149 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] |
| 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] |
| 14151 | Pure geometry is deductive, and neutral over what exists [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] |
| 14141 | Ordinals are defined through mathematical induction [Russell] |
| 14142 | Ordinals are types of series of terms in a row, rather than the 'nth' instance [Russell] |
| 14139 | Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic [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] |
| 14119 | We do not currently know whether, of two infinite numbers, one must be greater than the other [Russell] |
| 14133 | There are cardinal and ordinal theories of infinity (while continuity is entirely ordinal) [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] |
| 14147 | Denying mathematical induction gave us the transfinite [Russell] |
| 14125 | Finite numbers, unlike infinite numbers, obey mathematical induction [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] |
| 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] |
| 14111 | A proposition is a unity, and analysis destroys it [Russell] |
| 19157 | Russell said the proposition must explain its own unity - or else objective truth is impossible [Russell, by Davidson] |
| 19956 | True goodness is political, and consists of love of and submission to the laws [Montesquieu] |
| 5954 | All inventions of the mind aim at pleasure, and those that don't are worthless [Metrodorus of Lamp., by Plutarch] |
| 19961 | Primitive people would be too vulnerable and timid to attack anyone, so peace would reign [Montesquieu] |
| 19962 | Men do not desire to subjugate one another; domination is a complex and advanced idea [Montesquieu] |
| 19963 | People are drawn into society by needs, shared fears, pleasure, and knowledge [Montesquieu] |
| 20008 | People are guided by a multitude of influences, from which the spirit of a nation emerges [Montesquieu] |
| 19993 | In small republics citizens identify with the public good, and abuses are fewer [Montesquieu] |
| 19992 | In a large republic there is too much wealth for individuals to manage it [Montesquieu] |
| 20005 | The rich would never submit to a lottery deciding which part of their society should be slaves [Montesquieu] |
| 19995 | All states aim at preservation, and then have distinctive individual purposes [Montesquieu] |
| 19964 | The natural power of a father suggests rule by one person, but that authority can be spread [Montesquieu] |
| 19986 | Monarchies can act more quickly, because one person is in charge [Montesquieu] |
| 19972 | The nobility are an indispensable part of a monarchy [Montesquieu] |
| 19974 | Monarchs must not just have links to the people; they need a body which maintains the laws [Montesquieu] |
| 19976 | Ambition is good in a monarchy, because the monarch can always restrain it [Montesquieu] |
| 19978 | In monarchies, men's actions are judged by their grand appearance, not their virtues [Montesquieu] |
| 19985 | In a monarchy, the nobility must be hereditary, to bind them together [Montesquieu] |
| 19988 | A despot's agents must be given power, so they inevitably become corrupt [Montesquieu] |
| 19977 | Despotism and honour are incompatible, because honour scorns his power, and lives by rules [Montesquieu] |
| 20007 | Tyranny is either real violence, or the imposition of unpopular legislation [Montesquieu] |
| 19975 | Despots are always lazy and ignorant, so they always delegate their power to a vizier [Montesquieu] |
| 19989 | The will of a despot is an enigma, so magistrates can only follow their own will [Montesquieu] |
| 19970 | If the nobility is numerous, the senate is the artistocracy, and the nobles are a democracy [Montesquieu] |
| 19971 | Aristocracy is democratic if they resemble the people, but not if they resemble the monarch [Montesquieu] |
| 19984 | Great inequality between aristocrats and the rest is bad - and also among aristocrats themselves [Montesquieu] |
| 19980 | If a government is to be preserved, it must first be loved [Montesquieu] |
| 19996 | A government has a legislature, an international executive, and a domestic executive [Montesquieu] |
| 19997 | The judiciary must be separate from the legislature, to avoid arbitrary power [Montesquieu] |
| 19965 | The fundamental laws of a democracy decide who can vote [Montesquieu] |
| 19968 | It is basic to a democracy that the people themselves must name their ministers [Montesquieu] |
| 19969 | Voting should be public, so the lower classes can be influenced by the example of notable people [Montesquieu] |
| 19999 | All citizens (apart from the very humble poor) should choose their representatives [Montesquieu] |
| 19967 | In a democracy the people should manage themselves, and only delegate what they can't do [Montesquieu] |
| 19966 | A democratic assembly must have a fixed number, to see whether everyone has spoken [Montesquieu] |
| 19998 | If deputies represent people, they are accountable, but less so if they represent places [Montesquieu] |
| 20003 | Slaves are not members of the society, so no law can forbid them to run away [Montesquieu] |
| 20000 | Slavery is entirely bad; the master abandons the virtues, and they are pointless in the slave [Montesquieu] |
| 20006 | The demand for slavery is just the masters' demand for luxury [Montesquieu] |
| 20009 | Freedom of speech and writing, within the law, is essential to preserve liberty [Montesquieu] |
| 19994 | Freedom in society is ability to do what is right, and not having to do what is wrong [Montesquieu] |
| 19981 | No one even thinks of equality in monarchies and despotism; they all want superiority [Montesquieu] |
| 19991 | Equality is not command by everyone or no one, but command and obedience among equals [Montesquieu] |
| 19990 | Democracy is corrupted by lack of equality, or by extreme equality (between rulers and ruled) [Montesquieu] |
| 19983 | Democracies may sometimes need to restrict equality [Montesquieu] |
| 19982 | Some equality can be achieved by social categories, combined with taxes and poor relief [Montesquieu] |
| 19959 | Prior to positive laws there is natural equity, of obedience, gratitude, dependence and merit [Montesquieu] |
| 19960 | Sensation gives animals natural laws, but knowledge can make them break them [Montesquieu] |
| 20002 | The death penalty is permissible, because its victims enjoyed the protection of that law [Montesquieu] |
| 20010 | If religion teaches determinism, penalties must be severe; if free will, then that is different [Montesquieu] |
| 20001 | The only right victors have over captives is the protection of the former [Montesquieu] |
| 19973 | The clergy are essential to a monarchy, but dangerous in a republic [Montesquieu] |
| 19987 | Religion has the most influence in despotic states, and reinforces veneration for the ruler [Montesquieu] |
| 20011 | Religion can support the state when the law fails to do so [Montesquieu] |
| 20004 | French slavery was accepted because it was the best method of religious conversion [Montesquieu] |
| 19979 | In monarchies education ennobles people, and in despotisms it debases them [Montesquieu] |
| 19957 | Teaching is the best practice of the general virtue that leads us to love everyone [Montesquieu] |
| 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] |
| 19958 | Laws are the necessary relations that derive from the nature of things [Montesquieu] |
| 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] |