101 ideas
20771 | Six parts: dialectic, rhetoric, ethics, politics, physics, theology [Cleanthes, by Diog. Laertius] |
14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
14426 | A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell] |
14227 | We could refer to tables as 'xs that are arranged tablewise' [Inwagen] |
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] |
10662 | Mereology is 'nihilistic' (just atoms) or 'universal' (no restrictions on what is 'whole') [Inwagen, by Varzi] |
14452 | All the propositions of logic are completely general [Russell] |
14462 | In modern times, logic has become mathematical, and mathematics has become logical [Russell] |
12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
10057 | Logic can only assert hypothetical existence [Russell] |
14464 | Logic can be known a priori, without study of the actual world [Russell] |
17587 | The 'Law' of Excluded Middle needs all propositions to be definitely true or definitely false [Inwagen] |
17558 | Variables are just like pronouns; syntactic explanations get muddled over dummy letters [Inwagen] |
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] |
14458 | Asking 'Did Homer exist?' is employing an abbreviated description [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] |
17583 | There are no heaps [Inwagen] |
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] |
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] |
17578 | I reject talk of 'stuff', and treat it in terms of particles [Inwagen] |
14429 | Classes are logical fictions, made from defining characteristics [Russell] |
17582 | Singular terms can be vague, because they can contain predicates, which can be vague [Inwagen] |
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] |
17556 | Material objects are in space and time, move, have a surface and mass, and are made of some stuff [Inwagen] |
8264 | Maybe table-shaped particles exist, but not tables [Inwagen, by Lowe] |
17565 | Nihilism says composition between single things is impossible [Inwagen] |
14228 | If there are no tables, but tables are things arranged tablewise, the denial of tables is a contradiction [Liggins on Inwagen] |
14468 | Actions by artefacts and natural bodies are disguised cooperations, so we don't need them [Inwagen] |
17571 | Every physical thing is either a living organism or a simple [Inwagen] |
17562 | The statue and lump seem to share parts, but the statue is not part of the lump [Inwagen] |
17574 | If you knead clay you make an infinite series of objects, but they are rearrangements, not creations [Inwagen] |
17531 | I assume matter is particulate, made up of 'simples' [Inwagen] |
17560 | If contact causes composition, do two colliding balls briefly make one object? [Inwagen] |
17561 | If bricks compose a house, that is at least one thing, but it might be many things [Inwagen] |
17566 | I think parthood involves causation, and not just a reasonably stable spatial relationship [Inwagen] |
14230 | We can deny whole objects but accept parts, by referring to them as plurals within things [Inwagen, by Liggins] |
17557 | Special Composition Question: when is a thing part of something? [Inwagen] |
14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
17564 | The essence of a star includes the released binding energy which keeps it from collapse [Inwagen] |
17575 | The persistence of artifacts always covertly involves intelligent beings [Inwagen] |
17577 | When an electron 'leaps' to another orbit, is the new one the same electron? [Inwagen] |
17589 | If you reject transitivity of vague identity, there is no Ship of Theseus problem [Inwagen] |
17588 | We should talk of the transitivity of 'identity', and of 'definite identity' [Inwagen] |
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] |
17572 | Actuality proves possibility, but that doesn't explain how it is possible [Inwagen] |
14460 | If something is true in all possible worlds then it is logically necessary [Russell] |
17579 | Counterparts reduce counterfactual identity to problems about similarity relations [Inwagen] |
17590 | A merely possible object clearly isn't there, so that is a defective notion [Inwagen] |
17591 | Merely possible objects must be consistent properties, or haecceities [Inwagen] |
14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
6028 | Bodies interact with other bodies, and cuts cause pain, and shame causes blushing, so the soul is a body [Cleanthes, by Nemesius] |
20831 | The soul suffers when the body hurts, creates redness from shame, and pallor from fear [Cleanthes] |
14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
17563 | The strong force pulls, but also pushes apart if nucleons get too close together [Inwagen] |
17559 | Is one atom a piece of gold, or is a sizable group of atoms required? [Inwagen] |
17584 | Some events are only borderline cases of lives [Inwagen] |
17586 | At the lower level, life trails off into mere molecular interaction [Inwagen] |
17567 | A flame is like a life, but not nearly so well individuated [Inwagen] |
17568 | A tumour may spread a sort of life, but it is not a life, or an organism [Inwagen] |
17569 | Unlike waves, lives are 'jealous'; it is almost impossible for them to overlap [Inwagen] |
17580 | One's mental and other life is centred on the brain, unlike any other part of the body [Inwagen] |
17576 | If God were to 'reassemble' my atoms of ten years ago, the result would certainly not be me [Inwagen] |
17585 | Life is vague at both ends, but could it be totally vague? [Inwagen] |
17570 | The chemical reactions in a human life involve about sixteen elements [Inwagen] |
17581 | Being part of an organism's life is a matter of degree, and vague [Inwagen] |
17573 | There is no reason to think that mere existence is a valuable thing [Inwagen] |
5993 | The ascending scale of living creatures requires a perfect being [Cleanthes, by Tieleman] |