98 ideas
| 14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
| 19767 | Reason leads to prudent selfishness, which overrules natural compassion [Rousseau] |
| 14426 | A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 14534 | Shoemaker moved from properties as powers to properties bestowing powers [Shoemaker, by Mumford/Anjum] |
| 14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
| 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] |
| 19757 | No one would bother to reason, and try to know things, without a desire for enjoyment [Rousseau] |
| 14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
| 19760 | General ideas are purely intellectual; imagining them is immediately particular [Rousseau] |
| 19759 | Only words can introduce general ideas into the mind [Rousseau] |
| 19758 | Language may aid thinking, but powerful thought was needed to produce language [Rousseau] |
| 14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
| 19773 | Without love, what use is beauty? [Rousseau] |
| 19769 | Rational morality is OK for brainy people, but ordinary life can't rely on that [Rousseau] |
| 19752 | If we should not mistreat humans, it is mainly because of sentience, not rationality [Rousseau] |
| 19768 | The better Golden Rule is 'do good for yourself without harming others' [Rousseau] |
| 19766 | The fact that we weep (e.g. in theatres) shows that we are naturally compassionate [Rousseau] |
| 19756 | Humans are less distinguished from other animals by understanding, than by being free agents [Rousseau] |
| 19755 | Most human ills are self-inflicted; the simple, solitary, regular natural life is good [Rousseau] |
| 19762 | Is language a pre-requisite for society, or might it emerge afterwards? [Rousseau] |
| 19763 | I doubt whether a savage person ever complains of life, or considers suicide [Rousseau] |
| 19778 | Leisure led to envy, inequality, vice and revenge, which we now see in savages [Rousseau] |
| 19779 | Primitive man was very gentle [Rousseau] |
| 19751 | Our two starting principles are concern for self-interest, and compassion for others [Rousseau] |
| 19765 | Savages avoid evil because they are calm, and never think of it (not because they know goodness) [Rousseau] |
| 19771 | Savage men quietly pursue desires, without the havoc of modern frenzied imagination [Rousseau] |
| 19774 | A savage can steal fruit or a home, but there is no means of achieving obedience [Rousseau] |
| 19772 | In a state of nature people are much more equal; it is society which increases inequalities [Rousseau] |
| 19789 | It is against nature for children to rule old men, fools to rule the wise, and the rich to hog resources [Rousseau] |
| 19787 | People accept the right to be commanded, because they themselves wish to command [Rousseau] |
| 19780 | We seem to have made individual progress since savagery, but actually the species has decayed [Rousseau] |
| 19747 | Revolutionaries usually confuse liberty with total freedom, and end up with heavier chains [Rousseau] |
| 19748 | Plebiscites are bad, because they exclude the leaders from crucial decisions [Rousseau] |
| 19749 | In a direct democracy, only the leaders should be able to propose new laws [Rousseau] |
| 19775 | People must be made dependent before they can be enslaved [Rousseau] |
| 19784 | Enslaved peoples often boast of their condition, calling it a state of 'peace' [Rousseau] |
| 19785 | If the child of a slave woman is born a slave, then a man is not born a man [Rousseau] |
| 19746 | Like rich food, liberty can ruin people who are too weak to cope with it [Rousseau] |
| 19786 | Three stages of the state produce inequalities of wealth, power, and enslavement [Rousseau] |
| 19788 | The pleasure of wealth and power is largely seeing others deprived of them [Rousseau] |
| 19777 | Persuading other people that some land was 'owned' was the beginning of society [Rousseau] |
| 19782 | What else could property arise from, but the labour people add to it? [Rousseau] |
| 19781 | Land cultivation led to a general right of ownership, administered justly [Rousseau] |
| 19754 | If we have a natural right to property, what exactly does 'belonging to' mean? [Rousseau] |
| 19750 | Writers just propose natural law as the likely useful agreements among people [Rousseau] |
| 19770 | Primitive people simply redressed the evil caused by violence, without thought of punishing [Rousseau] |
| 19783 | A state of war remains after a conquest, if the losers don't accept the winners [Rousseau] |
| 19753 | Both men and animals are sentient, which should give the latter the right not to be mistreated [Rousseau] |
| 19761 | Men started with too few particular names, but later had too few natural kind names [Rousseau] |
| 19776 | Small uninterrupted causes can have big effects [Rousseau] |