87 ideas
14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
4767 | Traditionally, rational beliefs are those which are justified by reasons [Psillos] |
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] |
4810 | Valid deduction is monotonic - that is, it remains valid if further premises are added [Psillos] |
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] |
4768 | The 'epistemic fallacy' is inferring what does exist from what can be known to exist [Psillos] |
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] |
4807 | A good barometer will predict a storm, but not explain it [Psillos] |
4808 | If we say where Mars was two months ago, we offer an explanation without a prediction [Psillos] |
14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
4811 | Induction (unlike deduction) is non-monotonic - it can be invalidated by new premises [Psillos] |
4812 | Explanation is either showing predictability, or showing necessity, or showing causal relations [Psillos] |
4802 | Just citing a cause does not enable us to understand an event; we also need a relevant law [Psillos] |
4804 | The 'covering law model' says only laws can explain the occurrence of single events [Psillos] |
4805 | If laws explain the length of a flagpole's shadow, then the shadow also explains the length of the pole [Psillos] |
4395 | There are non-causal explanations, most typically mathematical explanations [Psillos] |
4806 | An explanation can just be a 'causal story', without laws, as when I knock over some ink [Psillos] |
4404 | Maybe explanation is entirely relative to the interests and presuppositions of the questioner [Psillos] |
4803 | An explanation is the removal of the surprise caused by the event [Psillos] |
4769 | It is hard to analyse causation, if it is presupposed in our theory of the functioning of the mind [Psillos] |
14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
4770 | Nothing is more usual than to apply to external bodies every internal sensation which they occasion [Psillos] |
4403 | We can't base our account of causation on explanation, because it is the wrong way round [Psillos] |
4399 | Causes clearly make a difference, are recipes for events, explain effects, and are evidence [Psillos] |
4400 | Theories of causation are based either on regularity, or on intrinsic relations of properties [Psillos] |
4789 | Three divisions of causal theories: generalist/singularist, intrinsic/extrinsic, reductive/non-reductive [Psillos] |
4790 | If causation is 'intrinsic' it depends entirely on the properties and relations of the cause and effect [Psillos] |
4402 | Empiricists tried to reduce causation to explanation, which they reduced to logic-plus-a-law [Psillos] |
4774 | Counterfactual claims about causation imply that it is more than just regular succession [Psillos] |
4793 | "All gold cubes are smaller than one cubic mile" is a true universal generalisation, but not a law [Psillos] |
4397 | Regularity doesn't seem sufficient for causation [Psillos] |
4792 | A Humean view of causation says it is regularities, and causal facts supervene on non-causal facts [Psillos] |
4801 | The regularity of a cock's crow is used to predict dawn, even though it doesn't cause it [Psillos] |
4401 | It is not a law of nature that all the coins in my pocket are euros, though it is a regularity [Psillos] |
4796 | Laws are sets of regularities within a simple and strong coherent system of wider regularities [Psillos] |
4799 | Dispositional essentialism can't explain its key distinction between essential and non-essential properties [Psillos] |
4780 | In some counterfactuals, the counterfactual event happens later than its consequent [Psillos] |
4791 | Counterfactual theories say causes make a difference - if c hadn't occurred, then e wouldn't occur [Psillos] |