18 ideas
13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
Full Idea: Von Neumann's decision was to start with the ordinals and to treat cardinals as a special sort of ordinal. | |
From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by William D. Hart - The Evolution of Logic 3 | |
A reaction: [see Hart 73-74 for an explication of this] |
12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
Full Idea: In Von Neumann's definition an ordinal is a transitive set in which all of the elements are transitive. | |
From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Alain Badiou - Briefings on Existence 11 |
18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
Full Idea: For Von Neumann the successor of n is n U {n} (rather than Zermelo's successor, which is {n}). | |
From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n8 |
18180 | Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann] |
Full Idea: Von Neumann's version of the natural numbers is in fact preferred because it carries over directly to the transfinite ordinals. | |
From: comment on John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n9 |
15925 | Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine] |
Full Idea: Each Von Neumann ordinal number is the set of its predecessors. ...He had shown how to introduce ordinal numbers as sets, making it possible to use them without leaving the domain of sets. | |
From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Shaughan Lavine - Understanding the Infinite V.3 |
8507 | Some think of reality as made of things; I prefer facts or states of affairs [Armstrong] |
Full Idea: Some philosophers (like Devitt) think of reality as made up of things. Others, like me, think of it as made up of facts or states of affairs. | |
From: David M. Armstrong (Against 'Ostrich Nominalism' [1980], §3) | |
A reaction: Devitt is a follower of Quine on this. Personally I rather like 'processes'. Unanalysed things with predication (Quine) don't look promising. I currently favour things with active powers, which give rise to properties. See Shoemaker and Ellis. |
8506 | Particulars and properties are distinguishable, but too close to speak of a relation [Armstrong] |
Full Idea: I favour the Realist view that while we can distinguish the particularity of a particular from its properties, but the two 'factors' are too intimately together to speak of a relation between them. | |
From: David M. Armstrong (Against 'Ostrich Nominalism' [1980], §3) | |
A reaction: Is Armstrong being a bit of an ostrich here? We could talk of part-whole relationships, or internal relations, or set membership, or coinciding objects, or bundles. We certainly ought to have a go. Armstrong approaches Quine here! |
8505 | Refusal to explain why different tokens are of the same type is to be an ostrich [Armstrong] |
Full Idea: A philosophical account of a general sort is required of what it is for different tokens to be of the same type. To refuse to give such an account is to be a metaphysical ostrich. | |
From: David M. Armstrong (Against 'Ostrich Nominalism' [1980], §1) | |
A reaction: This defines Ostrich Nominalism (a label Armstrong aims at Quine). I certainly sympathise with Armstrong. If there is no more to a class (a type) than just having members (tokens), nothing is explain. What is natural, essential, intensional etc.? |
23865 | Morality would improve if people could pursue private interests [Weil] |
Full Idea: The common run of moralists complain that man is moved by his private interest: would to heaven it were so! | |
From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.65) | |
A reaction: Her point is that currently people have to sacrifice their own interests to communal activities which offer dubious benefits. |
23866 | In oppressive societies the scope of actual control is extended by a religion of power [Weil] |
Full Idea: Every oppressive society is cemented by a religion of power, which falsifies all social relations by enabling the powerful to command over and above what they are able to impose. | |
From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.69) | |
A reaction: A rather acute and accurate observation, I think. Flashy cars, grand uniforms, lots of medals, rituals of deference….. Sometimes I like the order and security this brings, but Simone Weil could quickly change my view. |
23871 | No central authority can initiate decentralisation [Weil] |
Full Idea: It is quite patently impossible for decentralisation to be initiated by the central authority. | |
From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.113) | |
A reaction: This is contradicted by the creation of regional parliaments and mayors, but we see nothing beyond that. A state could crumble into small parts if there were'lots of autonomous regional groups. Easier for weird minorities to take control. |
23867 | After a bloody revolution the group which already had the power comes to the fore [Weil] |
Full Idea: There is no real break in continuity after a bloody struggle for regime change; for the victory just sanctions forces that before the struggle were the decisive factor in community life, patterns which were replacing those of the declining regime. | |
From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.73) | |
A reaction: [from Marx] I assume she has in mind the French Revolution, and perhaps the Russian Revolution, though in the latter the new bourgeois leaders also got swept away. So revolutions are not nearly as dramatic as they appear to be. |
23870 | Decentralisation is only possible by co-operation between strong and weak - which is absurd [Weil] |
Full Idea: The only possibility of salvation would lie in a co-operation between weak and strong, with a view to accomplishing a progressive decentralisation of social life; but the absurdity of such an idea strikes one immediately. | |
From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.113) | |
A reaction: I take this to be a judgement on the anarchist ideal, rather than a bit of modest devolution. The UK government set up regional parliaments. She says centralisation is remorseless. |
23863 | Only individual people of good will can achieve social progress [Weil] |
Full Idea: The enlightened goodwill of men acting in an individual capacity is the only possible principle of social progress. | |
From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.57) | |
A reaction: I identify with this. Virtually every admirable institution in a society can be traced back to the initiative of a few individuals. Every helpful technology was someone's brainwave. |
23869 | In the least evil societies people can think, control community life, and be autonomous [Weil] |
Full Idea: The least evil society is that in which the general run of men are most often obliged to think while acting, have the most opportunities for exercising control over collective life as a whole, and enjoy the greatest amount of independence. | |
From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.97) | |
A reaction: So Simone Weil was a liberal. How do you stop the most dynamic thinkers, social controllers, and exercisers of their own independence from coming to dominate the others? Only liberal institutions, such as the law and education, can do this. |
23861 | Marx showed that capitalist oppression, because of competition, is unstoppable [Weil] |
Full Idea: Marx gives a first-rate account of the mechanism of capitalist oppression; but so good is it that one finds it hard to visualise how this mechanism could cease to function. …The exploitation is the competitive need to expand as rapidly as possible. | |
From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.39) | |
A reaction: [Last bit compressed] This pinpoints the main motivation for desiring to overthrow capitalism. Resistance to that view is presumably the fear that an even worse oppression might replace it. |
23868 | The pleasure of completing tasks motivates just as well as the whip of slavery [Weil] |
Full Idea: The sight of the unfinished task attracts the free man as powerfully as the over-seer's whip stimulates the slave. | |
From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.94) | |
A reaction: This is Weil's key social idea - that freely performed productive work can be, and should be, a joy, as long as it is accompanied by respect and friendship, rather than oppression. Did this idea ever occur to a slave owner? |
23864 | Inequality could easily be mitigated, if it were not for the struggle for power [Weil] |
Full Idea: Inequality could easily be mitigated by the resistance of the weak and the feeling for justice of the strong, …were it not for the intervention of a further factor, namely, the struggle for power. | |
From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.62) | |
A reaction: The implication is that many of 'the strong' are inclined to diminish inequality, but find themselves trapped and unable to do so, because of irresistable capitalist forces. Sounds plausible. |