13 ideas
| 17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
| Full Idea: Zermelo's paper sets out to show that the standard set-theoretic axioms (what he calls the 'constitutive axioms', thus the ZF axioms minus the axiom of infinity) have an unending sequence of different models, thus that they are non-categorical. | |
| From: report of Ernst Zermelo (On boundary numbers and domains of sets [1930]) by Michael Hallett - Introduction to Zermelo's 1930 paper p.1209 | |
| A reaction: Hallett says later that Zermelo is working with second-order set theory. The addition of an Axiom of Infinity seems to have aimed at addressing the problem, and the complexities of that were pursued by Gödel. |
| 13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
| Full Idea: Zermelo included Replacement in 1930, after it was noticed that the sequence of power sets was needed, and Replacement gave the ordinal form of the well-ordering theorem, and justification for transfinite recursion. | |
| From: report of Ernst Zermelo (On boundary numbers and domains of sets [1930]) by Penelope Maddy - Believing the Axioms I §1.8 | |
| A reaction: Maddy says that this axiom suits the 'limitation of size' theorists very well, but is not so good for the 'iterative conception'. |
| 17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
| Full Idea: Two opposite tendencies of thought, the idea of creative advance and of collection and completion (underlying the Kantian 'antinomies') find their symbolic representation and their symbolic reconciliation in the transfinite numbers based on well-ordering. | |
| From: Ernst Zermelo (On boundary numbers and domains of sets [1930], §5) | |
| A reaction: [a bit compressed] It is this sort of idea, from one of the greatest set-theorists, that leads philosophers to think that the philosophy of mathematics may offer solutions to metaphysical problems. As an outsider, I am sceptical. |
| 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. |
| 7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
| Full Idea: Libet himself points out that the conscious decisions still have the power to 'endorse' or 'cancel', so to speak, the processes initiated by the earlier cortical activity: no action will result if the action's execution is consciously countermanded. | |
| From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by David Papineau - Thinking about Consciousness 1.4 | |
| A reaction: This is why Libet's findings do not imply 'epiphenomenalism'. It seems that part of a decisive action is non-conscious, undermining the all-or-nothing view of consciousness. Searle tries to smuggle in free will at this point (Idea 3817). |
| 6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |
| Full Idea: Libet found that a subject's conscious choice to move was about a fifth of a second before movement, and thus later than the onset of the brain's so-called 'readiness potential', which seems to imply that unconscious processes initiates action. | |
| From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.9 | |
| A reaction: Of great interest to philosophers! It seems to make conscious choices epiphenomenal. The key move, I think, is to give up the idea of consciousness as being all-or-nothing. My actions are still initiated by 'me', but 'me' shades off into unconsciousness. |
| 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. |