Combining Philosophers

All the ideas for Friedrich Schlegel, Simon Critchley and Bertrand Russell

expand these ideas     |    start again     |     specify just one area for these philosophers


583 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
A sense of timelessness is essential to wisdom [Russell]
1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / b. Pre-Socratic philosophy
Philosophy really got started as the rival mode of discourse to tragedy [Critchley]
1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / c. Eighteenth century philosophy
Irony is consciousness of abundant chaos [Schlegel,F]
1. Philosophy / C. History of Philosophy / 5. Modern Philosophy / b. Modern philosophy beginnings
Russell started a whole movement in philosophy by providing an analysis of descriptions [Read on Russell]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Philosophers must get used to absurdities [Russell]
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy verifies that our hierarchy of instinctive beliefs is harmonious and consistent [Russell]
Philosophy is logical analysis, followed by synthesis [Russell]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / d. Philosophy as puzzles
Philosophy begins in disappointment, notably in religion and politics [Critchley]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Philosophical disputes are mostly hopeless, because philosophers don't understand each other [Russell]
1. Philosophy / D. Nature of Philosophy / 8. Humour
Humour can give a phenomenological account of existence, and point to change [Critchley]
Humour is practically enacted philosophy [Critchley]
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
Metaphysics cannot give knowledge of the universe as a whole [Russell]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Plato has no system. Philosophy is the progression of a mind and development of thoughts [Schlegel,F]
Philosophical systems are interesting, but we now need a more objective scientific philosophy [Russell]
Hegel's confusions over 'is' show how vast systems can be built on simple errors [Russell]
Philosophers sometimes neglect truth and distort facts to attain a nice system [Russell]
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Physicists accept particles, points and instants, while pretending they don't do metaphysics [Russell]
The business of metaphysics is to describe the world [Russell]
1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
Analysis gives us nothing but the truth - but never the whole truth [Russell]
Only by analysing is progress possible in philosophy [Russell]
Analysis gives new knowledge, without destroying what we already have [Russell]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
All philosophy should begin with an analysis of propositions [Russell]
The study of grammar is underestimated in philosophy [Russell]
'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell]
Common speech is vague; its vocabulary and syntax must be modified, for precision [Russell]
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
We can't sharply distinguish variables, domains and values, if symbols frighten us [Russell]
When problems are analysed properly, they are either logical, or not philosophical at all [Russell]
A logical language would show up the fallacy of inferring reality from ordinary language [Russell]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
Analysis falsifies, if when the parts are broken down they are not equivalent to their sum [Russell]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
Philosophers usually learn science from each other, not from science [Russell]
Philosophy is similar to science, and has no special source of wisdom [Russell]
Philosophy should be built on science, to reduce error [Russell]
If infatuation with science leads to bad scientism, its rejection leads to obscurantism [Critchley]
Scientism is the view that everything can be explained causally through scientific method [Critchley]
Science gives us an excessively theoretical view of life [Critchley]
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
To meet the division in our life, try the Subject, Nature, Spirit, Will, Power, Praxis, Unconscious, or Being [Critchley]
The French keep returning, to Hegel or Nietzsche or Marx [Critchley]
German idealism aimed to find a unifying principle for Kant's various dualisms [Critchley]
Since Hegel, continental philosophy has been linked with social and historical enquiry. [Critchley]
Continental philosophy fights the threatened nihilism in the critique of reason [Critchley]
Continental philosophy is based on critique, praxis and emancipation [Critchley]
Continental philosophy has a bad tendency to offer 'one big thing' to explain everything [Critchley]
1. Philosophy / H. Continental Philosophy / 2. Phenomenology
Phenomenology is a technique of redescription which clarifies our social world [Critchley]
Phenomenology uncovers and redescribes the pre-theoretical layer of life [Critchley]
2. Reason / A. Nature of Reason / 6. Coherence
If one proposition is deduced from another, they are more certain together than alone [Russell]
2. Reason / B. Laws of Thought / 1. Laws of Thought
The law of contradiction is not a 'law of thought', but a belief about things [Russell]
Three Laws of Thought: identity, contradiction, and excluded middle [Russell]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Non-contradiction was learned from instances, and then found to be indubitable [Russell]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
Reducing entities and premisses makes error less likely [Russell]
2. Reason / D. Definition / 3. Types of Definition
A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell]
2. Reason / D. Definition / 7. Contextual Definition
Any linguistic expression may lack meaning when taken out of context [Russell]
2. Reason / D. Definition / 11. Ostensive Definition
Empirical words need ostensive definition, which makes them egocentric [Russell]
2. Reason / D. Definition / 13. Against Definition
Definition by analysis into constituents is useless, because it neglects the whole [Russell]
In mathematics definitions are superfluous, as they name classes, and it all reduces to primitives [Russell]
2. Reason / F. Fallacies / 2. Infinite Regress
Infinite regresses have propositions made of propositions etc, with the key term reappearing [Russell]
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 [Russell]
'The number one is bald' or 'the number one is fond of cream cheese' are meaningless [Russell]
The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false [Russell, by Orenstein]
The theory of types makes 'Socrates and killing are two' illegitimate [Russell]
3. Truth / A. Truth Problems / 1. Truth
Truth is a property of a belief, but dependent on its external relations, not its internal qualities [Russell]
3. Truth / A. Truth Problems / 5. Truth Bearers
Truth and falsehood are properties of beliefs and statements [Russell]
What is true or false is not mental, and is best called 'propositions' [Russell]
In its primary and formal sense, 'true' applies to propositions, not beliefs [Russell]
Truth belongs to beliefs, not to propositions and sentences [Russell]
3. Truth / A. Truth Problems / 7. Falsehood
A good theory of truth must make falsehood possible [Russell]
Asserting not-p is saying p is false [Russell]
3. Truth / B. Truthmakers / 1. For Truthmakers
The truth or falsehood of a belief depends upon a fact to which the belief 'refers' [Russell]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
Facts make propositions true or false, and are expressed by whole sentences [Russell]
3. Truth / B. Truthmakers / 6. Making Negative Truths
It seems that when a proposition is false, something must fail to subsist [Russell]
3. Truth / B. Truthmakers / 8. Making General Truths
Not only atomic truths, but also general and negative truths, have truth-makers [Russell, by Rami]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
For Russell, both propositions and facts are arrangements of objects, so obviously they correspond [Horwich on Russell]
Truth as congruence may work for complex beliefs, but not for simple beliefs about existence [Joslin on Russell]
Beliefs are true if they have corresponding facts, and false if they don't [Russell]
Propositions of existence, generalities, disjunctions and hypotheticals make correspondence tricky [Russell]
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 [Russell]
3. Truth / D. Coherence Truth / 2. Coherence Truth Critique
More than one coherent body of beliefs seems possible [Russell]
If we suspend the law of contradiction, nothing will appear to be incoherent [Russell]
Coherence is not the meaning of truth, but an important test for truth [Russell]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
An argument 'satisfies' a function φx if φa is true [Russell]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
"The death of Caesar is true" is not the same proposition as "Caesar died" [Russell]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
The mortality of Socrates is more certain from induction than it is from deduction [Russell]
The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell]
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 [Russell]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The null class is a fiction [Russell]
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 [Russell]
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 [Russell]
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 [Russell]
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 [Russell]
Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The British parliament has one representative selected from each constituency [Russell]
Choice is equivalent to the proposition that every class is well-ordered [Russell]
Choice shows that if any two cardinals are not equal, one must be the greater [Russell]
We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell]
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 [Russell]
Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
The 'no classes' theory says the propositions just refer to the members [Russell]
Propositions about classes can be reduced to propositions about their defining functions [Russell]
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 [Russell, by Lavine]
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
Order rests on 'between' and 'separation' [Russell]
Order depends on transitive asymmetrical relations [Russell]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Classes can be reduced to propositional functions [Russell, by Hanna]
Classes, grouped by a convenient property, are logical constructions [Russell]
Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell]
I gradually replaced classes with properties, and they ended as a symbolic convenience [Russell]
4. Formal Logic / G. Formal Mereology / 1. Mereology
The part-whole relation is ultimate and indefinable [Russell]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Subject-predicate logic (and substance-attribute metaphysics) arise from Aryan languages [Russell]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic gives the method of research in philosophy [Russell]
It is logic, not metaphysics, that is fundamental to philosophy [Russell]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
The physical world doesn't need logic, but the mental world does [Russell]
All the propositions of logic are completely general [Russell]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
In modern times, logic has become mathematical, and mathematics has become logical [Russell]
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
Demonstration always relies on the rule that anything implied by a truth is true [Russell]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
Implication cannot be defined [Russell]
It would be circular to use 'if' and 'then' to define material implication [Russell]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
Logic can only assert hypothetical existence [Russell]
Logic can be known a priori, without study of the actual world [Russell]
Logic is concerned with the real world just as truly as zoology [Russell]
Logic is highly general truths abstracted from reality [Russell, by Glock]
The only classes are things, predicates and relations [Russell]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Geometrical axioms imply the propositions, but the former may not be true [Russell]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Excluded middle can be stated psychologically, as denial of p implies assertion of not-p [Russell]
Russell's theories aim to preserve excluded middle (saying all sentences are T or F) [Sawyer on Russell]
Questions wouldn't lead anywhere without the law of excluded middle [Russell]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
'Elizabeth = Queen of England' is really a predication, not an identity-statement [Russell, by Lycan]
In a logically perfect language, there will be just one word for every simple object [Russell]
Romulus does not occur in the proposition 'Romulus did not exist' [Russell]
Vagueness, and simples being beyond experience, are obstacles to a logical language [Russell]
Leibniz bases everything on subject/predicate and substance/property propositions [Russell]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
The logical connectives are not objects, but are formal, and need a context [Russell]
Logical connectives have the highest precision, yet are infected by the vagueness of true and false [Russell, by Williamson]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
There seem to be eight or nine logical constants [Russell]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell]
Is it possible to state every possible truth about the whole course of nature without using 'not'? [Russell]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
'Or' expresses hesitation, in a dog at a crossroads, or birds risking grabbing crumbs [Russell]
A disjunction expresses indecision [Russell]
'Or' expresses a mental state, not something about the world [Russell]
Disjunction may also arise in practice if there is imperfect memory. [Russell]
Maybe the 'or' used to describe mental states is not the 'or' of logic [Russell]
5. Theory of Logic / E. Structures of Logic / 3. Constants in Logic
Constants are absolutely definite and unambiguous [Russell]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
The idea of a variable is fundamental [Russell]
Variables don't stand alone, but exist as parts of propositional functions [Russell]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
'Propositional functions' are ambiguous until the variable is given a value [Russell]
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 [Russell]
There are a set of criteria for pinning down a logically proper name [Russell, by Sainsbury]
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, by Sawyer]
Russell says names are not denotations, but definite descriptions in disguise [Russell, by Kripke]
Russell says a name contributes a complex of properties, rather than an object [Russell, by Sawyer]
Are names descriptions, if the description is unknown, false, not special, or contains names? [McCullogh on Russell]
Proper names are really descriptions, and can be replaced by a description in a person's mind [Russell]
Treat description using quantifiers, and treat proper names as descriptions [Russell, by McCullogh]
Asking 'Did Homer exist?' is employing an abbreviated description [Russell]
Russell admitted that even names could also be used as descriptions [Russell, by Bach]
Names are really descriptions, except for a few words like 'this' and 'that' [Russell]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
The meaning of a logically proper name is its referent, but most names are not logically proper [Russell, by Soames]
Logically proper names introduce objects; definite descriptions introduce quantifications [Russell, by Bach]
The only real proper names are 'this' and 'that'; the rest are really definite descriptions. [Russell, by Grayling]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
Russell rewrote singular term names as predicates [Russell, by Ayer]
"Nobody" is not a singular term, but a quantifier [Russell, by Lycan]
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
Russell implies that all sentences containing empty names are false [Sawyer on Russell]
Names are meaningless unless there is an object which they designate [Russell]
A name has got to name something or it is not a name [Russell]
5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
The only genuine proper names are 'this' and 'that' [Russell]
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 [Russell]
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 [Grayling on Russell]
Definite descriptions fail to refer in three situations, so they aren't essentially referring [Russell, by Sainsbury]
The phrase 'a so-and-so' is an 'ambiguous' description'; 'the so-and-so' (singular) is a 'definite' description [Russell]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
The theory of descriptions eliminates the name of the entity whose existence was presupposed [Russell, by Quine]
Russell's theory explains non-existents, negative existentials, identity problems, and substitutivity [Russell, by Lycan]
Russell showed how to define 'the', and thereby reduce the ontology of logic [Russell, by Lackey]
Russell's theory must be wrong if it says all statements about non-existents are false [Read on Russell]
The theory of definite descriptions reduces the definite article 'the' to the concepts of predicate logic [Russell, by Horwich]
Russell implies that 'the baby is crying' is only true if the baby is unique [Grayling on Russell]
Russell explained descriptions with quantifiers, where Frege treated them as names [Russell, by McCullogh]
Russell avoids non-existent objects by denying that definite descriptions are proper names [Russell, by Miller,A]
Denying definite description sentences are subject-predicate in form blocks two big problems [Russell, by Forbes,G]
Russell says apparent referring expressions are really assertions about properties [Russell, by Cooper,DE]
The theory of descriptions lacks conventions for the scope of quantifiers [Lackey on Russell]
Non-count descriptions don't threaten Russell's theory, which is only about singulars [Laycock on Russell]
Denoting is crucial in Russell's account of mathematics, for identifying classes [Russell, by Monk]
Russell's analysis means molecular sentences are ambiguous over the scope of the description [Kaplan on Russell]
5. Theory of Logic / G. Quantification / 1. Quantification
'Any' is better than 'all' where infinite classes are concerned [Russell]
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
Existence is entirely expressed by the existential quantifier [Russell, by McGinn]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths are known by their extreme generality [Russell]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The sources of a proof are the reasons why we believe its conclusion [Russell]
Which premises are ultimate varies with context [Russell]
Some axioms may only become accepted when they lead to obvious conclusions [Russell]
Finding the axioms may be the only route to some new results [Russell]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
The Achilles Paradox concerns the one-one correlation of infinite classes [Russell]
To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell]
The tortoise won't win, because infinite instants don't compose an infinitely long time [Russell]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / d. Richard's paradox
Richard's puzzle uses the notion of 'definition' - but that cannot be defined [Russell]
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 [Russell, by Lavine]
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 [Russell, by Grayling]
Russell's Paradox is a stripped-down version of Cantor's Paradox [Priest,G on Russell]
Russell's paradox means we cannot assume that every property is collectivizing [Potter on Russell]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
Vicious Circle: what involves ALL must not be one of those ALL [Russell]
'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell]
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! [Russell]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
In mathematic we are ignorant of both subject-matter and truth [Russell]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Geometry throws no light on the nature of actual space [Russell]
Two points have a line joining them (descriptive), a distance (metrical), and a whole line (projective) [Russell, by PG]
If straight lines were like ratios they might intersect at a 'gap', and have no point in common [Russell]
Pure geometry is deductive, and neutral over what exists [Russell]
In geometry, Kant and idealists aimed at the certainty of the premisses [Russell]
In geometry, empiricists aimed at premisses consistent with experience [Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
Russell's approach had to treat real 5/8 as different from rational 5/8 [Russell, by Dummett]
Ordinals result from likeness among relations, as cardinals from similarity among classes [Russell]
New numbers solve problems: negatives for subtraction, fractions for division, complex for equations [Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Some claim priority for the ordinals over cardinals, but there is no logical priority between them [Russell]
Ordinals presuppose two relations, where cardinals only presuppose one [Russell]
Properties of numbers don't rely on progressions, so cardinals may be more basic [Russell]
Could a number just be something which occurs in a progression? [Russell, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Ordinals are defined through mathematical induction [Russell]
Ordinals are types of series of terms in a row, rather than the 'nth' instance [Russell]
Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic [Russell]
For Cantor ordinals are types of order, not numbers [Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
We aren't sure if one cardinal number is always bigger than another [Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers are a class of rational numbers (and so not really numbers at all) [Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum [Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / j. Complex numbers
A complex number is simply an ordered couple of real numbers [Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
Discovering that 1 is a number was difficult [Russell]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / b. Quantity
Quantity is not part of mathematics, where it is replaced by order [Russell]
Some quantities can't be measured, and some non-quantities are measurable [Russell]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Counting explains none of the real problems about the foundations of arithmetic [Russell]
Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
We can define one-to-one without mentioning unity [Russell]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
We do not currently know whether, of two infinite numbers, one must be greater than the other [Russell]
Infinity and continuity used to be philosophy, but are now mathematics [Russell]
There are cardinal and ordinal theories of infinity (while continuity is entirely ordinal) [Russell]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
A collection is infinite if you can remove some terms without diminishing its number [Russell]
Infinite numbers are distinguished by disobeying induction, and the part equalling the whole [Russell]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
ω names the whole series, or the generating relation of the series of ordinal numbers [Russell]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
You can't get a new transfinite cardinal from an old one just by adding finite numbers to it [Russell]
For every transfinite cardinal there is an infinite collection of transfinite ordinals [Russell]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Geometry is united by the intuitive axioms of projective geometry [Russell, by Musgrave]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell]
Axiom of Archimedes: a finite multiple of a lesser magnitude can always exceed a greater [Russell]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
'0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell]
Russell tried to replace Peano's Postulates with the simple idea of 'class' [Russell, by Monk]
Dedekind failed to distinguish the numbers from other progressions [Shapiro on Russell]
Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
Finite numbers, unlike infinite numbers, obey mathematical induction [Russell]
Denying mathematical induction gave us the transfinite [Russell]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
Numbers were once defined on the basis of 1, but neglected infinities and + [Russell]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Numbers are properties of classes [Russell]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
A number is something which characterises collections of the same size [Russell]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Ordinals can't be defined just by progression; they have intrinsic qualities [Russell]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Mathematics doesn't care whether its entities exist [Russell]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Arithmetic was probably inferred from relationships between physical objects [Russell]
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 [Russell]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Pure mathematics is the class of propositions of the form 'p implies q' [Russell]
Maths can be deduced from logical axioms and the logic of relations [Russell]
We tried to define all of pure maths using logical premisses and concepts [Russell]
For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
For 'x is a u' to be meaningful, u must be one range of individuals (or 'type') higher than x [Russell]
In 'x is a u', x and u must be of different types, so 'x is an x' is generally meaningless [Russell, by Magidor]
Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell]
Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave]
Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Numbers are just verbal conveniences, which can be analysed away [Russell]
Formalism can't apply numbers to reality, so it is an evasion [Russell]
Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess [Russell]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Numbers are classes of classes, and hence fictions of fictions [Russell]
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 [Russell]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
We need rules for deciding which norms are predicative (unless none of them are) [Russell]
A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock]
Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock]
Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock]
A one-variable function is only 'predicative' if it is one order above its arguments [Russell]
'Predicative' norms are those which define a class [Russell]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / e. Psychologism
There is always something psychological about inference [Russell]
7. Existence / A. Nature of Existence / 1. Nature of Existence
Existence can only be asserted of something described, not of something named [Russell]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
Being is what belongs to every possible object of thought [Russell]
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 [Russell]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
What exists has causal relations, but non-existent things may also have them [Russell]
7. Existence / B. Change in Existence / 4. Events / b. Events as primitive
In 1927, Russell analysed force and matter in terms of events [Russell, by Grayling]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
General facts supervene on particular facts, but cannot be inferred from them [Russell, by Bennett,K]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
Russell gave up logical atomism because of negative, general and belief propositions [Russell, by Read]
Logical atomism aims at logical atoms as the last residue of analysis [Russell]
Once you have enumerated all the atomic facts, there is a further fact that those are all the facts [Russell]
Logical atoms aims to get down to ultimate simples, with their own unique reality [Russell]
To mean facts we assert them; to mean simples we name them [Russell]
'Simples' are not experienced, but are inferred at the limits of analysis [Russell]
Better to construct from what is known, than to infer what is unknown [Russell]
Given all true atomic propositions, in theory every other truth can thereby be deduced [Russell]
In 1899-1900 I adopted the philosophy of logical atomism [Russell]
Atomic facts may be inferrable from others, but never from non-atomic facts [Russell]
Russell's new logical atomist was of particulars, universals and facts (not platonic propositions) [Russell, by Linsky,B]
Russell's atomic facts are actually compounds, and his true logical atoms are sense data [Russell, by Quine]
Complex things can be known, but not simple things [Russell]
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 [Russell]
7. Existence / D. Theories of Reality / 1. Realism
If two people perceive the same object, the object of perception can't be in the mind [Russell]
7. Existence / D. Theories of Reality / 2. Reality
Space is neutral between touch and sight, so it cannot really be either of them [Russell]
7. Existence / D. Theories of Reality / 3. Anti-realism
Visible things are physical and external, but only exist when viewed [Russell]
7. Existence / D. Theories of Reality / 6. Fictionalism
Classes are logical fictions, made from defining characteristics [Russell]
7. Existence / D. Theories of Reality / 7. Facts / a. Facts
You can't name all the facts, so they are not real, but are what propositions assert [Russell]
As propositions can be put in subject-predicate form, we wrongly infer that facts have substance-quality form [Russell]
Facts are everything, except simples; they are either relations or qualities [Russell]
7. Existence / D. Theories of Reality / 7. Facts / b. Types of fact
Russell asserts atomic, existential, negative and general facts [Russell, by Armstrong]
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 [Russell]
7. Existence / D. Theories of Reality / 7. Facts / d. Negative facts
There can't be a negative of a complex, which is negated by its non-existence [Potter on Russell]
A positive and negative fact have the same constituents; their difference is primitive [Russell]
7. Existence / D. Theories of Reality / 8. States of Affairs
Modern trope theory tries, like logical atomism, to reduce things to elementary states [Russell, by Ellis]
7. Existence / D. Theories of Reality / 9. Vagueness / d. Vagueness as linguistic
Since natural language is not precise it cannot be in the province of logic [Russell, by Keefe/Smith]
Vagueness is only a characteristic of representations, such as language [Russell]
7. Existence / D. Theories of Reality / 10. Ontological Commitment / a. Ontological commitment
'Existence' means that a propositional function is sometimes true [Russell]
7. Existence / D. Theories of Reality / 10. Ontological Commitment / e. Ontological commitment problems
Russell showed that descriptions may not have ontological commitment [Russell, by Linsky,B]
7. Existence / E. Categories / 3. Proposed Categories
Four classes of terms: instants, points, terms at instants only, and terms at instants and points [Russell]
The Theory of Description dropped classes and numbers, leaving propositions, individuals and universals [Russell, by Monk]
8. Modes of Existence / A. Relations / 1. Nature of Relations
Philosophers of logic and maths insisted that a vocabulary of relations was essential [Russell, by Heil]
The only thing we can say about relations is that they relate [Russell]
Relational propositions seem to be 'about' their terms, rather than about the relation [Russell]
There is no complexity without relations, so no propositions, and no truth [Russell]
Because we depend on correspondence, we know relations better than we know the items that relate [Russell]
That Edinburgh is north of London is a non-mental fact, so relations are independent universals [Russell]
With asymmetrical relations (before/after) the reduction to properties is impossible [Russell]
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 [Russell]
'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness [Russell]
'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell]
8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation
Symmetrical and transitive relations are formally like equality [Russell]
8. Modes of Existence / B. Properties / 11. Properties as Sets
Russell refuted Frege's principle that there is a set for each property [Russell, by Sorensen]
When we attribute a common quality to a group, we can forget the quality and just talk of the group [Russell]
8. Modes of Existence / B. Properties / 12. Denial of Properties
Russell can't attribute existence to properties [McGinn on Russell]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
Trope theorists cannot explain how tropes resemble each other [Russell, by Mumford]
8. Modes of Existence / D. Universals / 1. Universals
Every complete sentence must contain at least one word (a verb) which stands for a universal [Russell]
Propositions express relations (prepositions and verbs) as well as properties (nouns and adjectives) [Russell]
Confused views of reality result from thinking that only nouns and adjectives represent universals [Russell]
All universals are like the relation "is north of", in having no physical location at all [Russell, by Loux]
8. Modes of Existence / D. Universals / 2. Need for Universals
We know a universal in 'yellow differs from blue' or 'yellow resembles blue less than green does' [Russell]
Russell claims that universals are needed to explain a priori knowledge (as their relations) [Russell, by Mellor/Oliver]
Every sentence contains at least one word denoting a universal, so we need universals to know truth [Russell]
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
Normal existence is in time, so we must say that universals 'subsist' [Russell]
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 [Russell]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
'Resemblance Nominalism' won't work, because the theory treats resemblance itself as a universal [Russell]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
Universals can't just be words, because words themselves are universals [Russell]
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 [Russell]
9. Objects / A. Existence of Objects / 1. Physical Objects
Physical things are series of appearances whose matter obeys physical laws [Russell]
A perceived physical object is events grouped around a centre [Russell]
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. [Russell]
When I perceive a melody, I do not perceive the notes as existing [Russell]
9. Objects / A. Existence of Objects / 4. Impossible objects
I prefer to deny round squares, and deal with the difficulties by the theory of denoting [Russell]
On Meinong's principles 'the existent round square' has to exist [Russell]
Common sense agrees with Meinong (rather than Russell) that 'Pegasus is a flying horse' is true [Lackey on Russell]
If the King of France is not bald, and not not-bald, this violates excluded middle [Linsky,B on Russell]
9. Objects / A. Existence of Objects / 5. Simples
Unities are only in propositions or concepts, and nothing that exists has unity [Russell]
9. Objects / A. Existence of Objects / 5. Individuation / c. Individuation by location
Objects only exist if they 'occupy' space and time [Russell]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
The only unities are simples, or wholes composed of parts [Russell]
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' [Russell]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
We need not deny substance, but there seems no reason to assert it [Russell]
The assumption by physicists of permanent substance is not metaphysically legitimate [Russell]
An object produces the same percepts with or without a substance, so that is irrelevant to science [Russell]
9. Objects / D. Essence of Objects / 3. Individual Essences
The essence of individuality is beyond description, and hence irrelevant to science [Russell]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Change is obscured by substance, a thing's nature, subject-predicate form, and by essences [Russell]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
It at least makes sense to say two objects have all their properties in common [Wittgenstein on Russell]
Terms are identical if they belong to all the same classes [Russell]
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 [Russell]
Modal terms are properties of propositional functions, not of propositions [Russell]
10. Modality / A. Necessity / 6. Logical Necessity
Some facts about experience feel like logical necessities [Russell]
10. Modality / B. Possibility / 1. Possibility
Only the actual exists, so possibilities always reduce to actuality after full analysis [Russell]
10. Modality / B. Possibility / 5. Contingency
Contingency arises from tensed verbs changing the propositions to which they refer [Russell]
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 [Russell]
All forms of implication are expressible as truth-functions [Russell]
10. Modality / B. Possibility / 9. Counterfactuals
It makes no sense to say that a true proposition could have been false [Russell]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
In any possible world we feel that two and two would be four [Russell]
If something is true in all possible worlds then it is logically necessary [Russell]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Knowledge cannot be precisely defined, as it merges into 'probable opinion' [Russell]
All our knowledge (if verbal) is general, because all sentences contain general words [Russell]
In epistemology we should emphasis the continuity between animal and human minds [Russell]
11. Knowledge Aims / A. Knowledge / 4. Belief / b. Elements of beliefs
Belief relates a mind to several things other than itself [Russell]
The three questions about belief are its contents, its success, and its character [Russell]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
We have an 'instinctive' belief in the external world, prior to all reflection [Russell]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
Descartes showed that subjective things are the most certain [Russell]
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 [Russell]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
I assume we perceive the actual objects, and not their 'presentations' [Russell]
'Acquaintance' is direct awareness, without inferences or judgements [Russell]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / c. Representative realism
Russell (1912) said phenomena only resemble reality in abstract structure [Russell, by Robinson,H]
There is no reason to think that objects have colours [Russell]
Science condemns sense-data and accepts matter, but a logical construction must link them [Russell]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Russell rejected phenomenalism because it couldn't account for causal relations [Russell, by Grayling]
Where possible, logical constructions are to be substituted for inferred entities [Russell]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
'Idealism' says that everything which exists is in some sense mental [Russell]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Poetry is transcendental when it connects the ideal to the real [Schlegel,F]
11. Knowledge Aims / C. Knowing Reality / 4. Solipsism
It is not illogical to think that only myself and my mental events exist [Russell]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Self-evidence is often a mere will-o'-the-wisp [Russell]
Particular instances are more clearly self-evident than any general principles [Russell]
Some propositions are self-evident, but their implications may also be self-evident [Russell]
As shown by memory, self-evidence comes in degrees [Russell]
If self-evidence has degrees, we should accept the more self-evident as correct [Russell]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
The rationalists were right, because we know logical principles without experience [Russell]
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
All a priori knowledge deals with the relations of universals [Russell]
We can know some general propositions by universals, when no instance can be given [Russell]
12. Knowledge Sources / B. Perception / 3. Representation
Russell's representationalism says primary qualities only show the structure of reality [Russell, by Robinson,H]
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 [Russell, by Grayling]
'Sense-data' are what are immediately known in sensation, such as colours or roughnesses [Russell]
In 1921 Russell abandoned sense-data, and the gap between sensation and object [Russell, by Grayling]
Seeing is not in itself knowledge, but is separate from what is seen, such as a patch of colour [Russell]
12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data
No sensibile is ever a datum to two people at once [Russell]
Sense-data are purely physical [Russell]
Sense-data are usually objects within the body, but are not part of the subject [Russell]
If my body literally lost its mind, the object seen when I see a flash would still exist [Russell]
Russell held that we are aware of states of our own brain [Russell, by Robinson,H]
Sense-data are qualities devoid of subjectivity, which are the basis of science [Russell, by Deleuze/Guattari]
Sense-data are not mental, but are part of the subject-matter of physics [Russell]
Sense-data are objects, and do not contain the subject as part, the way beliefs do [Russell]
12. Knowledge Sources / B. Perception / 4. Sense Data / c. Unperceived sense-data
When sense-data change, there must be indistinguishable sense-data in the process [Russell]
We do not know whether sense-data exist as objects when they are not data [Russell]
Ungiven sense-data can no more exist than unmarried husbands [Russell]
'Sensibilia' are identical to sense-data, without actually being data for any mind [Russell]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
My 'acquaintance' with sense-data is nothing like my knowing New York [Williams,M on Russell]
Individuating sense-data is difficult, because they divide when closely attended to [Russell]
Sense-data may be subjective, if closing our eyes can change them [Russell]
We cannot assume that the subject actually exists, so we cannot distinguish sensations from sense-data [Russell]
12. Knowledge Sources / B. Perception / 5. Interpretation
Perception goes straight to the fact, and not through the proposition [Russell]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Empirical truths are particular, so general truths need an a priori input of generality [Russell]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
If Russell rejects innate ideas and direct a priori knowledge, he is left with a tabula rasa [Russell, by Thompson]
Knowledge by descriptions enables us to transcend private experience [Russell]
It is natural to begin from experience, and presumably that is the basis of knowledge [Russell]
We are acquainted with outer and inner sensation, memory, Self, and universals [Russell, by PG]
For simple words, a single experience can show that they are true [Russell]
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
Pragmatism judges by effects, but I judge truth by causes [Russell]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Full empiricism is not tenable, but empirical investigation is always essential [Russell]
I can know the existence of something with which nobody is acquainted [Russell]
Perception can't prove universal generalisations, so abandon them, or abandon empiricism? [Russell]
It is hard to explain how a sentence like 'it is not raining' can be found true by observation [Russell]
Empiricists seem unclear what they mean by 'experience' [Russell]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
Images are not memory, because they are present, and memories are of the past [Russell]
It is possible the world came into existence five minutes ago, complete with false memories [Russell]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem
A true belief is not knowledge if it is reached by bad reasoning [Russell]
True belief is not knowledge when it is deduced from false belief [Russell]
True belief about the time is not knowledge if I luckily observe a stopped clock at the right moment [Russell]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
All knowledge (of things and of truths) rests on the foundations of acquaintance [Russell]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Believing a whole science is more than believing each of its propositions [Russell]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
Objects are treated as real when they connect with other experiences in a normal way [Russell]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
Knowledge needs more than a sensitive response; the response must also be appropriate [Russell]
13. Knowledge Criteria / D. Scepticism / 5. Dream Scepticism
Dreams can be explained fairly scientifically if we assume a physical world [Russell]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
Global scepticism is irrefutable, but can't replace our other beliefs, and just makes us hesitate [Russell]
14. Science / B. Scientific Theories / 1. Scientific Theory
Mathematically expressed propositions are true of the world, but how to interpret them? [Russell]
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 [Russell]
14. Science / C. Induction / 2. Aims of Induction
Induction is inferring premises from consequences [Russell]
14. Science / C. Induction / 3. Limits of Induction
We can't prove induction from experience without begging the question [Russell]
Chickens are not very good at induction, and are surprised when their feeder wrings their neck [Russell]
It doesn't follow that because the future has always resembled the past, that it always will [Russell]
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 [Russell]
Belief in real objects makes our account of experience simpler and more systematic [Russell]
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 [Russell]
Other minds seem to exist, because their testimony supports realism about the world [Russell, by Grayling]
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 [Russell]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
It is good to generalise truths as much as possible [Russell]
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 [Russell]
16. Persons / B. Nature of the Self / 6. Self as Higher Awareness
In seeing the sun, we are acquainted with our self, but not as a permanent person [Russell]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
In perceiving the sun, I am aware of sun sense-data, and of the perceiver of the data [Russell]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
A man is a succession of momentary men, bound by continuity and causation [Russell]
16. Persons / E. Rejecting the Self / 4. Denial of the Self
In perception, the self is just a logical fiction demanded by grammar [Russell]
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 [Russell]
Behaviourists struggle to explain memory and imagination, because they won't admit images [Russell]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
There are distinct sets of psychological and physical causal laws [Russell]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
We could probably, in principle, infer minds from brains, and brains from minds [Russell]
18. Thought / A. Modes of Thought / 5. Rationality
It is rational to believe in reality, despite the lack of demonstrative reasons for it [Russell]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
Knowledge of truths applies to judgements; knowledge by acquaintance applies to sensations and things [Russell]
Russell's 'multiple relations' theory says beliefs attach to ingredients, not to propositions [Russell, by Linsky,B]
Truth is when a mental state corresponds to a complex unity of external constituents [Russell]
18. Thought / A. Modes of Thought / 6. Judgement / b. Error
Do incorrect judgements have non-existent, or mental, or external objects? [Russell]
To explain false belief we should take belief as relating to a proposition's parts, not to the whole thing [Russell]
Surprise is a criterion of error [Russell]
In order to explain falsehood, a belief must involve several terms, not two [Russell]
The theory of error seems to need the existence of the non-existent [Russell]
18. Thought / C. Content / 1. Content
The complexity of the content correlates with the complexity of the object [Russell]
18. Thought / C. Content / 6. Broad Content
We don't assert private thoughts; the objects are part of what we assert [Russell]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
A universal of which we are aware is called a 'concept' [Russell]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Abstraction principles identify a common property, which is some third term with the right relation [Russell]
The principle of Abstraction says a symmetrical, transitive relation analyses into an identity [Russell]
A certain type of property occurs if and only if there is an equivalence relation [Russell]
19. Language / A. Nature of Meaning / 1. Meaning
Meaning takes many different forms, depending on different logical types [Russell]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Russell started philosophy of language, by declaring some plausible sentences to be meaningless [Russell, by Hart,WD]
Every understood proposition is composed of constituents with which we are acquainted [Russell]
Unverifiable propositions about the remote past are still either true or false [Russell]
19. Language / B. Reference / 1. Reference theories
Russell argued with great plausibility that we rarely, if ever, refer with our words [Russell, by Cooper,DE]
19. Language / B. Reference / 2. Denoting
A definite description 'denotes' an entity if it fits the description uniquely [Russell, by Recanati]
Referring is not denoting, and Russell ignores the referential use of definite descriptions [Donnellan on Russell]
Denoting phrases are meaningless, but guarantee meaning for propositions [Russell]
In 'Scott is the author of Waverley', denotation is identical, but meaning is different [Russell]
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
By eliminating descriptions from primitive notation, Russell seems to reject 'sense' [Russell, by Kripke]
19. Language / B. 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 [Russell]
19. Language / B. Reference / 5. Speaker's Reference
Russell assumes that expressions refer, but actually speakers refer by using expressions [Cooper,DE on Russell]
19. Language / C. Assigning Meanings / 3. Predicates
Russell uses 'propositional function' to refer to both predicates and to attributes [Quine on Russell]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Russell rejected sense/reference, because it made direct acquaintance with things impossible [Russell, by Recanati]
'Sense' is superfluous (rather than incoherent) [Russell, by Miller,A]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
The theory of definite descriptions aims at finding correct truth conditions [Russell, by Lycan]
19. Language / C. Assigning Meanings / 9. Indexical Semantics
Science reduces indexicals to a minimum, but they can never be eliminated from empirical matters [Russell]
19. Language / D. Propositions / 1. Propositions
Proposition contain entities indicated by words, rather than the words themselves [Russell]
If p is false, then believing not-p is knowing a truth, so negative propositions must exist [Russell]
Propositions don't name facts, because each fact corresponds to a proposition and its negation [Russell]
Our important beliefs all, if put into words, take the form of propositions [Russell]
A proposition expressed in words is a 'word-proposition', and one of images an 'image-proposition' [Russell]
A proposition is what we believe when we believe truly or falsely [Russell]
Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell]
19. Language / D. Propositions / 3. Concrete Propositions
If propositions are facts, then false and true propositions are indistinguishable [Davidson on Russell]
In graspable propositions the constituents are real entities of acquaintance [Russell]
In 1918 still believes in nonlinguistic analogues of sentences, but he now calls them 'facts' [Russell, by Quine]
19. Language / D. Propositions / 4. Mental Propositions
Propositions don't name facts, because two opposed propositions can match one fact [Russell]
You can believe the meaning of a sentence without thinking of the words [Russell]
19. Language / D. Propositions / 5. Unity of Propositions
A proposition is a unity, and analysis destroys it [Russell]
Russell said the proposition must explain its own unity - or else objective truth is impossible [Russell, by Davidson]
19. Language / D. Propositions / 6. Propositions Critique
In 1906, Russell decided that propositions did not, after all, exist [Russell, by Monk]
The main aim of the multiple relations theory of judgement was to dispense with propositions [Russell, by Linsky,B]
An inventory of the world does not need to include propositions [Russell]
I no longer believe in propositions, especially concerning falsehoods [Russell]
I know longer believe in shadowy things like 'that today is Wednesday' when it is actually Tuesday [Russell]
19. Language / F. Communication / 3. Denial
If we define 'this is not blue' as disbelief in 'this is blue', we eliminate 'not' as an ingredient of facts [Russell]
19. Language / F. Communication / 4. Private Language
The names in a logically perfect language would be private, and could not be shared [Russell]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
A mother cat is paralysed if equidistant between two needy kittens [Russell]
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
For poets free choice is supreme [Schlegel,F]
Wallace Stevens is the greatest philosophical poet of the twentieth century in English [Critchley]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Interesting art is always organised around ethical demands [Critchley]
22. Metaethics / A. Value / 2. Values / e. Love
True love is ironic, in the contrast between finite limitations and the infinity of love [Schlegel,F]
Unlike hate, all desires can be satisfied by love [Russell]
22. Metaethics / B. The Good / 1. Goodness / b. Types of good
Goodness is a combination of love and knowledge [Russell]
22. Metaethics / B. The Good / 2. Happiness / d. Routes to happiness
A happy and joyous life must largely be a quiet life [Russell]
In wartime, happiness is hating the enemy, because it gives the war a purpose [Russell]
22. Metaethics / C. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
The problems is not justifying ethics, but motivating it. Why should a self seek its good? [Critchley]
I doubt whether ethics is part of philosophy [Russell]
22. Metaethics / C. Ethics Foundations / 2. Source of Ethics / h. Expressivism
'You ought to do p' primarily has emotional content, expressing approval [Russell]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
Originally virtue was obedience, to gods, government, or custom [Russell]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
Individuals need creativity, reverence for others, and self-respect [Russell]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
Act so as to produce harmonious rather than discordant desires [Russell]
23. Ethics / E. Utilitarianism / 2. Ideal of Pleasure
Judgements of usefulness depend on judgements of value [Russell]
23. Ethics / F. Existentialism / 2. Nihilism
Perceiving meaninglessness is an achievement, which can transform daily life [Critchley]
23. Ethics / F. Existentialism / 3. Angst
Irony is the response to conflicts of involvement and attachment [Schlegel,F, by Pinkard]
23. Ethics / F. Existentialism / 4. Boredom
Happiness involves enduring boredom, and the young should be taught this [Russell]
Boredom always involves not being fully occupied [Russell]
Life is now more interesting, but boredom is more frightening [Russell]
Boredom is an increasingly strong motivating power [Russell]
24. Applied Ethics / A. Decision Conflicts / 1. Applied Ethics
Food first, then ethics [Critchley]
25. Society / B. The State / 7. Changing the State / b. Devolution
Democracy is inadequate without a great deal of devolution [Russell]
We would not want UK affairs to be settled by a world parliament [Russell]
25. Society / C. Social Justice / 3. Social Freedom / e. Freedom of lifestyle
We need security and liberty, and then encouragement of creativity [Russell]
25. Society / C. Social Justice / 5. Legal Rights / c. Property rights
The right to own land gives a legal right to a permanent income [Russell]
25. Society / C. Social Justice / 6. Right to Punish / d. Reform of offenders
Legally curbing people's desires is inferior to improving their desires [Russell]
25. Society / D. Political Doctrines / 3. Anarchism
Anarchy does not maximise liberty [Russell]
Anarchism used to be libertarian (especially for sexuality), but now concerns responsibility [Critchley]
The state, law, bureaucracy and capital are limitations on life, so I prefer federalist anarchism [Critchley]
25. Society / D. Political Doctrines / 4. Conservatism
Belief that humans are wicked leads to authoritarian politics [Critchley]
25. Society / D. Political Doctrines / 5. Democracy / a. Nature of democracy
On every new question the majority is always wrong at first [Russell]
Unfortunately ordinary voters can't detect insincerity [Russell]
25. Society / D. Political Doctrines / 5. Democracy / c. Direct democracy
Groups should be autonomous, with a neutral authority as arbitrator [Russell]
25. Society / D. Political Doctrines / 6. Liberalism
Theoretical and practical politics are both concerned with the best lives for individuals [Russell]
25. Society / D. Political Doctrines / 8. Socialism
When the state is the only employer, there is no refuge from the prejudices of other people [Russell]
25. Society / D. Political Doctrines / 11. Capitalism
Men unite in pursuit of material things, and idealise greed as part of group loyalty [Russell]
26. Natural Theory / C. Causation / 7. Eliminating causation
Moments and points seem to imply other moments and points, but don't cause them [Russell]
We can drop 'cause', and just make inferences between facts [Russell]
The law of causality is a source of confusion, and should be dropped from philosophy [Russell]
If causes are contiguous with events, only the last bit is relevant, or the event's timing is baffling [Russell]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
Striking a match causes its igniting, even if it sometimes doesn't work [Russell]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
The law of gravity has many consequences beyond its grounding observations [Russell]
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 [Russell]
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 [Russell]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
The laws of motion and gravitation are just parts of the definition of a kind of matter [Russell]
We can't know that our laws are exceptionless, or even that there are any laws [Russell]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
Occupying a place and change are prior to motion, so motion is just occupying places at continuous times [Russell]
Russell's 'at-at' theory says motion is to be at the intervening points at the intervening instants [Russell, by Psillos]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
Force is supposed to cause acceleration, but acceleration is a mathematical fiction [Russell]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
Matter is the limit of appearances as distance from the object diminishes [Russell]
Matter is a logical construction [Russell]
Matter requires a division into time-corpuscles as well as space-corpuscles [Russell]
At first matter is basic and known by sense-data; later Russell says matter is constructed [Russell, by Linsky,B]
27. Natural Reality / C. Space-Time / 1. Space / b. Space
There is 'private space', and there is also the 'space of perspectives' [Russell]
Six dimensions are needed for a particular, three within its own space, and three to locate that space [Russell]
27. Natural Reality / C. Space-Time / 1. Space / c. Points in space
Space is the extension of 'point', and aggregates of points seem necessary for geometry [Russell]
27. Natural Reality / C. Space-Time / 2. Time / a. Time
We never experience times, but only succession of events [Russell]
27. Natural Reality / C. Space-Time / 3. Space-Time
Mathematicians don't distinguish between instants of time and points on a line [Russell]
27. Natural Reality / D. Cosmology / 1. Cosmology
The 'universe' can mean what exists now, what always has or will exist [Russell]
28. God / A. Divine Nature / 6. 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 [Russell]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
The ontological argument begins with an unproven claim that 'there exists an x..' [Russell]
You can discuss 'God exists', so 'God' is a description, not a name [Russell]
29. Religion / D. Religious Issues / 2. Immortality / d. Heaven
That our heaven is a dull place reflects the misery of excessive work in life [Russell]