11 ideas
| 9148 | I think of variables as objects rather than as signs [Fine,K] |
| Full Idea: It is natural nowadays to think of variables as a certain kind of sign, but I wish to think of them as a certain kind of object. | |
| From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §2) | |
| A reaction: Fine has a theory based on 'arbitrary objects', which is a rather charming idea. The cell of a spreadsheet is a kind of object, I suppose. A variable might be analogous to a point in space, where objects can locate themselves. |
| 9152 | If green is abstracted from a thing, it is only seen as a type if it is common to many things [Fine,K] |
| Full Idea: In traditional abstraction, the colour green merely has the intrinsic property of being green, other properties of things being abstracted away. But why should that be regarded as a type? It must be because the property is common to the instances. | |
| From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §5) | |
| A reaction: A nice question which shows that the much-derided single act of abstraction is not sufficient to arrive at a concept, so that abstraction is a more complex matter (perhaps even a rational one) than simple empiricists believe. |
| 9149 | To obtain the number 2 by abstraction, we only want to abstract the distinctness of a pair of objects [Fine,K] |
| Full Idea: In abstracting from the elements of a doubleton to obtain 2, we do not wish to abstract away from all features of the objects. We wish to take account of the fact that the two objects are distinct; this alone should be preserved under abstraction. | |
| From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §3) | |
| A reaction: This is Fine's strategy for meeting Frege's objection to abstraction, summarised in Idea 9146. It seems to use the common sense idea that abstraction is not all-or-nothing. Abstraction has degrees (and levels). |
| 9150 | We should define abstraction in general, with number abstraction taken as a special case [Fine,K] |
| Full Idea: Number abstraction can be taken to be a special case of abstraction in general, which can then be defined without recourse to the concept of number. | |
| From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §3) | |
| A reaction: At last, a mathematical logician recognising that they don't have a monopoly on abstraction. It is perfectly obvious that abstractions of simple daily concepts must be chronologically and logically prior to number abstraction. Number of what? |
| 9146 | After abstraction all numbers seem identical, so only 0 and 1 will exist! [Fine,K] |
| Full Idea: In Cantor's abstractionist account there can only be two numbers, 0 and 1. For abs(Socrates) = abs(Plato), since their numbers are the same. So the number of {Socrates,Plato} is {abs(Soc),abs(Plato)}, which is the same number as {Socrates}! | |
| From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §1) | |
| A reaction: Fine tries to answer this objection, which arises from §45 of Frege's Grundlagen. Fine summarises that "indistinguishability without identity appears to be impossible". Maybe we should drop talk of numbers in terms of sets. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 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. |