88 ideas
8558 | One system has properties, powers, events, similarity and substance [Shoemaker] |
8559 | Analysis aims at internal relationships, not reduction [Shoemaker] |
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] |
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] |
15092 | Formerly I said properties are individuated by essential causal powers and causing instantiation [Shoemaker, by Shoemaker] |
8543 | Genuine properties are closely related to genuine changes [Shoemaker] |
8551 | Properties must be essentially causal if we can know and speak about them [Shoemaker] |
8557 | To ascertain genuine properties, examine the object directly [Shoemaker] |
15761 | We should abandon the idea that properties are the meanings of predicate expressions [Shoemaker] |
15756 | Some truths are not because of a thing's properties, but because of the properties of related things [Shoemaker] |
15758 | Things have powers in virtue of (which are entailed by) their properties [Shoemaker] |
8547 | One power can come from different properties; a thing's powers come from its properties [Shoemaker] |
8549 | Properties are functions producing powers, and powers are functions producing effects [Shoemaker] |
12678 | Shoemaker says all genuine properties are dispositional [Shoemaker, by Ellis] |
8545 | A causal theory of properties focuses on change, not (say) on abstract properties of numbers [Shoemaker] |
15757 | 'Square', 'round' and 'made of copper' show that not all properties are dispositional [Shoemaker] |
15759 | The identity of a property concerns its causal powers [Shoemaker] |
15760 | Properties are clusters of conditional powers [Shoemaker] |
15762 | Could properties change without the powers changing, or powers change without the properties changing? [Shoemaker] |
8552 | If properties are separated from causal powers, this invites total elimination [Shoemaker] |
4040 | The notions of property and of causal power are parts of a single system of related concepts [Shoemaker] |
15765 | Actually, properties are individuated by causes as well as effects [Shoemaker] |
8548 | Dispositional predicates ascribe powers, and the rest ascribe properties [Shoemaker] |
9485 | Universals concern how things are, and how they could be [Shoemaker, by Bird] |
8550 | Triangular and trilateral are coextensive, but different concepts; but powers and properties are the same [Shoemaker] |
14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
8555 | There is no subset of properties which guarantee a thing's identity [Shoemaker] |
8554 | Possible difference across worlds depends on difference across time in the actual world [Shoemaker] |
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] |
15764 | 'Conceivable' is either not-provably-false, or compatible with what we know? [Shoemaker] |
8562 | It is possible to conceive what is not possible [Shoemaker] |
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] |
8556 | Grueness is not, unlike green and blue, associated with causal potential [Shoemaker] |
14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
8542 | If causality is between events, there must be reference to the properties involved [Shoemaker] |
8560 | If causal laws describe causal potentialities, the same laws govern properties in all possible worlds [Shoemaker] |
15763 | If properties are causal, then causal necessity is a species of logical necessity [Shoemaker] |
8561 | If a world has different causal laws, it must have different properties [Shoemaker] |
8553 | It looks as if the immutability of the powers of a property imply essentiality [Shoemaker] |