801 ideas
21584 | A sense of timelessness is essential to wisdom [Russell] |
7536 | If you hope to improve the world, all you can do is improve yourself [Wittgenstein] |
16010 | While faith is a passion (as Kierkegaard says), wisdom is passionless [Wittgenstein] |
18730 | The history of philosophy only matters if the subject is a choice between rival theories [Wittgenstein] |
11006 | Russell started a whole movement in philosophy by providing an analysis of descriptions [Read on Russell] |
5361 | Philosophers must get used to absurdities [Russell] |
2937 | What we cannot speak about we must pass over in silence [Wittgenstein] |
2626 | A philosopher is outside any community of ideas [Wittgenstein] |
5368 | Philosophy verifies that our hierarchy of instinctive beliefs is harmonious and consistent [Russell] |
7085 | The main problem of philosophy is what can and cannot be thought and expressed [Wittgenstein, by Grayling] |
6870 | I say (contrary to Wittgenstein) that philosophy expresses what we thought we must be silent about [Ansell Pearson on Wittgenstein] |
2512 | Philosophy is a battle against the bewitchment of our intelligence by means of language [Wittgenstein] |
23025 | Philosophers should be more inductive, and test results by their conclusions, not their self-evidence [Russell] |
18704 | Philosophy tries to be rid of certain intellectual puzzles, irrelevant to daily life [Wittgenstein] |
17641 | Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell] |
2944 | If a question can be framed at all, it is also possible to answer it [Wittgenstein] |
9810 | The 'Tractatus' is a masterpiece of anti-philosophy [Badiou on Wittgenstein] |
4148 | What is your aim in philosophy? - To show the fly the way out of the fly-bottle [Wittgenstein] |
21572 | Philosophical disputes are mostly hopeless, because philosophers don't understand each other [Russell] |
23459 | This work solves all the main problems, but that has little value [Wittgenstein] |
23512 | Once you understand my book you will see that it is nonsensical [Wittgenstein] |
18710 | Philosophers express puzzlement, but don't clearly state the puzzle [Wittgenstein] |
5432 | Metaphysics cannot give knowledge of the universe as a whole [Russell] |
21571 | Philosophical systems are interesting, but we now need a more objective scientific philosophy [Russell] |
21574 | Hegel's confusions over 'is' show how vast systems can be built on simple errors [Russell] |
21587 | Philosophers sometimes neglect truth and distort facts to attain a nice system [Russell] |
21582 | Physicists accept particles, points and instants, while pretending they don't do metaphysics [Russell] |
6095 | The business of metaphysics is to describe the world [Russell] |
14122 | Analysis gives us nothing but the truth - but never the whole truth [Russell] |
6118 | Philosophy is logical analysis, followed by synthesis [Russell] |
6420 | Only by analysing is progress possible in philosophy [Russell] |
6432 | Analysis gives new knowledge, without destroying what we already have [Russell] |
23492 | Our language is an aspect of biology, and so its inner logic is opaque [Wittgenstein] |
23510 | Most philosophical questions arise from failing to understand the logic of language [Wittgenstein] |
2938 | The limits of my language means the limits of my world [Wittgenstein] |
18732 | We don't need a theory of truth, because we use the word perfectly well [Wittgenstein] |
22490 | Bring words back from metaphysics to everyday use [Wittgenstein] |
7529 | All philosophy should begin with an analysis of propositions [Russell] |
14109 | The study of grammar is underestimated in philosophy [Russell] |
14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
21552 | Common speech is vague; its vocabulary and syntax must be modified, for precision [Russell] |
18274 | Analysis complicates a statement, but only as far as the complexity of its meaning [Wittgenstein] |
6429 | All complex statements can be resolved into constituents and descriptions [Wittgenstein] |
21546 | We can't sharply distinguish variables, domains and values, if symbols frighten us [Russell] |
21573 | When problems are analysed properly, they are either logical, or not philosophical at all [Russell] |
6116 | A logical language would show up the fallacy of inferring reality from ordinary language [Russell] |
18714 | We already know what we want to know, and analysis gives us no new facts [Wittgenstein] |
14165 | Analysis falsifies, if when the parts are broken down they are not equivalent to their sum [Russell] |
23499 | This book says we should either say it clearly, or shut up [Wittgenstein] |
8378 | Philosophers usually learn science from each other, not from science [Russell] |
5434 | Philosophy is similar to science, and has no special source of wisdom [Russell] |
6117 | Philosophy should be built on science, to reduce error [Russell] |
23508 | Science is all the true propositions [Wittgenstein] |
17638 | If one proposition is deduced from another, they are more certain together than alone [Russell] |
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] |
17632 | Non-contradiction was learned from instances, and then found to be indubitable [Russell] |
6566 | The problem is to explain the role of contradiction in social life [Wittgenstein] |
2939 | If a sign is useless it is meaningless; that is the point of Ockham's maxim [Wittgenstein] |
6106 | Reducing entities and premisses makes error less likely [Russell] |
14426 | A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell] |
21560 | Any linguistic expression may lack meaning when taken out of context [Russell] |
21551 | Empirical words need ostensive definition, which makes them egocentric [Russell] |
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] |
21561 | 'The number one is bald' or 'the number one is fond of cream cheese' are meaningless [Russell] |
8468 | The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false [Russell, by Orenstein] |
6437 | The theory of types makes 'Socrates and killing are two' illegitimate [Russell] |
18706 | Words of the same kind can be substituted in a proposition without producing nonsense [Wittgenstein] |
18719 | Grammar says that saying 'sound is red' is not false, but nonsense [Wittgenstein] |
18735 | Talking nonsense is not following the rules [Wittgenstein] |
5420 | Truth is a property of a belief, but dependent on its external relations, not its internal qualities [Russell] |
18731 | There is no theory of truth, because it isn't a concept [Wittgenstein] |
5784 | In its primary and formal sense, 'true' applies to propositions, not beliefs [Russell] |
6442 | Truth belongs to beliefs, not to propositions and sentences [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] |
16477 | Asserting not-p is saying p is false [Russell] |
5777 | The truth or falsehood of a belief depends upon a fact to which the belief 'refers' [Russell] |
10910 | The best account of truth-making is isomorphism [Wittgenstein, by Mulligan/Simons/Smith] |
6090 | Facts make propositions true or false, and are expressed by whole sentences [Russell] |
23462 | He says the world is the facts because it is the facts which fix all the truths [Wittgenstein, by Morris,M] |
21544 | It seems that when a proposition is false, something must fail to subsist [Russell] |
18348 | Not only atomic truths, but also general and negative truths, have truth-makers [Russell, by Rami] |
18349 | All truths have truth-makers, but only atomic truths correspond to them [Wittgenstein, by Rami] |
6343 | For Russell, both propositions and facts are arrangements of objects, so obviously they correspond [Horwich on 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] |
5783 | Propositions of existence, generalities, disjunctions and hypotheticals make correspondence tricky [Russell] |
10967 | Wittgenstein's picture theory is the best version of the correspondence theory of truth [Read on Wittgenstein] |
7087 | Language is [propositions-elementary propositions-names]; reality is [facts-states of affairs-objects] [Wittgenstein, by Grayling] |
4702 | The account of truth in the 'Tractatus' seems a perfect example of the correspondence theory [Wittgenstein, by O'Grady] |
7056 | Pictures reach out to or feel reality, touching at the edges, correlating in its parts [Wittgenstein] |
18707 | All thought has the logical form of reality [Wittgenstein] |
23483 | Proposition elements correlate with objects, but the whole picture does not correspond to a fact [Wittgenstein, by Morris,M] |
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] |
14454 | An argument 'satisfies' a function φx if φa is true [Russell] |
11074 | 'It is true that this follows' means simply: this follows [Wittgenstein] |
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] |
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] |
16484 | There are four experiences that lead us to talk of 'some' things [Russell] |
14113 | The null class is a fiction [Russell] |
6103 | Normally a class with only one member is a problem, because the class and the member are identical [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] |
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] |
18130 | Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock] |
14459 | Reducibility: a family of functions is equivalent to a single type of function [Russell] |
21563 | The 'no classes' theory says the propositions just refer to the members [Russell] |
14461 | Propositions about classes can be reduced to propositions about their defining functions [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] |
8469 | Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein] |
11064 | Classes can be reduced to propositional functions [Russell, by Hanna] |
7548 | Classes, grouped by a convenient property, are logical constructions [Russell] |
8745 | Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell] |
6436 | I gradually replaced classes with properties, and they ended as a symbolic convenience [Russell] |
14121 | The part-whole relation is ultimate and indefinable [Russell] |
23502 | Logic fills the world, to its limits [Wittgenstein] |
6110 | Subject-predicate logic (and substance-attribute metaphysics) arise from Aryan languages [Russell] |
16908 | We can dispense with self-evidence, if language itself prevents logical mistakes [Jeshion on Wittgenstein] |
23504 | Logic concerns everything that is subject to law; the rest is accident [Wittgenstein] |
18724 | In logic nothing is hidden [Wittgenstein] |
21588 | Logic gives the method of research in philosophy [Russell] |
6107 | It is logic, not metaphysics, that is fundamental to philosophy [Russell] |
6428 | Wittgenstein is right that logic is just tautologies [Wittgenstein, by Russell] |
14452 | All the propositions of logic are completely general [Russell] |
16486 | The physical world doesn't need logic, but the mental world does [Russell] |
11062 | Logic is a priori because it is impossible to think illogically [Wittgenstein] |
21495 | Theoretical and practical politics are both concerned with the best lives for individuals [Russell] |
14462 | In modern times, logic has become mathematical, and mathematics has become logical [Russell] |
18277 | If q implies p, that is justified by q and p, not by some 'laws' of inference [Wittgenstein] |
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] |
14464 | Logic can be known a priori, without study of the actual world [Russell] |
22329 | Logic is highly general truths abstracted from reality [Russell, by Glock] |
12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
10057 | Logic can only assert hypothetical existence [Russell] |
18162 | The propositions of logic are analytic tautologies [Wittgenstein] |
7537 | Wittgenstein convinced Russell that logic is tautologies, not Platonic forms [Wittgenstein, by Monk] |
10053 | Geometrical axioms imply the propositions, but the former may not be true [Russell] |
18709 | Laws of logic are like laws of chess - if you change them, it's just a different game [Wittgenstein] |
21539 | Excluded middle can be stated psychologically, as denial of p implies assertion of not-p [Russell] |
18944 | Russell's theories aim to preserve excluded middle (saying all sentences are T or F) [Sawyer on Russell] |
2947 | Questions wouldn't lead anywhere without the law of excluded middle [Russell] |
23496 | Two colours in the same place is ruled out by the logical structure of colour [Wittgenstein] |
18736 | Contradiction is between two rules, not between rule and reality [Wittgenstein] |
18154 | The sign of identity is not allowed in 'Tractatus' [Wittgenstein, by Bostock] |
13429 | The identity sign is not essential in logical notation, if every sign has a different meaning [Wittgenstein, by Ramsey] |
7758 | 'Elizabeth = Queen of England' is really a predication, not an identity-statement [Russell, by Lycan] |
6092 | In a logically perfect language, there will be just one word for every simple object [Russell] |
6101 | Romulus does not occur in the proposition 'Romulus did not exist' [Russell] |
6115 | Vagueness, and simples being beyond experience, are obstacles to a logical language [Russell] |
7528 | Leibniz bases everything on subject/predicate and substance/property propositions [Russell] |
18276 | A statement's logical form derives entirely from its constituents [Wittgenstein] |
18743 | Wittgenstein says we want the grammar of problems, not their first-order logical structure [Wittgenstein, by Horsten/Pettigrew] |
18268 | Apparent logical form may not be real logical form [Wittgenstein] |
23476 | Logical constants seem to be entities in propositions, but are actually pure form [Russell] |
23477 | We use logical notions, so they must be objects - but I don't know what they really are [Russell] |
21586 | The logical connectives are not objects, but are formal, and need a context [Russell] |
21597 | Logical connectives have the highest precision, yet are infected by the vagueness of true and false [Russell, by Williamson] |
10905 | My fundamental idea is that the 'logical constants' do not represent [Wittgenstein] |
6563 | 'And' and 'not' are non-referring terms, which do not represent anything [Wittgenstein, by Fogelin] |
14105 | There seem to be eight or nine logical constants [Russell] |
18723 | We may correctly use 'not' without making the rule explicit [Wittgenstein] |
18722 | Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell] |
16489 | Is it possible to state every possible truth about the whole course of nature without using 'not'? [Russell] |
23493 | 'Not' isn't an object, because not-not-p would then differ from p [Wittgenstein] |
18718 | Saying 'and' has meaning is just saying it works in a sentence [Wittgenstein] |
16479 | 'Or' expresses hesitation, in a dog at a crossroads, or birds risking grabbing crumbs [Russell] |
16480 | A disjunction expresses indecision [Russell] |
16483 | Disjunction may also arise in practice if there is imperfect memory. [Russell] |
16481 | 'Or' expresses a mental state, not something about the world [Russell] |
16487 | Maybe the 'or' used to describe mental states is not the 'or' of logic [Russell] |
14104 | Constants are absolutely definite and unambiguous [Russell] |
14114 | Variables don't stand alone, but exist as parts of propositional functions [Russell] |
5772 | The idea of a variable is fundamental [Russell] |
7784 | 'Object' is a pseudo-concept, properly indicated in logic by the variable x [Wittgenstein] |
21566 | 'Propositional functions' are ambiguous until the variable is given a value [Russell] |
6102 | You can understand 'author of Waverley', but to understand 'Scott' you must know who it applies to [Russell] |
10423 | There are a set of criteria for pinning down a logically proper name [Russell, by Sainsbury] |
23506 | Names are primitive, and cannot be analysed [Wittgenstein] |
18727 | A person's name doesn't mean their body; bodies don't sit down, and their existence can be denied [Wittgenstein] |
4139 | Naming is a preparation for description [Wittgenstein] |
18941 | Names don't have a sense, but are disguised definite descriptions [Russell, by Sawyer] |
4945 | Russell says names are not denotations, but definite descriptions in disguise [Russell, by Kripke] |
18942 | Russell says a name contributes a complex of properties, rather than an object [Russell, by Sawyer] |
7745 | Are names descriptions, if the description is unknown, false, not special, or contains names? [McCullogh on Russell] |
5386 | Proper names are really descriptions, and can be replaced by a description in a person's mind [Russell] |
7744 | Treat description using quantifiers, and treat proper names as descriptions [Russell, by McCullogh] |
10450 | Russell admitted that even names could also be used as descriptions [Russell, by Bach] |
14458 | Asking 'Did Homer exist?' is employing an abbreviated description [Russell] |
14457 | Names are really descriptions, except for a few words like 'this' and 'that' [Russell] |
4946 | A name is not determined by a description, but by a cluster or family [Wittgenstein, by Kripke] |
10449 | Logically proper names introduce objects; definite descriptions introduce quantifications [Russell, by Bach] |
6410 | The only real proper names are 'this' and 'that'; the rest are really definite descriptions. [Russell, by Grayling] |
7089 | A name is primitive, and its meaning is the object [Wittgenstein] |
15159 | The meaning of a logically proper name is its referent, but most names are not logically proper [Russell, by Soames] |
2612 | Russell rewrote singular term names as predicates [Russell, by Ayer] |
7757 | "Nobody" is not a singular term, but a quantifier [Russell, by Lycan] |
18943 | Russell implies that all sentences containing empty names are false [Sawyer on Russell] |
10426 | A name has got to name something or it is not a name [Russell] |
6439 | Names are meaningless unless there is an object which they designate [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] |
6411 | Critics say definite descriptions can refer, and may not embody both uniqueness and existence claims [Grayling on Russell] |
10433 | Definite descriptions fail to refer in three situations, so they aren't essentially referring [Russell, by Sainsbury] |
5385 | The phrase 'a so-and-so' is an 'ambiguous' description'; 'the so-and-so' (singular) is a 'definite' description [Russell] |
11009 | Russell's theory must be wrong if it says all statements about non-existents are false [Read on Russell] |
1608 | The theory of descriptions eliminates the name of the entity whose existence was presupposed [Russell, by Quine] |
7754 | Russell's theory explains non-existents, negative existentials, identity problems, and substitutivity [Russell, by Lycan] |
21529 | Russell showed how to define 'the', and thereby reduce the ontology of logic [Russell, by Lackey] |
6333 | The theory of definite descriptions reduces the definite article 'the' to the concepts of predicate logic [Russell, by Horwich] |
6412 | Russell implies that 'the baby is crying' is only true if the baby is unique [Grayling on Russell] |
7743 | Russell explained descriptions with quantifiers, where Frege treated them as names [Russell, by McCullogh] |
7310 | Russell avoids non-existent objects by denying that definite descriptions are proper names [Russell, by Miller,A] |
12006 | Denying definite description sentences are subject-predicate in form blocks two big problems [Russell, by Forbes,G] |
4569 | Russell says apparent referring expressions are really assertions about properties [Russell, by Cooper,DE] |
21549 | The theory of descriptions lacks conventions for the scope of quantifiers [Lackey on Russell] |
12796 | Non-count descriptions don't threaten Russell's theory, which is only about singulars [Laycock on Russell] |
7532 | Denoting is crucial in Russell's account of mathematics, for identifying classes [Russell, by Monk] |
11988 | Russell's analysis means molecular sentences are ambiguous over the scope of the description [Kaplan on Russell] |
14137 | 'Any' is better than 'all' where infinite classes are concerned [Russell] |
9467 | Wittgenstein tried unsuccessfully to reduce quantifiers to conjunctions and disjunctions [Wittgenstein, by Jacquette] |
6061 | Existence is entirely expressed by the existential quantifier [Russell, by McGinn] |
15089 | Logical proof just explicates complicated tautologies [Wittgenstein] |
18273 | Logical truths are known by their extreme generality [Russell] |
13830 | Logical truths are just 'by-products' of the introduction rules for logical constants [Wittgenstein, by Hacking] |
17640 | Finding the axioms may be the only route to some new results [Russell] |
17629 | Which premises are ultimate varies with context [Russell] |
17630 | The sources of a proof are the reasons why we believe its conclusion [Russell] |
6109 | Some axioms may only become accepted when they lead to obvious conclusions [Russell] |
19292 | Logic doesn't split into primitive and derived propositions; they all have the same status [Wittgenstein] |
7557 | To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell] |
14149 | The Achilles Paradox concerns the one-one correlation of infinite classes [Russell] |
21585 | The tortoise won't win, because infinite instants don't compose an infinitely long time [Russell] |
21565 | Richard's puzzle uses the notion of 'definition' - but that cannot be defined [Russell] |
15895 | Russell discovered the paradox suggested by Burali-Forti's work [Russell, by Lavine] |
13365 | Russell's Paradox is a stripped-down version of Cantor's Paradox [Priest,G on Russell] |
10711 | Russell's paradox means we cannot assume that every property is collectivizing [Potter on Russell] |
6407 | The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling] |
21564 | Vicious Circle: what involves ALL must not be one of those ALL [Russell] |
21567 | 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell] |
6569 | 'This sentence is false' sends us in a looping search for its proposition [Wittgenstein, by Fogelin] |
16475 | A 'heterological' predicate can't be predicated of itself; so is 'heterological' heterological? Yes=no! [Russell] |
10059 | In mathematic we are ignorant of both subject-matter and truth [Russell] |
18281 | In mathematics everything is algorithm and nothing is meaning [Wittgenstein] |
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] |
14442 | If straight lines were like ratios they might intersect at a 'gap', and have no point in common [Russell] |
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] |
14438 | New numbers solve problems: negatives for subtraction, fractions for division, complex for equations [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] |
13510 | Could a number just be something which occurs in a progression? [Russell, by Hart,WD] |
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] |
18738 | We don't get 'nearer' to something by adding decimals to 1.1412... (root-2) [Wittgenstein] |
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] |
14123 | Some quantities can't be measured, and some non-quantities are measurable [Russell] |
14158 | Quantity is not part of mathematics, where it is replaced by order [Russell] |
14120 | Counting explains none of the real problems about the foundations of arithmetic [Russell] |
14424 | Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell] |
14118 | We can define one-to-one without mentioning unity [Russell] |
14441 | The formal laws of arithmetic are the Commutative, the Associative and the Distributive [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] |
14420 | Infinity and continuity used to be philosophy, but are now mathematics [Russell] |
18708 | Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein] |
14134 | Infinite numbers are distinguished by disobeying induction, and the part equalling the whole [Russell] |
7556 | A collection is infinite if you can remove some terms without diminishing its number [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] |
17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
10052 | Geometry is united by the intuitive axioms of projective geometry [Russell, by Musgrave] |
14431 | The definition of order needs a transitive relation, to leap over infinite intermediate terms [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] |
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] |
14125 | Finite numbers, unlike infinite numbers, obey mathematical induction [Russell] |
14147 | Denying mathematical induction gave us the transfinite [Russell] |
18160 | The concept of number is just what all numbers have in common [Wittgenstein] |
18153 | A number is a repeated operation [Wittgenstein] |
14116 | Numbers were once defined on the basis of 1, but neglected infinities and + [Russell] |
14117 | Numbers are properties of classes [Russell] |
14425 | A number is something which characterises collections of the same size [Russell] |
18161 | The theory of classes is superfluous in mathematics [Wittgenstein] |
14434 | What matters is the logical interrelation of mathematical terms, not their intrinsic nature [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] |
17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
5399 | Maths is not known by induction, because further instances are not needed to support it [Russell] |
14465 | Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell] |
14103 | Pure mathematics is the class of propositions of the form 'p implies q' [Russell] |
13414 | For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf] |
6108 | Maths can be deduced from logical axioms and the logic of relations [Russell] |
6423 | We tried to define all of pure maths using logical premisses and concepts [Russell] |
11073 | Two and one making three has the necessity of logical inference [Wittgenstein] |
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] |
10418 | Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell] |
10047 | Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave] |
23478 | Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell] |
23457 | Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell] |
21556 | Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey] |
21718 | Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B] |
6849 | Wittgenstein hated logicism, and described it as a cancerous growth [Wittgenstein, by Monk] |
23509 | The logic of the world is shown by tautologies in logic, and by equations in mathematics [Wittgenstein] |
21570 | Numbers are just verbal conveniences, which can be analysed away [Russell] |
6424 | Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess [Russell] |
6425 | Formalism can't apply numbers to reality, so it is an evasion [Russell] |
6104 | Numbers are classes of classes, and hence fictions of fictions [Russell] |
6426 | Intuitionism says propositions are only true or false if there is a method of showing it [Russell] |
21559 | We need rules for deciding which norms are predicative (unless none of them are) [Russell] |
21558 | 'Predicative' norms are those which define a class [Russell] |
18126 | A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock] |
18128 | Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock] |
18124 | Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock] |
21568 | A one-variable function is only 'predicative' if it is one order above its arguments [Russell] |
14449 | There is always something psychological about inference [Russell] |
13133 | The world is facts, not things. Facts determine the world, and the world divides into facts [Wittgenstein] |
14463 | Existence can only be asserted of something described, not of something named [Russell] |
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] |
6402 | In 1927, Russell analysed force and matter in terms of events [Russell, by Grayling] |
16045 | General facts supervene on particular facts, but cannot be inferred from them [Russell, by Bennett,K] |
10968 | Russell gave up logical atomism because of negative, general and belief propositions [Russell, by Read] |
21684 | Atomic facts may be inferrable from others, but never from non-atomic facts [Russell] |
21708 | Russell's new logical atomist was of particulars, universals and facts (not platonic propositions) [Russell, by Linsky,B] |
19051 | Russell's atomic facts are actually compounds, and his true logical atoms are sense data [Russell, by Quine] |
6089 | Logical atomism aims at logical atoms as the last residue of analysis [Russell] |
6100 | Once you have enumerated all the atomic facts, there is a further fact that those are all the facts [Russell] |
6105 | Logical atoms aims to get down to ultimate simples, with their own unique reality [Russell] |
6113 | To mean facts we assert them; to mean simples we name them [Russell] |
6114 | 'Simples' are not experienced, but are inferred at the limits of analysis [Russell] |
21722 | Better to construct from what is known, than to infer what is unknown [Russell] |
23463 | Atomic facts correspond to true elementary propositions [Wittgenstein] |
21681 | Given all true atomic propositions, in theory every other truth can thereby be deduced [Russell] |
6419 | In 1899-1900 I adopted the philosophy of logical atomism [Russell] |
6438 | Complex things can be known, but not simple things [Russell] |
23472 | The sense of propositions relies on the world's basic logical structure [Wittgenstein] |
7090 | The 'Tractatus' is an extreme example of 'Logical Atomism' [Wittgenstein, by Grayling] |
23464 | In atomic facts the objects hang together like chain links [Wittgenstein] |
23471 | The structure of an atomic fact is how its objects combine; this possibility is its form [Wittgenstein] |
21682 | If a proposition is elementary, no other elementary proposition contradicts it [Wittgenstein] |
22319 | Analysis must end in elementary propositions, which are combinations of names [Wittgenstein] |
21683 | Nothing can be inferred from an elementary proposition [Wittgenstein] |
6472 | Continuity is a sufficient criterion for the identity of a rock, but not for part of a smooth fluid [Russell] |
21538 | If two people perceive the same object, the object of perception can't be in the mind [Russell] |
5370 | Space is neutral between touch and sight, so it cannot really be either of them [Russell] |
7545 | Visible things are physical and external, but only exist when viewed [Russell] |
14429 | Classes are logical fictions, made from defining characteristics [Russell] |
21709 | You can't name all the facts, so they are not real, but are what propositions assert [Russell] |
6111 | As propositions can be put in subject-predicate form, we wrongly infer that facts have substance-quality form [Russell] |
6434 | Facts are everything, except simples; they are either relations or qualities [Russell] |
23473 | Do his existent facts constitute the world, or determine the world? [Morris,M on Wittgenstein] |
18376 | Russell asserts atomic, existential, negative and general facts [Russell, by Armstrong] |
18737 | There are no positive or negative facts; these are just the forms of propositions [Wittgenstein] |
5418 | In a world of mere matter there might be 'facts', but no truths [Russell] |
22315 | There can't be a negative of a complex, which is negated by its non-existence [Potter on Russell] |
22316 | A positive and negative fact have the same constituents; their difference is primitive [Russell] |
22312 | Facts can be both positive and negative [Wittgenstein, by Potter] |
22311 | The world is determined by the facts, and there are no further facts [Wittgenstein] |
22313 | The existence of atomic facts is a positive fact, their non-existence a negative fact [Wittgenstein] |
22314 | On white paper a black spot is a positive fact and a white spot a negative fact [Wittgenstein] |
5465 | Modern trope theory tries, like logical atomism, to reduce things to elementary states [Russell, by Ellis] |
9051 | Since natural language is not precise it cannot be in the province of logic [Russell, by Keefe/Smith] |
9054 | Vagueness is only a characteristic of representations, such as language [Russell] |
6060 | 'Existence' means that a propositional function is sometimes true [Russell] |
18775 | Russell showed that descriptions may not have ontological commitment [Russell, by Linsky,B] |
7533 | The Theory of Description dropped classes and numbers, leaving propositions, individuals and universals [Russell, by Monk] |
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] |
21534 | The only thing we can say about relations is that they relate [Russell] |
21540 | Relational propositions seem to be 'about' their terms, rather than about the relation [Russell] |
21562 | There is no complexity without relations, so no propositions, and no truth [Russell] |
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] |
21576 | With asymmetrical relations (before/after) the reduction to properties is impossible [Russell] |
7969 | The order of numbers is an internal relation, not an external one [Wittgenstein] |
7968 | A relation is internal if it is unthinkable that its object should not possess it [Wittgenstein] |
14430 | If a relation is symmetrical and transitive, it has to be reflexive [Russell] |
10586 | 'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness [Russell] |
14432 | 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell] |
10585 | Symmetrical and transitive relations are formally like equality [Russell] |
9127 | Russell refuted Frege's principle that there is a set for each property [Russell, by Sorensen] |
21575 | When we attribute a common quality to a group, we can forget the quality and just talk of the group [Russell] |
6063 | Russell can't attribute existence to properties [McGinn on Russell] |
14327 | Trope theorists cannot explain how tropes resemble each other [Russell, by Mumford] |
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] |
21710 | We know a universal in 'yellow differs from blue' or 'yellow resembles blue less than green does' [Russell] |
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] |
18715 | Using 'green' is a commitment to future usage of 'green' [Wittgenstein] |
4441 | 'Resemblance Nominalism' won't work, because the theory treats resemblance itself as a universal [Russell] |
6440 | Universals can't just be words, because words themselves are universals [Russell] |
4429 | If we consider whiteness to be merely a mental 'idea', we rob it of its universality [Russell] |
6473 | Physical things are series of appearances whose matter obeys physical laws [Russell] |
14732 | A perceived physical object is events grouped around a centre [Russell] |
23466 | Objects are the substance of the world [Wittgenstein] |
7781 | I call an object of thought a 'term'. This is a wide concept implying unity and existence. [Russell] |
21536 | When I perceive a melody, I do not perceive the notes as existing [Russell] |
22320 | An 'object' is just what can be referred to without possible non-existence [Wittgenstein] |
21531 | Common sense agrees with Meinong (rather than Russell) that 'Pegasus is a flying horse' is true [Lackey on Russell] |
18777 | If the King of France is not bald, and not not-bald, this violates excluded middle [Linsky,B on Russell] |
21545 | I prefer to deny round squares, and deal with the difficulties by the theory of denoting [Russell] |
21547 | On Meinong's principles 'the existent round square' has to exist [Russell] |
23467 | Objects are simple [Wittgenstein] |
14166 | Unities are only in propositions or concepts, and nothing that exists has unity [Russell] |
21535 | Objects only exist if they 'occupy' space and time [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] |
23468 | Apart from the facts, there is only substance [Wittgenstein] |
10710 | We accept substance, to avoid infinite backwards chains of meaning [Wittgenstein, by Potter] |
6465 | We need not deny substance, but there seems no reason to assert it [Russell] |
6471 | The assumption by physicists of permanent substance is not metaphysically legitimate [Russell] |
14733 | An object produces the same percepts with or without a substance, so that is irrelevant to science [Russell] |
14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
15106 | Essence is expressed by grammar [Wittgenstein] |
22321 | To know an object we must know the form and content of its internal properties [Wittgenstein, by Potter] |
14170 | Change is obscured by substance, a thing's nature, subject-predicate form, and by essences [Russell] |
6056 | Identity is not a relation between objects [Wittgenstein] |
22322 | You can't define identity by same predicates, because two objects with same predicates is assertable [Wittgenstein] |
6057 | Two things can't be identical, and self-identity is an empty concept [Wittgenstein] |
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] |
8375 | 'Necessary' is a predicate of a propositional function, saying it is true for all values of its argument [Russell] |
6099 | Modal terms are properties of propositional functions, not of propositions [Russell] |
9442 | The only necessity is logical necessity [Wittgenstein] |
16490 | Some facts about experience feel like logical necessities [Russell] |
22308 | Only the actual exists, so possibilities always reduce to actuality after full analysis [Russell] |
21533 | Contingency arises from tensed verbs changing the propositions to which they refer [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] |
22303 | It makes no sense to say that a true proposition could have been false [Russell] |
18726 | For each necessity in the world there is an arbitrary rule of language [Wittgenstein] |
23495 | The tautologies of logic show the logic of language and the world [Wittgenstein] |
23487 | What is thinkable is possible [Wittgenstein] |
14460 | If something is true in all possible worlds then it is logically necessary [Russell] |
5400 | In any possible world we feel that two and two would be four [Russell] |
23470 | Each thing is in a space of possible facts [Wittgenstein] |
23507 | Unlike the modern view of a set of worlds, Wittgenstein thinks of a structured manifold of them [Wittgenstein, by White,RM] |
23469 | An imagined world must have something in common with the real world [Wittgenstein] |
11027 | To know an object you must know all its possible occurrences [Wittgenstein] |
23465 | The 'form' of an object is its possible roles in facts [Wittgenstein] |
12869 | Two objects may only differ in being different [Wittgenstein] |
5431 | Knowledge cannot be precisely defined, as it merges into 'probable opinion' [Russell] |
16482 | All our knowledge (if verbal) is general, because all sentences contain general words [Russell] |
6430 | In epistemology we should emphasis the continuity between animal and human minds [Russell] |
18712 | Understanding is translation, into action or into other symbols [Wittgenstein] |
5426 | Belief relates a mind to several things other than itself [Russell] |
5780 | The three questions about belief are its contents, its success, and its character [Russell] |
6600 | The belief that fire burns is like the fear that it burns [Wittgenstein] |
5366 | We have an 'instinctive' belief in the external world, prior to all reflection [Russell] |
17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
5359 | Descartes showed that subjective things are the most certain [Russell] |
4758 | Naïve realism leads to physics, but physics then shows that naïve realism is false [Russell] |
21537 | I assume we perceive the actual objects, and not their 'presentations' [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] |
21580 | Science condemns sense-data and accepts matter, but a logical construction must link them [Russell] |
6466 | Where possible, logical constructions are to be substituted for inferred entities [Russell] |
6418 | Russell rejected phenomenalism because it couldn't account for causal relations [Russell, by Grayling] |
4153 | Are sense-data the material of which the universe is made? [Wittgenstein] |
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] |
23503 | Strict solipsism is pure realism, with the self as a mere point in surrounding reality [Wittgenstein] |
7554 | Self-evidence is often a mere will-o'-the-wisp [Russell] |
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] |
16907 | If the truth doesn't follow from self-evidence, then self-evidence cannot justify a truth [Wittgenstein] |
5397 | The rationalists were right, because we know logical principles without experience [Russell] |
23500 | My main problem is the order of the world, and whether it is knowable a priori [Wittgenstein] |
23479 | The Tractatus aims to reveal the necessities, without appealing to synthetic a priori truths [Wittgenstein, by Morris,M] |
23501 | There is no a priori order of things [Wittgenstein] |
7088 | Logic and maths can't say anything about the world, since, as tautologies, they are consistent with all realities [Wittgenstein, by Grayling] |
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] |
16909 | Logic is a priori because we cannot think illogically [Wittgenstein] |
23485 | No pictures are true a priori [Wittgenstein] |
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] |
6417 | In 1921 Russell abandoned sense-data, and the gap between sensation and object [Russell, by Grayling] |
6474 | Seeing is not in itself knowledge, but is separate from what is seen, such as a patch of colour [Russell] |
18280 | We live in sense-data, but talk about physical objects [Wittgenstein] |
6483 | Russell held that we are aware of states of our own brain [Russell, by Robinson,H] |
8244 | Sense-data are qualities devoid of subjectivity, which are the basis of science [Russell, by Deleuze/Guattari] |
6462 | Sense-data are not mental, but are part of the subject-matter of physics [Russell] |
6463 | Sense-data are objects, and do not contain the subject as part, the way beliefs do [Russell] |
6464 | Sense-data are usually objects within the body, but are not part of the subject [Russell] |
7549 | If my body literally lost its mind, the object seen when I see a flash would still exist [Russell] |
7553 | Sense-data are purely physical [Russell] |
6467 | No sensibile is ever a datum to two people at once [Russell] |
6459 | We do not know whether sense-data exist as objects when they are not data [Russell] |
6460 | 'Sensibilia' are identical to sense-data, without actually being data for any mind [Russell] |
6461 | Ungiven sense-data can no more exist than unmarried husbands [Russell] |
21583 | When sense-data change, there must be indistinguishable sense-data in the process [Russell] |
8854 | My 'acquaintance' with sense-data is nothing like my knowing New York [Williams,M on Russell] |
6458 | Individuating sense-data is difficult, because they divide when closely attended to [Russell] |
6469 | Sense-data may be subjective, if closing our eyes can change them [Russell] |
6476 | We cannot assume that the subject actually exists, so we cannot distinguish sensations from sense-data [Russell] |
18729 | Part of what we mean by stating the facts is the way we tend to experience them [Wittgenstein] |
6501 | As sense-data are necessarily private, they are attacked by Wittgenstein's objections [Wittgenstein, by Robinson,H] |
6098 | Perception goes straight to the fact, and not through the proposition [Russell] |
21577 | Empirical truths are particular, so general truths need an a priori input of generality [Russell] |
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] |
16476 | For simple words, a single experience can show that they are true [Russell] |
6441 | Pragmatism judges by effects, but I judge truth by causes [Russell] |
16488 | It is hard to explain how a sentence like 'it is not raining' can be found true by observation [Russell] |
6431 | Empiricists seem unclear what they mean by 'experience' [Russell] |
21532 | Full empiricism is not tenable, but empirical investigation is always essential [Russell] |
5376 | I can know the existence of something with which nobody is acquainted [Russell] |
16485 | Perception can't prove universal generalisations, so abandon them, or abandon empiricism? [Russell] |
11079 | How do I decide when to accept or obey an intuition? [Wittgenstein] |
5414 | Images are not memory, because they are present, and memories are of the past [Russell] |
2792 | It is possible the world came into existence five minutes ago, complete with false memories [Russell] |
18734 | If you remember wrongly, then there must be some other criterion than your remembering [Wittgenstein] |
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] |
6444 | True belief about the time is not knowledge if I luckily observe a stopped clock at the right moment [Russell] |
3597 | Foundations need not precede other beliefs [Wittgenstein] |
5378 | All knowledge (of things and of truths) rests on the foundations of acquaintance [Russell] |
17639 | Believing a whole science is more than believing each of its propositions [Russell] |
21579 | Objects are treated as real when they connect with other experiences in a normal way [Russell] |
3790 | Causes of beliefs are irrelevant to their contents [Wittgenstein] |
22326 | Knowledge needs more than a sensitive response; the response must also be appropriate [Russell] |
6591 | Doubts can't exist if they are inexpressible or unanswerable [Wittgenstein] |
5365 | Dreams can be explained fairly scientifically if we assume a physical world [Russell] |
21578 | Global scepticism is irrefutable, but can't replace our other beliefs, and just makes us hesitate [Russell] |
3596 | Total doubt can't even get started [Wittgenstein, by Williams,M] |
4160 | One can mistrust one's own senses, but not one's own beliefs [Wittgenstein] |
14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
5391 | Science aims to find uniformities to which (within the limits of experience) there are no exceptions [Russell] |
17665 | The 'Tractatus' is instrumentalist about laws of nature [Wittgenstein, by Armstrong] |
2941 | Induction accepts the simplest law that fits our experiences [Wittgenstein] |
17631 | Induction is inferring premises from consequences [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] |
18721 | Explanation and understanding are the same [Wittgenstein] |
18720 | Explanation gives understanding by revealing the full multiplicity of the thing [Wittgenstein] |
17673 | The modern worldview is based on the illusion that laws explain nature [Wittgenstein] |
18716 | A machine strikes us as being a rule of movement [Wittgenstein] |
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] |
18713 | If an explanation is good, the symbol is used properly in the future [Wittgenstein] |
5364 | It is hard not to believe that speaking humans are expressing thoughts, just as we do ourselves [Russell] |
6416 | Other minds seem to exist, because their testimony supports realism about the world [Russell, by Grayling] |
19273 | I don't have the opinion that people have minds; I just treat them as such [Wittgenstein] |
5379 | If we didn't know our own minds by introspection, we couldn't know that other people have minds [Russell] |
5663 | It is irresponsible to generalise from my own case of pain to other people's [Wittgenstein] |
19272 | To imagine another's pain by my own, I must imagine a pain I don't feel, by one I do feel [Wittgenstein] |
4161 | If a lion could talk, we could not understand him [Wittgenstein] |
7392 | If a lion could talk, it would be nothing like other lions [Dennett on Wittgenstein] |
21569 | It is good to generalise truths as much as possible [Russell] |
5410 | I learn the universal 'resemblance' by seeing two shades of green, and their contrast with red [Russell] |
22323 | The philosophical I is the metaphysical subject, the limit - not a part of the world [Wittgenstein] |
2940 | The subject stands outside our understanding of the world [Wittgenstein] |
5381 | In seeing the sun, we are acquainted with our self, but not as a permanent person [Russell] |
5676 | To say that I 'know' I am in pain means nothing more than that I AM in pain [Wittgenstein] |
5380 | In perceiving the sun, I am aware of sun sense-data, and of the perceiver of the data [Russell] |
7546 | A man is a succession of momentary men, bound by continuity and causation [Russell] |
22419 | 'I' is a subject in 'I am in pain' and an object in 'I am bleeding' [Wittgenstein, by McGinn] |
6475 | In perception, the self is just a logical fiction demanded by grammar [Russell] |
23498 | The modern idea of the subjective soul is composite, and impossible [Wittgenstein] |
5778 | If we object to all data which is 'introspective' we will cease to believe in toothaches [Russell] |
6433 | Behaviourists struggle to explain memory and imagination, because they won't admit images [Russell] |
5779 | There are distinct sets of psychological and physical causal laws [Russell] |
4154 | Why are we not aware of the huge gap between mind and brain in ordinary life? [Wittgenstein] |
7550 | We could probably, in principle, infer minds from brains, and brains from minds [Russell] |
18717 | Thought is an activity which we perform by the expression of it [Wittgenstein] |
5369 | It is rational to believe in reality, despite the lack of demonstrative reasons for it [Russell] |
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] |
21542 | Do incorrect judgements have non-existent, or mental, or external objects? [Russell] |
22306 | To explain false belief we should take belief as relating to a proposition's parts, not to the whole thing [Russell] |
5425 | In order to explain falsehood, a belief must involve several terms, not two [Russell] |
6097 | The theory of error seems to need the existence of the non-existent [Russell] |
6443 | Surprise is a criterion of error [Russell] |
23475 | The form of a proposition must show why nonsense is unjudgeable [Wittgenstein] |
6165 | Every course of action can either accord or conflict with a rule, so there is no accord or conflict [Wittgenstein] |
4143 | One cannot obey a rule 'privately', because that is a practice, not the same as thinking one is obeying [Wittgenstein] |
7092 | If individuals can't tell if they are following a rule, how does a community do it? [Grayling on Wittgenstein] |
4158 | An 'inner process' stands in need of outward criteria [Wittgenstein] |
21541 | The complexity of the content correlates with the complexity of the object [Russell] |
4138 | Is white simple, or does it consist of the colours of the rainbow? [Wittgenstein] |
7531 | We don't assert private thoughts; the objects are part of what we assert [Russell] |
7055 | Externalist accounts of mental content begin in Wittgenstein [Wittgenstein, by Heil] |
5384 | A universal of which we are aware is called a 'concept' [Russell] |
12576 | Possessing a concept is knowing how to go on [Wittgenstein, by Peacocke] |
4157 | Concepts direct our interests and investigations, and express those interests [Wittgenstein] |
12606 | Man learns the concept of the past by remembering [Wittgenstein] |
4141 | Various games have a 'family resemblance', as their similarities overlap and criss-cross [Wittgenstein] |
7084 | What can be said is what can be thought, so language shows the limits of thought [Wittgenstein, by Grayling] |
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] |
6112 | Meaning takes many different forms, depending on different logical types [Russell] |
23450 | Wittgenstein rejected his earlier view that the form of language is the form of the world [Wittgenstein, by Morris,M] |
23482 | The 'form' of the picture is its possible combinations [Wittgenstein] |
18283 | Language pictures the essence of the world [Wittgenstein] |
23481 | Propositions assemble a world experimentally, like the model of a road accident [Wittgenstein] |
8172 | To understand a proposition means to know what is the case if it is true [Wittgenstein] |
18725 | A proposition draws a line around the facts which agree with it [Wittgenstein] |
18282 | You can't believe it if you can't imagine a verification for it [Wittgenstein] |
18728 | The meaning of a proposition is the mode of its verification [Wittgenstein] |
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] |
6427 | Unverifiable propositions about the remote past are still either true or false [Russell] |
7086 | Good philosophy asserts science, and demonstrates the meaninglessness of metaphysics [Wittgenstein] |
4150 | Asking about verification is only one way of asking about the meaning of a proposition [Wittgenstein] |
6567 | For Wittgenstein, words are defined by their use, just as chess pieces are [Wittgenstein, by Fogelin] |
6169 | We do not achieve meaning and understanding in our heads, but in the world [Wittgenstein, by Rowlands] |
4155 | We all seem able to see quite clearly how sentences represent things when we use them [Wittgenstein] |
4137 | In the majority of cases the meaning of a word is its use in the language [Wittgenstein] |
18705 | Words function only in propositions, like levers in a machine [Wittgenstein] |
4142 | To understand a sentence means to understand a language [Wittgenstein] |
4721 | If you are not certain of any fact, you cannot be certain of the meaning of your words either [Wittgenstein] |
4149 | We don't have 'meanings' in our minds in addition to verbal expressions [Wittgenstein] |
4156 | Make the following experiment: say "It's cold here" and mean "It's warm here" [Wittgenstein] |
4567 | Russell argued with great plausibility that we rarely, if ever, refer with our words [Russell, by Cooper,DE] |
4145 | How do words refer to sensations? [Wittgenstein] |
5810 | Referring is not denoting, and Russell ignores the referential use of definite descriptions [Donnellan on Russell] |
5774 | Denoting phrases are meaningless, but guarantee meaning for propositions [Russell] |
5775 | In 'Scott is the author of Waverley', denotation is identical, but meaning is different [Russell] |
16385 | A definite description 'denotes' an entity if it fits the description uniquely [Russell, by Recanati] |
4140 | The standard metre in Paris is neither one metre long nor not one metre long [Wittgenstein] |
16987 | By eliminating descriptions from primitive notation, Russell seems to reject 'sense' [Russell, by Kripke] |
5387 | It is pure chance which descriptions in a person's mind make a name apply to an individual [Russell] |
4570 | Russell assumes that expressions refer, but actually speakers refer by using expressions [Cooper,DE on Russell] |
9022 | Russell uses 'propositional function' to refer to both predicates and to attributes [Quine on Russell] |
23511 | Propositions use old expressions for a new sense [Wittgenstein] |
23488 | Propositions are understood via their constituents [Wittgenstein] |
16349 | Russell rejected sense/reference, because it made direct acquaintance with things impossible [Russell, by Recanati] |
7313 | 'Sense' is superfluous (rather than incoherent) [Russell, by Miller,A] |
7767 | The theory of definite descriptions aims at finding correct truth conditions [Russell, by Lycan] |
21550 | Science reduces indexicals to a minimum, but they can never be eliminated from empirical matters [Russell] |
14110 | Proposition contain entities indicated by words, rather than the words themselves [Russell] |
21543 | If p is false, then believing not-p is knowing a truth, so negative propositions must exist [Russell] |
6091 | Propositions don't name facts, because each fact corresponds to a proposition and its negation [Russell] |
5781 | Our important beliefs all, if put into words, take the form of propositions [Russell] |
18711 | A proposition is any expression which can be significantly negated [Wittgenstein] |
5782 | A proposition expressed in words is a 'word-proposition', and one of images an 'image-proposition' [Russell] |
5776 | A proposition is what we believe when we believe truly or falsely [Russell] |
14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
23486 | Pictures are possible situations in logical space [Wittgenstein] |
19164 | If propositions are facts, then false and true propositions are indistinguishable [Davidson on Russell] |
21726 | In graspable propositions the constituents are real entities of acquaintance [Russell] |
21702 | In 1918 still believes in nonlinguistic analogues of sentences, but he now calls them 'facts' [Russell, by Quine] |
6435 | You can believe the meaning of a sentence without thinking of the words [Russell] |
22307 | Propositions don't name facts, because two opposed propositions can match one fact [Russell] |
23490 | A thought is mental constituents that relate to reality as words do [Wittgenstein] |
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] |
7534 | In 1906, Russell decided that propositions did not, after all, exist [Russell, by Monk] |
21724 | The main aim of the multiple relations theory of judgement was to dispense with propositions [Russell, by Linsky,B] |
6094 | An inventory of the world does not need to include propositions [Russell] |
6096 | I no longer believe in propositions, especially concerning falsehoods [Russell] |
21712 | I know longer believe in shadowy things like 'that today is Wednesday' when it is actually Tuesday [Russell] |
16491 | If we define 'this is not blue' as disbelief in 'this is blue', we eliminate 'not' as an ingredient of facts [Russell] |
6093 | The names in a logically perfect language would be private, and could not be shared [Russell] |
23497 | Solipsism is correct, but can only be shown, not said, by the limits of my personal language [Wittgenstein] |
4136 | To imagine a language means to imagine a form of life [Wittgenstein] |
6166 | Was Wittgenstein's problem between individual and community, or between occasions for an individual? [Rowlands on Wittgenstein] |
7875 | If a brilliant child invented a name for a private sensation, it couldn't communicate it [Wittgenstein] |
4146 | We cannot doublecheck mental images for correctness (or confirm news with many copies of the paper) [Wittgenstein] |
4147 | If we only named pain by our own case, it would be like naming beetles by looking in a private box [Wittgenstein] |
5659 | If the reference is private, that is incompatible with the sense being public [Wittgenstein, by Scruton] |
4152 | Getting from perceptions to words cannot be a private matter; the rules need an institution of use [Wittgenstein] |
23489 | We translate by means of proposition constituents, not by whole propositions [Wittgenstein] |
6318 | The doctrine of indeterminacy of translation seems implied by the later Wittgenstein [Wittgenstein, by Quine] |
4144 | Common human behaviour enables us to interpret an unknown language [Wittgenstein] |
11049 | To communicate, language needs agreement in judgment as well as definition [Wittgenstein] |
6658 | What is left over if I subtract my arm going up from my raising my arm? [Wittgenstein] |
16478 | A mother cat is paralysed if equidistant between two needy kittens [Russell] |
6606 | Consider: "Imagine this butterfly exactly as it is, but ugly instead of beautiful" [Wittgenstein] |
2943 | Ethics cannot be put into words [Wittgenstein] |
21740 | I doubt whether ethics is part of philosophy [Russell] |
23154 | We divide mankind into friend and foe, and cooperate with one and compete with the other [Russell] |
21741 | 'You ought to do p' primarily has emotional content, expressing approval [Russell] |
2942 | The sense of the world must lie outside the world [Wittgenstein] |
21746 | Unlike hate, all desires can be satisfied by love [Russell] |
21747 | Goodness is a combination of love and knowledge [Russell] |
21743 | In wartime, happiness is hating the enemy, because it gives the war a purpose [Russell] |
20180 | A happy and joyous life must largely be a quiet life [Russell] |
21742 | Originally virtue was obedience, to gods, government, or custom [Russell] |
21517 | Individuals need creativity, reverence for others, and self-respect [Russell] |
21745 | Act so as to produce harmonious rather than discordant desires [Russell] |
5398 | Judgements of usefulness depend on judgements of value [Russell] |
20179 | Happiness involves enduring boredom, and the young should be taught this [Russell] |
20177 | Boredom always involves not being fully occupied [Russell] |
20176 | Boredom is an increasingly strong motivating power [Russell] |
20178 | Life is now more interesting, but boredom is more frightening [Russell] |
23153 | Gradually loyalty to a creed increased, which could even outweigh nationality [Russell] |
23152 | Increasingly war expands communities, and unifies them through fear [Russell] |
23155 | In early societies the leaders needed cohesion, but the rest just had to obey [Russell] |
23156 | The economic and political advantages of great size seem to have no upper limit [Russell] |
23157 | Government has a negative purpose, to prevent trouble, and a positive aim of realising our desires [Russell] |
23151 | A monarch is known to everyone in the group, and can thus unite large groups [Russell] |
21522 | Democracy is inadequate without a great deal of devolution [Russell] |
21523 | We would not want UK affairs to be settled by a world parliament [Russell] |
23167 | Power should be with smaller bodies, as long as it doesn't restrict central powers [Russell] |
23168 | A state is essential, to control greedy or predatory impulses [Russell] |
21521 | Anarchy does not maximise liberty [Russell] |
23163 | In an anarchy universities, research, books, and even seaside holidays, would be impossible [Russell] |
21528 | Groups should be autonomous, with a neutral authority as arbitrator [Russell] |
21526 | Unfortunately ordinary voters can't detect insincerity [Russell] |
23166 | In democracy we are more aware of being governed than of our tiny share in government [Russell] |
23169 | Democratic institutions become impossible in a fanatical democracy [Russell] |
21527 | On every new question the majority is always wrong at first [Russell] |
23170 | Liberal opinions are tentative rather than dogmatic, and are always responsive to new evidence [Russell] |
23171 | Empiricism is ethically superior, because dogmatism favours persecution and hatred [Russell] |
23172 | Empiricist Liberalism is the only view for someone who favours scientific evidence and happiness [Russell] |
23162 | Managers are just as remote from workers under nationalisation as under capitalism [Russell] |
23165 | Socialists say economic justice needs some state control of industries, and of foreign trade [Russell] |
21525 | When the state is the only employer, there is no refuge from the prejudices of other people [Russell] |
23160 | Being a slave of society is hardly better than being a slave of a despot [Russell] |
21518 | Men unite in pursuit of material things, and idealise greed as part of group loyalty [Russell] |
23158 | Slavery began the divorce between the work and the purposes of the worker [Russell] |
21519 | We need security and liberty, and then encouragement of creativity [Russell] |
23161 | Slaves can be just as equal as free people [Russell] |
23159 | Scarce goods may be denied entirely, to avoid their unequal distribution [Russell] |
21524 | The right to own land gives a legal right to a permanent income [Russell] |
23164 | Modern justice is seen as equality, apart from modest extra rewards for exceptional desert [Russell] |
21744 | Legally curbing people's desires is inferior to improving their desires [Russell] |
4678 | Absolute prohibitions are the essence of ethics, and suicide is the most obvious example [Wittgenstein] |
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] |
4396 | The law of causality is a source of confusion, and should be dropped from philosophy [Russell] |
8376 | If causes are contiguous with events, only the last bit is relevant, or the event's timing is baffling [Russell] |
8380 | Striking a match causes its igniting, even if it sometimes doesn't work [Russell] |
17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |
8379 | In causal laws, 'events' must recur, so they have to be universals, not particulars [Russell] |
8381 | The constancy of scientific laws rests on differential equations, not on cause and effect [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] |
18733 | Laws of nature are an aspect of the phenomena, and are just our mode of description [Wittgenstein] |
14168 | Occupying a place and change are prior to motion, so motion is just occupying places at continuous times [Russell] |
4786 | Russell's 'at-at' theory says motion is to be at the intervening points at the intervening instants [Russell, by Psillos] |
14171 | Force is supposed to cause acceleration, but acceleration is a mathematical fiction [Russell] |
7547 | Matter requires a division into time-corpuscles as well as space-corpuscles [Russell] |
7551 | Matter is a logical construction [Russell] |
21706 | At first matter is basic and known by sense-data; later Russell says matter is constructed [Russell, by Linsky,B] |
6470 | Matter is the limit of appearances as distance from the object diminishes [Russell] |
6468 | There is 'private space', and there is also the 'space of perspectives' [Russell] |
7552 | Six dimensions are needed for a particular, three within its own space, and three to locate that space [Russell] |
14160 | Space is the extension of 'point', and aggregates of points seem necessary for geometry [Russell] |
21581 | We never experience times, but only succession of events [Russell] |
14156 | Mathematicians don't distinguish between instants of time and points on a line [Russell] |
22891 | We could be aware of time if senses briefly vibrated, extending their experience of movement [Russell, by Bardon] |
14169 | The 'universe' can mean what exists now, what always has or will exist [Russell] |
2609 | If God's decrees are good, and this is not a mere tautology, then goodness is separate from God's decrees [Russell] |
5773 | The ontological argument begins with an unproven claim that 'there exists an x..' [Russell] |
6119 | You can discuss 'God exists', so 'God' is a description, not a name [Russell] |
4151 | Grammar tells what kind of object anything is - and theology is a kind of grammar [Wittgenstein] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
4159 | The human body is the best picture of the human soul [Wittgenstein] |
21520 | That our heaven is a dull place reflects the misery of excessive work in life [Russell] |