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.]

idea number gives full details    |    back to list of philosophers    |     expand these ideas
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Philosophers must get used to absurdities
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy verifies that our hierarchy of instinctive beliefs is harmonious and consistent
Philosophy is logical analysis, followed by synthesis
1. Philosophy / D. Nature of Philosophy / 4. Aims of Philosophy / e. Philosophy as reason
Discoveries in mathematics can challenge philosophy, and offer it a new foundation
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
Metaphysics cannot give knowledge of the universe as a whole
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysics as Science
The business of metaphysics is to describe the world
1. Philosophy / F. Analytic Philosophy / 1. Analysis
All philosophy should begin with an analysis of propositions
The study of grammar is underestimated in philosophy
Analysis gives us nothing but the truth - but never the whole truth
Only by analysing is progress possible in philosophy
Analysis gives new knowledge, without destroying what we already have
1. Philosophy / F. Analytic Philosophy / 4. Ordinary Language
'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity
A logical language would show up the fallacy of inferring reality from ordinary language
1. Philosophy / F. Analytic Philosophy / 5. Against Analysis
Analysis falsifies, if when the parts are broken down they are not equivalent to their sum
1. Philosophy / G. Scientific Philosophy / 3. Scientism
Philosophy should be built on science, to reduce error
Philosophy is similar to science, and has no special source of wisdom
Philosophers usually learn science from each other, not from science
2. Reason / A. Nature of Reason / 6. Coherence
If one proposition is deduced from another, they are more certain together than alone
2. Reason / B. Laws of Thought / 1. Laws of Thought
Three Laws of Thought: identity, contradiction, and excluded middle
The law of contradiction is not a 'law of thought', but a belief about things
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Non-contradiction was learned from instances, and then found to be indubitable
2. Reason / B. Laws of Thought / 6. Ockham's Razor
Reducing entities and premisses makes error less likely
2. Reason / D. Definition / 3. Types of Definition
A definition by 'extension' enumerates items, and one by 'intension' gives a defining property
2. Reason / D. Definition / 12. Against Definition
Definition by analysis into constituents is useless, because it neglects the whole
In mathematics definitions are superfluous, as they name classes, and it all reduces to primitives
2. Reason / F. Fallacies / 2. Infinite Regress
Infinite regresses have propositions made of propositions etc, with the key term reappearing
2. Reason / F. Fallacies / 8. Category Mistake / a. Category mistakes
As well as a truth value, propositions have a range of significance for their variables
The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false
The theory of types makes 'Socrates and killing are two' illegitimate
3. Truth / A. Truth Problems / 1. Truth
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
What is true or false is not mental, and is best called 'propositions'
Truth and falsehood are properties of beliefs and statements
In its primary and formal sense, 'true' applies to propositions, not beliefs
Truth belongs to beliefs, not to propositions and sentences
3. Truth / A. Truth Problems / 7. Falsehood
A good theory of truth must make falsehood possible
Asserting not-p is saying p is false
3. Truth / B. Truthmakers / 1. For Truthmakers
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
Facts make propositions true or false, and are expressed by whole sentences
3. Truth / B. Truthmakers / 8. Making General Truths
Not only atomic truths, but also general and negative truths, have truth-makers
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
For Russell, both propositions and facts are arrangements of objects, so obviously they correspond
Truth as congruence may work for complex beliefs, but not for simple beliefs about existence
Truth is when a mental state corresponds to a complex unity of external constituents
Beliefs are true if they have corresponding facts, and false if they don't
Propositions of existence, generalities, disjunctions and hypotheticals make correspondence tricky
3. Truth / D. Coherence Truth / 1. Coherence Truth
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
If we suspend the law of contradiction, nothing will appear to be incoherent
Coherence is not the meaning of truth, but an important test for truth
More than one coherent body of beliefs seems possible
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
An argument 'satisfies' a function φx if φa is true
3. Truth / H. Deflationary Truth / 1. Redundant Truth
"The death of Caesar is true" is not the same proposition as "Caesar died"
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
The mortality of Socrates is more certain from induction than it is from deduction
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 ∃
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
The null class is a fiction
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Set
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
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
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
We may assume that there are infinite collections, as there is no logical reason against them
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
Choice is equivalent to the proposition that every class is well-ordered
Choice shows that if any two cardinals are not equal, one must be the greater
We can pick all the right or left boots, but socks need Choice to insure the representative class
The British parliament has one representative selected from each constituency
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
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
Propositions about classes can be reduced to propositions about their defining functions
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Na´ve logical sets
Russell invented the na´ve set theory usually attributed to Cantor
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
Order rests on 'between' and 'separation'
Order depends on transitive asymmetrical relations
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Russell's proposal was that only meaningful predicates have sets as their extensions
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Classes can be reduced to propositional functions
Classes, grouped by a convenient property, are logical constructions
Classes are logical fictions, and are not part of the ultimate furniture of the world
I gradually replaced classes with properties, and they ended as a symbolic convenience
4. Formal Logic / G. Formal Mereology / 1. Mereology
The part-whole relation is ultimate and indefinable
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Subject-predicate logic (and substance-attribute metaphysics) arise from Aryan languages
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
It is logic, not metaphysics, that is fundamental to philosophy
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
The physical world doesn't need logic, but the mental world does
All the propositions of logic are completely general
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
In modern times, logic has become mathematical, and mathematics has become logical
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
Demonstration always relies on the rule that anything implied by a truth is true
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
Implication cannot be defined
It would be circular to use 'if' and 'then' to define material implication
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
The only classes are things, predicates and relations
Logic is concerned with the real world just as truly as zoology
Logic can only assert hypothetical existence
Logic can be known a priori, without study of the actual world
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Geometrical axioms imply the propositions, but the former may not be true
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Questions wouldn't lead anywhere without the law of excluded middle
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
'Elizabeth = Queen of England' is really a predication, not an identity-statement
In a logically perfect language, there will be just one word for every simple object
Romulus does not occur in the proposition 'Romulus did not exist'
Vagueness, and simples being beyond experience, are obstacles to a logical language
Leibniz bases everything on subject/predicate and substance/property propositions
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
There seem to be eight or nine logical constants
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
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
A disjunction expresses indecision
'Or' expresses hesitation, in a dog at a crossroads, or birds risking grabbing crumbs
'Or' expresses a mental state, not something about the world
Disjunction may also arise in practice if there is imperfect memory.
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
Constants are absolutely definite and unambiguous
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
Variables don't stand alone, but exist as parts of propositional functions
The idea of a variable is fundamental
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
You can understand 'author of Waverley', but to understand 'Scott' you must know who it applies to
There are a set of criteria for pinning down a logically proper name
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
Names don't have a sense, but are disguised definite descriptions
Russell says names are not denotations, but definite descriptions in disguise
Russell says a name contributes a complex of properties, rather than an object
Are names descriptions, if the description is unknown, false, not special, or contains names?
Proper names are really descriptions, and can be replaced by a description in a person's mind
Treat description using quantifiers, and treat proper names as descriptions
Russell admitted that even names could also be used as descriptions
Asking 'Did Homer exist?' is employing an abbreviated description
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
The only real proper names are 'this' and 'that'; the rest are really definite descriptions.
The meaning of a logically proper name is its referent, but most names are not logically proper
Logically proper names introduce objects; definite descriptions introduce quantifications
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
"Nobody" is not a singular term, but a quantifier
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
A name has got to name something or it is not a name
Names are meaningless unless there is an object which they designate
5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
The only genuine proper names are 'this' and 'that'
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / a. Descriptions
'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
Critics say definite descriptions can refer, and may not embody both uniqueness and existence claims
Definite descriptions fail to refer in three situations, so they aren't essentially referring
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
Russell's theory must be wrong if it says all statements about non-existents are false
The theory of descriptions eliminates the name of the entity whose existence was presupposed
Russell's theory explains non-existents, negative existentials, identity problems, and substitutivity
Russell implies that 'the baby is crying' is only true if the baby is unique
Russell explained descriptions with quantifiers, where Frege treated them as names
Russell avoids non-existent objects by denying that definite descriptions are proper names
Non-count descriptions don't threaten Russell's theory, which is only about singulars
Denoting is crucial in Russell's account of mathematics, for identifying classes
5. Theory of Logic / G. Quantification / 1. Quantification
'Any' is better than 'all' where infinite classes are concerned
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
Existence is entirely expressed by the existential quantifier
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths are known by their extreme generality
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Some axioms may only become accepted when they lead to obvious conclusions
The sources of a proof are the reasons why we believe its conclusion
Which premises are ultimate varies with context
Finding the axioms may be the only route to some new results
5. Theory of Logic / L. Paradox / 3. Antinomies
Plato's 'Parmenides' is perhaps the best collection of antinomies ever made
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
The Achilles Paradox concerns the one-one correlation of infinite classes
To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
Russell discovered the paradox suggested by Burali-Forti's work
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
The class of classes which lack self-membership leads to a contradiction
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
A 'heterological' predicate can't be predicated of itself; so is 'heterological' heterological? Yes=no!
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
In mathematic we are ignorant of both subject-matter and truth
6. Mathematics / A. Nature of Mathematics / 2. Quantity
Quantity is not part of mathematics, where it is replaced by order
Some quantities can't be measured, and some non-quantities are measurable
6. Mathematics / A. Nature of Mathematics / 3. Numbers / b. Types of number
Russell's approach had to treat real 5/8 as different from rational 5/8
Ordinals result from likeness among relations, as cardinals from similarity among classes
New numbers solve problems: negatives for subtraction, fractions for division, complex for equations
6. Mathematics / A. Nature of Mathematics / 3. Numbers / c. Priority of numbers
Some claim priority for the ordinals over cardinals, but there is no logical priority between them
Ordinals presuppose two relations, where cardinals only presuppose one
Properties of numbers don't rely on progressions, so cardinals may be more basic
Could a number just be something which occurs in a progression?
6. Mathematics / A. Nature of Mathematics / 3. Numbers / e. Ordinal numbers
For Cantor ordinals are types of order, not numbers
Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic
Ordinals are defined through mathematical induction
Dedekind's ordinals are just members of any progression whatever
Ordinals are types of series of terms in a row, rather than than the 'nth' instance
6. Mathematics / A. Nature of Mathematics / 3. Numbers / f. Cardinal numbers
We aren't sure if one cardinal number is always bigger than another
6. Mathematics / A. Nature of Mathematics / 3. Numbers / g. Real numbers
Real numbers are a class of rational numbers (and so not really numbers at all)
6. Mathematics / A. Nature of Mathematics / 3. Numbers / i. Reals from cuts
A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum
Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil
6. Mathematics / A. Nature of Mathematics / 3. Numbers / j. Complex numbers
A complex number is simply an ordered couple of real numbers
6. Mathematics / A. Nature of Mathematics / 3. Numbers / m. One
Discovering that 1 is a number was difficult
6. Mathematics / A. Nature of Mathematics / 3. Numbers / o. Units
We can define one-to-one without mentioning unity
6. Mathematics / A. Nature of Mathematics / 3. Numbers / p. Counting
Counting explains none of the real problems about the foundations of arithmetic
Numbers are needed for counting, so they need a meaning, and not just formal properties
6. Mathematics / A. Nature of Mathematics / 3. Numbers / q. Arithmetic
The formal laws of arithmetic are the Commutative, the Associative and the Distributive
6. Mathematics / A. Nature of Mathematics / 4. The Infinite / a. The Infinite
Zeno achieved the statement of the problems of infinitesimals, infinity and continuity
There are cardinal and ordinal theories of infinity (while continuity is entirely ordinal)
We do not currently know whether, of two infinite numbers, one must be greater than the other
Infinity and continuity used to be philosophy, but are now mathematics
6. Mathematics / A. Nature of Mathematics / 4. The Infinite / b. Mark of the infinite
A collection is infinite if you can remove some terms without diminishing its number
Infinite numbers are distinguished by disobeying induction, and the part equalling the whole
6. Mathematics / A. Nature of Mathematics / 4. The Infinite / h. Ordinal infinity
ω names the whole series, or the generating relation of the series of ordinal numbers
6. Mathematics / A. Nature of Mathematics / 4. The Infinite / i. Cardinal infinity
You can't get a new transfinite cardinal from an old one just by adding finite numbers to it
For every transfinite cardinal there is an infinite collection of transfinite ordinals
6. Mathematics / A. Nature of Mathematics / 5. Geometry
Geometry throws no light on the nature of actual space
Pure geometry is deductive, and neutral over what exists
In geometry, empiricists aimed at premisses consistent with experience
Two points have a line joining them (descriptive), a distance (metrical), and a whole line (projective)
If straight lines were like ratios they might intersect at a 'gap', and have no point in common
In geometry, Kant and idealists aimed at the certainty of the premisses
6. Mathematics / A. Nature of Mathematics / 6. Proof in Mathematics
It seems absurd to prove 2+2=4, where the conclusion is more certain than premises
6. Mathematics / B. Foundations for Mathematics / 2. Axioms for Geometry
Geometry is united by the intuitive axioms of projective geometry
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / a. Axioms for numbers
The definition of order needs a transitive relation, to leap over infinite intermediate terms
Axiom of Archimedes: a finite multiple of a lesser magnitude can always exceed a greater
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / d. Peano arithmetic
'0', 'number' and 'successor' cannot be defined by Peano's axioms
Peano axioms not only support arithmetic, but are also fairly obvious
Russell tried to replace Peano's Postulates with the simple idea of 'class'
Dedekind failed to distinguish the numbers from other progressions
Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / f. Mathematical induction
Denying mathematical induction gave us the transfinite
Finite numbers, unlike infinite numbers, obey mathematical induction
Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / b. Greek arithmetic
Numbers were once defined on the basis of 1, but neglected infinities and +
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / c. Fregean numbers
Numbers are properties of classes
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / d. Hume's Principle
A number is something which characterises collections of the same size
6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / a. Structuralism
What matters is the logical interrelation of mathematical terms, not their intrinsic nature
6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / e. Structuralism critique
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
Mathematics doesn't care whether its entities exist
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Arithmetic was probably inferred from relationships between physical objects
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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
Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men'
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Arithmetic can have even simpler logical premises than the Peano Axioms
Pure mathematics is the class of propositions of the form 'p implies q'
Maths can be deduced from logical axioms and the logic of relations
We tried to define all of pure maths using logical premisses and concepts
For Russell, numbers are sets of equivalent sets
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
In 'x is a u', x and u must be of different types, so 'x is an x' is generally meaningless
Type theory seems an extreme reaction, since self-exemplification is often innocuous
Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess
Formalism can't apply numbers to reality, so it is an evasion
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Numbers are classes of classes, and hence fictions of fictions
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
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
A set does not exist unless at least one of its specifications is predicative
Russell is a conceptualist here, saying some abstracta only exist because definitions create them
Vicious Circle says if it is expressed using the whole collection, it can't be in the collection
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / e. Psychologism
There is always something psychological about inference
7. Existence / A. Nature of Existence / 1. Nature of Existence
Existence can only be asserted of something described, not of something named
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
Being is what belongs to every possible object of thought
7. Existence / A. Nature of Existence / 3. Being / b. Being and existence
Many things have being (as topics of propositions), but may not have actual existence
7. Existence / A. Nature of Existence / 8. Criterion for Existence
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
In 1927, Russell analysed force and matter in terms of events
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
Russell gave up logical atomism because of negative, general and belief propositions
Once you have enumerated all the atomic facts, there is a further fact that those are all the facts
Logical atoms aims to get down to ultimate simples, with their own unique reality
Russell's atomic facts are actually compounds, and his true logical atoms are sense data
Logical atomism aims at logical atoms as the last residue of analysis
To mean facts we assert them; to mean simples we name them
'Simples' are not experienced, but are inferred at the limits of analysis
In 1899-1900 I adopted the philosophy of logical atomism
Complex things can be known, but not simple things
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
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 / 2. Reality
Space is neutral between touch and sight, so it cannot really be either of them
7. Existence / D. Theories of Reality / 3. Anti-realism
Visible things are physical and external, but only exist when viewed
7. Existence / D. Theories of Reality / 6. Fictionalism
Classes are logical fictions, made from defining characteristics
7. Existence / D. Theories of Reality / 7. Facts / a. Facts
As propositions can be put in subject-predicate form, we wrongly infer that facts have substance-quality form
Facts are everything, except simples; they are either relations or qualities
7. Existence / D. Theories of Reality / 7. Facts / b. Types of fact
Russell asserts atomic, existential, negative and general facts
7. Existence / D. Theories of Reality / 7. Facts / c. Facts and truths
In a world of mere matter there might be 'facts', but no truths
7. Existence / D. Theories of Reality / 9. Vagueness / c. Vagueness as semantic
Since natural language is not precise it cannot be in the province of logic
Vagueness is only a characteristic of representations, such as language
7. Existence / D. Theories of Reality / 10. Ontological Commitment / a. Ontological commitment
'Existence' means that a propositional function is sometimes true
7. Existence / E. Categories / 3. Proposed Categories
Four classes of terms: instants, points, terms at instants only, and terms at instants and points
The Theory of Description dropped classes and numbers, leaving propositions, individuals and universals
8. Modes of Existence / A. Relations / 1. Nature of Relations
Because we depend on correspondence, we know relations better than we know the items that relate
That Edinburgh is north of London is a non-mental fact, so relations are independent universals
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
If a relation is symmetrical and transitive, it has to be reflexive
'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness
'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a
8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation
Symmetrical and transitive relations are formally like equality
8. Modes of Existence / B. Properties / 11. Properties as Sets
Russell refuted Frege's principle that there is a set for each property
8. Modes of Existence / B. Properties / 12. Denial of Properties
Russell can't attribute existence to properties
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
Trope theorists cannot explain how tropes resemble each other
8. Modes of Existence / D. Universals / 1. Universals
Every complete sentence must contain at least one word (a verb) which stands for a universal
Propositions express relations (prepositions and verbs) as well as properties (nouns and adjectives)
Confused views of reality result from thinking that only nouns and adjectives represent universals
All universals are like the relation "is north of", in having no physical location at all
8. Modes of Existence / D. Universals / 2. Need for Universals
Russell claims that universals are needed to explain a priori knowledge (as their relations)
Every sentence contains at least one word denoting a universal, so we need universals to know truth
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
Normal existence is in time, so we must say that universals 'subsist'
8. Modes of Existence / D. Universals / 5. Universals as Concepts
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
'Resemblance Nominalism' won't work, because the theory treats resemblance itself as a universal
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
Universals can't just be words, because words themselves are universals
8. Modes of Existence / E. Nominalism / 4. Concept Nominalism
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
Physical things are series of appearances whose matter obeys physical laws
A perceived physical object is events grouped around a centre
9. Objects / A. Existence of Objects / 3. Objects in Thought
I call an object of thought a 'term'. This is a wide concept implying unity and existence.
9. Objects / A. Existence of Objects / 5. Simples
Unities are only in propositions or concepts, and nothing that exists has unity
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
The only unities are simples, or wholes composed of parts
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
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
We need not deny substance, but there seems no reason to assert it
The assumption by physicists of permanent substance is not metaphysically legitimate
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
The essence of individuality is beyond description, and hence irrelevant to science
9. Objects / D. Essence of Objects / 15. Against Essentialism
Change is obscured by substance, a thing's nature, subject-predicate form, and by essences
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
Terms are identical if they belong to all the same classes
10. Modality / A. Necessity / 2. Nature of Necessity
'Necessary' is a predicate of a propositional function, saying it is true for all values of its argument
Modal terms are properties of propositional functions, not of propositions
10. Modality / A. Necessity / 6. Logical Necessity
Some facts about experience feel like logical necessities
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
Inferring q from p only needs p to be true, and 'not-p or q' to be true
All forms of implication are expressible as truth-functions
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
If something is true in all possible worlds then it is logically necessary
In any possible world we feel that two and two would be four
11. Knowledge Aims / A. Knowledge / 1. Knowledge
In epistemology we should emphasis the continuity between animal and human minds
Knowledge of truths applies to judgements; knowledge by acquaintance applies to sensations and things
Knowledge cannot be precisely defined, as it merges into 'probable opinion'
All our knowledge (if verbal) is general, because all sentences contain general words
11. Knowledge Aims / A. Knowledge / 4. Belief / b. Elements of beliefs
Belief relates a mind to several things other than itself
The three questions about belief are its contents, its success, and its character
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
We have an 'instinctive' belief in the external world, prior to all reflection
11. Knowledge Aims / B. Certain Knowledge / 3. Error
In order to explain falsehood, a belief must involve several terms, not two
The theory of error seems to need the existence of the non-existent
Surprise is a criterion of error
11. Knowledge Aims / B. Certain Knowledge / 4. Fallibilism
The most obvious beliefs are not infallible, as other obvious beliefs may conflict
11. Knowledge Aims / B. Certain Knowledge / 5. The Cogito
Descartes showed that subjective things are the most certain
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / a. Na´ve realism
Na´ve realism leads to physics, but physics then shows that na´ve realism is false
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
'Acquaintance' is direct awareness, without inferences or judgements
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / c. Representative realism
There is no reason to think that objects have colours
Russell (1912) said phenomena only resemble reality in abstract structure
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Where possible, logical constructions are to be substituted for inferred entities
Russell rejected phenomenalism because it couldn't account for causal relations
11. Knowledge Aims / C. Knowing Reality / 3. Idealism
'Idealism' says that everything which exists is in some sense mental
11. Knowledge Aims / C. Knowing Reality / 4. Solipsism
It is not illogical to think that only myself and my mental events exist
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Self-evidence is often a mere will-o'-the-wisp
Some propositions are just self-evident, but some proven propositions are also self-evident
Particular instances are more clearly self-evident than any general principles
As shown by memory, self-evidence comes in degrees
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
The rationalists were right, because we know logical principles without experience
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
Kant showed that we have a priori knowledge which is not purely analytic
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
All a priori knowledge deals with the relations of universals
We can know some general propositions by universals, when no instance can be given
12. Knowledge Sources / B. Perception / 3. Representation
Russell's representationalism says primary qualities only show the structure of reality
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
After 1912, Russell said sense-data are last in analysis, not first in experience
'Sense-data' are what are immediately known in sensation, such as colours or roughnesses
In 1921 Russell abandoned sense-data, and the gap between sensation and object
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
Russell held that we are aware of states of our own brain
Sense-data are qualities devoid of subjectivity, which are the basis of science
No sensibile is ever a datum to two people at once
Sense-data are not mental, but are part of the subject-matter of physics
Sense-data are objects, and do not contain the subject as part, the way beliefs do
Sense-data are usually objects within the body, but are not part of the subject
If my body literally lost its mind, the object seen when I see a flash would still exist
Sense-data are purely physical
12. Knowledge Sources / B. Perception / 4. Sense Data / c. Unperceived sense-data
We do not know whether sense-data exist as objects when they are not data
'Sensibilia' are identical to sense-data, without actually being data for any mind
Ungiven sense-data can no more exist than unmarried husbands
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
My 'acquaintance' with sense-data is nothing like my knowing New York
Individuating sense-data is difficult, because they divide when closely attended to
Sense-data may be subjective, if closing our eyes can change them
We cannot assume that the subject actually exists, so we cannot distinguish sensations from sense-data
12. Knowledge Sources / B. Perception / 5. Interpretation
Perception goes straight to the fact, and not through the proposition
12. Knowledge Sources / D. Empiricism / 1. Empiricism
Knowledge by descriptions enables us to transcend private experience
If Russell rejects innate ideas and direct a priori knowledge, he is left with a tabula rasa
It is natural to begin from experience, and presumably that is the basis of knowledge
We are acquainted with outer and inner sensation, memory, Self, and universals
For simple words, a single experience can show that they are true
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
Pragmatism judges by effects, but I judge truth by causes
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
I can know the existence of something with which nobody is acquainted
Perception can't prove universal generalisations, so abandon them, or abandon empiricism?
It is hard to explain how a sentence like 'it is not raining' can be found true be observation
Empiricists seem unclear what they mean by 'experience'
12. Knowledge Sources / E. Direct Knowledge / 3. Memory
Images are not memory, because they are present, and memories are of the past
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
True belief is not knowledge when it is deduced from false belief
A true belief is not knowledge if it is reached by bad reasoning
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
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
Believing a whole science is more than believing each of its propositions
13. Knowledge Criteria / D. Scepticism / 5. Dream Scepticism
Dreams can be explained fairly scientifically if we assume a physical world
14. Science / B. Scientific Theories / 1. Scientific Theory
Mathematically expressed propositions are true of the world, but how to interpret them?
14. Science / B. Scientific Theories / 2. Aim of Science
Science aims to find uniformities to which (within the limits of experience) there are no exceptions
14. Science / C. Induction / 2. Aims of Induction
Induction is inferring premises from consequences
14. Science / C. Induction / 3. Limits of Induction
We can't prove induction from experience without begging the question
Chickens are not very good at induction, and are surprised when their feeder wrings their neck
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
If the cat reappears in a new position, presumably it has passed through the intermediate positions
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
It is hard not to believe that speaking humans are expressing thoughts, just as we do ourselves
Other minds seem to exist, because their testimony supports realism about the world
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / d. Other minds by analogy
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 / 7. Seeing Resemblance
I learn the universal 'resemblance' by seeing two shades of green, and their contrast with red
16. Persons / B. Concept of the Self / 5. Persistence of Self
In seeing the sun, we are acquainted with our self, but not as a permanent person
16. Persons / B. Concept of the Self / 6. Denial of the Self
In perception, the self is just a logical fiction demanded by grammar
16. Persons / C. Self-Awareness / 3. Undetectable Self
In perceiving the sun, I am aware of sun sense-data, and of the perceiver of the data
16. Persons / E. Self as Mind / 2. Psychological Continuity
A man is a succession of momentary men, bound by continuity and causation
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
If we object to all data which is 'introspective' we will cease to believe in toothaches
Behaviourists struggle to explain memory and imagination, because they won't admit images
17. Mind and Body / D. Property Dualism / 3. Property Dualism
There are distinct sets of psychological and physical causal laws
17. Mind and Body / E. Physicalism / 2. Reduction of Mind
We could probably, in principle, infer minds from brains, and brains from minds
18. Thought / A. Modes of Thought / 6. Rationality
It is rational to believe in reality, despite the lack of demonstrative reasons for it
18. Thought / C. Content / 6. Broad Content
We don't assert private thoughts; the objects are part of what we assert
18. Thought / D. Concepts / 1. Concepts / a. Concepts
A universal of which we are aware is called a 'concept'
18. Thought / D. Concepts / 6. Abstract Concepts / g. Abstracta by equivalence
The principle of Abstraction says a symmetrical, transitive relation analyses into an identity
Abstraction principles identify a common property, which is some third term with the right relation
A certain type of property occurs if and only if there is an equivalence relation
19. Language / A. Language / 1. Language
Russell started philosophy of language, by declaring some plausible sentences to be meaningless
19. Language / A. Language / 6. Predicates
Russell uses 'propositional function' to refer to both predicates and to attributes
19. Language / A. Language / 7. Private Language
The names in a logically perfect language would be private, and could not be shared
19. Language / B. Meaning / 1. Meaning
Meaning takes many different forms, depending on different logical types.
19. Language / B. Meaning / 3. Meaning as Verification
Every understood proposition is composed of constituents with which we are acquainted
Unverifiable propositions about the remote past are still either true or false
19. Language / C. Semantics / 2. Fregean Semantics
'Sense' is superfluous (rather than incoherent)
Russell rejected sense/reference, because it made direct acquaintance with things impossible
19. Language / C. Semantics / 4. Truth-Conditions Semantics
The theory of definite descriptions aims at finding correct truth conditions
19. Language / D. Theories of Reference / 2. Denoting
A definite description 'denotes' an entity if it fits the description uniquely
Referring is not denoting, and Russell ignores the referential use of definite descriptions
In 'Scott is the author of Waverley', denotation is identical, but meaning is different
19. Language / D. Theories of Reference / 4. Descriptive Reference / a. Sense and reference
By eliminating descriptions from primitive notation, Russell seems to reject 'sense'
19. Language / D. Theories of Reference / 4. Descriptive Reference / b. Reference by description
It is pure chance which descriptions in a person's mind make a name apply to an individual
19. Language / D. Theories of Reference / 5. Speaker's Reference
Russell assumes that expressions refer, but actually speakers refer by using expressions
19. Language / E. Propositions / 1. Propositions
Denoting phrases are meaningless, but guarantee meaning for propositions
Propositions don't name facts, because each fact corresponds to a proposition and its negation
Our important beliefs all, if put into words, take the form of propositions
A proposition is what we believe when we believe truly or falsely
19. Language / E. Propositions / 2. Nature of Propositions
I take Mont Blanc to be an actual part of any assertion about it
Proposition contain entities indicated by words, rather than the words themselves
A proposition is a unity, and analysis destroys it
Russell said the proposition must explain its own unity - or else objective truth is impossible
Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts
19. Language / E. Propositions / 3. Types of Proposition
A proposition expressed in words is a 'word-proposition', and one of images an 'image-proposition'
19. Language / E. Propositions / 4. Support for Propositions
You can believe the meaning of a sentence without thinking of the words
19. Language / E. Propositions / 5. Propositions Critique
In 1906, Russell decided that propositions did not, after all, exist
An inventory of the world does not need to include propositions
I no longer believe in propositions, especially concerning falsehoods
19. Language / H. Pragmatics / 2. Denial
If we define 'this is not blue' as disbelief in 'this is blue', we eliminate 'not' as an ingredient of facts
20. Action / B. Motives for Action / 3. Acting on Reason / b. Intellectualism
A mother cat is paralysed if equidistant between two needy kittens
22. Metaethics / A. Ethical Ends / 5. Happiness / d. Routes to happiness
A happy and joyous life must largely be a quiet life
23. Ethics / E. Utilitarianism / 2. Ideal of Pleasure
Judgements of usefulness depend on judgements of value
23. Ethics / F. Existentialism / 4. Boredom
Boredom is an increasingly strong motivating power
Life is now more interesting, but boredom is more frightening
Happiness involves enduring boredom, and the young should be taught this
Boredom always involves not being fully occupied
26. Natural Theory / B. Concepts of Nature / 3. Space / a. Space
There is 'private space', and there is also the 'space of perspectives'
Six dimensions are needed for a particular, three within its own space, and three to locate that space
26. Natural Theory / B. Concepts of Nature / 3. Space / b. Points in space
Space is the extension of 'point', and aggregates of points seem necessary for geometry
26. Natural Theory / B. Concepts of Nature / 5. Space-Time
Mathematicians don't distinguish between instants of time and points on a line
26. Natural Theory / C. Causation / 1. Causation / g. Eliminating causation
Moments and points seem to imply other moments and points, but don't cause them
We can drop 'cause', and just make inferences between facts
The law of causality is a source of confusion, and should be dropped from philosophy
If causes are contiguous with events, only the last bit is relevant, or the event's timing is baffling
26. Natural Theory / C. Causation / 3. General Causation / a. Constant conjunction
Striking a match causes its igniting, even if it sometimes doesn't work
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
The law of gravity has many consequences beyond its grounding observations
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
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
The constancy of scientific laws rests on differential equations, not on cause and effect
26. Natural Theory / D. Laws of Nature / 12. Against Laws of Nature
The laws of motion and gravitation are just parts of the definition of a kind of matter
We can't know that our laws are exceptionless, or even that there are any laws
27. Natural Reality / A. Physics / 1. Matter / i. Modern matter
Matter is the limit of appearances as distance from the object diminishes
Matter requires a division into time-corpuscles as well as space-corpuscles
Matter is a logical construction
27. Natural Reality / A. Physics / 2. Movement
Occupying a place and change are prior to motion, so motion is just occupying places at continuous times
Russell's 'at-at' theory says motion is to be at the intervening points at the intervening instants
27. Natural Reality / A. Physics / 3. Force
Force is supposed to cause acceleration, but acceleration is a mathematical fiction.
27. Natural Reality / D. Cosmology / 1. Cosmology
The 'universe' can mean what exists now, what always has or will exist
28. God / A. Divine Nature / 5. Divine Morality / b. Euthyphro question
If God's decrees are good, and this is not a mere tautology, then goodness is separate from God's decrees
28. God / C. Proofs of Reason / 2. Ontological Proof critique
The ontological argument begins with an unproven claim that 'there exists an x..'
You can discuss 'God exists', so 'God' is a description, not a name