204 ideas
| 19693 | There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb] |
| 5361 | Philosophers must get used to absurdities [Russell] |
| 5368 | Philosophy verifies that our hierarchy of instinctive beliefs is harmonious and consistent [Russell] |
| 5432 | Metaphysics cannot give knowledge of the universe as a whole [Russell] |
| 14122 | Analysis gives us nothing but the truth - but never the whole truth [Russell] |
| 14109 | The study of grammar is underestimated in philosophy [Russell] |
| 14165 | Analysis falsifies, if when the parts are broken down they are not equivalent to their sum [Russell] |
| 5434 | Philosophy is similar to science, and has no special source of wisdom [Russell] |
| 1575 | For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle] |
| 1589 | Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle] |
| 5405 | The law of contradiction is not a 'law of thought', but a belief about things [Russell] |
| 5396 | Three Laws of Thought: identity, contradiction, and excluded middle [Russell] |
| 8200 | Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine] |
| 4385 | Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson] |
| 14115 | Definition by analysis into constituents is useless, because it neglects the whole [Russell] |
| 14159 | In mathematics definitions are superfluous, as they name classes, and it all reduces to primitives [Russell] |
| 14148 | Infinite regresses have propositions made of propositions etc, with the key term reappearing [Russell] |
| 18002 | As well as a truth value, propositions have a range of significance for their variables [Russell] |
| 5420 | Truth is a property of a belief, but dependent on its external relations, not its internal qualities [Russell] |
| 14102 | What is true or false is not mental, and is best called 'propositions' [Russell] |
| 5419 | Truth and falsehood are properties of beliefs and statements [Russell] |
| 5417 | A good theory of truth must make falsehood possible [Russell] |
| 7395 | Truth as congruence may work for complex beliefs, but not for simple beliefs about existence [Joslin on Russell] |
| 5428 | Beliefs are true if they have corresponding facts, and false if they don't [Russell] |
| 5421 | The coherence theory says falsehood is failure to cohere, and truth is fitting into a complete system of Truth [Russell] |
| 5422 | More than one coherent body of beliefs seems possible [Russell] |
| 5423 | If we suspend the law of contradiction, nothing will appear to be incoherent [Russell] |
| 5424 | Coherence is not the meaning of truth, but an important test for truth [Russell] |
| 14176 | "The death of Caesar is true" is not the same proposition as "Caesar died" [Russell] |
| 5401 | The mortality of Socrates is more certain from induction than it is from deduction [Russell] |
| 14113 | The null class is a fiction [Russell] |
| 15894 | Russell invented the naïve set theory usually attributed to Cantor [Russell, by Lavine] |
| 14126 | Order rests on 'between' and 'separation' [Russell] |
| 14127 | Order depends on transitive asymmetrical relations [Russell] |
| 14121 | The part-whole relation is ultimate and indefinable [Russell] |
| 13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
| 5395 | Demonstration always relies on the rule that anything implied by a truth is true [Russell] |
| 14106 | Implication cannot be defined [Russell] |
| 14108 | It would be circular to use 'if' and 'then' to define material implication [Russell] |
| 14167 | The only classes are things, predicates and relations [Russell] |
| 4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
| 14105 | There seem to be eight or nine logical constants [Russell] |
| 18722 | Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell] |
| 14104 | Constants are absolutely definite and unambiguous [Russell] |
| 14114 | Variables don't stand alone, but exist as parts of propositional functions [Russell] |
| 5386 | Proper names are really descriptions, and can be replaced by a description in a person's mind [Russell] |
| 5385 | The phrase 'a so-and-so' is an 'ambiguous' description'; 'the so-and-so' (singular) is a 'definite' description [Russell] |
| 14137 | 'Any' is better than 'all' where infinite classes are concerned [Russell] |
| 14149 | The Achilles Paradox concerns the one-one correlation of infinite classes [Russell] |
| 15895 | Russell discovered the paradox suggested by Burali-Forti's work [Russell, by Lavine] |
| 14151 | Pure geometry is deductive, and neutral over what exists [Russell] |
| 14152 | In geometry, Kant and idealists aimed at the certainty of the premisses [Russell] |
| 14154 | Geometry throws no light on the nature of actual space [Russell] |
| 14153 | In geometry, empiricists aimed at premisses consistent with experience [Russell] |
| 14155 | Two points have a line joining them (descriptive), a distance (metrical), and a whole line (projective) [Russell, by PG] |
| 18254 | Russell's approach had to treat real 5/8 as different from rational 5/8 [Russell, by Dummett] |
| 14144 | Ordinals result from likeness among relations, as cardinals from similarity among classes [Russell] |
| 14128 | Some claim priority for the ordinals over cardinals, but there is no logical priority between them [Russell] |
| 14129 | Ordinals presuppose two relations, where cardinals only presuppose one [Russell] |
| 14132 | Properties of numbers don't rely on progressions, so cardinals may be more basic [Russell] |
| 14139 | Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic [Russell] |
| 14142 | Ordinals are types of series of terms in a row, rather than the 'nth' instance [Russell] |
| 14141 | Ordinals are defined through mathematical induction [Russell] |
| 14145 | For Cantor ordinals are types of order, not numbers [Russell] |
| 14146 | We aren't sure if one cardinal number is always bigger than another [Russell] |
| 14135 | Real numbers are a class of rational numbers (and so not really numbers at all) [Russell] |
| 14158 | Quantity is not part of mathematics, where it is replaced by order [Russell] |
| 14123 | Some quantities can't be measured, and some non-quantities are measurable [Russell] |
| 14120 | Counting explains none of the real problems about the foundations of arithmetic [Russell] |
| 14118 | We can define one-to-one without mentioning unity [Russell] |
| 14133 | There are cardinal and ordinal theories of infinity (while continuity is entirely ordinal) [Russell] |
| 14119 | We do not currently know whether, of two infinite numbers, one must be greater than the other [Russell] |
| 14134 | Infinite numbers are distinguished by disobeying induction, and the part equalling the whole [Russell] |
| 14143 | ω names the whole series, or the generating relation of the series of ordinal numbers [Russell] |
| 14138 | You can't get a new transfinite cardinal from an old one just by adding finite numbers to it [Russell] |
| 14140 | For every transfinite cardinal there is an infinite collection of transfinite ordinals [Russell] |
| 14124 | Axiom of Archimedes: a finite multiple of a lesser magnitude can always exceed a greater [Russell] |
| 7530 | Russell tried to replace Peano's Postulates with the simple idea of 'class' [Russell, by Monk] |
| 18246 | Dedekind failed to distinguish the numbers from other progressions [Shapiro on Russell] |
| 14125 | Finite numbers, unlike infinite numbers, obey mathematical induction [Russell] |
| 14147 | Denying mathematical induction gave us the transfinite [Russell] |
| 14116 | Numbers were once defined on the basis of 1, but neglected infinities and + [Russell] |
| 14117 | Numbers are properties of classes [Russell] |
| 9977 | Ordinals can't be defined just by progression; they have intrinsic qualities [Russell] |
| 14162 | Mathematics doesn't care whether its entities exist [Russell] |
| 5399 | Maths is not known by induction, because further instances are not needed to support it [Russell] |
| 14103 | Pure mathematics is the class of propositions of the form 'p implies q' [Russell] |
| 21555 | For 'x is a u' to be meaningful, u must be one range of individuals (or 'type') higher than x [Russell] |
| 18003 | In 'x is a u', x and u must be of different types, so 'x is an x' is generally meaningless [Russell, by Magidor] |
| 11010 | Being is what belongs to every possible object of thought [Russell] |
| 14161 | Many things have being (as topics of propositions), but may not have actual existence [Russell] |
| 14173 | What exists has causal relations, but non-existent things may also have them [Russell] |
| 5370 | Space is neutral between touch and sight, so it cannot really be either of them [Russell] |
| 5418 | In a world of mere matter there might be 'facts', but no truths [Russell] |
| 14163 | Four classes of terms: instants, points, terms at instants only, and terms at instants and points [Russell] |
| 21341 | Philosophers of logic and maths insisted that a vocabulary of relations was essential [Russell, by Heil] |
| 5371 | Because we depend on correspondence, we know relations better than we know the items that relate [Russell] |
| 5407 | That Edinburgh is north of London is a non-mental fact, so relations are independent universals [Russell] |
| 10586 | 'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness [Russell] |
| 10585 | Symmetrical and transitive relations are formally like equality [Russell] |
| 5383 | Every complete sentence must contain at least one word (a verb) which stands for a universal [Russell] |
| 4428 | Propositions express relations (prepositions and verbs) as well as properties (nouns and adjectives) [Russell] |
| 5406 | Confused views of reality result from thinking that only nouns and adjectives represent universals [Russell] |
| 4479 | All universals are like the relation "is north of", in having no physical location at all [Russell, by Loux] |
| 4030 | Russell claims that universals are needed to explain a priori knowledge (as their relations) [Russell, by Mellor/Oliver] |
| 4427 | Every sentence contains at least one word denoting a universal, so we need universals to know truth [Russell] |
| 5409 | Normal existence is in time, so we must say that universals 'subsist' [Russell] |
| 5408 | If we identify whiteness with a thought, we can never think of it twice; whiteness is the object of a thought [Russell] |
| 4441 | 'Resemblance Nominalism' won't work, because the theory treats resemblance itself as a universal [Russell] |
| 4429 | If we consider whiteness to be merely a mental 'idea', we rob it of its universality [Russell] |
| 7781 | I call an object of thought a 'term'. This is a wide concept implying unity and existence. [Russell] |
| 14166 | Unities are only in propositions or concepts, and nothing that exists has unity [Russell] |
| 14164 | The only unities are simples, or wholes composed of parts [Russell] |
| 14112 | A set has some sort of unity, but not enough to be a 'whole' [Russell] |
| 13276 | The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki] |
| 13277 | The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki] |
| 14170 | Change is obscured by substance, a thing's nature, subject-predicate form, and by essences [Russell] |
| 14107 | Terms are identical if they belong to all the same classes [Russell] |
| 11849 | It at least makes sense to say two objects have all their properties in common [Wittgenstein on Russell] |
| 22303 | It makes no sense to say that a true proposition could have been false [Russell] |
| 5400 | In any possible world we feel that two and two would be four [Russell] |
| 5991 | For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code] |
| 5431 | Knowledge cannot be precisely defined, as it merges into 'probable opinion' [Russell] |
| 5426 | Belief relates a mind to several things other than itself [Russell] |
| 5366 | We have an 'instinctive' belief in the external world, prior to all reflection [Russell] |
| 5359 | Descartes showed that subjective things are the most certain [Russell] |
| 5377 | 'Acquaintance' is direct awareness, without inferences or judgements [Russell] |
| 6510 | Russell (1912) said phenomena only resemble reality in abstract structure [Russell, by Robinson,H] |
| 5372 | There is no reason to think that objects have colours [Russell] |
| 5373 | 'Idealism' says that everything which exists is in some sense mental [Russell] |
| 5362 | It is not illogical to think that only myself and my mental events exist [Russell] |
| 11239 | The notion of a priori truth is absent in Aristotle [Aristotle, by Politis] |
| 5412 | Some propositions are self-evident, but their implications may also be self-evident [Russell] |
| 5413 | Particular instances are more clearly self-evident than any general principles [Russell] |
| 5415 | As shown by memory, self-evidence comes in degrees [Russell] |
| 5416 | If self-evidence has degrees, we should accept the more self-evident as correct [Russell] |
| 5397 | The rationalists were right, because we know logical principles without experience [Russell] |
| 4430 | All a priori knowledge deals with the relations of universals [Russell] |
| 5411 | We can know some general propositions by universals, when no instance can be given [Russell] |
| 6514 | Russell's representationalism says primary qualities only show the structure of reality [Russell, by Robinson,H] |
| 6415 | After 1912, Russell said sense-data are last in analysis, not first in experience [Russell, by Grayling] |
| 5358 | 'Sense-data' are what are immediately known in sensation, such as colours or roughnesses [Russell] |
| 23312 | Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M] |
| 7290 | If Russell rejects innate ideas and direct a priori knowledge, he is left with a tabula rasa [Russell, by Thompson] |
| 5357 | It is natural to begin from experience, and presumably that is the basis of knowledge [Russell] |
| 5382 | We are acquainted with outer and inner sensation, memory, Self, and universals [Russell, by PG] |
| 5389 | Knowledge by descriptions enables us to transcend private experience [Russell] |
| 5376 | I can know the existence of something with which nobody is acquainted [Russell] |
| 16111 | Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML] |
| 5414 | Images are not memory, because they are present, and memories are of the past [Russell] |
| 5430 | A true belief is not knowledge if it is reached by bad reasoning [Russell] |
| 5429 | True belief is not knowledge when it is deduced from false belief [Russell] |
| 5378 | All knowledge (of things and of truths) rests on the foundations of acquaintance [Russell] |
| 5365 | Dreams can be explained fairly scientifically if we assume a physical world [Russell] |
| 16971 | Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik] |
| 5391 | Science aims to find uniformities to which (within the limits of experience) there are no exceptions [Russell] |
| 5390 | Chickens are not very good at induction, and are surprised when their feeder wrings their neck [Russell] |
| 5394 | We can't prove induction from experience without begging the question [Russell] |
| 5392 | It doesn't follow that because the future has always resembled the past, that it always will [Russell] |
| 11243 | Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis] |
| 3320 | Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA] |
| 12000 | Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung] |
| 5363 | If the cat reappears in a new position, presumably it has passed through the intermediate positions [Russell] |
| 5367 | Belief in real objects makes our account of experience simpler and more systematic [Russell] |
| 5364 | It is hard not to believe that speaking humans are expressing thoughts, just as we do ourselves [Russell] |
| 5379 | If we didn't know our own minds by introspection, we couldn't know that other people have minds [Russell] |
| 5410 | I learn the universal 'resemblance' by seeing two shades of green, and their contrast with red [Russell] |
| 5381 | In seeing the sun, we are acquainted with our self, but not as a permanent person [Russell] |
| 5380 | In perceiving the sun, I am aware of sun sense-data, and of the perceiver of the data [Russell] |
| 5369 | It is rational to believe in reality, despite the lack of demonstrative reasons for it [Russell] |
| 23300 | Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji] |
| 5375 | Knowledge of truths applies to judgements; knowledge by acquaintance applies to sensations and things [Russell] |
| 21711 | Russell's 'multiple relations' theory says beliefs attach to ingredients, not to propositions [Russell, by Linsky,B] |
| 5427 | Truth is when a mental state corresponds to a complex unity of external constituents [Russell] |
| 5425 | In order to explain falsehood, a belief must involve several terms, not two [Russell] |
| 5384 | A universal of which we are aware is called a 'concept' [Russell] |
| 10583 | Abstraction principles identify a common property, which is some third term with the right relation [Russell] |
| 10582 | The principle of Abstraction says a symmetrical, transitive relation analyses into an identity [Russell] |
| 10584 | A certain type of property occurs if and only if there is an equivalence relation [Russell] |
| 13468 | Russell started philosophy of language, by declaring some plausible sentences to be meaningless [Russell, by Hart,WD] |
| 5388 | Every understood proposition is composed of constituents with which we are acquainted [Russell] |
| 5387 | It is pure chance which descriptions in a person's mind make a name apply to an individual [Russell] |
| 14110 | Proposition contain entities indicated by words, rather than the words themselves [Russell] |
| 19164 | If propositions are facts, then false and true propositions are indistinguishable [Davidson on Russell] |
| 19157 | Russell said the proposition must explain its own unity - or else objective truth is impossible [Russell, by Davidson] |
| 14111 | A proposition is a unity, and analysis destroys it [Russell] |
| 21724 | The main aim of the multiple relations theory of judgement was to dispense with propositions [Russell, by Linsky,B] |
| 11240 | The notion of analytic truth is absent in Aristotle [Aristotle, by Politis] |
| 6559 | Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin] |
| 5398 | Judgements of usefulness depend on judgements of value [Russell] |
| 11150 | It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle] |
| 3037 | Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius] |
| 8660 | There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend] |
| 12058 | Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins] |
| 14175 | We can drop 'cause', and just make inferences between facts [Russell] |
| 14172 | Moments and points seem to imply other moments and points, but don't cause them [Russell] |
| 14174 | The laws of motion and gravitation are just parts of the definition of a kind of matter [Russell] |
| 5393 | We can't know that our laws are exceptionless, or even that there are any laws [Russell] |
| 14168 | Occupying a place and change are prior to motion, so motion is just occupying places at continuous times [Russell] |
| 14171 | Force is supposed to cause acceleration, but acceleration is a mathematical fiction [Russell] |
| 14160 | Space is the extension of 'point', and aggregates of points seem necessary for geometry [Russell] |
| 14156 | Mathematicians don't distinguish between instants of time and points on a line [Russell] |
| 14169 | The 'universe' can mean what exists now, what always has or will exist [Russell] |
| 22729 | The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus] |