141 ideas
| 14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
| 19807 | Both nature and reason require that everything has a cause [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] |
| 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] |
| 14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
| 6027 | From the fact that some men die, we cannot infer that they all do [Philodemus] |
| 14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
| 7235 | Without freedom of will actions lack moral significance [Rousseau] |
| 19791 | Natural mankind is too fragmented for states of peace, or of war and enmity [Rousseau] |
| 20501 | Rousseau assumes that laws need a people united by custom and tradition [Rousseau, by Wolff,J] |
| 7237 | The act of becoming 'a people' is the real foundation of society [Rousseau] |
| 19792 | To overcome obstacles, people must unite their forces into a single unified power [Rousseau] |
| 19812 | Human nature changes among a people, into a moral and partial existence [Rousseau] |
| 19814 | A state must be big enough to preserve itself, but small enough to be governable [Rousseau] |
| 19815 | Too much land is a struggle, producing defensive war; too little makes dependence, and offensive war [Rousseau] |
| 19822 | If the state enlarges, the creators of the general will become less individually powerful [Rousseau] |
| 19823 | If the population is larger, the government needs to be more powerful [Rousseau] |
| 7232 | Man is born free, and he is everywhere in chains [Rousseau] |
| 7234 | No man has any natural authority over his fellows [Rousseau] |
| 19816 | A state's purpose is liberty and equality - liberty for strength, and equality for liberty [Rousseau] |
| 7247 | The greatest social good comes down to freedom and equality [Rousseau] |
| 19838 | The measure of a successful state is increase in its population [Rousseau] |
| 19848 | The sovereignty does not appoint the leaders [Rousseau] |
| 20567 | Rousseau insists that popular sovereignty needs a means of expressing consent [Rousseau, by Oksala] |
| 19801 | Sovereignty is the exercise of the general will, which can never be delegated [Rousseau] |
| 19805 | Just as people control their limbs, the general-will state has total control of its members [Rousseau] |
| 19818 | Political laws are fundamental, as they firmly organise the state - but they could still be changed [Rousseau] |
| 19790 | Force can only dominate if it is seen as a right, and obedience as a duty [Rousseau] |
| 7233 | The social order is a sacred right, but based on covenants, not nature [Rousseau] |
| 19842 | The government is instituted by a law, not by a contract [Rousseau] |
| 7239 | The social pact is the total subjection of individuals to the general will [Rousseau] |
| 19793 | We need a protective association which unites forces, but retains individual freedom [Rousseau] |
| 7240 | To foreign powers a state is seen as a simple individual [Rousseau] |
| 19795 | The act of association commits citizens to the state, and the state to its citizens [Rousseau] |
| 19797 | Citizens must ultimately for forced to accept the general will (so freedom is compulsory!) [Rousseau] |
| 19796 | Individual citizens still retain a private will, which may be contrary to the general will [Rousseau] |
| 7244 | The general will is common interest; the will of all is the sum of individual desires [Rousseau] |
| 19802 | The general will is always right, but the will of all can err, because it includes private interests [Rousseau] |
| 19803 | If the state contains associations there are fewer opinions, undermining the general will [Rousseau] |
| 19804 | If a large knowledgeable population votes in isolation, their many choices will have good results [Rousseau] |
| 19808 | The general will changes its nature when it focuses on particulars [Rousseau] |
| 7246 | The general will is always good, but sometimes misunderstood [Rousseau] |
| 7250 | Laws are authentic acts of the general will [Rousseau] |
| 19844 | Assemblies must always confirm the form of government, and the current administration [Rousseau] |
| 19846 | The more unanimous the assembly, the stronger the general will becomes [Rousseau] |
| 19817 | Citizens should be independent of each other, and very dependent on the state [Rousseau] |
| 19840 | A citizen is a subject who is also sovereign [Rousseau] |
| 19839 | The flourishing of arts and letters is too much admired [Rousseau] |
| 19798 | Ancient monarchs were kings of peoples; modern monarchs more cleverly rule a land [Rousseau] |
| 19831 | The highest officers under a monarchy are normally useless; the public could choose much better [Rousseau] |
| 19833 | Hereditary monarchy is easier, but can lead to dreadful monarchs [Rousseau] |
| 19834 | Attempts to train future kings don't usually work, and the best have been unprepared [Rousseau] |
| 19829 | Natural aristocracy is primitive, and hereditary is dreadful, but elective aristocracy is best [Rousseau] |
| 7249 | Natural aristocracy is primitive, hereditary is bad, and elective aristocracy is the best [Rousseau] |
| 19830 | Large states need a nobility to fill the gap between a single prince and the people [Rousseau] |
| 19827 | Law makers and law implementers should be separate [Rousseau] |
| 19820 | The state has a legislature and an executive, just like the will and physical power in a person [Rousseau] |
| 19821 | I call the executive power the 'government', which is the 'prince' - a single person, or a group [Rousseau] |
| 19824 | Large populations needs stronger control, which means power should be concentrated [Rousseau] |
| 19826 | Democracy for small states, aristocracy for intermediate, monarchy for large [Rousseau] |
| 19837 | If inhabitants are widely dispersed, organising a revolt is much more difficult [Rousseau] |
| 19843 | The state is not bound to leave civil authority to its leaders [Rousseau] |
| 19825 | If the sovereign entrusts government to at least half the citizens, that is 'democracy' [Rousseau] |
| 19832 | Democratic elections are dangerous intervals in government [Rousseau] |
| 7243 | Silence of the people implies their consent [Rousseau] |
| 7251 | The English are actually slaves in between elections [Rousseau] |
| 7238 | Minorities only accept majority-voting because of a prior unanimous agreement [Rousseau] |
| 19828 | Democracy leads to internal strife, as people struggle to maintain or change ways of ruling [Rousseau] |
| 19835 | When ministers change the state changes, because they always reverse policies [Rousseau] |
| 19849 | In early theocracies the god was the king, and there were as many gods as nations [Rousseau] |
| 19841 | Sometimes full liberty is only possible at the expense of some complete enslavement [Rousseau] |
| 19847 | We can never assume that the son of a slave is a slave [Rousseau] |
| 7242 | Appetite alone is slavery, and self-prescribed laws are freedom [Rousseau] |
| 19800 | The social compact imposes conventional equality of rights on people who may start unequally [Rousseau] |
| 7248 | No citizen should be rich enough to buy another, and none so poor as forced to sell himself [Rousseau] |
| 19794 | If we all give up all of our rights together to the community, we will always support one another [Rousseau] |
| 7241 | In society man loses natural liberty, but gains a right to civil liberty and property [Rousseau] |
| 19806 | We alienate to society only what society needs - but society judges that, not us [Rousseau] |
| 19799 | Private property must always be subordinate to ownership by the whole community [Rousseau] |
| 19819 | The state ensures liberty, so civil law separates citizens, and binds them to the state [Rousseau] |
| 7245 | Natural justice, without sanctions, benefits the wicked, who exploit it [Rousseau] |
| 19809 | We accept the death penalty to prevent assassinations, so we must submit to it if necessary [Rousseau] |
| 19810 | A trial proves that a criminal has broken the social treaty, and is no longer a member of the state [Rousseau] |
| 19811 | Only people who are actually dangerous should be executed, even as an example [Rousseau] |
| 7236 | War gives no right to inflict more destruction than is necessary for victory [Rousseau] |
| 23607 | Wars are between States, not people, and the individuals are enemies by accident [Rousseau] |
| 19850 | By separating theological and political systems, Jesus caused divisions in the state [Rousseau] |
| 19852 | Civil religion needs one supreme god, an afterlife, justice, and the sanctity of the social contract [Rousseau] |
| 19853 | All religions should be tolerated, if they tolerate each other, and support citizenship [Rousseau] |
| 19851 | Every society has a religion as its base [Rousseau] |
| 19836 | The amount of taxation doesn't matter, if it quickly circulates back to the citizens [Rousseau] |
| 7252 | A tyrant exploits Christians because they don't value this life, and are made to be slaves [Rousseau] |