Ideas of Bertrand Russell, by Theme

[British, 1872 - 1970, Born at Trelleck. Professor at Cambridge (Trinity). Taught Wittgenstein. Imprisoned for pacificism. Campaigner against nuclear weapons. Died in N. Wales.]

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1. Philosophy / A. Wisdom / 1. Nature of Wisdom
21584 A sense of timelessness is essential to wisdom
1. Philosophy / C. History of Philosophy / 5. Modern Philosophy / b. Modern philosophy beginnings
11006 Russell started a whole movement in philosophy by providing an analysis of descriptions [Read]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
5361 Philosophers must get used to absurdities
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
5368 Philosophy verifies that our hierarchy of instinctive beliefs is harmonious and consistent
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
23025 Philosophers should be more inductive, and test results by their conclusions, not their self-evidence
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
17641 Discoveries in mathematics can challenge philosophy, and offer it a new foundation
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
21572 Philosophical disputes are mostly hopeless, because philosophers don't understand each other
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
5432 Metaphysics cannot give knowledge of the universe as a whole
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
21571 Philosophical systems are interesting, but we now need a more objective scientific philosophy
21574 Hegel's confusions over 'is' show how vast systems can be built on simple errors
21587 Philosophers sometimes neglect truth and distort facts to attain a nice system
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
21582 Physicists accept particles, points and instants, while pretending they don't do metaphysics
6095 The business of metaphysics is to describe the world
1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
14122 Analysis gives us nothing but the truth - but never the whole truth
6118 Philosophy is logical analysis, followed by synthesis
6420 Only by analysing is progress possible in philosophy
6432 Analysis gives new knowledge, without destroying what we already have
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
7529 All philosophy should begin with an analysis of propositions
14109 The study of grammar is underestimated in philosophy
14456 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity
21552 Common speech is vague; its vocabulary and syntax must be modified, for precision
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
21546 We can't sharply distinguish variables, domains and values, if symbols frighten us
21573 When problems are analysed properly, they are either logical, or not philosophical at all
6116 A logical language would show up the fallacy of inferring reality from ordinary language
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
14165 Analysis falsifies, if when the parts are broken down they are not equivalent to their sum
1. Philosophy / G. Scientific Philosophy / 3. Scientism
5434 Philosophy is similar to science, and has no special source of wisdom
8378 Philosophers usually learn science from each other, not from science
6117 Philosophy should be built on science, to reduce error
2. Reason / A. Nature of Reason / 6. Coherence
17638 If one proposition is deduced from another, they are more certain together than alone
2. Reason / B. Laws of Thought / 1. Laws of Thought
5396 Three Laws of Thought: identity, contradiction, and excluded middle
5405 The law of contradiction is not a 'law of thought', but a belief about things
2. Reason / B. Laws of Thought / 3. Non-Contradiction
17632 Non-contradiction was learned from instances, and then found to be indubitable
2. Reason / B. Laws of Thought / 6. Ockham's Razor
6106 Reducing entities and premisses makes error less likely
2. Reason / D. Definition / 3. Types of Definition
14426 A definition by 'extension' enumerates items, and one by 'intension' gives a defining property
2. Reason / D. Definition / 7. Contextual Definition
21560 Any linguistic expression may lack meaning when taken out of context
2. Reason / D. Definition / 11. Ostensive Definition
21551 Empirical words need ostensive definition, which makes them egocentric
2. Reason / D. Definition / 13. Against Definition
14115 Definition by analysis into constituents is useless, because it neglects the whole
14159 In mathematics definitions are superfluous, as they name classes, and it all reduces to primitives
2. Reason / F. Fallacies / 2. Infinite Regress
14148 Infinite regresses have propositions made of propositions etc, with the key term reappearing
2. Reason / F. Fallacies / 8. Category Mistake / a. Category mistakes
18002 As well as a truth value, propositions have a range of significance for their variables
21561 'The number one is bald' or 'the number one is fond of cream cheese' are meaningless
8468 The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false [Orenstein]
6437 The theory of types makes 'Socrates and killing are two' illegitimate
3. Truth / A. Truth Problems / 1. Truth
5420 Truth is a property of a belief, but dependent on its external relations, not its internal qualities
3. Truth / A. Truth Problems / 5. Truth Bearers
14102 What is true or false is not mental, and is best called 'propositions'
5419 Truth and falsehood are properties of beliefs and statements
5784 In its primary and formal sense, 'true' applies to propositions, not beliefs
6442 Truth belongs to beliefs, not to propositions and sentences
3. Truth / A. Truth Problems / 7. Falsehood
5417 A good theory of truth must make falsehood possible
16477 Asserting not-p is saying p is false
3. Truth / B. Truthmakers / 1. For Truthmakers
5777 The truth or falsehood of a belief depends upon a fact to which the belief 'refers'
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
6090 Facts make propositions true or false, and are expressed by whole sentences
3. Truth / B. Truthmakers / 6. Making Negative Truths
21544 It seems that when a proposition is false, something must fail to subsist
3. Truth / B. Truthmakers / 8. Making General Truths
18348 Not only atomic truths, but also general and negative truths, have truth-makers [Rami]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
6343 For Russell, both propositions and facts are arrangements of objects, so obviously they correspond [Horwich]
7395 Truth as congruence may work for complex beliefs, but not for simple beliefs about existence [Joslin]
5428 Beliefs are true if they have corresponding facts, and false if they don't
5783 Propositions of existence, generalities, disjunctions and hypotheticals make correspondence tricky
3. Truth / D. Coherence Truth / 1. Coherence Truth
5421 The coherence theory says falsehood is failure to cohere, and truth is fitting into a complete system of Truth
3. Truth / D. Coherence Truth / 2. Coherence Truth Critique
5423 If we suspend the law of contradiction, nothing will appear to be incoherent
5422 More than one coherent body of beliefs seems possible
5424 Coherence is not the meaning of truth, but an important test for truth
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
14454 An argument 'satisfies' a function φx if φa is true
3. Truth / H. Deflationary Truth / 1. Redundant Truth
14176 "The death of Caesar is true" is not the same proposition as "Caesar died"
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
5401 The mortality of Socrates is more certain from induction than it is from deduction
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?
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / e. Existential quantifier ∃
16484 There are four experiences that lead us to talk of 'some' things
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14113 The null class is a fiction
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
6103 Normally a class with only one member is a problem, because the class and the member are identical
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
14427 We can enumerate finite classes, but an intensional definition is needed for infinite classes
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
14428 Members define a unique class, whereas defining characteristics are numerous
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
14440 We may assume that there are infinite collections, as there is no logical reason against them
14447 Infinity says 'for any inductive cardinal, there is a class having that many terms'
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
14443 The British parliament has one representative selected from each constituency
14445 Choice shows that if any two cardinals are not equal, one must be the greater
14444 Choice is equivalent to the proposition that every class is well-ordered
14446 We can pick all the right or left boots, but socks need Choice to insure the representative class
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
18130 Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Bostock]
14459 Reducibility: a family of functions is equivalent to a single type of function
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
21563 The 'no classes' theory says the propositions just refer to the members
14461 Propositions about classes can be reduced to propositions about their defining functions
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
15894 Russell invented the naïve set theory usually attributed to Cantor [Lavine]
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
14126 Order rests on 'between' and 'separation'
14127 Order depends on transitive asymmetrical relations
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
8469 Russell's proposal was that only meaningful predicates have sets as their extensions [Orenstein]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
11064 Classes can be reduced to propositional functions [Hanna]
7548 Classes, grouped by a convenient property, are logical constructions
8745 Classes are logical fictions, and are not part of the ultimate furniture of the world
6436 I gradually replaced classes with properties, and they ended as a symbolic convenience
4. Formal Logic / G. Formal Mereology / 1. Mereology
14121 The part-whole relation is ultimate and indefinable
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
6110 Subject-predicate logic (and substance-attribute metaphysics) arise from Aryan languages
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
21588 Logic gives the method of research in philosophy
6107 It is logic, not metaphysics, that is fundamental to philosophy
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
14452 All the propositions of logic are completely general
16486 The physical world doesn't need logic, but the mental world does
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
21495 Theoretical and practical politics are both concerned with the best lives for individuals
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
14462 In modern times, logic has become mathematical, and mathematics has become logical
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
5395 Demonstration always relies on the rule that anything implied by a truth is true
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
14108 It would be circular to use 'if' and 'then' to define material implication
14106 Implication cannot be defined
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
14167 The only classes are things, predicates and relations
22329 Logic is highly general truths abstracted from reality [Glock]
12444 Logic is concerned with the real world just as truly as zoology
10057 Logic can only assert hypothetical existence
14464 Logic can be known a priori, without study of the actual world
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
10053 Geometrical axioms imply the propositions, but the former may not be true
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
21539 Excluded middle can be stated psychologically, as denial of p implies assertion of not-p
18944 Russell's theories aim to preserve excluded middle (saying all sentences are T or F) [Sawyer]
2947 Questions wouldn't lead anywhere without the law of excluded middle
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
7758 'Elizabeth = Queen of England' is really a predication, not an identity-statement [Lycan]
6092 In a logically perfect language, there will be just one word for every simple object
6101 Romulus does not occur in the proposition 'Romulus did not exist'
6115 Vagueness, and simples being beyond experience, are obstacles to a logical language
7528 Leibniz bases everything on subject/predicate and substance/property propositions
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
23476 Logical constants seem to be entities in propositions, but are actually pure form
23477 We use logical notions, so they must be objects - but I don't know what they really are
21586 The logical connectives are not objects, but are formal, and need a context
21597 Logical connectives have the highest precision, yet are infected by the vagueness of true and false [Williamson]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
14105 There seem to be eight or nine logical constants
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
18722 Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein]
16489 Is it possible to state every possible truth about the whole course of nature without using 'not'?
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
16479 'Or' expresses hesitation, in a dog at a crossroads, or birds risking grabbing crumbs
16480 A disjunction expresses indecision
16481 'Or' expresses a mental state, not something about the world
16483 Disjunction may also arise in practice if there is imperfect memory.
16487 Maybe the 'or' used to describe mental states is not the 'or' of logic
5. Theory of Logic / E. Structures of Logic / 3. Constants in Logic
14104 Constants are absolutely definite and unambiguous
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
14114 Variables don't stand alone, but exist as parts of propositional functions
5772 The idea of a variable is fundamental
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
21566 'Propositional functions' are ambiguous until the variable is given a value
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
6102 You can understand 'author of Waverley', but to understand 'Scott' you must know who it applies to
10423 There are a set of criteria for pinning down a logically proper name [Sainsbury]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
18941 Names don't have a sense, but are disguised definite descriptions [Sawyer]
4945 Russell says names are not denotations, but definite descriptions in disguise [Kripke]
18942 Russell says a name contributes a complex of properties, rather than an object [Sawyer]
7745 Are names descriptions, if the description is unknown, false, not special, or contains names? [McCullogh]
5386 Proper names are really descriptions, and can be replaced by a description in a person's mind
7744 Treat description using quantifiers, and treat proper names as descriptions [McCullogh]
10450 Russell admitted that even names could also be used as descriptions [Bach]
14458 Asking 'Did Homer exist?' is employing an abbreviated description
14457 Names are really descriptions, except for a few words like 'this' and 'that'
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
10449 Logically proper names introduce objects; definite descriptions introduce quantifications [Bach]
15159 The meaning of a logically proper name is its referent, but most names are not logically proper [Soames]
6410 The only real proper names are 'this' and 'that'; the rest are really definite descriptions. [Grayling]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
7757 "Nobody" is not a singular term, but a quantifier [Lycan]
2612 Russell rewrote singular term names as predicates [Ayer]
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
18943 Russell implies that all sentences containing empty names are false [Sawyer]
10426 A name has got to name something or it is not a name
6439 Names are meaningless unless there is an object which they designate
5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
7311 The only genuine proper names are 'this' and 'that'
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / a. Descriptions
14455 'I met a unicorn' is meaningful, and so is 'unicorn', but 'a unicorn' is not
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
6411 Critics say definite descriptions can refer, and may not embody both uniqueness and existence claims [Grayling]
10433 Definite descriptions fail to refer in three situations, so they aren't essentially referring [Sainsbury]
5385 The phrase 'a so-and-so' is an 'ambiguous' description'; 'the so-and-so' (singular) is a 'definite' description
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
1608 The theory of descriptions eliminates the name of the entity whose existence was presupposed [Quine]
7754 Russell's theory explains non-existents, negative existentials, identity problems, and substitutivity [Lycan]
21529 Russell showed how to define 'the', and thereby reduce the ontology of logic [Lackey]
6333 The theory of definite descriptions reduces the definite article 'the' to the concepts of predicate logic [Horwich]
6412 Russell implies that 'the baby is crying' is only true if the baby is unique [Grayling]
7743 Russell explained descriptions with quantifiers, where Frege treated them as names [McCullogh]
7310 Russell avoids non-existent objects by denying that definite descriptions are proper names [Miller,A]
12006 Denying definite description sentences are subject-predicate in form blocks two big problems [Forbes,G]
4569 Russell says apparent referring expressions are really assertions about properties [Cooper,DE]
11009 Russell's theory must be wrong if it says all statements about non-existents are false [Read]
21549 The theory of descriptions lacks conventions for the scope of quantifiers [Lackey]
12796 Non-count descriptions don't threaten Russell's theory, which is only about singulars [Laycock]
7532 Denoting is crucial in Russell's account of mathematics, for identifying classes [Monk]
11988 Russell's analysis means molecular sentences are ambiguous over the scope of the description [Kaplan]
5. Theory of Logic / G. Quantification / 1. Quantification
14137 'Any' is better than 'all' where infinite classes are concerned
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
6061 Existence is entirely expressed by the existential quantifier [McGinn]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
18273 Logical truths are known by their extreme generality
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17640 Finding the axioms may be the only route to some new results
17629 Which premises are ultimate varies with context
17630 The sources of a proof are the reasons why we believe its conclusion
6109 Some axioms may only become accepted when they lead to obvious conclusions
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
7557 To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts
14149 The Achilles Paradox concerns the one-one correlation of infinite classes
21585 The tortoise won't win, because infinite instants don't compose an infinitely long time
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / d. Richard's paradox
21565 Richard's puzzle uses the notion of 'definition' - but that cannot be defined
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
15895 Russell discovered the paradox suggested by Burali-Forti's work [Lavine]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
13365 Russell's Paradox is a stripped-down version of Cantor's Paradox [Priest,G]
10711 Russell's paradox means we cannot assume that every property is collectivizing [Potter]
6407 The class of classes which lack self-membership leads to a contradiction [Grayling]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
21564 Vicious Circle: what involves ALL must not be one of those ALL
21567 'All judgements made by Epimenedes are true' needs the judgements to be of the same type
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
16475 A 'heterological' predicate can't be predicated of itself; so is 'heterological' heterological? Yes=no!
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10059 In mathematic we are ignorant of both subject-matter and truth
6. Mathematics / A. Nature of Mathematics / 2. Geometry
14151 Pure geometry is deductive, and neutral over what exists
14153 In geometry, empiricists aimed at premisses consistent with experience
14152 In geometry, Kant and idealists aimed at the certainty of the premisses
14154 Geometry throws no light on the nature of actual space
14155 Two points have a line joining them (descriptive), a distance (metrical), and a whole line (projective) [PG]
14442 If straight lines were like ratios they might intersect at a 'gap', and have no point in common
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
14144 Ordinals result from likeness among relations, as cardinals from similarity among classes
18254 Russell's approach had to treat real 5/8 as different from rational 5/8 [Dummett]
14438 New numbers solve problems: negatives for subtraction, fractions for division, complex for equations
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
14128 Some claim priority for the ordinals over cardinals, but there is no logical priority between them
14129 Ordinals presuppose two relations, where cardinals only presuppose one
14132 Properties of numbers don't rely on progressions, so cardinals may be more basic
13510 Could a number just be something which occurs in a progression? [Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
14139 Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic
14141 Ordinals are defined through mathematical induction
14142 Ordinals are types of series of terms in a row, rather than the 'nth' instance
14145 For Cantor ordinals are types of order, not numbers
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
14146 We aren't sure if one cardinal number is always bigger than another
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
14135 Real numbers are a class of rational numbers (and so not really numbers at all)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
14436 A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / j. Complex numbers
14439 A complex number is simply an ordered couple of real numbers
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
14421 Discovering that 1 is a number was difficult
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / b. Quantity
14123 Some quantities can't be measured, and some non-quantities are measurable
14158 Quantity is not part of mathematics, where it is replaced by order
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
14120 Counting explains none of the real problems about the foundations of arithmetic
14424 Numbers are needed for counting, so they need a meaning, and not just formal properties
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
14118 We can define one-to-one without mentioning unity
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
14441 The formal laws of arithmetic are the Commutative, the Associative and the Distributive
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
14119 We do not currently know whether, of two infinite numbers, one must be greater than the other
14133 There are cardinal and ordinal theories of infinity (while continuity is entirely ordinal)
14420 Infinity and continuity used to be philosophy, but are now mathematics
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
7556 A collection is infinite if you can remove some terms without diminishing its number
14134 Infinite numbers are distinguished by disobeying induction, and the part equalling the whole
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
14143 ω names the whole series, or the generating relation of the series of ordinal numbers
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
14138 You can't get a new transfinite cardinal from an old one just by adding finite numbers to it
14140 For every transfinite cardinal there is an infinite collection of transfinite ordinals
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
17627 It seems absurd to prove 2+2=4, where the conclusion is more certain than premises
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
10052 Geometry is united by the intuitive axioms of projective geometry [Musgrave]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
14124 Axiom of Archimedes: a finite multiple of a lesser magnitude can always exceed a greater
14431 The definition of order needs a transitive relation, to leap over infinite intermediate terms
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
7530 Russell tried to replace Peano's Postulates with the simple idea of 'class' [Monk]
18246 Dedekind failed to distinguish the numbers from other progressions [Shapiro]
14422 Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms
14423 '0', 'number' and 'successor' cannot be defined by Peano's axioms
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
14125 Finite numbers, unlike infinite numbers, obey mathematical induction
14147 Denying mathematical induction gave us the transfinite
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
14116 Numbers were once defined on the basis of 1, but neglected infinities and +
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
14117 Numbers are properties of classes
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
14425 A number is something which characterises collections of the same size
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
14434 What matters is the logical interrelation of mathematical terms, not their intrinsic nature
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9977 Ordinals can't be defined just by progression; they have intrinsic qualities
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
14162 Mathematics doesn't care whether its entities exist
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17628 Arithmetic was probably inferred from relationships between physical objects
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
5399 Maths is not known by induction, because further instances are not needed to support it
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
14465 Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men'
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
14103 Pure mathematics is the class of propositions of the form 'p implies q'
13414 For Russell, numbers are sets of equivalent sets [Benacerraf]
6108 Maths can be deduced from logical axioms and the logic of relations
6423 We tried to define all of pure maths using logical premisses and concepts
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
21555 For 'x is a u' to be meaningful, u must be one range of individuals (or 'type') higher than x
18003 In 'x is a u', x and u must be of different types, so 'x is an x' is generally meaningless [Magidor]
10418 Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer]
10047 Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Musgrave]
23478 Type theory means that features shared by different levels cannot be expressed [Morris,M]
23457 Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M]
21556 Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Lackey]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
21718 Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Linsky,B]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
21570 Numbers are just verbal conveniences, which can be analysed away
6425 Formalism can't apply numbers to reality, so it is an evasion
6424 Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
6104 Numbers are classes of classes, and hence fictions of fictions
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
6426 Intuitionism says propositions are only true or false if there is a method of showing it
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
21559 We need rules for deciding which norms are predicative (unless none of them are)
21558 'Predicative' norms are those which define a class
18126 A set does not exist unless at least one of its specifications is predicative [Bostock]
18128 Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Bostock]
18124 Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Bostock]
21568 A one-variable function is only 'predicative' if it is one order above its arguments
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / e. Psychologism
14449 There is always something psychological about inference
7. Existence / A. Nature of Existence / 1. Nature of Existence
14463 Existence can only be asserted of something described, not of something named
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
11010 Being is what belongs to every possible object of thought
7. Existence / A. Nature of Existence / 3. Being / b. Being and existence
14161 Many things have being (as topics of propositions), but may not have actual existence
7. Existence / A. Nature of Existence / 6. Criterion for Existence
14173 What exists has causal relations, but non-existent things may also have them
7. Existence / B. Change in Existence / 4. Events / b. Events as primitive
6402 In 1927, Russell analysed force and matter in terms of events [Grayling]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
16045 General facts supervene on particular facts, but cannot be inferred from them [Bennett,K]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
21684 Atomic facts may be inferrable from others, but never from non-atomic facts
21708 Russell's new logical atomist was of particulars, universals and facts (not platonic propositions) [Linsky,B]
19051 Russell's atomic facts are actually compounds, and his true logical atoms are sense data [Quine]
6089 Logical atomism aims at logical atoms as the last residue of analysis
6100 Once you have enumerated all the atomic facts, there is a further fact that those are all the facts
6105 Logical atoms aims to get down to ultimate simples, with their own unique reality
6113 To mean facts we assert them; to mean simples we name them
6114 'Simples' are not experienced, but are inferred at the limits of analysis
21722 Better to construct from what is known, than to infer what is unknown
10968 Russell gave up logical atomism because of negative, general and belief propositions [Read]
21681 Given all true atomic propositions, in theory every other truth can thereby be deduced
6419 In 1899-1900 I adopted the philosophy of logical atomism
6438 Complex things can be known, but not simple things
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
6472 Continuity is a sufficient criterion for the identity of a rock, but not for part of a smooth fluid
7. Existence / D. Theories of Reality / 1. Realism
21538 If two people perceive the same object, the object of perception can't be in the mind
7. Existence / D. Theories of Reality / 2. Reality
5370 Space is neutral between touch and sight, so it cannot really be either of them
7. Existence / D. Theories of Reality / 3. Anti-realism
7545 Visible things are physical and external, but only exist when viewed
7. Existence / D. Theories of Reality / 6. Fictionalism
14429 Classes are logical fictions, made from defining characteristics
7. Existence / D. Theories of Reality / 7. Facts / a. Facts
21709 You can't name all the facts, so they are not real, but are what propositions assert
6111 As propositions can be put in subject-predicate form, we wrongly infer that facts have substance-quality form
6434 Facts are everything, except simples; they are either relations or qualities
7. Existence / D. Theories of Reality / 7. Facts / b. Types of fact
18376 Russell asserts atomic, existential, negative and general facts [Armstrong]
7. Existence / D. Theories of Reality / 7. Facts / c. Facts and truths
5418 In a world of mere matter there might be 'facts', but no truths
7. Existence / D. Theories of Reality / 7. Facts / d. Negative facts
22315 There can't be a negative of a complex, which is negated by its non-existence [Potter]
22316 A positive and negative fact have the same constituents; their difference is primitive
7. Existence / D. Theories of Reality / 8. States of Affairs
5465 Modern trope theory tries, like logical atomism, to reduce things to elementary states [Ellis]
7. Existence / D. Theories of Reality / 9. Vagueness / d. Vagueness as linguistic
9051 Since natural language is not precise it cannot be in the province of logic [Keefe/Smith]
9054 Vagueness is only a characteristic of representations, such as language
7. Existence / D. Theories of Reality / 10. Ontological Commitment / a. Ontological commitment
6060 'Existence' means that a propositional function is sometimes true
7. Existence / D. Theories of Reality / 10. Ontological Commitment / e. Ontological commitment problems
18775 Russell showed that descriptions may not have ontological commitment [Linsky,B]
7. Existence / E. Categories / 3. Proposed Categories
14163 Four classes of terms: instants, points, terms at instants only, and terms at instants and points
7533 The Theory of Description dropped classes and numbers, leaving propositions, individuals and universals [Monk]
8. Modes of Existence / A. Relations / 1. Nature of Relations
21341 Philosophers of logic and maths insisted that a vocabulary of relations was essential [Heil]
21534 The only thing we can say about relations is that they relate
21540 Relational propositions seem to be 'about' their terms, rather than about the relation
21562 There is no complexity without relations, so no propositions, and no truth
5371 Because we depend on correspondence, we know relations better than we know the items that relate
5407 That Edinburgh is north of London is a non-mental fact, so relations are independent universals
21576 With asymmetrical relations (before/after) the reduction to properties is impossible
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
10586 'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness
14432 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a
14430 If a relation is symmetrical and transitive, it has to be reflexive
8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation
10585 Symmetrical and transitive relations are formally like equality
8. Modes of Existence / B. Properties / 11. Properties as Sets
9127 Russell refuted Frege's principle that there is a set for each property [Sorensen]
21575 When we attribute a common quality to a group, we can forget the quality and just talk of the group
8. Modes of Existence / B. Properties / 12. Denial of Properties
6063 Russell can't attribute existence to properties [McGinn]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
14327 Trope theorists cannot explain how tropes resemble each other [Mumford]
8. Modes of Existence / D. Universals / 1. Universals
5383 Every complete sentence must contain at least one word (a verb) which stands for a universal
4428 Propositions express relations (prepositions and verbs) as well as properties (nouns and adjectives)
5406 Confused views of reality result from thinking that only nouns and adjectives represent universals
4479 All universals are like the relation "is north of", in having no physical location at all [Loux]
8. Modes of Existence / D. Universals / 2. Need for Universals
21710 We know a universal in 'yellow differs from blue' or 'yellow resembles blue less than green does'
4427 Every sentence contains at least one word denoting a universal, so we need universals to know truth
4030 Russell claims that universals are needed to explain a priori knowledge (as their relations) [Mellor/Oliver]
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
5409 Normal existence is in time, so we must say that universals 'subsist'
8. Modes of Existence / D. Universals / 5. Universals as Concepts
5408 If we identify whiteness with a thought, we can never think of it twice; whiteness is the object of a thought
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
4441 'Resemblance Nominalism' won't work, because the theory treats resemblance itself as a universal
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
6440 Universals can't just be words, because words themselves are universals
8. Modes of Existence / E. Nominalism / 4. Concept Nominalism
4429 If we consider whiteness to be merely a mental 'idea', we rob it of its universality
9. Objects / A. Existence of Objects / 1. Physical Objects
6473 Physical things are series of appearances whose matter obeys physical laws
14732 A perceived physical object is events grouped around a centre
9. Objects / A. Existence of Objects / 3. Objects in Thought
7781 I call an object of thought a 'term'. This is a wide concept implying unity and existence.
21536 When I perceive a melody, I do not perceive the notes as existing
9. Objects / A. Existence of Objects / 4. Impossible objects
21531 Common sense agrees with Meinong (rather than Russell) that 'Pegasus is a flying horse' is true [Lackey]
18777 If the King of France is not bald, and not not-bald, this violates excluded middle [Linsky,B]
21545 I prefer to deny round squares, and deal with the difficulties by the theory of denoting
21547 On Meinong's principles 'the existent round square' has to exist
9. Objects / A. Existence of Objects / 5. Simples
14166 Unities are only in propositions or concepts, and nothing that exists has unity
9. Objects / A. Existence of Objects / 5. Individuation / c. Individuation by location
21535 Objects only exist if they 'occupy' space and time
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
14164 The only unities are simples, or wholes composed of parts
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
14112 A set has some sort of unity, but not enough to be a 'whole'
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
6465 We need not deny substance, but there seems no reason to assert it
6471 The assumption by physicists of permanent substance is not metaphysically legitimate
14733 An object produces the same percepts with or without a substance, so that is irrelevant to science
9. Objects / D. Essence of Objects / 3. Individual Essences
14435 The essence of individuality is beyond description, and hence irrelevant to science
9. Objects / D. Essence of Objects / 15. Against Essentialism
14170 Change is obscured by substance, a thing's nature, subject-predicate form, and by essences
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
14107 Terms are identical if they belong to all the same classes
11849 It at least makes sense to say two objects have all their properties in common [Wittgenstein]
10. Modality / A. Necessity / 2. Nature of Necessity
8375 'Necessary' is a predicate of a propositional function, saying it is true for all values of its argument
6099 Modal terms are properties of propositional functions, not of propositions
10. Modality / A. Necessity / 6. Logical Necessity
16490 Some facts about experience feel like logical necessities
10. Modality / B. Possibility / 1. Possibility
22308 Only the actual exists, so possibilities always reduce to actuality after full analysis
10. Modality / B. Possibility / 5. Contingency
21533 Contingency arises from tensed verbs changing the propositions to which they refer
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
12197 Inferring q from p only needs p to be true, and 'not-p or q' to be true
14450 All forms of implication are expressible as truth-functions
10. Modality / B. Possibility / 9. Counterfactuals
22303 It makes no sense to say that a true proposition could have been false
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
5400 In any possible world we feel that two and two would be four
14460 If something is true in all possible worlds then it is logically necessary
11. Knowledge Aims / A. Knowledge / 1. Knowledge
5431 Knowledge cannot be precisely defined, as it merges into 'probable opinion'
16482 All our knowledge (if verbal) is general, because all sentences contain general words
6430 In epistemology we should emphasis the continuity between animal and human minds
11. Knowledge Aims / A. Knowledge / 4. Belief / b. Elements of beliefs
5426 Belief relates a mind to several things other than itself
5780 The three questions about belief are its contents, its success, and its character
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
5366 We have an 'instinctive' belief in the external world, prior to all reflection
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
17637 The most obvious beliefs are not infallible, as other obvious beliefs may conflict
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
5359 Descartes showed that subjective things are the most certain
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / a. Naïve realism
4758 Naïve realism leads to physics, but physics then shows that naïve realism is false
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
21537 I assume we perceive the actual objects, and not their 'presentations'
5377 'Acquaintance' is direct awareness, without inferences or judgements
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / c. Representative realism
6510 Russell (1912) said phenomena only resemble reality in abstract structure [Robinson,H]
5372 There is no reason to think that objects have colours
21580 Science condemns sense-data and accepts matter, but a logical construction must link them
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
6466 Where possible, logical constructions are to be substituted for inferred entities
6418 Russell rejected phenomenalism because it couldn't account for causal relations [Grayling]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
5373 'Idealism' says that everything which exists is in some sense mental
11. Knowledge Aims / C. Knowing Reality / 4. Solipsism
5362 It is not illogical to think that only myself and my mental events exist
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
7554 Self-evidence is often a mere will-o'-the-wisp
5412 Some propositions are self-evident, but their implications may also be self-evident
5413 Particular instances are more clearly self-evident than any general principles
5415 As shown by memory, self-evidence comes in degrees
5416 If self-evidence has degrees, we should accept the more self-evident as correct
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
5397 The rationalists were right, because we know logical principles without experience
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
4430 All a priori knowledge deals with the relations of universals
5411 We can know some general propositions by universals, when no instance can be given
12. Knowledge Sources / B. Perception / 3. Representation
6514 Russell's representationalism says primary qualities only show the structure of reality [Robinson,H]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
6415 After 1912, Russell said sense-data are last in analysis, not first in experience [Grayling]
5358 'Sense-data' are what are immediately known in sensation, such as colours or roughnesses
6417 In 1921 Russell abandoned sense-data, and the gap between sensation and object [Grayling]
6474 Seeing is not in itself knowledge, but is separate from what is seen, such as a patch of colour
12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data
6483 Russell held that we are aware of states of our own brain [Robinson,H]
8244 Sense-data are qualities devoid of subjectivity, which are the basis of science [Deleuze/Guattari]
6467 No sensibile is ever a datum to two people at once
6462 Sense-data are not mental, but are part of the subject-matter of physics
6464 Sense-data are usually objects within the body, but are not part of the subject
6463 Sense-data are objects, and do not contain the subject as part, the way beliefs do
7549 If my body literally lost its mind, the object seen when I see a flash would still exist
7553 Sense-data are purely physical
12. Knowledge Sources / B. Perception / 4. Sense Data / c. Unperceived sense-data
6459 We do not know whether sense-data exist as objects when they are not data
6460 'Sensibilia' are identical to sense-data, without actually being data for any mind
6461 Ungiven sense-data can no more exist than unmarried husbands
21583 When sense-data change, there must be indistinguishable sense-data in the process
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
8854 My 'acquaintance' with sense-data is nothing like my knowing New York [Williams,M]
6458 Individuating sense-data is difficult, because they divide when closely attended to
6469 Sense-data may be subjective, if closing our eyes can change them
6476 We cannot assume that the subject actually exists, so we cannot distinguish sensations from sense-data
12. Knowledge Sources / B. Perception / 5. Interpretation
6098 Perception goes straight to the fact, and not through the proposition
12. Knowledge Sources / C. Rationalism / 1. Rationalism
21577 Empirical truths are particular, so general truths need an a priori input of generality
12. Knowledge Sources / D. Empiricism / 1. Empiricism
7290 If Russell rejects innate ideas and direct a priori knowledge, he is left with a tabula rasa [Thompson]
5357 It is natural to begin from experience, and presumably that is the basis of knowledge
5389 Knowledge by descriptions enables us to transcend private experience
5382 We are acquainted with outer and inner sensation, memory, Self, and universals [PG]
16476 For simple words, a single experience can show that they are true
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
6441 Pragmatism judges by effects, but I judge truth by causes
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
21532 Full empiricism is not tenable, but empirical investigation is always essential
5376 I can know the existence of something with which nobody is acquainted
16485 Perception can't prove universal generalisations, so abandon them, or abandon empiricism?
16488 It is hard to explain how a sentence like 'it is not raining' can be found true by observation
6431 Empiricists seem unclear what they mean by 'experience'
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
5414 Images are not memory, because they are present, and memories are of the past
2792 It is possible the world came into existence five minutes ago, complete with false memories
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem
5430 A true belief is not knowledge if it is reached by bad reasoning
5429 True belief is not knowledge when it is deduced from false belief
6444 True belief about the time is not knowledge if I luckily observe a stopped clock at the right moment
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
5378 All knowledge (of things and of truths) rests on the foundations of acquaintance
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
17639 Believing a whole science is more than believing each of its propositions
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
21579 Objects are treated as real when they connect with other experiences in a normal way
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
22326 Knowledge needs more than a sensitive response; the response must also be appropriate
13. Knowledge Criteria / D. Scepticism / 5. Dream Scepticism
5365 Dreams can be explained fairly scientifically if we assume a physical world
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
21578 Global scepticism is irrefutable, but can't replace our other beliefs, and just makes us hesitate
14. Science / B. Scientific Theories / 1. Scientific Theory
14433 Mathematically expressed propositions are true of the world, but how to interpret them?
14. Science / B. Scientific Theories / 2. Aim of Science
5391 Science aims to find uniformities to which (within the limits of experience) there are no exceptions
14. Science / C. Induction / 2. Aims of Induction
17631 Induction is inferring premises from consequences
14. Science / C. Induction / 3. Limits of Induction
5394 We can't prove induction from experience without begging the question
5390 Chickens are not very good at induction, and are surprised when their feeder wrings their neck
5392 It doesn't follow that because the future has always resembled the past, that it always will
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
5363 If the cat reappears in a new position, presumably it has passed through the intermediate positions
5367 Belief in real objects makes our account of experience simpler and more systematic
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
5364 It is hard not to believe that speaking humans are expressing thoughts, just as we do ourselves
6416 Other minds seem to exist, because their testimony supports realism about the world [Grayling]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / d. Other minds by analogy
5379 If we didn't know our own minds by introspection, we couldn't know that other people have minds
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
21569 It is good to generalise truths as much as possible
15. Nature of Minds / C. Capacities of Minds / 7. Seeing Resemblance
5410 I learn the universal 'resemblance' by seeing two shades of green, and their contrast with red
16. Persons / B. Nature of the Self / 6. Self as Higher Awareness
5381 In seeing the sun, we are acquainted with our self, but not as a permanent person
16. Persons / C. Self-Awareness / 3. Limits of Introspection
5380 In perceiving the sun, I am aware of sun sense-data, and of the perceiver of the data
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
7546 A man is a succession of momentary men, bound by continuity and causation
16. Persons / E. Rejecting the Self / 4. Denial of the Self
6475 In perception, the self is just a logical fiction demanded by grammar
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
5778 If we object to all data which is 'introspective' we will cease to believe in toothaches
6433 Behaviourists struggle to explain memory and imagination, because they won't admit images
17. Mind and Body / D. Property Dualism / 3. Property Dualism
5779 There are distinct sets of psychological and physical causal laws
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
7550 We could probably, in principle, infer minds from brains, and brains from minds
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
5369 It is rational to believe in reality, despite the lack of demonstrative reasons for it
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
5375 Knowledge of truths applies to judgements; knowledge by acquaintance applies to sensations and things
21711 Russell's 'multiple relations' theory says beliefs attach to ingredients, not to propositions [Linsky,B]
5427 Truth is when a mental state corresponds to a complex unity of external constituents
18. Thought / A. Modes of Thought / 6. Judgement / b. Error
21542 Do incorrect judgements have non-existent, or mental, or external objects?
22306 To explain false belief we should take belief as relating to a proposition's parts, not to the whole thing
5425 In order to explain falsehood, a belief must involve several terms, not two
6097 The theory of error seems to need the existence of the non-existent
6443 Surprise is a criterion of error
18. Thought / C. Content / 1. Content
21541 The complexity of the content correlates with the complexity of the object
18. Thought / C. Content / 6. Broad Content
7531 We don't assert private thoughts; the objects are part of what we assert
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
5384 A universal of which we are aware is called a 'concept'
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10583 Abstraction principles identify a common property, which is some third term with the right relation
10582 The principle of Abstraction says a symmetrical, transitive relation analyses into an identity
10584 A certain type of property occurs if and only if there is an equivalence relation
19. Language / A. Nature of Meaning / 1. Meaning
6112 Meaning takes many different forms, depending on different logical types
19. Language / A. Nature of Meaning / 5. Meaning as Verification
13468 Russell started philosophy of language, by declaring some plausible sentences to be meaningless [Hart,WD]
5388 Every understood proposition is composed of constituents with which we are acquainted
6427 Unverifiable propositions about the remote past are still either true or false
19. Language / B. Reference / 1. Reference theories
4567 Russell argued with great plausibility that we rarely, if ever, refer with our words [Cooper,DE]
19. Language / B. Reference / 2. Denoting
16385 A definite description 'denotes' an entity if it fits the description uniquely [Recanati]
5810 Referring is not denoting, and Russell ignores the referential use of definite descriptions [Donnellan]
5774 Denoting phrases are meaningless, but guarantee meaning for propositions
5775 In 'Scott is the author of Waverley', denotation is identical, but meaning is different
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
16987 By eliminating descriptions from primitive notation, Russell seems to reject 'sense' [Kripke]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
5387 It is pure chance which descriptions in a person's mind make a name apply to an individual
19. Language / B. Reference / 5. Speaker's Reference
4570 Russell assumes that expressions refer, but actually speakers refer by using expressions [Cooper,DE]
19. Language / C. Assigning Meanings / 3. Predicates
9022 Russell uses 'propositional function' to refer to both predicates and to attributes [Quine]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
16349 Russell rejected sense/reference, because it made direct acquaintance with things impossible [Recanati]
7313 'Sense' is superfluous (rather than incoherent) [Miller,A]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
7767 The theory of definite descriptions aims at finding correct truth conditions [Lycan]
19. Language / C. Assigning Meanings / 9. Indexical Semantics
21550 Science reduces indexicals to a minimum, but they can never be eliminated from empirical matters
19. Language / D. Propositions / 1. Propositions
14110 Proposition contain entities indicated by words, rather than the words themselves
21543 If p is false, then believing not-p is knowing a truth, so negative propositions must exist
6091 Propositions don't name facts, because each fact corresponds to a proposition and its negation
5781 Our important beliefs all, if put into words, take the form of propositions
5782 A proposition expressed in words is a 'word-proposition', and one of images an 'image-proposition'
5776 A proposition is what we believe when we believe truly or falsely
14451 Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts
19. Language / D. Propositions / 3. Concrete Propositions
19164 If propositions are facts, then false and true propositions are indistinguishable [Davidson]
21726 In graspable propositions the constituents are real entities of acquaintance
21702 In 1918 still believes in nonlinguistic analogues of sentences, but he now calls them 'facts' [Quine]
19. Language / D. Propositions / 4. Mental Propositions
22307 Propositions don't name facts, because two opposed propositions can match one fact
6435 You can believe the meaning of a sentence without thinking of the words
19. Language / D. Propositions / 5. Unity of Propositions
19157 Russell said the proposition must explain its own unity - or else objective truth is impossible [Davidson]
14111 A proposition is a unity, and analysis destroys it
19. Language / D. Propositions / 6. Propositions Critique
7534 In 1906, Russell decided that propositions did not, after all, exist [Monk]
21724 The main aim of the multiple relations theory of judgement was to dispense with propositions [Linsky,B]
6094 An inventory of the world does not need to include propositions
6096 I no longer believe in propositions, especially concerning falsehoods
21712 I know longer believe in shadowy things like 'that today is Wednesday' when it is actually Tuesday
19. Language / F. Communication / 3. Denial
16491 If we define 'this is not blue' as disbelief in 'this is blue', we eliminate 'not' as an ingredient of facts
19. Language / F. Communication / 4. Private Language
6093 The names in a logically perfect language would be private, and could not be shared
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
16478 A mother cat is paralysed if equidistant between two needy kittens
22. Metaethics / A. Value / 2. Values / f. Love
21746 Unlike hate, all desires can be satisfied by love
22. Metaethics / B. The Good / 1. Goodness / b. Types of good
21747 Goodness is a combination of love and knowledge
22. Metaethics / B. The Good / 2. Happiness / d. Routes to happiness
21743 In wartime, happiness is hating the enemy, because it gives the war a purpose
20180 A happy and joyous life must largely be a quiet life
22. Metaethics / C. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
21740 I doubt whether ethics is part of philosophy
22. Metaethics / C. Ethics Foundations / 2. Source of Ethics / e. Human nature
23154 We divide mankind into friend and foe, and cooperate with one and compete with the other
22. Metaethics / C. Ethics Foundations / 2. Source of Ethics / h. Expressivism
21741 'You ought to do p' primarily has emotional content, expressing approval
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
21742 Originally virtue was obedience, to gods, government, or custom
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
21517 Individuals need creativity, reverence for others, and self-respect
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
21745 Act so as to produce harmonious rather than discordant desires
23. Ethics / E. Utilitarianism / 2. Ideal of Pleasure
5398 Judgements of usefulness depend on judgements of value
23. Ethics / F. Existentialism / 4. Boredom
20177 Boredom always involves not being fully occupied
20178 Life is now more interesting, but boredom is more frightening
20179 Happiness involves enduring boredom, and the young should be taught this
20176 Boredom is an increasingly strong motivating power
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
23152 Increasingly war expands communities, and unifies them through fear
23153 Gradually loyalty to a creed increased, which could even outweigh nationality
23155 In early societies the leaders needed cohesion, but the rest just had to obey
24. Political Theory / A. Basis of a State / 2. Population / b. State population
23156 The economic and political advantages of great size seem to have no upper limit
24. Political Theory / B. Nature of a State / 1. Purpose of a State
23157 Government has a negative purpose, to prevent trouble, and a positive aim of realising our desires
24. Political Theory / C. Ruling a State / 2. Leaders / b. Monarchy
23151 A monarch is known to everyone in the group, and can thus unite large groups
24. Political Theory / C. Ruling a State / 4. Changing the State / b. Devolution
21522 Democracy is inadequate without a great deal of devolution
21523 We would not want UK affairs to be settled by a world parliament
23167 Power should be with smaller bodies, as long as it doesn't restrict central powers
24. Political Theory / D. Ideologies / 2. Anarchism
21521 Anarchy does not maximise liberty
23163 In an anarchy universities, research, books, and even seaside holidays, would be impossible
23168 A state is essential, to control greedy or predatory impulses
24. Political Theory / D. Ideologies / 5. Democracy / c. Direct democracy
21528 Groups should be autonomous, with a neutral authority as arbitrator
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
21526 Unfortunately ordinary voters can't detect insincerity
21527 On every new question the majority is always wrong at first
23166 In democracy we are more aware of being governed than of our tiny share in government
23169 Democratic institutions become impossible in a fanatical democracy
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
23170 Liberal opinions are tentative rather than dogmatic, and are always responsive to new evidence
23171 Empiricism is ethically superior, because dogmatism favours persecution and hatred
23172 Empiricist Liberalism is the only view for someone who favours scientific evidence and happiness
24. Political Theory / D. Ideologies / 8. Socialism
21525 When the state is the only employer, there is no refuge from the prejudices of other people
23160 Being a slave of society is hardly better than being a slave of a despot
23162 Managers are just as remote from workers under nationalisation as under capitalism
23165 Socialists say economic justice needs some state control of industries, and of foreign trade
24. Political Theory / D. Ideologies / 11. Capitalism
21518 Men unite in pursuit of material things, and idealise greed as part of group loyalty
25. Social Practice / A. Freedoms / 1. Slavery
23158 Slavery began the divorce between the work and the purposes of the worker
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
21519 We need security and liberty, and then encouragement of creativity
25. Social Practice / B. Equalities / 1. Grounds of equality
23161 Slaves can be just as equal as free people
25. Social Practice / B. Equalities / 4. Economic equality
23159 Scarce goods may be denied entirely, to avoid their unequal distribution
25. Social Practice / C. Rights / 4. Property rights
21524 The right to own land gives a legal right to a permanent income
25. Social Practice / D. Justice / 1. Basis of justice
23164 Modern justice is seen as equality, apart from modest extra rewards for exceptional desert
25. Social Practice / D. Justice / 3. Punishment / d. Reform of offenders
21744 Legally curbing people's desires is inferior to improving their desires
26. Natural Theory / C. Causation / 7. Eliminating causation
14172 Moments and points seem to imply other moments and points, but don't cause them
14175 We can drop 'cause', and just make inferences between facts
4396 The law of causality is a source of confusion, and should be dropped from philosophy
8376 If causes are contiguous with events, only the last bit is relevant, or the event's timing is baffling
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
8380 Striking a match causes its igniting, even if it sometimes doesn't work
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
17633 The law of gravity has many consequences beyond its grounding observations
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
8379 In causal laws, 'events' must recur, so they have to be universals, not particulars
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
8381 The constancy of scientific laws rests on differential equations, not on cause and effect
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
14174 The laws of motion and gravitation are just parts of the definition of a kind of matter
5393 We can't know that our laws are exceptionless, or even that there are any laws
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
14168 Occupying a place and change are prior to motion, so motion is just occupying places at continuous times
4786 Russell's 'at-at' theory says motion is to be at the intervening points at the intervening instants [Psillos]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
14171 Force is supposed to cause acceleration, but acceleration is a mathematical fiction
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
6470 Matter is the limit of appearances as distance from the object diminishes
7551 Matter is a logical construction
7547 Matter requires a division into time-corpuscles as well as space-corpuscles
21706 At first matter is basic and known by sense-data; later Russell says matter is constructed [Linsky,B]
27. Natural Reality / C. Space / 2. Space
6468 There is 'private space', and there is also the 'space of perspectives'
7552 Six dimensions are needed for a particular, three within its own space, and three to locate that space
27. Natural Reality / C. Space / 3. Points in Space
14160 Space is the extension of 'point', and aggregates of points seem necessary for geometry
27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time
21581 We never experience times, but only succession of events
27. Natural Reality / D. Time / 3. Parts of Time / b. Instants
14156 Mathematicians don't distinguish between instants of time and points on a line
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
22891 We could be aware of time if senses briefly vibrated, extending their experience of movement [Bardon]
27. Natural Reality / E. Cosmology / 1. Cosmology
14169 The 'universe' can mean what exists now, what always has or will exist
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
2609 If God's decrees are good, and this is not a mere tautology, then goodness is separate from God's decrees
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
5773 The ontological argument begins with an unproven claim that 'there exists an x..'
6119 You can discuss 'God exists', so 'God' is a description, not a name
29. Religion / D. Religious Issues / 2. Immortality / d. Heaven
21520 That our heaven is a dull place reflects the misery of excessive work in life