91 ideas
| 8605 | In addition to analysis of a concept, one can deny it, or accept it as primitive [Lewis] |
| 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] |
| 8607 | Supervenience is reduction without existence denials, ontological priorities, or translatability [Lewis] |
| 8606 | A supervenience thesis is a denial of independent variation [Lewis] |
| 8580 | Materialism is (roughly) that two worlds cannot differ without differing physically [Lewis] |
| 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] |
| 8571 | Universals are wholly present in their instances, whereas properties are spread around [Lewis] |
| 10717 | Natural properties figure in the analysis of similarity in intrinsic respects [Lewis, by Oliver] |
| 16217 | Lewisian natural properties fix reference of predicates, through a principle of charity [Lewis, by Hawley] |
| 8613 | Objects are demarcated by density and chemistry, and natural properties belong in what is well demarcated [Lewis] |
| 8585 | Reference partly concerns thought and language, partly eligibility of referent by natural properties [Lewis] |
| 8586 | Natural properties tend to belong to well-demarcated things, typically loci of causal chains [Lewis] |
| 8589 | For us, a property being natural is just an aspect of its featuring in the contents of our attitudes [Lewis] |
| 15460 | All perfectly natural properties are intrinsic [Lewis, by Lewis] |
| 15726 | Natural properties fix resemblance and powers, and are picked out by universals [Lewis] |
| 7031 | Lewis says properties are sets of actual and possible objects [Lewis, by Heil] |
| 8572 | Any class of things is a property, no matter how whimsical or irrelevant [Lewis] |
| 18433 | There are far more properties than any brain could ever encodify [Lewis] |
| 8604 | We need properties as semantic values for linguistic expressions [Lewis] |
| 14499 | Properties are classes of possible and actual concrete particulars [Lewis, by Koslicki] |
| 15120 | Lewisian properties have powers because of their relationships to other properties [Lewis, by Hawthorne] |
| 8573 | Most properties are causally irrelevant, and we can't spot the relevant ones. [Lewis] |
| 8569 | I suspend judgements about universals, but their work must be done [Lewis] |
| 21961 | Physics aims to discover which universals actually exist [Lewis, by Moore,AW] |
| 8576 | The One over Many problem (in predication terms) deserves to be neglected (by ostriches) [Lewis] |
| 8570 | To have a property is to be a member of a class, usually a class of things [Lewis] |
| 8574 | Class Nominalism and Resemblance Nominalism are pretty much the same [Lewis] |
| 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] |
| 8579 | Psychophysical identity implies the possibility of idealism or panpsychism [Lewis] |
| 14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
| 1554 | Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind] |
| 8614 | A sophisticated principle of charity sometimes imputes error as well as truth [Lewis] |
| 8615 | We need natural properties in order to motivate the principle of charity [Lewis] |
| 8608 | Counterfactuals 'backtrack' if a different present implies a different past [Lewis] |
| 8584 | Causal counterfactuals must avoid backtracking, to avoid epiphenomena and preemption [Lewis] |
| 8581 | Physics discovers laws and causal explanations, and also the natural properties required [Lewis] |
| 15727 | Physics aims for a list of natural properties [Lewis] |
| 8611 | A law of nature is any regularity that earns inclusion in the ideal system [Lewis] |
| 1555 | People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus] |
| 1543 | He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus] |
| 535 | The gods are just personified human benefits [Prodicus] |