121 ideas
14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
24047 | An account is either a definition or a demonstration [Aristotle] |
192 | Only one thing can be contrary to something [Plato] |
24052 | From one thing alone we can infer its contrary [Aristotle] |
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] |
14440 | We may assume that there are infinite collections, as there is no logical reason against them [Russell] |
14447 | Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell] |
14443 | The British parliament has one representative selected from each constituency [Russell] |
14444 | Choice is equivalent to the proposition that every class is well-ordered [Russell] |
14445 | Choice shows that if any two cardinals are not equal, one must be the greater [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] |
14464 | Logic can be known a priori, without study of the actual world [Russell] |
12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
10057 | Logic can only assert hypothetical existence [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] |
1729 | We perceive number by the denial of continuity [Aristotle] |
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] |
14423 | '0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell] |
14422 | Any founded, non-repeating series all reachable in steps will satisfy 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] |
24057 | What is prior is always potentially present in what is next in order [Aristotle] |
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] |
16752 | Sight is the essence of the eye, fitting its definition; the eye itself is just the matter [Aristotle] |
190 | If asked whether justice itself is just or unjust, you would have to say that it is just [Plato] |
24058 | The substance is the cause of a thing's being [Aristotle] |
24055 | Matter is potential, form is actual [Aristotle] |
24040 | Scientists explain anger by the matter, dialecticians by the form and the account [Aristotle] |
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] |
20184 | The only real evil is loss of knowledge [Plato] |
20185 | The most important things in life are wisdom and knowledge [Plato] |
5051 | The intellect has potential to think, like a tablet on which nothing has yet been written [Aristotle] |
1732 | Sense organs aren't the end of sensation, or they would know what does the sensing [Aristotle] |
17711 | Our minds take on the form of what is being perceived [Aristotle, by Mares] |
1725 | Why can't we sense the senses? And why do senses need stimuli? [Aristotle] |
1724 | Perception necessitates pleasure and pain, which necessitates appetite [Aristotle] |
1730 | Why do we have many senses, and not just one? [Aristotle] |
16723 | Perception of sensible objects is virtually never wrong [Aristotle] |
1728 | Many objects of sensation are common to all the senses [Aristotle] |
1727 | Some objects of sensation are unique to one sense, where deception is impossible [Aristotle] |
1734 | In moral thought images are essential, to be pursued or avoided [Aristotle] |
1726 | We may think when we wish, but not perceive, because universals are within the mind [Aristotle] |
16647 | Demonstration starts from a definition of essence, so we can derive (or conjecture about) the properties [Aristotle] |
24048 | Demonstrations move from starting-points to deduced conclusions [Aristotle] |
14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
16646 | To understand a triangle summing to two right angles, we need to know the essence of a line [Aristotle] |
1714 | Mind involves movement, perception, incorporeality [Aristotle] |
5507 | Aristotle led to the view that there are several souls, all somewhat physical [Aristotle, by Martin/Barresi] |
24051 | Soul is seen as what moves, or what is least physical, or a combination of elements [Aristotle] |
12086 | Psuché is the form and actuality of a body which potentially has life [Aristotle] |
16754 | The soul is the cause or source of movement, the essence of body, and its end [Aristotle] |
24046 | Understanding is impossible, if it involves the understanding having parts [Aristotle] |
1717 | If the soul is composed of many physical parts, it can't be a true unity [Aristotle] |
24053 | If a soul have parts, what unites them? [Aristotle] |
1721 | What unifies the soul would have to be a super-soul, which seems absurd [Aristotle] |
1735 | In a way the soul is everything which exists, through its perceptions and thoughts [Aristotle] |
24061 | If we divide the mind up according to its capacities, there are a lot of them [Aristotle] |
24062 | Self-moving animals must have desires, and that entails having imagination [Aristotle] |
191 | Everything resembles everything else up to a point [Plato] |
1710 | Emotion involves the body, thinking uses the mind, imagination hovers between them [Aristotle] |
24039 | All the emotions seem to involve the body, simultaneously with the feeling [Aristotle] |
24056 | The soul (or parts of it) is not separable from the body [Aristotle] |
24050 | If soul is separate from body, why does it die when the body dies? [Aristotle] |
24049 | Thinkers place the soul within the body, but never explain how they are attached [Aristotle] |
1514 | Early thinkers concentrate on the soul but ignore the body, as if it didn't matter what body received the soul [Aristotle] |
2683 | Aristotle has a problem fitting his separate reason into the soul, which is said to be the form of the body [Ackrill on Aristotle] |
1718 | Does the mind think or pity, or does the whole man do these things? [Aristotle] |
13275 | The soul and the body are inseparable, like the imprint in some wax [Aristotle] |
1733 | Thinking is not perceiving, but takes the form of imagination and speculation [Aristotle] |
23307 | Aristotle makes belief a part of reason, but sees desires as separate [Aristotle, by Sorabji] |
14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
24060 | Self-controlled follow understanding, when it is opposed to desires [Aristotle] |
203 | Courage is knowing what should or shouldn't be feared [Plato] |
202 | No one willingly and knowingly embraces evil [Plato] |
193 | Some things are good even though they are not beneficial to men [Plato] |
4376 | Pleasure and pain are perceptions of things as good or bad [Aristotle] |
197 | Some pleasures are not good, and some pains are not evil [Plato] |
200 | People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato] |
188 | Socrates did not believe that virtue could be taught [Plato] |
189 | If we punish wrong-doers, it shows that we believe virtue can be taught [Plato] |
204 | Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato] |
1740 | Nature does nothing in vain [Aristotle] |
24044 | Movement can be intrinsic (like a ship) or relative (like its sailors) [Aristotle] |
24045 | Movement is spatial, alteration, withering or growth [Aristotle] |
1738 | Practical reason is based on desire, so desire must be the ultimate producer of movement [Aristotle] |
1739 | If all movement is either pushing or pulling, there must be a still point in between where it all starts [Aristotle] |
24064 | If something is pushed, it pushes back [Aristotle] |
24063 | What is born has growth, a prime, and a withering away [Aristotle] |