Combining Texts

All the ideas for 'A Dictionary of Political Thought', 'Introduction to Mathematical Philosophy' and 'Possibility'

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


92 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
If an analysis shows the features of a concept, it doesn't seem to 'reduce' the concept [Jubien]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [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 / F. Fallacies / 8. Category Mistake / a. Category mistakes
The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false [Russell, by Orenstein]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
An argument 'satisfies' a function φx if φa is true [Russell]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
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 / 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
Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell]
We may assume that there are infinite collections, as there is no logical reason against them [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 shows that if any two cardinals are not equal, one must be the greater [Russell]
Choice is equivalent to the proposition that every class is well-ordered [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]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
Propositions about classes can be reduced to propositions about their defining functions [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 are logical fictions, and are not part of the ultimate furniture of the world [Russell]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
It is a mistake to think that the logic developed for mathematics can clarify language and philosophy [Jubien]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
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 / C. Ontology of Logic / 1. Ontology of Logic
Logic can only assert hypothetical existence [Russell]
Logic is concerned with the real world just as truly as zoology [Russell]
Logic can be known a priori, without study of the actual world [Russell]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
We only grasp a name if we know whether to apply it when the bearer changes [Jubien]
The baptiser picks the bearer of a name, but social use decides the category [Jubien]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
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
Examples show that ordinary proper names are not rigid designators [Jubien]
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
We could make a contingent description into a rigid and necessary one by adding 'actual' to it [Jubien]
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
Philosophers reduce complex English kind-quantifiers to the simplistic first-order quantifier [Jubien]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
If straight lines were like ratios they might intersect at a 'gap', and have no point in common [Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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
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 / 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 / c. Counting procedure
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 / 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
Infinity and continuity used to be philosophy, but are now mathematics [Russell]
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]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell]
'0', 'number' and 'successor' cannot be defined by Peano's axioms [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 / 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
For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf]
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 / g. Particular being
To exist necessarily is to have an essence whose own essence must be instantiated [Jubien]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
If objects are just conventional, there is no ontological distinction between stuff and things [Jubien]
7. Existence / D. Theories of Reality / 7. Fictionalism
Classes are logical fictions, made from defining characteristics [Russell]
7. Existence / E. Categories / 1. Categories
The category of Venus is not 'object', or even 'planet', but a particular class of good-sized object [Jubien]
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]
'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
The idea that every entity must have identity conditions is an unfortunate misunderstanding [Jubien]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
Any entity has the unique property of being that specific entity [Jubien]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
It is incoherent to think that a given entity depends on its kind for its existence [Jubien]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
Objects need conventions for their matter, their temporal possibility, and their spatial possibility [Jubien]
Basically, the world doesn't have ready-made 'objects'; we carve objects any way we like [Jubien]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
If the statue is loved and the clay hated, that is about the object first qua statue, then qua clay [Jubien]
If one entity is an object, a statue, and some clay, these come apart in at least three ways [Jubien]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
The idea of coincident objects is a last resort, as it is opposed to commonsense naturalism [Jubien]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
Parts seem to matter when it is just an object, but not matter when it is a kind of object [Jubien]
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 / 7. Essence and Necessity / b. Essence not necessities
We should not regard essentialism as just nontrivial de re necessity [Jubien]
9. Objects / E. Objects over Time / 9. Ship of Theseus
Thinking of them as 'ships' the repaired ship is the original, but as 'objects' the reassembly is the original [Jubien]
Rearranging the planks as a ship is confusing; we'd say it was the same 'object' with a different arrangement [Jubien]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
If two objects are indiscernible across spacetime, how could we decide whether or not they are the same? [Jubien]
10. Modality / A. Necessity / 6. Logical Necessity
Entailment does not result from mutual necessity; mutual necessity ensures entailment [Jubien]
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 / C. Sources of Modality / 1. Sources of Necessity
Modality concerns relations among platonic properties [Jubien]
To analyse modality, we must give accounts of objects, properties and relations [Jubien]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
If something is true in all possible worlds then it is logically necessary [Russell]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
The love of possible worlds is part of the dream that technical logic solves philosophical problems [Jubien]
Possible worlds don't explain necessity, because they are a bunch of parallel contingencies [Jubien]
14. Science / B. Scientific Theories / 1. Scientific Theory
Mathematically expressed propositions are true of the world, but how to interpret them? [Russell]
17. Mind and Body / E. Mind as Physical / 6. Conceptual Dualism
Analysing mental concepts points to 'inclusionism' - that mental phenomena are part of the physical [Jubien]
19. Language / B. Reference / 3. Direct Reference / a. Direct reference
First-order logic tilts in favour of the direct reference theory, in its use of constants for objects [Jubien]
19. Language / D. Propositions / 1. Propositions
Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
Consequentialism emphasises value rather than obligation in morality [Scruton]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
Altruism is either emotional (where your interests are mine) or moral (where they are reasons for me) [Scruton]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton]
24. Political Theory / D. Ideologies / 3. Conservatism
Allegiance is fundamental to the conservative view of society [Scruton]
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
Democrats are committed to a belief and to its opposite, if the majority prefer the latter [Scruton]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG]
25. Social Practice / D. Justice / 2. The Law / d. Legal positivism
For positivists law is a matter of form, for naturalists it is a matter of content [Scruton]
25. Social Practice / F. Life Issues / 3. Abortion
The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton]