139 ideas
2845 | Free and great-souled men do not keep asking "what is the use of it?" [Aristotle] |
22521 | Our method of inquiry is to examine the smallest parts that make up the whole [Aristotle] |
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] |
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] |
17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
17928 | Ordinal numbers represent order relations [Colyvan] |
17923 | Intuitionists only accept a few safe infinities [Colyvan] |
17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
12354 | A 'categorial' property is had by virtue of being or having an item from a category [Wedin] |
12358 | Substance is a principle and a kind of cause [Wedin] |
12346 | Form explains why some matter is of a certain kind, and that is explanatory bedrock [Wedin] |
22525 | The whole is prior to its parts, because parts are defined by their role [Aristotle] |
22587 | Understanding is the aim of our nature [Aristotle] |
17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
22522 | To grasp something, trace it back to its natural origins [Aristotle] |
22524 | The nature of each thing is its mature state [Aristotle] |
17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
22528 | The nature of all animate things is to have one part which rules it [Aristotle] |
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] |
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] |
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] |
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] |
22563 | The middle classes are neither ambitious nor anarchic, which is good [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] |
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] |