160 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] |
| 9738 | Each line of a truth table is a model [Fitting/Mendelsohn] |
| 9727 | Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn] |
| 9726 | We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn] |
| 9737 | The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn] |
| 13136 | The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn] |
| 13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn] |
| 9734 | Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn] |
| 9736 | A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn] |
| 9735 | A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn] |
| 9741 | Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn] |
| 13149 | S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn] |
| 13141 | Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn] |
| 13138 | Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn] |
| 13142 | Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn] |
| 13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn] |
| 13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn] |
| 13146 | B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn] |
| 13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 13148 | 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 9740 | If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn] |
| 9739 | If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn] |
| 13137 | Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn] |
| 13140 | Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn] |
| 13139 | Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn] |
| 13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn] |
| 9742 | The system K has no accessibility conditions [Fitting/Mendelsohn] |
| 13114 | □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn] |
| 9743 | The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9744 | The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9746 | The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn] |
| 9745 | The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9748 | System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9404 | Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn] |
| 13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
| 13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
| 13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
| 13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
| 13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 22525 | The whole is prior to its parts, because parts are defined by their role [Aristotle] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 13725 | □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn] |
| 13731 | Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn] |
| 13726 | Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn] |
| 22587 | Understanding is the aim of our nature [Aristotle] |
| 11052 | Psychological logic can't distinguish justification from causes of a belief [Frege] |
| 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] |
| 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] |
| 22550 | It is dreadful to neither give a share nor receive a share [Aristotle] |
| 22569 | The Heraeans replaced election with lot, to thwart campaigning [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] |