19 ideas
9987 | An aggregate in which order does not matter I call a 'set' [Bolzano] |
Full Idea: An aggregate whose basic conception renders the arrangement of its members a matter of indifference, and whose permutation therefore produces no essential difference, I call a 'set'. | |
From: Bernard Bolzano (Paradoxes of the Infinite [1846], §4), quoted by William W. Tait - Frege versus Cantor and Dedekind IX | |
A reaction: The idea of 'sets' was emerging before Cantor formalised it, and clarified it by thinking about infinite sets. Nowadays we also have 'ordered' sets, which rather contradicts Bolzano, and we also expect the cardinality to be determinate. |
10856 | A truly infinite quantity does not need to be a variable [Bolzano] |
Full Idea: A truly infinite quantity (for example, the length of a straight line, unbounded in either direction) does not by any means need to be a variable. | |
From: Bernard Bolzano (Paradoxes of the Infinite [1846]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable §10 | |
A reaction: This is an important idea, followed up by Cantor, which relegated to the sidelines the view of infinity as simply something that could increase without limit. Personally I like the old view, but there is something mathematically stable about infinity. |
22673 | Wherever there is a small community, the association of the people is natural [Tocqueville] |
Full Idea: The village or township is the only association which is so perfectly natural that, wherever a number of men are collected, it seems to constitute itself. | |
From: Alexis de Tocqueville (Democracy in America (abr Renshaw) [1840], 1.04) | |
A reaction: Seems like a chicken and egg issue. I would have thought that association precedes the development of a village. |
22676 | The people are just individuals, and only present themselves as united to foreigners [Tocqueville] |
Full Idea: The people in themselves are only individuals; and the special reason why they need to be united under one government is that they may appear to advantage before foreigners. | |
From: Alexis de Tocqueville (Democracy in America (abr Renshaw) [1840], 1.07) | |
A reaction: I take this to be an observation on 1830s America, rather than a universal truth. It fits modern western societies rather well though. |
22679 | Vast empires are bad for well-being and freedom, though they may promote glory [Tocqueville] |
Full Idea: Nothing is more opposed to the well-being and the freedom of men than vast empires. …But there is a love of glory in those who regard the applause of a great people as a worthy reward. | |
From: Alexis de Tocqueville (Democracy in America (abr Renshaw) [1840], 1.07) | |
A reaction: Presumably the main the problem is the central dominance over distant colonies. There may also be some freedom in being distant from the centres, especially in 1830. The Wild West. |
22680 | People would be much happier and freer in small nations [Tocqueville] |
Full Idea: If none but small nations existed, I do not doubt that mankind would be more happy and more free. | |
From: Alexis de Tocqueville (Democracy in America (abr Renshaw) [1840], 1.07) | |
A reaction: In modern times many small states have appeared in Europe (in the Balkans and on the Baltic), and it looks to me a good thing. The prospect of Scottish independence may currently be looming, and De Tocqueville would approve. |
22675 | In American judges rule according to the Constitution, not the law [Tocqueville] |
Full Idea: The Americans have acknowledged the right of judges to found their decisions on the Constitution, rather than on the laws. | |
From: Alexis de Tocqueville (Democracy in America (abr Renshaw) [1840], 1.05) | |
A reaction: Obviously the Constitution is one short document, so the details must be enshrined in the laws (which presumably defer to the Constitution). |
22677 | A monarchical family is always deeply concerned with the interests of the state [Tocqueville] |
Full Idea: The advantages of a monarchy are that the private interests of a family are connected with the interests of the state, …and at least there is always someone available to conduct the affairs of a monarchy. | |
From: Alexis de Tocqueville (Democracy in America (abr Renshaw) [1840], 1.07) | |
A reaction: The second one is not much of a reason! The same defence can be given for the dominance of the Mafia. His defences are deliberately feeble, I suspect. England had plenty of monarchs who showed limited interest. |
22683 | Despots like to see their own regulations ignored, by themselves and their agents [Tocqueville] |
Full Idea: In despotic states the sovereign is so much attached to his power that he dislikes the constraints even of his own regulations, and likes to see his agents acting irregularly. | |
From: Alexis de Tocqueville (Democracy in America (abr Renshaw) [1840], 1.11) | |
A reaction: A nice observation. What would Machiavelli say? At least the citizens can see where the real power resides. |
22669 | Aristocracy is constituted by inherited landed property [Tocqueville] |
Full Idea: Land is the basis of an aristocracy; …it is by landed property handed down from generation to generation that an aristocracy is constituted. | |
From: Alexis de Tocqueville (Democracy in America (abr Renshaw) [1840], 1.01) | |
A reaction: Presumably there can be aristocrats by mere royal patronage, who have perhaps gambled away their land. They need protection by the other aristocrats. |
22674 | In Europe it is thought that local government is best handled centrally [Tocqueville] |
Full Idea: The partisans of centralisation in Europe are wont to maintain that the government can administer the affairs of each locality better than the citizens can do it for themselves. | |
From: Alexis de Tocqueville (Democracy in America (abr Renshaw) [1840], 1.04) | |
A reaction: In the modern UK we have lots of local government, which is thoroughly starved of funds by the central government. He is contrasting it with the strong local system in the U.S. |
22678 | An election, and its lead up time, are always a national crisis [Tocqueville] |
Full Idea: The period which immediately precedes an election, and that during which the election is taking place, must always be considered as a national crisis. | |
From: Alexis de Tocqueville (Democracy in America (abr Renshaw) [1840], 1.07) | |
A reaction: Rousseau said something similar. Election day in modern Britain is very peaceful and civilised, but it used to be chaotic. The weeks preceding it are invariably nasty. |
22682 | Universal suffrage is no guarantee of wise choices [Tocqueville] |
Full Idea: Universal suffrage is by no means a guarantee of the wisdom of the popular choice. | |
From: Alexis de Tocqueville (Democracy in America (abr Renshaw) [1840], 1.11) | |
A reaction: This was precisely Plato's fear about democracy. There seems no way at all of preventing the people from electing representatives on superficial grounds of personality. |
22670 | Slavery undermines the morals and energy of a society [Tocqueville] |
Full Idea: Slavery dishonours labour; it introduces idleness into society, and with idleness, ignorance and pride, luxury and distress. | |
From: Alexis de Tocqueville (Democracy in America (abr Renshaw) [1840], 1.01) | |
A reaction: A pretty feeble reason (in the 1830s) for disliking slavery. He seems only concerned with the adverse effects on the slave-owning society, and shows no interest in the slaves themselves. |
22681 | The liberty of the press is more valuable for what it prevents than what it promotes [Tocqueville] |
Full Idea: I approve of the liberty of the press from a consideration more of the evils it prevents than of the advantages it ensures. | |
From: Alexis de Tocqueville (Democracy in America (abr Renshaw) [1840], 1.10) | |
A reaction: He accepts the freedom of the press as inevitable in a democracy, but he found U.S. newspapers to be nearly as bad then as they are now. |
22672 | It is admirable to elevate the humble to the level of the great, but the opposite is depraved [Tocqueville] |
Full Idea: One manly and lawful passion for equality elevates the humble to the rank of the great. But there exists also a depraved taste for equality, which impels the weak to attempt to lower the powerful to their own level. | |
From: Alexis de Tocqueville (Democracy in America (abr Renshaw) [1840], 1.02) | |
A reaction: There is a distinction in modern political rhetoric between 'levelling down' and 'levelling up'. Since levelling down is just destructive, and levelling up is unaffordable, it seems obvious that true equality needs to be a compromise. |
22671 | Equality can only be established by equal rights for all (or no rights for anyone) [Tocqueville] |
Full Idea: I know of only two methods of establishing equality in the political world; rights must be given to every citizen, or none at all to anyone. | |
From: Alexis de Tocqueville (Democracy in America (abr Renshaw) [1840], 1.02) | |
A reaction: We may have a vague concept of 'natural' rights, but primarily they are a tool of social engineering. You could grant equal rights on inheritance, for example, which turn out in practice to hugely favour the rich. |
16713 | Philosophers are the forefathers of heretics [Tertullian] |
Full Idea: Philosophers are the forefathers of heretics. | |
From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
6610 | I believe because it is absurd [Tertullian] |
Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |