction: Once you are faced with distinct 'objects' of some sort, they can play the role of 'unit' in counting, so his challenge is that nothing is 'intrinsically' an object, which is the nihilism explored by Unger, Van Inwagen and Merricks. Aristotle disagrees... |
| 17817 | Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau] |
| Full Idea: The Frege-Maddy definition of number (as the 'property' of being-three) explains why the definitions of Von Neumann, Zermelo and others work, by giving the 'principle of collection' that ties together all threes. | |
| From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'A Fregean') | |
| A reaction: [compressed two or three sentences] I am strongly in favour of the best definition being the one which explains the target, rather than just pinning it down. I take this to be Aristotle's view. |
| 17815 | We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau] |
| Full Idea: Sets could hardly serve as a foundation for number theory if we had to await detailed results in the upper reaches of the edifice before we could make our first move. | |
| From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'Two') |
| 17821 | You can ask all sorts of numerical questions about any one given set [Yourgrau] |
| Full Idea: We can address a set with any question at all that admits of a numerical reply. Thus we can ask of {Carter, Reagan} 'How many feet do the members have?'. | |
| From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'On Numbering') | |
| A reaction: This is his objection to the Fregean idea that once you have fixed the members of a set, you have thereby fixed the unique number that belongs with the set. |
| 22252 | Capitalism may actually be the best way to foster community [Conway,D] |
| Full Idea: Not only is there no good reason for supposing capitalism inimical to community, but there is reason to think it more conducive to community than the feasible alternatives to it. | |
| From: David Conway (Capitalism and Community [1996], I) | |
| A reaction: Conway is defending an obviously unorthodox view, while attacking the hopes of communitarians. |
| 22253 | Capitalism is just the market, with optional limited government, and perhaps democracy [Conway,D] |
| Full Idea: There are three types of capitalism: 1) the market - private ownership, labor contracts and profit, 2) limited government - the state provides goods the market cannot do, 3) limited government with democracy - with political freedom and elections. | |
| From: David Conway (Capitalism and Community [1996], II) | |
| A reaction: [compressed] I would have thought that capitalism is compatible with a fair degree of workplace democracy, which would make a fourth type. |
| 22256 | Capitalism prefers representative democracy, which avoids community decision-making [Conway,D] |
| Full Idea: By opting for representative rather than direct democracy, capitalism is said to preclude political community, for which the citizens of a state must possess a common will, which needs their direct participation in decisions. | |
| From: David Conway (Capitalism and Community [1996], V) | |
| A reaction: Conway does not accept this claim. I'm beginning to wonder whether the famous British electoral system is actually a capitalist conspiracy against the people. |
| 22255 | Capitalism breaks up extended families, and must then provide welfare for the lonely people [Conway,D] |
| Full Idea: It is said that capitalism encourages the breakup of extended families, which creates the need for extensive state welfare for those indigent members of society who can no longer rely on their own family to take care of them. | |
| From: David Conway (Capitalism and Community [1996], V) | |
| A reaction: Conway does not accept this claim. It seems to simplistic to say that capitalism is the sole culprit. Any rise of mechanisation in agriculture would break up rural extended families. |
| 22257 | Capitalism is anti-community, by only valuing individuals, and breaking up families [Conway,D] |
| Full Idea: Communitarns say capitalism is inimical to family community, because it encourages an individualistic mentality which only values self-fulfilment, and because it demands labour mobility which is disruptive of families. | |
| From: David Conway (Capitalism and Community [1996], VI) | |
| A reaction: Chicken-and-egg with the first one. Small entrepreneurs are individualists who seek their own gain. It is big capitalism that sucks in the others. Traditional community is based on labour-intensive agriculture. |