17 ideas
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
A reaction: Each expansion brings a limitation, but then you can expand again. |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
21507 | Scientific explanation aims at a unifying account of underlying structures and processes [Hempel] |
Full Idea: What theoretical scientific explanation aims at is an objective kind of insight that is achieved by a systematic unification, by exhibiting the phenomena as manifestations of common underlying structures and processes that conform to testable principles. | |
From: Carl Hempel (Philosophy of Natural Science [1967], p.83), quoted by Laurence Bonjour - The Structure of Empirical Knowledge 5.3 | |
A reaction: This is a pretty good statement of scientific essentialism, and structures and processes are what I take Aristotle to have had in mind when he sought 'what it is to be that thing'. Structures and processes give stability and powers. |
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. |