143 ideas
14122 | Analysis gives us nothing but the truth - but never the whole truth [Russell] |
14109 | The study of grammar is underestimated in philosophy [Russell] |
14165 | Analysis falsifies, if when the parts are broken down they are not equivalent to their sum [Russell] |
14115 | Definition by analysis into constituents is useless, because it neglects the whole [Russell] |
14159 | In mathematics definitions are superfluous, as they name classes, and it all reduces to primitives [Russell] |
14148 | Infinite regresses have propositions made of propositions etc, with the key term reappearing [Russell] |
18002 | As well as a truth value, propositions have a range of significance for their variables [Russell] |
14102 | What is true or false is not mental, and is best called 'propositions' [Russell] |
14176 | "The death of Caesar is true" is not the same proposition as "Caesar died" [Russell] |
14113 | The null class is a fiction [Russell] |
15894 | Russell invented the naïve set theory usually attributed to Cantor [Russell, by Lavine] |
14126 | Order rests on 'between' and 'separation' [Russell] |
14127 | Order depends on transitive asymmetrical relations [Russell] |
14121 | The part-whole relation is ultimate and indefinable [Russell] |
14106 | Implication cannot be defined [Russell] |
14108 | It would be circular to use 'if' and 'then' to define material implication [Russell] |
14167 | The only classes are things, predicates and relations [Russell] |
14105 | There seem to be eight or nine logical constants [Russell] |
18722 | Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell] |
14104 | Constants are absolutely definite and unambiguous [Russell] |
14114 | Variables don't stand alone, but exist as parts of propositional functions [Russell] |
14137 | 'Any' is better than 'all' where infinite classes are concerned [Russell] |
14149 | The Achilles Paradox concerns the one-one correlation of infinite classes [Russell] |
15895 | Russell discovered the paradox suggested by Burali-Forti's work [Russell, by Lavine] |
14151 | Pure geometry is deductive, and neutral over what exists [Russell] |
14152 | In geometry, Kant and idealists aimed at the certainty of the premisses [Russell] |
14154 | Geometry throws no light on the nature of actual space [Russell] |
14153 | In geometry, empiricists aimed at premisses consistent with experience [Russell] |
14155 | Two points have a line joining them (descriptive), a distance (metrical), and a whole line (projective) [Russell, by PG] |
18254 | Russell's approach had to treat real 5/8 as different from rational 5/8 [Russell, by Dummett] |
14144 | Ordinals result from likeness among relations, as cardinals from similarity among classes [Russell] |
14128 | Some claim priority for the ordinals over cardinals, but there is no logical priority between them [Russell] |
14129 | Ordinals presuppose two relations, where cardinals only presuppose one [Russell] |
14132 | Properties of numbers don't rely on progressions, so cardinals may be more basic [Russell] |
14139 | Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic [Russell] |
14142 | Ordinals are types of series of terms in a row, rather than the 'nth' instance [Russell] |
14141 | Ordinals are defined through mathematical induction [Russell] |
14145 | For Cantor ordinals are types of order, not numbers [Russell] |
14146 | We aren't sure if one cardinal number is always bigger than another [Russell] |
14135 | Real numbers are a class of rational numbers (and so not really numbers at all) [Russell] |
14123 | Some quantities can't be measured, and some non-quantities are measurable [Russell] |
14158 | Quantity is not part of mathematics, where it is replaced by order [Russell] |
14120 | Counting explains none of the real problems about the foundations of arithmetic [Russell] |
14118 | We can define one-to-one without mentioning unity [Russell] |
14133 | There are cardinal and ordinal theories of infinity (while continuity is entirely ordinal) [Russell] |
14119 | We do not currently know whether, of two infinite numbers, one must be greater than the other [Russell] |
14134 | Infinite numbers are distinguished by disobeying induction, and the part equalling the whole [Russell] |
14143 | ω names the whole series, or the generating relation of the series of ordinal numbers [Russell] |
14138 | You can't get a new transfinite cardinal from an old one just by adding finite numbers to it [Russell] |
14140 | For every transfinite cardinal there is an infinite collection of transfinite ordinals [Russell] |
14124 | Axiom of Archimedes: a finite multiple of a lesser magnitude can always exceed a greater [Russell] |
7530 | Russell tried to replace Peano's Postulates with the simple idea of 'class' [Russell, by Monk] |
18246 | Dedekind failed to distinguish the numbers from other progressions [Shapiro on Russell] |
14125 | Finite numbers, unlike infinite numbers, obey mathematical induction [Russell] |
14147 | Denying mathematical induction gave us the transfinite [Russell] |
14116 | Numbers were once defined on the basis of 1, but neglected infinities and + [Russell] |
14117 | Numbers are properties of classes [Russell] |
9977 | Ordinals can't be defined just by progression; they have intrinsic qualities [Russell] |
14162 | Mathematics doesn't care whether its entities exist [Russell] |
14103 | Pure mathematics is the class of propositions of the form 'p implies q' [Russell] |
21555 | For 'x is a u' to be meaningful, u must be one range of individuals (or 'type') higher than x [Russell] |
18003 | In 'x is a u', x and u must be of different types, so 'x is an x' is generally meaningless [Russell, by Magidor] |
11010 | Being is what belongs to every possible object of thought [Russell] |
14161 | Many things have being (as topics of propositions), but may not have actual existence [Russell] |
14173 | What exists has causal relations, but non-existent things may also have them [Russell] |
14163 | Four classes of terms: instants, points, terms at instants only, and terms at instants and points [Russell] |
21341 | Philosophers of logic and maths insisted that a vocabulary of relations was essential [Russell, by Heil] |
10586 | 'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness [Russell] |
10585 | Symmetrical and transitive relations are formally like equality [Russell] |
7781 | I call an object of thought a 'term'. This is a wide concept implying unity and existence. [Russell] |
14166 | Unities are only in propositions or concepts, and nothing that exists has unity [Russell] |
14164 | The only unities are simples, or wholes composed of parts [Russell] |
14112 | A set has some sort of unity, but not enough to be a 'whole' [Russell] |
14170 | Change is obscured by substance, a thing's nature, subject-predicate form, and by essences [Russell] |
14107 | Terms are identical if they belong to all the same classes [Russell] |
11849 | It at least makes sense to say two objects have all their properties in common [Wittgenstein on Russell] |
22303 | It makes no sense to say that a true proposition could have been false [Russell] |
3102 | Why don't we experience or remember going to sleep at night? [Magee] |
10583 | Abstraction principles identify a common property, which is some third term with the right relation [Russell] |
10582 | The principle of Abstraction says a symmetrical, transitive relation analyses into an identity [Russell] |
10584 | A certain type of property occurs if and only if there is an equivalence relation [Russell] |
14110 | Proposition contain entities indicated by words, rather than the words themselves [Russell] |
19164 | If propositions are facts, then false and true propositions are indistinguishable [Davidson on Russell] |
19157 | Russell said the proposition must explain its own unity - or else objective truth is impossible [Russell, by Davidson] |
14111 | A proposition is a unity, and analysis destroys it [Russell] |
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] |
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] |
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] |
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] |
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] |
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] |
19912 | Self-defence is natural, but not the punishment of superiors by inferiors [Locke] |
19867 | Reparation and restraint are the only justifications for punishment [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] |
14175 | We can drop 'cause', and just make inferences between facts [Russell] |
14172 | Moments and points seem to imply other moments and points, but don't cause them [Russell] |
14174 | The laws of motion and gravitation are just parts of the definition of a kind of matter [Russell] |
14168 | Occupying a place and change are prior to motion, so motion is just occupying places at continuous times [Russell] |
14171 | Force is supposed to cause acceleration, but acceleration is a mathematical fiction [Russell] |
14160 | Space is the extension of 'point', and aggregates of points seem necessary for geometry [Russell] |
14156 | Mathematicians don't distinguish between instants of time and points on a line [Russell] |
14169 | The 'universe' can mean what exists now, what always has or will exist [Russell] |