82 ideas
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| 9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
| 9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
| 9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
| 9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
| 9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| 9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
| 9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
| 9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
| 9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
| 9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
| 9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| 9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| 9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
| 9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
| 9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| 6610 | I believe because it is absurd [Tertullian] |