122 ideas
21979 | Wisdom emerges at the end of a process [Hegel] |
22766 | Philosophy is exploration of the rational [Hegel] |
6947 | Metaphysics does not rest on facts, but on what we are inclined to believe [Peirce] |
14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
6937 | Reason aims to discover the unknown by thinking about the known [Peirce] |
22768 | Subjective and objective are not firmly opposed, but merge into one another [Hegel] |
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] |
22772 | Personality overcomes subjective limitations and posits Dasein as its own [Hegel] |
21492 | Realism is basic to the scientific method [Peirce] |
6949 | If someone doubted reality, they would not actually feel dissatisfaction [Peirce] |
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] |
6940 | The feeling of belief shows a habit which will determine our actions [Peirce] |
6941 | We are entirely satisfied with a firm belief, even if it is false [Peirce] |
6942 | We want true beliefs, but obviously we think our beliefs are true [Peirce] |
6943 | A mere question does not stimulate a struggle for belief; there must be a real doubt [Peirce] |
6598 | We need our beliefs to be determined by some external inhuman permanency [Peirce] |
6944 | Demonstration does not rest on first principles of reason or sensation, but on freedom from actual doubt [Peirce] |
6948 | Doubts should be satisfied by some external permanency upon which thinking has no effect [Peirce] |
22780 | It is a rejection of intellectual dignity to say that we cannot know the truth [Hegel] |
6945 | Once doubt ceases, there is no point in continuing to argue [Peirce] |
14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
22770 | A person is a being which is aware of its own self-directed and free subjectivity [Hegel] |
22788 | A human only become a somebody as a member of a social estate [Hegel] |
22792 | Individuals attain their right by discovering their self-consciousness in institutions [Hegel] |
21780 | A free will primarily wills its own freedoom [Hegel, by Houlgate] |
14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
22769 | The concept of the will is the free will which wills its freedom [Hegel] |
21787 | Evil enters a good will when we believe we are doing right, but allow no criticism of our choice [Hegel, by Houlgate] |
21786 | Conscience is the right of the self to know what is right and obligatory, and thus make them true [Hegel] |
22784 | Love is ethical life in its natural form [Hegel] |
8029 | You can't have a morality which is supplied by the individual, but is also genuinely universal [Hegel, by MacIntyre] |
22771 | Be a person, and respect other persons [Hegel] |
22051 | The categorical imperative lacks roots in a historical culture [Hegel, by Bowie] |
22781 | The categorical imperative is fine if you already have a set of moral principles [Hegel] |
22779 | The good is realised freedom [Hegel] |
22787 | The family is the first basis of the state, but estates are a necessary second [Hegel] |
22790 | We cannot assert rights which are unnatural [Hegel] |
22767 | I aim to portray the state as a rational entity [Hegel] |
22789 | Society draws people, and requires their work, making them wholly dependent on it [Hegel] |
22791 | The state is the march of God in the world [Hegel] |
22778 | Individuals can't leave the state, because they are natural citizens, and humans require a state [Hegel] |
22794 | A fully developed state is conscious and knows what it wills [Hegel] |
22799 | The people do not have the ability to know the general will [Hegel] |
22801 | The great man of the ages is the one who reveals and accomplishes the will of his time [Hegel] |
22796 | A constitution embodies a nation's rights and condition [Hegel] |
22777 | Individuals must dedicate themselves to the ethical whole, and give their lives when asked [Hegel] |
21791 | Social groups must focus on the state, which must in turn respect their inclusion and their will [Hegel] |
22795 | People can achieve respect for their state by insight into its essence [Hegel] |
21988 | In the 1840s Hegel seemed to defend society being right as it is, as a manifestation of Mind [Hegel, by Singer] |
22800 | Majority rule means obligations can be imposed on me [Hegel] |
21792 | The state should reflect all interests, and not just popular will, or a popular party [Hegel, by Houlgate] |
22797 | In modern states an individual's actions should be their choice [Hegel] |
21790 | Moral individuals become ethical when they see the social aspect of a matter [Hegel, by Houlgate] |
8030 | For Hegel, the moral life can only be led within a certain type of community [Hegel, by MacIntyre] |
22785 | Even educated women are unsuited to science, philosophy, art and government [Hegel] |
21789 | Slaves have no duties because they have no rights [Hegel] |
22776 | Slaves are partly responsible for their own condition [Hegel] |
21778 | True liberal freedom is to pursue something, while being free to cease the pursuit [Hegel, by Houlgate] |
21779 | People assume they are free, but the options available are not under their control [Hegel] |
22085 | Freedom requires us to submit to a family, or a corporation, or a state [Hegel, by Houlgate] |
22798 | Money is the best way to achieve just equality [Hegel] |
22783 | Rights imply duties, and duties imply rights [Hegel] |
21782 | Man has an absolute right to appropriate things [Hegel] |
22773 | Because only human beings can own property, everything else can become our property [Hegel] |
22774 | A community does not have the property-owning rights that a person has [Hegel] |
22775 | The owner of a thing is obviously the first person to freely take possession of it [Hegel] |
22802 | Wars add strength to a nation, and cure internal dissension [Hegel] |
22786 | Children need discipline, to break their self-will and eradicate sensuousness [Hegel] |
6939 | What is true of one piece of copper is true of another (unlike brass) [Peirce] |
6938 | Natural selection might well fill an animal's mind with pleasing thoughts rather than true ones [Peirce] |
6946 | If death is annihilation, belief in heaven is a cheap pleasure with no disappointment [Peirce] |
22782 | To have pagan beliefs and be a pagan are quite different [Hegel] |
22793 | Some religions lead to harsh servitude and the debasement of human beings [Hegel] |