71 ideas
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 16764 | The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus] |
| 19906 | All countries are in a mutual state of nature [Locke] |
| 19882 | We are not created for solitude, but are driven into society by our needs [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] |
| 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] |
| 19892 | Children are not born into citizenship of a state [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] |
| 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] |
| 19901 | The people have supreme power, to depose a legislature which has breached their trust [Locke] |
| 19887 | Unanimous consent makes a united community, which is then ruled by the majority [Locke] |
| 19913 | A master forfeits ownership of slaves he abandons [Locke] |
| 19883 | Slaves captured in a just war have no right to property, so are not part of civil society [Locke] |
| 19870 | If you try to enslave me, you have declared war on me [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] |
| 19884 | There is only a civil society if the members give up all of their natural executive rights [Locke] |
| 19873 | We all own our bodies, and the work we do is our own [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] |
| 19875 | A man's labour gives ownership rights - as long as there are fair shares for all [Locke] |
| 19874 | If a man mixes his labour with something in Nature, he thereby comes to own it [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] |
| 19898 | Soldiers can be commanded to die, but not to hand over their money [Locke] |
| 19879 | A man owns land if he cultivates it, to the limits of what he needs [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] |
| 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] |