12 ideas
| 17809 | Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel] |
| Full Idea: Usually Gödel's incompleteness theorems are taken as showing a limitation on the syntactic approach to an understanding of the concept of infinity. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 05) |
| 17810 | The study of mathematical foundations needs new non-mathematical concepts [Kreisel] |
| Full Idea: It is necessary to use non-mathematical concepts, i.e. concepts lacking the precision which permit mathematical manipulation, for a significant approach to foundations. We currently have no concepts of this kind which we can take seriously. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 06) | |
| A reaction: Music to the ears of any philosopher of mathematics, because it means they are not yet out of a job. |
| 19347 | Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins] |
| Full Idea: For individuation, substance needs three properties: independence, to separate it from other things; unity, to call it one thing, rather than an aggregate; and permanence or stability over time. Its other role is as subject for predicates. | |
| From: Franklin Perkins (Leibniz: Guide for the Perplexed [2007], 3.1) | |
| A reaction: Perkins is describing the Aristotelian view, which is taken up by Leibniz. 'Substance' is not a controversial idea, if we see that it only means that the world is full of 'things'. It is an unusual philosopher wholly totally denies that. |
| 5303 | For the proletariate, law, morality and religion are just expressions of bourgeois interests [Marx/Engels] |
| Full Idea: Law, morality, religion are to the proletarian so many bourgeois prejudices, behind which lurk in ambush just as many bourgeois interests. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], §1) | |
| A reaction: This Marxist idea has been the main driving force in spreading relativist views through modern culture. There is a lot of truth here, but philosophy is plausibly the search for truths which both the bourgeois and the proletarian will accept. |
| 21998 | Bourgeois interests create our morality, law and religion [Marx/Engels] |
| Full Idea: Morality, law and religion are bourgeois prejudices, behind which lurk in ambush just as many bourgeois interests. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], p.230), quoted by Peter Singer - Marx 9 | |
| A reaction: The obvious question is whether this creation of values is conscious or unconscious. Personally I believe in conspiracies. Some cynical conversations go on behind the scenes, of which historians will never hear. |
| 5302 | Modern governments are just bourgeois management committees [Marx/Engels] |
| Full Idea: The executive of the modern State is but a committee for managing the common affairs of the whole bourgeoisie. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], §1) | |
| A reaction: In Britain the Labour Party and the Trade Unions have appeared since 1848, but bourgeoisie control of the media has pushed us a long way back towards Marx's time. Government will always be someone's management committee. |
| 5304 | Communism aims to abolish not all property, but bourgeois property [Marx/Engels] |
| Full Idea: The distinguishing feature of Communism is not the abolition of property generally, but the abolition of bourgeois property. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], §2) | |
| A reaction: This is a sinister remark which has led to huge numbers of murders in the Soviet Union and China. People resent having their property 'abolished', especially if they have worked hard for it. But most of our wealth is owned by about 2% of our people. |
| 5307 | Many of the bourgeois rights grievances are a form of self-defence [Marx/Engels] |
| Full Idea: A part of the bourgeoisie is desirous of redressing social grievances, in order to secure the continued existence of bourgeois society. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], §3.II) | |
| A reaction: …so don't try being nice to us. No TRUE bourgeois would actually want to help the proletariate… Nevertheless, he is probably largely right. Do we want the poor to suffer? No. Do we want them to be as rich as us? No! |
| 5306 | The free development of each should be the condition for the free development of all [Marx/Engels] |
| Full Idea: In a communist society we shall have an association, in which the free development of each is the condition for the free development of all. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], §2) | |
| A reaction: This ringing slogan is remarkably close to John Stuart Mill's defence of liberalism, where liberty is an absolute, as long as it avoids the liberty of others. Personally I think freedom is marginal in political philosophy, like food and shelter. |
| 5305 | Communists want to rescue education from the ruling class [Marx/Engels] |
| Full Idea: Communists seek to rescue education from the influence of the ruling class. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], §2) | |
| A reaction: Someone has to control education, and I would personally prefer it if the controllers were well educated themselves. Neutral education is an idle dream. We must educate for democracy, if we really want democracy. |
| 5301 | The history of all existing society is the history of class struggles [Marx/Engels] |
| Full Idea: The history of all existing society is the history of class struggles. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], §1) | |
| A reaction: This seems to make, say, the English Peasants' Revolt of 1481 crucial, and the building of Lincoln Cathedral fairly minor. Where does the advent of the telephone figure? Etc. Still, we must concede his point. Most medieval history is about power. |
| 17811 | The natural conception of points ducks the problem of naming or constructing each point [Kreisel] |
| Full Idea: In analysis, the most natural conception of a point ignores the matter of naming the point, i.e. how the real number is represented or by what constructions the point is reached from given points. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 13) | |
| A reaction: This problem has bothered me. There are formal ways of constructing real numbers, but they don't seem to result in a name for each one. |