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Single Idea 14112

[filed under theme 9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates ]

Full Idea

In a class as many, the component terms, though they have some kind of unity, have less than is required for a whole.

Gist of Idea

A set has some sort of unity, but not enough to be a 'whole'

Source

Bertrand Russell (The Principles of Mathematics [1903], §070)

Book Ref

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.69

A Reaction

This is interesting because (among many other things), sets are used to stand for numbers, but numbers are usually reqarded as wholes.

The 581 ideas from Bertrand Russell

6410 The only real proper names are 'this' and 'that'; the rest are really definite descriptions. [Russell, by Grayling]
6417 In 1921 Russell abandoned sense-data, and the gap between sensation and object [Russell, by Grayling]
6475 In perception, the self is just a logical fiction demanded by grammar [Russell]
6474 Seeing is not in itself knowledge, but is separate from what is seen, such as a patch of colour [Russell]
6476 We cannot assume that the subject actually exists, so we cannot distinguish sensations from sense-data [Russell]
2792 It is possible the world came into existence five minutes ago, complete with false memories [Russell]
22326 Knowledge needs more than a sensitive response; the response must also be appropriate [Russell]
21706 At first matter is basic and known by sense-data; later Russell says matter is constructed [Russell, by Linsky,B]
6418 Russell rejected phenomenalism because it couldn't account for causal relations [Russell, by Grayling]
6402 In 1927, Russell analysed force and matter in terms of events [Russell, by Grayling]
14732 A perceived physical object is events grouped around a centre [Russell]
14733 An object produces the same percepts with or without a substance, so that is irrelevant to science [Russell]
23154 We divide mankind into friend and foe, and cooperate with one and compete with the other [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]
23151 A monarch is known to everyone in the group, and can thus unite large groups [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]
23162 Managers are just as remote from workers under nationalisation as under capitalism [Russell]
23159 Scarce goods may be denied entirely, to avoid their unequal distribution [Russell]
23161 Slaves can be just as equal as free people [Russell]
23160 Being a slave of society is hardly better than being a slave of a despot [Russell]
23158 Slavery began the divorce between the work and the purposes of the worker [Russell]
23165 Socialists say economic justice needs some state control of industries, and of foreign trade [Russell]
23163 In an anarchy universities, research, books, and even seaside holidays, would be impossible [Russell]
23164 Modern justice is seen as equality, apart from modest extra rewards for exceptional desert [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]
23166 In democracy we are more aware of being governed than of our tiny share in government [Russell]
20179 Happiness involves enduring boredom, and the young should be taught this [Russell]
20178 Life is now more interesting, but boredom is more frightening [Russell]
20177 Boredom always involves not being fully occupied [Russell]
20180 A happy and joyous life must largely be a quiet life [Russell]
20176 Boredom is an increasingly strong motivating power [Russell]
10052 Geometry is united by the intuitive axioms of projective geometry [Russell, by Musgrave]
10053 Geometrical axioms imply the propositions, but the former may not be true [Russell]
2609 If God's decrees are good, and this is not a mere tautology, then goodness is separate from God's decrees [Russell]
4786 Russell's 'at-at' theory says motion is to be at the intervening points at the intervening instants [Russell, by Psillos]
16491 If we define 'this is not blue' as disbelief in 'this is blue', we eliminate 'not' as an ingredient of facts [Russell]
16489 Is it possible to state every possible truth about the whole course of nature without using 'not'? [Russell]
16490 Some facts about experience feel like logical necessities [Russell]
16488 It is hard to explain how a sentence like 'it is not raining' can be found true by observation [Russell]
16478 A mother cat is paralysed if equidistant between two needy kittens [Russell]
16476 For simple words, a single experience can show that they are true [Russell]
16485 Perception can't prove universal generalisations, so abandon them, or abandon empiricism? [Russell]
16482 All our knowledge (if verbal) is general, because all sentences contain general words [Russell]
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]
16486 The physical world doesn't need logic, but the mental world does [Russell]
16477 Asserting not-p is saying p is false [Russell]
16484 There are four experiences that lead us to talk of 'some' things [Russell]
16475 A 'heterological' predicate can't be predicated of itself; so is 'heterological' heterological? Yes=no! [Russell]
2947 Questions wouldn't lead anywhere without the law of excluded middle [Russell]
4758 Naïve realism leads to physics, but physics then shows that naïve realism is false [Russell]
21563 The 'no classes' theory says the propositions just refer to the members [Russell]
21564 Vicious Circle: what involves ALL must not be one of those ALL [Russell]
21565 Richard's puzzle uses the notion of 'definition' - but that cannot be defined [Russell]
13414 For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf]
8469 Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein]
8468 The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false [Russell, by Orenstein]
14420 Infinity and continuity used to be philosophy, but are now mathematics [Russell]
8745 Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell]
14423 '0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell]
14421 Discovering that 1 is a number was difficult [Russell]
14424 Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell]
14422 Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell]
14425 A number is something which characterises collections of the same size [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]
14426 A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell]
14430 If a relation is symmetrical and transitive, it has to be reflexive [Russell]
14429 Classes are logical fictions, made from defining characteristics [Russell]
14431 The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell]
14441 The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell]
10450 Russell admitted that even names could also be used as descriptions [Russell, by Bach]
13510 Could a number just be something which occurs in a progression? [Russell, by Hart,WD]
14432 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell]
14433 Mathematically expressed propositions are true of the world, but how to interpret them? [Russell]
14435 The essence of individuality is beyond description, and hence irrelevant to science [Russell]
14434 What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell]
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]
14438 New numbers solve problems: negatives for subtraction, fractions for division, complex for equations [Russell]
14440 We may assume that there are infinite collections, as there is no logical reason against them [Russell]
14442 If straight lines were like ratios they might intersect at a 'gap', and have no point in common [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]
14447 Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell]
14449 There is always something psychological about inference [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]
14451 Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell]
14454 An argument 'satisfies' a function φx if φa is true [Russell]
14453 The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell]
14452 All the propositions of logic are completely general [Russell]
12444 Logic is concerned with the real world just as truly as zoology [Russell]
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]
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]
14456 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell]
14459 Reducibility: a family of functions is equivalent to a single type of function [Russell]
14461 Propositions about classes can be reduced to propositions about their defining functions [Russell]
14460 If something is true in all possible worlds then it is logically necessary [Russell]
14462 In modern times, logic has become mathematical, and mathematics has become logical [Russell]
10057 Logic can only assert hypothetical existence [Russell]
14464 Logic can be known a priori, without study of the actual world [Russell]
14465 Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell]
14463 Existence can only be asserted of something described, not of something named [Russell]
21570 Numbers are just verbal conveniences, which can be analysed away [Russell]
8854 My 'acquaintance' with sense-data is nothing like my knowing New York [Williams,M on Russell]
21710 We know a universal in 'yellow differs from blue' or 'yellow resembles blue less than green does' [Russell]
21571 Philosophical systems are interesting, but we now need a more objective scientific philosophy [Russell]
21572 Philosophical disputes are mostly hopeless, because philosophers don't understand each other [Russell]
21573 When problems are analysed properly, they are either logical, or not philosophical at all [Russell]
21576 With asymmetrical relations (before/after) the reduction to properties is impossible [Russell]
21575 When we attribute a common quality to a group, we can forget the quality and just talk of the group [Russell]
21577 Empirical truths are particular, so general truths need an a priori input of generality [Russell]
21574 Hegel's confusions over 'is' show how vast systems can be built on simple errors [Russell]
21579 Objects are treated as real when they connect with other experiences in a normal way [Russell]
21578 Global scepticism is irrefutable, but can't replace our other beliefs, and just makes us hesitate [Russell]
6416 Other minds seem to exist, because their testimony supports realism about the world [Russell, by Grayling]
21581 We never experience times, but only succession of events [Russell]
21582 Physicists accept particles, points and instants, while pretending they don't do metaphysics [Russell]
21580 Science condemns sense-data and accepts matter, but a logical construction must link them [Russell]
21583 When sense-data change, there must be indistinguishable sense-data in the process [Russell]
21584 A sense of timelessness is essential to wisdom [Russell]
21585 The tortoise won't win, because infinite instants don't compose an infinitely long time [Russell]
21586 The logical connectives are not objects, but are formal, and need a context [Russell]
21588 Logic gives the method of research in philosophy [Russell]
21587 Philosophers sometimes neglect truth and distort facts to attain a nice system [Russell]
21684 Atomic facts may be inferrable from others, but never from non-atomic facts [Russell]
22316 A positive and negative fact have the same constituents; their difference is primitive [Russell]
10968 Russell gave up logical atomism because of negative, general and belief propositions [Russell, by Read]
6107 It is logic, not metaphysics, that is fundamental to philosophy [Russell]
6108 Maths can be deduced from logical axioms and the logic of relations [Russell]
6109 Some axioms may only become accepted when they lead to obvious conclusions [Russell]
6110 Subject-predicate logic (and substance-attribute metaphysics) arise from Aryan languages [Russell]
6111 As propositions can be put in subject-predicate form, we wrongly infer that facts have substance-quality form [Russell]
6112 Meaning takes many different forms, depending on different logical types [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]
6115 Vagueness, and simples being beyond experience, are obstacles to a logical language [Russell]
6116 A logical language would show up the fallacy of inferring reality from ordinary language [Russell]
6117 Philosophy should be built on science, to reduce error [Russell]
21722 Better to construct from what is known, than to infer what is unknown [Russell]
6118 Philosophy is logical analysis, followed by synthesis [Russell]
10059 In mathematic we are ignorant of both subject-matter and truth [Russell]
7554 Self-evidence is often a mere will-o'-the-wisp [Russell]
7556 A collection is infinite if you can remove some terms without diminishing its number [Russell]
7557 To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell]
21532 Full empiricism is not tenable, but empirical investigation is always essential [Russell]
21533 Contingency arises from tensed verbs changing the propositions to which they refer [Russell]
21534 The only thing we can say about relations is that they relate [Russell]
21535 Objects only exist if they 'occupy' space and time [Russell]
21536 When I perceive a melody, I do not perceive the notes as existing [Russell]
21537 I assume we perceive the actual objects, and not their 'presentations' [Russell]
21538 If two people perceive the same object, the object of perception can't be in the mind [Russell]
21539 Excluded middle can be stated psychologically, as denial of p implies assertion of not-p [Russell]
21540 Relational propositions seem to be 'about' their terms, rather than about the relation [Russell]
21541 The complexity of the content correlates with the complexity of the object [Russell]
21542 Do incorrect judgements have non-existent, or mental, or external objects? [Russell]
21543 If p is false, then believing not-p is knowing a truth, so negative propositions must exist [Russell]
21544 It seems that when a proposition is false, something must fail to subsist [Russell]
21531 Common sense agrees with Meinong (rather than Russell) that 'Pegasus is a flying horse' is true [Lackey on Russell]
21545 I prefer to deny round squares, and deal with the difficulties by the theory of denoting [Russell]
21546 We can't sharply distinguish variables, domains and values, if symbols frighten us [Russell]
21547 On Meinong's principles 'the existent round square' has to exist [Russell]
21550 Science reduces indexicals to a minimum, but they can never be eliminated from empirical matters [Russell]
21551 Empirical words need ostensive definition, which makes them egocentric [Russell]
21552 Common speech is vague; its vocabulary and syntax must be modified, for precision [Russell]
6420 Only by analysing is progress possible in philosophy [Russell]
6419 In 1899-1900 I adopted the philosophy of logical atomism [Russell]
6426 Intuitionism says propositions are only true or false if there is a method of showing it [Russell]
7528 Leibniz bases everything on subject/predicate and substance/property propositions [Russell]
6423 We tried to define all of pure maths using logical premisses and concepts [Russell]
6427 Unverifiable propositions about the remote past are still either true or false [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]
6432 Analysis gives new knowledge, without destroying what we already have [Russell]
6430 In epistemology we should emphasis the continuity between animal and human minds [Russell]
6431 Empiricists seem unclear what they mean by 'experience' [Russell]
6433 Behaviourists struggle to explain memory and imagination, because they won't admit images [Russell]
6435 You can believe the meaning of a sentence without thinking of the words [Russell]
6434 Facts are everything, except simples; they are either relations or qualities [Russell]
6438 Complex things can be known, but not simple things [Russell]
6439 Names are meaningless unless there is an object which they designate [Russell]
6437 The theory of types makes 'Socrates and killing are two' illegitimate [Russell]
6436 I gradually replaced classes with properties, and they ended as a symbolic convenience [Russell]
6440 Universals can't just be words, because words themselves are universals [Russell]
6444 True belief about the time is not knowledge if I luckily observe a stopped clock at the right moment [Russell]
6443 Surprise is a criterion of error [Russell]
6441 Pragmatism judges by effects, but I judge truth by causes [Russell]
6442 Truth belongs to beliefs, not to propositions and sentences [Russell]
4396 The law of causality is a source of confusion, and should be dropped from philosophy [Russell]
8375 'Necessary' is a predicate of a propositional function, saying it is true for all values of its argument [Russell]
8376 If causes are contiguous with events, only the last bit is relevant, or the event's timing is baffling [Russell]
8378 Philosophers usually learn science from each other, not from science [Russell]
8379 In causal laws, 'events' must recur, so they have to be universals, not particulars [Russell]
8380 Striking a match causes its igniting, even if it sometimes doesn't work [Russell]
8381 The constancy of scientific laws rests on differential equations, not on cause and effect [Russell]
16385 A definite description 'denotes' an entity if it fits the description uniquely [Russell, by Recanati]
4567 Russell argued with great plausibility that we rarely, if ever, refer with our words [Russell, by Cooper,DE]
5810 Referring is not denoting, and Russell ignores the referential use of definite descriptions [Donnellan on Russell]
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]
16987 By eliminating descriptions from primitive notation, Russell seems to reject 'sense' [Russell, by Kripke]
4570 Russell assumes that expressions refer, but actually speakers refer by using expressions [Cooper,DE on Russell]
7767 The theory of definite descriptions aims at finding correct truth conditions [Russell, by Lycan]
11006 Russell started a whole movement in philosophy by providing an analysis of descriptions [Read on Russell]
7758 'Elizabeth = Queen of England' is really a predication, not an identity-statement [Russell, by Lycan]
18944 Russell's theories aim to preserve excluded middle (saying all sentences are T or F) [Sawyer on Russell]
15159 The meaning of a logically proper name is its referent, but most names are not logically proper [Russell, by Soames]
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]
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]
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]
10449 Logically proper names introduce objects; definite descriptions introduce quantifications [Russell, by Bach]
6061 Existence is entirely expressed by the existential quantifier [Russell, by McGinn]
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]
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]
18777 If the King of France is not bald, and not not-bald, this violates excluded middle [Linsky,B on Russell]
6063 Russell can't attribute existence to properties [McGinn on Russell]
5772 The idea of a variable is fundamental [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]
5773 The ontological argument begins with an unproven claim that 'there exists an x..' [Russell]
21726 In graspable propositions the constituents are real entities of acquaintance [Russell]
5779 There are distinct sets of psychological and physical causal laws [Russell]
5778 If we object to all data which is 'introspective' we will cease to believe in toothaches [Russell]
5781 Our important beliefs all, if put into words, take the form of propositions [Russell]
5782 A proposition expressed in words is a 'word-proposition', and one of images an 'image-proposition' [Russell]
5780 The three questions about belief are its contents, its success, and its character [Russell]
5783 Propositions of existence, generalities, disjunctions and hypotheticals make correspondence tricky [Russell]
5784 In its primary and formal sense, 'true' applies to propositions, not beliefs [Russell]
5776 A proposition is what we believe when we believe truly or falsely [Russell]
5777 The truth or falsehood of a belief depends upon a fact to which the belief 'refers' [Russell]
22891 We could be aware of time if senses briefly vibrated, extending their experience of movement [Russell, by Bardon]
21744 Legally curbing people's desires is inferior to improving their desires [Russell]
21741 'You ought to do p' primarily has emotional content, expressing approval [Russell]
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]
21742 Originally virtue was obedience, to gods, government, or custom [Russell]
21745 Act so as to produce harmonious rather than discordant desires [Russell]
21740 I doubt whether ethics is part of philosophy [Russell]
22306 To explain false belief we should take belief as relating to a proposition's parts, not to the whole thing [Russell]
22308 Only the actual exists, so possibilities always reduce to actuality after full analysis [Russell]
22307 Propositions don't name facts, because two opposed propositions can match one fact [Russell]
21702 In 1918 still believes in nonlinguistic analogues of sentences, but he now calls them 'facts' [Russell, by Quine]
9022 Russell uses 'propositional function' to refer to both predicates and to attributes [Quine on Russell]
18348 Not only atomic truths, but also general and negative truths, have truth-makers [Russell, by Rami]
7744 Treat description using quantifiers, and treat proper names as descriptions [Russell, by McCullogh]
5465 Modern trope theory tries, like logical atomism, to reduce things to elementary states [Russell, by Ellis]
18376 Russell asserts atomic, existential, negative and general facts [Russell, by Armstrong]
6060 'Existence' means that a propositional function is sometimes true [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]
6091 Propositions don't name facts, because each fact corresponds to a proposition and its negation [Russell]
6089 Logical atomism aims at logical atoms as the last residue of analysis [Russell]
6090 Facts make propositions true or false, and are expressed by whole sentences [Russell]
6093 The names in a logically perfect language would be private, and could not be shared [Russell]
6092 In a logically perfect language, there will be just one word for every simple object [Russell]
6094 An inventory of the world does not need to include propositions [Russell]
6095 The business of metaphysics is to describe the world [Russell]
6096 I no longer believe in propositions, especially concerning falsehoods [Russell]
6097 The theory of error seems to need the existence of the non-existent [Russell]
6098 Perception goes straight to the fact, and not through the proposition [Russell]
6099 Modal terms are properties of propositional functions, not of propositions [Russell]
6100 Once you have enumerated all the atomic facts, there is a further fact that those are all the facts [Russell]
6119 You can discuss 'God exists', so 'God' is a description, not a name [Russell]
6101 Romulus does not occur in the proposition 'Romulus did not exist' [Russell]
6102 You can understand 'author of Waverley', but to understand 'Scott' you must know who it applies to [Russell]
6103 Normally a class with only one member is a problem, because the class and the member are identical [Russell]
6106 Reducing entities and premisses makes error less likely [Russell]
6105 Logical atoms aims to get down to ultimate simples, with their own unique reality [Russell]
6104 Numbers are classes of classes, and hence fictions of fictions [Russell]
10423 There are a set of criteria for pinning down a logically proper name [Russell, by Sainsbury]
10426 A name has got to name something or it is not a name [Russell]
21712 I know longer believe in shadowy things like 'that today is Wednesday' when it is actually Tuesday [Russell]
21709 You can't name all the facts, so they are not real, but are what propositions assert [Russell]
23169 Democratic institutions become impossible in a fanatical democracy [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]
22329 Logic is highly general truths abstracted from reality [Russell, by Glock]
21569 It is good to generalise truths as much as possible [Russell]
7529 All philosophy should begin with an analysis of propositions [Russell]
21520 That our heaven is a dull place reflects the misery of excessive work in life [Russell]
21521 Anarchy does not maximise liberty [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]
21517 Individuals need creativity, reverence for others, and self-respect [Russell]
21518 Men unite in pursuit of material things, and idealise greed as part of group loyalty [Russell]
21519 We need security and liberty, and then encouragement of creativity [Russell]
21495 Theoretical and practical politics are both concerned with the best lives for individuals [Russell]
21524 The right to own land gives a legal right to a permanent income [Russell]
21525 When the state is the only employer, there is no refuge from the prejudices of other people [Russell]
21526 Unfortunately ordinary voters can't detect insincerity [Russell]
21528 Groups should be autonomous, with a neutral authority as arbitrator [Russell]
21527 On every new question the majority is always wrong at first [Russell]
21681 Given all true atomic propositions, in theory every other truth can thereby be deduced [Russell]
19164 If propositions are facts, then false and true propositions are indistinguishable [Davidson on Russell]
11010 Being is what belongs to every possible object of thought [Russell]
15895 Russell discovered the paradox suggested by Burali-Forti's work [Russell, by Lavine]
18254 Russell's approach had to treat real 5/8 as different from rational 5/8 [Russell, by Dummett]
7530 Russell tried to replace Peano's Postulates with the simple idea of 'class' [Russell, by Monk]
15894 Russell invented the naïve set theory usually attributed to Cantor [Russell, by Lavine]
18722 Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell]
11849 It at least makes sense to say two objects have all their properties in common [Wittgenstein on Russell]
14102 What is true or false is not mental, and is best called 'propositions' [Russell]
14103 Pure mathematics is the class of propositions of the form 'p implies q' [Russell]
14104 Constants are absolutely definite and unambiguous [Russell]
14105 There seem to be eight or nine logical constants [Russell]
14106 Implication cannot be defined [Russell]
14107 Terms are identical if they belong to all the same classes [Russell]
14108 It would be circular to use 'if' and 'then' to define material implication [Russell]
14109 The study of grammar is underestimated in philosophy [Russell]
7781 I call an object of thought a 'term'. This is a wide concept implying unity and existence. [Russell]
14110 Proposition contain entities indicated by words, rather than the words themselves [Russell]
14111 A proposition is a unity, and analysis destroys it [Russell]
14112 A set has some sort of unity, but not enough to be a 'whole' [Russell]
14113 The null class is a fiction [Russell]
14114 Variables don't stand alone, but exist as parts of propositional functions [Russell]
14115 Definition by analysis into constituents is useless, because it neglects the whole [Russell]
14116 Numbers were once defined on the basis of 1, but neglected infinities and + [Russell]
14117 Numbers are properties of classes [Russell]
14118 We can define one-to-one without mentioning unity [Russell]
14119 We do not currently know whether, of two infinite numbers, one must be greater than the other [Russell]
14120 Counting explains none of the real problems about the foundations of arithmetic [Russell]
14121 The part-whole relation is ultimate and indefinable [Russell]
14122 Analysis gives us nothing but the truth - but never the whole truth [Russell]
14123 Some quantities can't be measured, and some non-quantities are measurable [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]
14124 Axiom of Archimedes: a finite multiple of a lesser magnitude can always exceed a greater [Russell]
14125 Finite numbers, unlike infinite numbers, obey mathematical induction [Russell]
14126 Order rests on 'between' and 'separation' [Russell]
14127 Order depends on transitive asymmetrical relations [Russell]
10585 Symmetrical and transitive relations are formally like equality [Russell]
10586 'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness [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]
9977 Ordinals can't be defined just by progression; they have intrinsic qualities [Russell]
14132 Properties of numbers don't rely on progressions, so cardinals may be more basic [Russell]
14133 There are cardinal and ordinal theories of infinity (while continuity is entirely ordinal) [Russell]
14134 Infinite numbers are distinguished by disobeying induction, and the part equalling the whole [Russell]
14135 Real numbers are a class of rational numbers (and so not really numbers at all) [Russell]
14137 'Any' is better than 'all' where infinite classes are concerned [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]
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]
14143 ω names the whole series, or the generating relation of the series of ordinal numbers [Russell]
14144 Ordinals result from likeness among relations, as cardinals from similarity among classes [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]
14147 Denying mathematical induction gave us the transfinite [Russell]
14149 The Achilles Paradox concerns the one-one correlation of infinite classes [Russell]
14148 Infinite regresses have propositions made of propositions etc, with the key term reappearing [Russell]
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]
14156 Mathematicians don't distinguish between instants of time and points on a line [Russell]
14158 Quantity is not part of mathematics, where it is replaced by order [Russell]
14159 In mathematics definitions are superfluous, as they name classes, and it all reduces to primitives [Russell]
14160 Space is the extension of 'point', and aggregates of points seem necessary for geometry [Russell]
14161 Many things have being (as topics of propositions), but may not have actual existence [Russell]
22303 It makes no sense to say that a true proposition could have been false [Russell]
14162 Mathematics doesn't care whether its entities exist [Russell]
14163 Four classes of terms: instants, points, terms at instants only, and terms at instants and points [Russell]
14165 Analysis falsifies, if when the parts are broken down they are not equivalent to their sum [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]
14167 The only classes are things, predicates and relations [Russell]
14169 The 'universe' can mean what exists now, what always has or will exist [Russell]
14168 Occupying a place and change are prior to motion, so motion is just occupying places at continuous times [Russell]
14170 Change is obscured by substance, a thing's nature, subject-predicate form, and by essences [Russell]
14171 Force is supposed to cause acceleration, but acceleration is a mathematical fiction [Russell]
14172 Moments and points seem to imply other moments and points, but don't cause them [Russell]
14173 What exists has causal relations, but non-existent things may also have them [Russell]
14174 The laws of motion and gravitation are just parts of the definition of a kind of matter [Russell]
14175 We can drop 'cause', and just make inferences between facts [Russell]
14176 "The death of Caesar is true" is not the same proposition as "Caesar died" [Russell]
21555 For 'x is a u' to be meaningful, u must be one range of individuals (or 'type') higher than x [Russell]
18002 As well as a truth value, propositions have a range of significance for their variables [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]
21341 Philosophers of logic and maths insisted that a vocabulary of relations was essential [Russell, by Heil]
18246 Dedekind failed to distinguish the numbers from other progressions [Shapiro on Russell]
19157 Russell said the proposition must explain its own unity - or else objective truth is impossible [Russell, by Davidson]
21724 The main aim of the multiple relations theory of judgement was to dispense with propositions [Russell, by Linsky,B]
13468 Russell started philosophy of language, by declaring some plausible sentences to be meaningless [Russell, by Hart,WD]
6510 Russell (1912) said phenomena only resemble reality in abstract structure [Russell, by Robinson,H]
7290 If Russell rejects innate ideas and direct a priori knowledge, he is left with a tabula rasa [Russell, by Thompson]
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]
5357 It is natural to begin from experience, and presumably that is the basis of knowledge [Russell]
5365 Dreams can be explained fairly scientifically if we assume a physical world [Russell]
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]
5359 Descartes showed that subjective things are the most certain [Russell]
5362 It is not illogical to think that only myself and my mental events exist [Russell]
5366 We have an 'instinctive' belief in the external world, prior to all reflection [Russell]
5361 Philosophers must get used to absurdities [Russell]
5368 Philosophy verifies that our hierarchy of instinctive beliefs is harmonious and consistent [Russell]
5369 It is rational to believe in reality, despite the lack of demonstrative reasons for it [Russell]
5371 Because we depend on correspondence, we know relations better than we know the items that relate [Russell]
5370 Space is neutral between touch and sight, so it cannot really be either of them [Russell]
5372 There is no reason to think that objects have colours [Russell]
5375 Knowledge of truths applies to judgements; knowledge by acquaintance applies to sensations and things [Russell]
5373 'Idealism' says that everything which exists is in some sense mental [Russell]
5376 I can know the existence of something with which nobody is acquainted [Russell]
5387 It is pure chance which descriptions in a person's mind make a name apply to an individual [Russell]
5378 All knowledge (of things and of truths) rests on the foundations of acquaintance [Russell]
5379 If we didn't know our own minds by introspection, we couldn't know that other people have minds [Russell]
5380 In perceiving the sun, I am aware of sun sense-data, and of the perceiver of the data [Russell]
5381 In seeing the sun, we are acquainted with our self, but not as a permanent person [Russell]
5384 A universal of which we are aware is called a 'concept' [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]
5377 'Acquaintance' is direct awareness, without inferences or judgements [Russell]
5383 Every complete sentence must contain at least one word (a verb) which stands for a universal [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]
5393 We can't know that our laws are exceptionless, or even that there are any laws [Russell]
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]
5388 Every understood proposition is composed of constituents with which we are acquainted [Russell]
5398 Judgements of usefulness depend on judgements of value [Russell]
5395 Demonstration always relies on the rule that anything implied by a truth is true [Russell]
5396 Three Laws of Thought: identity, contradiction, and excluded middle [Russell]
5401 The mortality of Socrates is more certain from induction than it is from deduction [Russell]
5399 Maths is not known by induction, because further instances are not needed to support it [Russell]
5400 In any possible world we feel that two and two would be four [Russell]
5397 The rationalists were right, because we know logical principles without experience [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]
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]
4427 Every sentence contains at least one word denoting a universal, so we need universals to know truth [Russell]
4429 If we consider whiteness to be merely a mental 'idea', we rob it of its universality [Russell]
5407 That Edinburgh is north of London is a non-mental fact, so relations are independent universals [Russell]
5405 The law of contradiction is not a 'law of thought', but a belief about things [Russell]
5410 I learn the universal 'resemblance' by seeing two shades of green, and their contrast with red [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]
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]
5414 Images are not memory, because they are present, and memories are of the past [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]
5426 Belief relates a mind to several things other than itself [Russell]
5419 Truth and falsehood are properties of beliefs and statements [Russell]
5420 Truth is a property of a belief, but dependent on its external relations, not its internal qualities [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]
5417 A good theory of truth must make falsehood possible [Russell]
5421 The coherence theory says falsehood is failure to cohere, and truth is fitting into a complete system of Truth [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]
5418 In a world of mere matter there might be 'facts', but no truths [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]
5431 Knowledge cannot be precisely defined, as it merges into 'probable opinion' [Russell]
5434 Philosophy is similar to science, and has no special source of wisdom [Russell]
5432 Metaphysics cannot give knowledge of the universe as a whole [Russell]
17628 Arithmetic was probably inferred from relationships between physical objects [Russell]
17627 It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [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]
17632 Non-contradiction was learned from instances, and then found to be indubitable [Russell]
17631 Induction is inferring premises from consequences [Russell]
17633 The law of gravity has many consequences beyond its grounding observations [Russell]
17639 Believing a whole science is more than believing each of its propositions [Russell]
17637 The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell]
17638 If one proposition is deduced from another, they are more certain together than alone [Russell]
17640 Finding the axioms may be the only route to some new results [Russell]
17641 Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell]
23025 Philosophers should be more inductive, and test results by their conclusions, not their self-evidence [Russell]
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]
6458 Individuating sense-data is difficult, because they divide when closely attended to [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]
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]
6470 Matter is the limit of appearances as distance from the object diminishes [Russell]
6465 We need not deny substance, but there seems no reason to assert it [Russell]
6466 Where possible, logical constructions are to be substituted for inferred entities [Russell]
6468 There is 'private space', and there is also the 'space of perspectives' [Russell]
6467 No sensibile is ever a datum to two people at once [Russell]
6469 Sense-data may be subjective, if closing our eyes can change them [Russell]
6471 The assumption by physicists of permanent substance is not metaphysically legitimate [Russell]
6473 Physical things are series of appearances whose matter obeys physical laws [Russell]
6472 Continuity is a sufficient criterion for the identity of a rock, but not for part of a smooth fluid [Russell]
18130 Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock]
21560 Any linguistic expression may lack meaning when taken out of context [Russell]
21561 'The number one is bald' or 'the number one is fond of cream cheese' are meaningless [Russell]
21562 There is no complexity without relations, so no propositions, and no truth [Russell]
22315 There can't be a negative of a complex, which is negated by its non-existence [Potter on Russell]
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]
18273 Logical truths are known by their extreme generality [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]
21566 'Propositional functions' are ambiguous until the variable is given a value [Russell]
21567 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell]
21568 A one-variable function is only 'predicative' if it is one order above its arguments [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]
21718 Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
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]
6407 The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
11064 Classes can be reduced to propositional functions [Russell, by Hanna]
18124 Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock]
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]
7531 We don't assert private thoughts; the objects are part of what we assert [Russell]
9127 Russell refuted Frege's principle that there is a set for each property [Russell, by Sorensen]
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]
7534 In 1906, Russell decided that propositions did not, after all, exist [Russell, by Monk]
6343 For Russell, both propositions and facts are arrangements of objects, so obviously they correspond [Horwich on Russell]
7545 Visible things are physical and external, but only exist when viewed [Russell]
7546 A man is a succession of momentary men, bound by continuity and causation [Russell]
7547 Matter requires a division into time-corpuscles as well as space-corpuscles [Russell]
7548 Classes, grouped by a convenient property, are logical constructions [Russell]
7549 If my body literally lost its mind, the object seen when I see a flash would still exist [Russell]
7550 We could probably, in principle, infer minds from brains, and brains from minds [Russell]
7551 Matter is a logical construction [Russell]
7552 Six dimensions are needed for a particular, three within its own space, and three to locate that space [Russell]
7553 Sense-data are purely physical [Russell]
14327 Trope theorists cannot explain how tropes resemble each other [Russell, by Mumford]
16045 General facts supervene on particular facts, but cannot be inferred from them [Russell, by Bennett,K]
9051 Since natural language is not precise it cannot be in the province of logic [Russell, by Keefe/Smith]
21597 Logical connectives have the highest precision, yet are infected by the vagueness of true and false [Russell, by Williamson]
9054 Vagueness is only a characteristic of representations, such as language [Russell]