208 ideas
| 2845 | Free and great-souled men do not keep asking "what is the use of it?" [Aristotle] |
| 14122 | Analysis gives us nothing but the truth - but never the whole truth [Russell] |
| 22521 | Our method of inquiry is to examine the smallest parts that make up the whole [Aristotle] |
| 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] |
| 1570 | Human beings, alone of the animals, have logos [Aristotle] |
| 1574 | Reasoning distinguishes what is beneficial, and hence what is right [Aristotle] |
| 2801 | Intelligence which looks ahead is a natural master, while bodily strength is a natural slave [Aristotle] |
| 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] |
| 22529 | Men are natural leaders (apart from the unnatural ones) [Aristotle] |
| 22571 | 'If each is small, so too are all' is in one way false, for the whole composed of all is not small [Aristotle] |
| 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] |
| 10121 | Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal] |
| 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] |
| 22525 | The whole is prior to its parts, because parts are defined by their role [Aristotle] |
| 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] |
| 22587 | Understanding is the aim of our nature [Aristotle] |
| 22522 | To grasp something, trace it back to its natural origins [Aristotle] |
| 22524 | The nature of each thing is its mature state [Aristotle] |
| 22528 | The nature of all animate things is to have one part which rules it [Aristotle] |
| 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] |
| 22570 | Rhetoric now enables good speakers to become popular leaders [Aristotle] |
| 22574 | A community can lack self-control [Aristotle] |
| 2837 | Nothing contrary to nature is beautiful [Aristotle] |
| 2824 | The collective judgement of many people on art is better than that of an individual [Aristotle] |
| 2846 | Music can mould the character to be virtuous (just as gymnastics trains the body) [Aristotle] |
| 2807 | Some say slavery is unnatural and created by convention, and is therefore forced, and unjust [Aristotle] |
| 22582 | Spirit [thumos] is the capacity by which we love [Aristotle] |
| 2810 | Selfishness is wrong not because it is self-love, but because it is excessive [Aristotle] |
| 22555 | The function of good men is to confer benefits [Aristotle] |
| 22557 | Virtuous people are like the citizens of the best city [Aristotle] |
| 2841 | People become good because of nature, habit and reason [Aristotle] |
| 2829 | The law is the mean [Aristotle] |
| 22590 | Virtue is concerned with correct feelings [Aristotle] |
| 2813 | It is quite possible to live a moderate life and yet be miserable [Aristotle] |
| 22553 | Justice is a virtue of communities [Aristotle] |
| 22561 | The rich are seen as noble, because they don't need to commit crimes [Aristotle] |
| 2808 | Master and slave can have friendship through common interests [Aristotle] |
| 2803 | Man is by nature a political animal [Aristotle] |
| 2820 | People want to live together, even when they don't want mutual help [Aristotle] |
| 22586 | Only humans have reason [Aristotle] |
| 22523 | The community (of villages) becomes a city when it is totally self-sufficient [Aristotle] |
| 2805 | A community must share a common view of good and justice [Aristotle] |
| 22526 | People who are anti-social or wholly self-sufficient are no part of a city [Aristotle] |
| 22535 | Friendship is the best good for cities, because it reduces factions [Aristotle] |
| 22532 | A city can't become entirely one, because its very nature is to be a multitude [Aristotle] |
| 22584 | A community should all share to some extent in something like land or food [Aristotle] |
| 22581 | The size of a city is decided by the maximum self-sufficient community that can be surveyed [Aristotle] |
| 22548 | A city aims at living well [Aristotle] |
| 22577 | What is the best life for everyone, and is that a communal or an individual problem? [Aristotle] |
| 22579 | The same four cardinal virtues which apply to individuals also apply to a city [Aristotle] |
| 2431 | Every state is an association formed for some good purpose [Aristotle] |
| 22578 | The happiest city is the one that acts most nobly [Aristotle] |
| 2832 | The state aims to consist as far as possible of those who are like and equal [Aristotle] |
| 2821 | The six constitutions are monarchy/tyranny, aristocracy/oligarchy, and polity/democracy [Aristotle] |
| 22546 | A city is a community of free people, and the constitution should aim at the common advantage [Aristotle] |
| 2835 | Any constitution can be made to last for a day or two [Aristotle] |
| 22580 | The best constitution enables everyone to live the best life [Aristotle] |
| 22558 | Constitutions specify distribution of offices, the authorities, and the community's aim [Aristotle] |
| 22566 | The greed of the rich is more destructive than the greed of the people [Aristotle] |
| 2973 | We must decide the most desirable human life before designing a constitution [Aristotle] |
| 22563 | The middle classes are neither ambitious nor anarchic, which is good [Aristotle] |
| 2818 | The virtues of a good citizen are relative to a particular constitution [Aristotle] |
| 22545 | A person can be an excellent citizen without being an excellent man [Aristotle] |
| 22544 | A citizen is someone who is allowed to hold official posts in a city [Aristotle] |
| 22541 | Kings should be selected according to character [Aristotle] |
| 2819 | The only virtue special to a ruler is practical wisdom [Aristotle] |
| 22542 | People who buy public office will probably expect to profit from it [Aristotle] |
| 22552 | The rich can claim to rule, because of land ownership, and being more trustworthy [Aristotle] |
| 22583 | The guardians should not be harsh to strangers, as no one should behave like that [Aristotle] |
| 22543 | In large communities it is better if more people participate in the offices [Aristotle] |
| 22539 | Election of officials by the elected is dangerous, because factions can control it [Aristotle] |
| 22572 | Officers should like the constitution, be capable, and have appropriate virtues and justice [Aristotle] |
| 2826 | Like water, large numbers of people are harder to corrupt than a few [Aristotle] |
| 22567 | Democracy arises when people who are given equal freedom assume unconditional equality [Aristotle] |
| 22560 | Popular leaders only arise in democracies that are not in accord with the law [Aristotle] |
| 22562 | Choosing officials by lot is democratic [Aristotle] |
| 2823 | The many may add up to something good, even if they are inferior as individuals [Aristotle] |
| 22533 | If the people are equal in nature, then they should all share in ruling [Aristotle] |
| 2817 | It is wrong that a worthy officer of state should seek the office [Aristotle] |
| 22576 | No office is permanent in a democracy [Aristotle] |
| 22549 | In many cases, the claim that the majority is superior would apply equally to wild beasts [Aristotle] |
| 22575 | Ultimate democracy is tyranny [Aristotle] |
| 22531 | We aim to understand the best possible community for free people [Aristotle] |
| 22564 | Community is based on friends, who are equal and similar, and share things [Aristotle] |
| 22585 | Look at all of the citizens before judging a city to be happy [Aristotle] |
| 22565 | The best communities rely on a large and strong middle class [Aristotle] |
| 22589 | Citizens do not just own themselves, but are also parts of the city [Aristotle] |
| 22534 | People care less about what is communal, and more about what is their own [Aristotle] |
| 22538 | Owning and sharing property communally increases disagreements [Aristotle] |
| 22536 | There could be private land and public crops, or public land and private crops, or both public [Aristotle] |
| 22530 | Both women and children should be educated, as this contributes to a city's excellence [Aristotle] |
| 21358 | Natural slaves are those naturally belonging to another, or who can manage no more than labouring [Aristotle] |
| 20092 | One principle of liberty is to take turns ruling and being ruled [Aristotle] |
| 2833 | Equality is obviously there to help people who do not get priority in the constitution [Aristotle] |
| 2834 | It is always the weak who want justice and equality, not the strong [Aristotle] |
| 2830 | We can claim an equal right to aristocratic virtue, as well as to wealth or freedom [Aristotle] |
| 22569 | The Heraeans replaced election with lot, to thwart campaigning [Aristotle] |
| 22550 | It is dreadful to neither give a share nor receive a share [Aristotle] |
| 22568 | Faction is for inferiors to be equal, and equals to become superior [Aristotle] |
| 2814 | Phaleas proposed equality of property, provided there is equality of education [Aristotle] |
| 22540 | Wealth could be quickly leveled by only the rich giving marriage dowries [Aristotle] |
| 2828 | Law is intelligence without appetite [Aristotle] |
| 22537 | Property should be owned privately, but used communally [Aristotle] |
| 22573 | The virtue of justice may be relative to a particular constitution [Aristotle] |
| 22527 | Justice is the order in a political community [Aristotle] |
| 22547 | Justice is equality for equals, and inequality for unequals [Aristotle] |
| 2825 | The good is obviously justice, which benefits the whole community, and involves equality in some sense [Aristotle] |
| 2816 | If it is easy to change the laws, that makes them weaker [Aristotle] |
| 2806 | Man is the worst of all animals when divorced from law and justice [Aristotle] |
| 22556 | Laws that match people's habits are more effective than mere written rules [Aristotle] |
| 2827 | It is preferable that law should rule rather than any single citizen [Aristotle] |
| 22551 | Correct law should be in control, with rulers only deciding uncertain issues [Aristotle] |
| 22554 | It is said that we should not stick strictly to written law, as it is too vague [Aristotle] |
| 2840 | The whole state should pay for the worship of the gods [Aristotle] |
| 2811 | A state is plural, and needs education to make it a community [Aristotle] |
| 22588 | A city has a single end, so education must focus on that, and be communal, not private [Aristotle] |
| 2847 | The aim of serious childhood play is the amusement of the complete adult [Aristotle] |
| 2842 | Men learn partly by habit, and partly by listening [Aristotle] |
| 2844 | Abortions should be procured before the embryo has acquired life and sensation [Aristotle] |
| 2809 | If nature makes everything for a purpose, then plants and animals must have been made for man [Aristotle] |
| 2800 | The best instruments have one purpose, not many [Aristotle] |
| 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] |
| 2836 | God is not blessed and happy because of external goods, but because of his own nature [Aristotle] |
| 2802 | Men imagine gods to be of human shape, with a human lifestyle [Aristotle] |