220 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] |
14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [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] |
14426 | A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [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] |
8468 | The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false [Russell, by Orenstein] |
14454 | An argument 'satisfies' a function φx if φa is true [Russell] |
14453 | The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell] |
14427 | We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell] |
14428 | Members define a unique class, whereas defining characteristics are numerous [Russell] |
14447 | Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell] |
14440 | We may assume that there are infinite collections, as there is no logical reason against them [Russell] |
14443 | The British parliament has one representative selected from each constituency [Russell] |
14445 | Choice shows that if any two cardinals are not equal, one must be the greater [Russell] |
14444 | Choice is equivalent to the proposition that every class is well-ordered [Russell] |
14446 | We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell] |
14459 | Reducibility: a family of functions is equivalent to a single type of function [Russell] |
14461 | Propositions about classes can be reduced to propositions about their defining functions [Russell] |
8625 | What physical facts could underlie 0 or 1, or very large numbers? [Frege on Mill] |
8469 | Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein] |
8745 | Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell] |
14452 | All the propositions of logic are completely general [Russell] |
14462 | In modern times, logic has become mathematical, and mathematics has become logical [Russell] |
10057 | Logic can only assert hypothetical existence [Russell] |
12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
14464 | Logic can be known a priori, without study of the actual world [Russell] |
17895 | Combining two distinct assertions does not necessarily lead to a single 'complex proposition' [Mill] |
10427 | All names are names of something, real or imaginary [Mill] |
14458 | Asking 'Did Homer exist?' is employing an abbreviated description [Russell] |
10450 | Russell admitted that even names could also be used as descriptions [Russell, by Bach] |
14457 | Names are really descriptions, except for a few words like 'this' and 'that' [Russell] |
4944 | Mill says names have denotation but not connotation [Mill, by Kripke] |
7762 | Proper names are just labels for persons or objects, and the meaning is the object [Mill, by Lycan] |
7311 | The only genuine proper names are 'this' and 'that' [Russell] |
14455 | 'I met a unicorn' is meaningful, and so is 'unicorn', but 'a unicorn' is not [Russell] |
14442 | If straight lines were like ratios they might intersect at a 'gap', and have no point in common [Russell] |
14438 | New numbers solve problems: negatives for subtraction, fractions for division, complex for equations [Russell] |
13510 | Could a number just be something which occurs in a progression? [Russell, by Hart,WD] |
14436 | A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum [Russell] |
14439 | A complex number is simply an ordered couple of real numbers [Russell] |
14421 | Discovering that 1 is a number was difficult [Russell] |
9801 | Numbers must be assumed to have identical units, as horses are equalised in 'horse-power' [Mill] |
14424 | Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell] |
14441 | The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell] |
14420 | Infinity and continuity used to be philosophy, but are now mathematics [Russell] |
8742 | The only axioms needed are for equality, addition, and successive numbers [Mill, by Shapiro] |
14431 | The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell] |
14422 | Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell] |
14423 | '0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell] |
9800 | Arithmetic is based on definitions, and Sums of equals are equal, and Differences of equals are equal [Mill] |
14425 | A number is something which characterises collections of the same size [Russell] |
14434 | What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell] |
5201 | Mill says logic and maths is induction based on a very large number of instances [Mill, by Ayer] |
9360 | If two black and two white objects in practice produced five, what colour is the fifth one? [Lewis,CI on Mill] |
9888 | Mill mistakes particular applications as integral to arithmetic, instead of general patterns [Dummett on Mill] |
9794 | There are no such things as numbers in the abstract [Mill] |
9796 | Things possess the properties of numbers, as quantity, and as countable parts [Mill] |
9795 | Numbers have generalised application to entities (such as bodies or sounds) [Mill] |
9798 | Different parcels made from three pebbles produce different actual sensations [Mill] |
9797 | '2 pebbles and 1 pebble' and '3 pebbles' name the same aggregation, but different facts [Mill] |
9799 | 3=2+1 presupposes collections of objects ('Threes'), which may be divided thus [Mill] |
9802 | Numbers denote physical properties of physical phenomena [Mill] |
9803 | We can't easily distinguish 102 horses from 103, but we could arrange them to make it obvious [Mill] |
9804 | Arithmetical results give a mode of formation of a given number [Mill] |
9805 | 12 is the cube of 1728 means pebbles can be aggregated a certain way [Mill] |
8741 | Numbers must be of something; they don't exist as abstractions [Mill] |
12411 | Mill is too imprecise, and is restricted to simple arithmetic [Kitcher on Mill] |
5656 | Empirical theories of arithmetic ignore zero, limit our maths, and need probability to get started [Frege on Mill] |
9624 | Numbers are a very general property of objects [Mill, by Brown,JR] |
14465 | Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell] |
13414 | For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf] |
14449 | There is always something psychological about inference [Russell] |
14463 | Existence can only be asserted of something described, not of something named [Russell] |
14429 | Classes are logical fictions, made from defining characteristics [Russell] |
14430 | If a relation is symmetrical and transitive, it has to be reflexive [Russell] |
14432 | 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell] |
9806 | Whatever is made up of parts is made up of parts of those parts [Mill] |
22525 | The whole is prior to its parts, because parts are defined by their role [Aristotle] |
14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
11156 | The essence is that without which a thing can neither be, nor be conceived to be [Mill] |
12190 | Necessity is what will be, despite any alternative suppositions whatever [Mill] |
22623 | Necessity can only mean what must be, without conditions of any kind [Mill] |
12197 | Inferring q from p only needs p to be true, and 'not-p or q' to be true [Russell] |
14450 | All forms of implication are expressible as truth-functions [Russell] |
14460 | If something is true in all possible worlds then it is logically necessary [Russell] |
22587 | Understanding is the aim of our nature [Aristotle] |
16859 | Most perception is one-tenth observation and nine-tenths inference [Mill] |
9082 | Clear concepts result from good observation, extensive experience, and accurate memory [Mill] |
16860 | Inductive generalisation is more reliable than one of its instances; they can't all be wrong [Mill] |
14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
16845 | The whole theory of induction rests on causes [Mill] |
16843 | Mill's methods (Difference,Agreement,Residues,Concomitance,Hypothesis) don't nail induction [Mill, by Lipton] |
17086 | Surprisingly, empiricists before Mill ignore explanation, which seems to transcend experience [Mill, by Ruben] |
17091 | Explanation is fitting of facts into ever more general patterns of regularity [Mill, by Ruben] |
16805 | Causal inference is by spotting either Agreements or Differences [Mill, by Lipton] |
22522 | To grasp something, trace it back to its natural origins [Aristotle] |
22524 | The nature of each thing is its mature state [Aristotle] |
16835 | The Methods of Difference and of Agreement are forms of inference to the best explanation [Mill, by Lipton] |
9079 | We can focus our minds on what is common to a whole class, neglecting other aspects [Mill] |
9081 | We don't recognise comparisons by something in our minds; the concepts result from the comparisons [Mill] |
22528 | The nature of all animate things is to have one part which rules it [Aristotle] |
9080 | General conceptions are a necessary preliminary to Induction [Mill] |
9078 | The study of the nature of Abstract Ideas does not belong to logic, but to a different science [Mill] |
14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
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] |
8345 | A cause is the total of all the conditions which inevitably produce the result [Mill] |
10391 | Causes and conditions are not distinct, because we select capriciously from among them [Mill] |
14547 | The strict cause is the total positive and negative conditions which ensure the consequent [Mill] |
8377 | Causation is just invariability of succession between every natural fact and a preceding fact [Mill] |
14545 | A cause is an antecedent which invariably and unconditionally leads to a phenomenon [Mill] |
4773 | Mill's regularity theory of causation is based on an effect preceded by a conjunction of causes [Mill, by Psillos] |
4775 | In Mill's 'Method of Agreement' cause is the common factor in a range of different cases [Mill, by Psillos] |
4776 | In Mill's 'Method of Difference' the cause is what stops the effect when it is removed [Mill, by Psillos] |
9417 | What are the fewest propositions from which all natural uniformities could be inferred? [Mill] |
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] |