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 selfevidence

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. NonContradiction
17632

Noncontradiction 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 notp 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 truthmakers [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
5424

Coherence is not the meaning of truth, but an important test for truth

5422

More than one coherent body of beliefs seems possible

5423

If we suspend the law of contradiction, nothing will appear to be incoherent

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
14447

Infinity says 'for any inductive cardinal, there is a class having that many terms'

14440

We may assume that there are infinite collections, as there is no logical reason against them

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 wellordered

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 partwhole relation is ultimate and indefinable

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
6110

Subjectpredicate logic (and substanceattribute 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. FirstOrder 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
14106

Implication cannot be defined

14108

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
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

14464

Logic can be known a priori, without study of the actual world

10057

Logic can only assert hypothetical existence

5. Theory of Logic / C. Ontology of Logic / 3. IfThenism
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 notp

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 identitystatement [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 truthvalue, 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

16481

'Or' expresses a mental state, not something about the world

16487

Maybe the 'or' used to describe mental states is not the 'or' of logic

16480

A disjunction expresses indecision

16483

Disjunction may also arise in practice if there is imperfect memory.

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]

14457

Names are really descriptions, except for a few words like 'this' and 'that'

14458

Asking 'Did Homer exist?' is employing an abbreviated description

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
2612

Russell rewrote singular term names as predicates [Ayer]

7757

"Nobody" is not a singular term, but a quantifier [Lycan]

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 soandso' is an 'ambiguous' description'; 'the soandso' (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 nonexistents, 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 nonexistent objects by denying that definite descriptions are proper names [Miller,A]

12006

Denying definite description sentences are subjectpredicate 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 nonexistents are false [Read]

21549

The theory of descriptions lacks conventions for the scope of quantifiers [Lackey]

12796

Noncount 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
17629

Which premises are ultimate varies with context

17630

The sources of a proof are the reasons why we believe its conclusion

17640

Finding the axioms may be the only route to some new results

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 oneone 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. BuraliForti's paradox
15895

Russell discovered the paradox suggested by BuraliForti's work [Lavine]

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
13365

Russell's Paradox is a strippeddown 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 selfmembership 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 subjectmatter and truth

6. Mathematics / A. Nature of Mathematics / 2. Geometry
14152

In geometry, Kant and idealists aimed at the certainty of the premisses

14154

Geometry throws no light on the nature of actual space

14151

Pure geometry is deductive, and neutral over what exists

14153

In geometry, empiricists aimed at premisses consistent with experience

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
18254

Russell's approach had to treat real 5/8 as different from rational 5/8 [Dummett]

14144

Ordinals result from likeness among relations, as cardinals from similarity among classes

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
14141

Ordinals are defined through mathematical induction

14142

Ordinals are types of series of terms in a row, rather than the 'nth' instance

14139

Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic

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 nonquantities 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 onetoone 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, nonrepeating 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
14147

Denying mathematical induction gave us the transfinite

14125

Finite numbers, unlike infinite numbers, obey mathematical induction

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 selfexemplification 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. Neologicism
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

6424

Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess

6425

Formalism can't apply numbers to reality, so it is an evasion

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 onevariable 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 nonexistent 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 nonatomic 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 18991900 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 / 2. 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 / 3. Reality
5370

Space is neutral between touch and sight, so it cannot really be either of them

7. Existence / D. Theories of Reality / 4. Antirealism
7545

Visible things are physical and external, but only exist when viewed

7. Existence / D. Theories of Reality / 7. Fictionalism
14429

Classes are logical fictions, made from defining characteristics

7. Existence / D. Theories of Reality / 8. 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 subjectpredicate form, we wrongly infer that facts have substancequality form

6434

Facts are everything, except simples; they are either relations or qualities

7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact
18376

Russell asserts atomic, existential, negative and general facts [Armstrong]

7. Existence / D. Theories of Reality / 8. 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 / 8. Facts / d. Negative facts
22315

There can't be a negative of a complex, which is negated by its nonexistence [Potter]

22316

A positive and negative fact have the same constituents; their difference is primitive

7. Existence / D. Theories of Reality / 9. States of Affairs
5465

Modern trope theory tries, like logical atomism, to reduce things to elementary states [Ellis]

7. Existence / D. Theories of Reality / 10. 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 / 11. Ontological Commitment / a. Ontological commitment
6060

'Existence' means that a propositional function is sometimes true

7. Existence / D. Theories of Reality / 11. 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 nonmental 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'

4030

Russell claims that universals are needed to explain a priori knowledge (as their relations) [Mellor/Oliver]

4427

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
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 notbald, 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, subjectpredicate 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. Truthfunction conditionals
12197

Inferring q from p only needs p to be true, and 'notp or q' to be true

14450

All forms of implication are expressible as truthfunctions

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 sensedata 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. SelfEvidence
7554

Selfevidence is often a mere willo'thewisp

5412

Some propositions are selfevident, but their implications may also be selfevident

5413

Particular instances are more clearly selfevident than any general principles

5415

As shown by memory, selfevidence comes in degrees

5416

If selfevidence has degrees, we should accept the more selfevident 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. Sensedata theory
6415

After 1912, Russell said sensedata are last in analysis, not first in experience [Grayling]

5358

'Sensedata' are what are immediately known in sensation, such as colours or roughnesses

6417

In 1921 Russell abandoned sensedata, 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 sensedata
6467

No sensibile is ever a datum to two people at once

6483

Russell held that we are aware of states of our own brain [Robinson,H]

8244

Sensedata are qualities devoid of subjectivity, which are the basis of science [Deleuze/Guattari]

6462

Sensedata are not mental, but are part of the subjectmatter of physics

6463

Sensedata are objects, and do not contain the subject as part, the way beliefs do

6464

Sensedata are usually objects within the body, but are not part of the subject

7549

If my body literally lost its mind, the object seen when I see a flash would still exist

7553

Sensedata are purely physical

12. Knowledge Sources / B. Perception / 4. Sense Data / c. Unperceived sensedata
6459

We do not know whether sensedata exist as objects when they are not data

6460

'Sensibilia' are identical to sensedata, without actually being data for any mind

6461

Ungiven sensedata can no more exist than unmarried husbands

21583

When sensedata change, there must be indistinguishable sensedata in the process

12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sensedata problems
8854

My 'acquaintance' with sensedata is nothing like my knowing New York [Williams,M]

6458

Individuating sensedata is difficult, because they divide when closely attended to

6469

Sensedata 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 sensedata

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

5382

We are acquainted with outer and inner sensation, memory, Self, and universals [PG]

5389

Knowledge by descriptions enables us to transcend private experience

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. Procoherentism
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. Antireliabilism
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. SelfAwareness / 3. Limits of Introspection
5380

In perceiving the sun, I am aware of sun sensedata, 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 nonexistent, 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 nonexistent

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
5810

Referring is not denoting, and Russell ignores the referential use of definite descriptions [Donnellan]

16385

A definite description 'denotes' an entity if it fits the description uniquely [Recanati]

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. TruthConditions 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 notp 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 'wordproposition', and one of images an 'imageproposition'

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
14111

A proposition is a unity, and analysis destroys it

19157

Russell said the proposition must explain its own unity  or else objective truth is impossible [Davidson]

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. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
21740

I doubt whether ethics is part of philosophy

22. Metaethics / A. 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 / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
21741

'You ought to do p' primarily has emotional content, expressing approval

22. Metaethics / B. Value / 2. Values / g. Love
21746

Unlike hate, all desires can be satisfied by love

22. Metaethics / C. The Good / 1. Goodness / b. Types of good
21747

Goodness is a combination of love and knowledge

22. Metaethics / C. 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

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 selfrespect

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
20176

Boredom is an increasingly strong motivating power

20178

Life is now more interesting, but boredom is more frightening

20177

Boredom always involves not being fully occupied

20179

Happiness involves enduring boredom, and the young should be taught this

24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
23153

Gradually loyalty to a creed increased, which could even outweigh nationality

23152

Increasingly war expands communities, and unifies them through fear

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
21523

We would not want UK affairs to be settled by a world parliament

21522

Democracy is inadequate without a great deal of devolution

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
21527

On every new question the majority is always wrong at first

21526

Unfortunately ordinary voters can't detect insincerity

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

23172

Empiricist Liberalism is the only view for someone who favours scientific evidence and happiness

23171

Empiricism is ethically superior, because dogmatism favours persecution and hatred

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

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

23160

Being a slave of society is hardly better than being a slave of a despot

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
14175

We can drop 'cause', and just make inferences between facts

14172

Moments and points seem to imply other moments and points, but don't cause them

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 'atat' 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 timecorpuscles as well as spacecorpuscles

21706

At first matter is basic and known by sensedata; 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
