74 ideas
10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
10763 | Completeness and compactness together give axiomatizability [Tharp] |
10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
7590 | Consequentialism emphasises value rather than obligation in morality [Scruton] |
7589 | Altruism is either emotional (where your interests are mine) or moral (where they are reasons for me) [Scruton] |
19882 | We are not created for solitude, but are driven into society by our needs [Locke] |
19906 | All countries are in a mutual state of nature [Locke] |
19864 | In nature men can dispose of possessions and their persons in any way that is possible [Locke] |
19865 | There is no subjection in nature, and all creatures of the same species are equal [Locke] |
19866 | The rational law of nature says we are all equal and independent, and should show mutual respect [Locke] |
19872 | The animals and fruits of the earth belong to mankind [Locke] |
19907 | There is a natural right to inheritance within a family [Locke] |
7595 | The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton] |
19863 | Politics is the right to make enforceable laws to protect property and the state, for the common good [Locke] |
5654 | The Second Treatise explores the consequences of the contractual view of the state [Locke, by Scruton] |
19888 | A society only begins if there is consent of all the individuals to join it [Locke] |
6702 | If anyone enjoys the benefits of government (even using a road) they give tacit assent to its laws [Locke] |
19909 | A politic society is created from a state of nature by a unanimous agreement [Locke] |
19910 | A single will creates the legislature, which is duty-bound to preserve that will [Locke] |
19893 | Anyone who enjoys the benefits of a state has given tacit consent to be part of it [Locke] |
19894 | You can only become an actual member of a commonwealth by an express promise [Locke] |
19892 | Children are not born into citizenship of a state [Locke] |
19885 | Absolute monarchy is inconsistent with civil society [Locke] |
19886 | The idea that absolute power improves mankind is confuted by history [Locke] |
19903 | Despotism is arbitrary power to kill, based neither on natural equality, nor any social contract [Locke] |
19905 | People stripped of their property are legitimately subject to despotism [Locke] |
19904 | Legitimate prisoners of war are subject to despotism, because that continues the state of war [Locke] |
19895 | Even the legislature must be preceded by a law which gives it power to make laws [Locke] |
19900 | The executive must not be the legislature, or they may exempt themselves from laws [Locke] |
19902 | Any obstruction to the operation of the legislature can be removed forcibly by the people [Locke] |
19908 | Rebelling against an illegitimate power is no sin [Locke] |
19911 | If legislators confiscate property, or enslave people, they are no longer owed obedience [Locke] |
7588 | Allegiance is fundamental to the conservative view of society [Scruton] |
19887 | Unanimous consent makes a united community, which is then ruled by the majority [Locke] |
19901 | The people have supreme power, to depose a legislature which has breached their trust [Locke] |
7594 | Democrats are committed to a belief and to its opposite, if the majority prefer the latter [Scruton] |
7593 | Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG] |
19870 | If you try to enslave me, you have declared war on me [Locke] |
19883 | Slaves captured in a just war have no right to property, so are not part of civil society [Locke] |
19913 | A master forfeits ownership of slaves he abandons [Locke] |
19871 | Freedom is not absence of laws, but living under laws arrived at by consent [Locke] |
19880 | All value depends on the labour involved [Locke] |
19873 | We all own our bodies, and the work we do is our own [Locke] |
19884 | There is only a civil society if the members give up all of their natural executive rights [Locke] |
19879 | A man owns land if he cultivates it, to the limits of what he needs [Locke] |
19898 | Soldiers can be commanded to die, but not to hand over their money [Locke] |
6580 | Locke (and Marx) held that ownership of objects is a natural relation, based on the labour put into it [Locke, by Fogelin] |
20520 | Locke says 'mixing of labour' entitles you to land, as well as nuts and berries [Wolff,J on Locke] |
19874 | If a man mixes his labour with something in Nature, he thereby comes to own it [Locke] |
19875 | A man's labour gives ownership rights - as long as there are fair shares for all [Locke] |
19877 | Fountain water is everyone's, but a drawn pitcher of water has an owner [Locke] |
19876 | Gathering natural fruits gives ownership; the consent of other people is irrelevant [Locke] |
19878 | Mixing labour with a thing bestows ownership - as long as the thing is not wasted [Locke] |
19881 | The aim of law is not restraint, but to make freedom possible [Locke] |
19868 | It is only by a law of Nature that we can justify punishing foreigners [Locke] |
7592 | For positivists law is a matter of form, for naturalists it is a matter of content [Scruton] |
19867 | Reparation and restraint are the only justifications for punishment [Locke] |
19912 | Self-defence is natural, but not the punishment of superiors by inferiors [Locke] |
19869 | Punishment should make crime a bad bargain, leading to repentance and deterrence [Locke] |
19899 | The consent of the people is essential for any tax [Locke] |
7587 | The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton] |