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All the ideas for 'Explaining the A Priori', 'Treatise of Human Nature' and 'Introduction to Mathematical Philosophy'

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115 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell]
2. Reason / A. Nature of Reason / 7. Status of Reason
Reason is and ought to be the slave of the passions [Hume]
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 / 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 / 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 / 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]
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
Two numbers are equal if all of their units correspond to one another [Hume]
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 / 2. Types of Existence
There is no medium state between existence and non-existence [Hume]
7. Existence / D. Theories of Reality / 7. Fictionalism
Classes are logical fictions, made from defining characteristics [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]
'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
Power is the possibility of action, as discovered by experience [Hume]
There may well be powers in things, with which we are quite unacquainted [Hume]
8. Modes of Existence / C. Powers and Dispositions / 7. Against Powers
We have no idea of powers, because we have no impressions of them [Hume]
The distinction between a power and its exercise is entirely frivolous [Hume]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
Momentary impressions are wrongly identified with one another on the basis of resemblance [Hume, by Quine]
If we see a resemblance among objects, we apply the same name to them, despite their differences [Hume]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
Individuation is only seeing that a thing is stable and continuous over time [Hume]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
The only meaning we have for substance is a collection of qualities [Hume]
Aristotelians propose accidents supported by substance, but they don't understand either of them [Hume]
9. Objects / D. Essence of Objects / 3. Individual Essences
The essence of individuality is beyond description, and hence irrelevant to science [Russell]
9. Objects / E. Objects over Time / 1. Objects over Time
A change more obviously destroys an identity if it is quick and observed [Hume]
Changing a part can change the whole, not absolutely, but by its proportion of the whole [Hume]
9. Objects / E. Objects over Time / 2. Objects that Change
If a republic can retain identity through many changes, so can an individual [Hume]
If identity survives change or interruption, then resemblance, contiguity or causation must unite the parts of it [Hume]
9. Objects / E. Objects over Time / 7. Intermittent Objects
If a ruined church is rebuilt, its relation to its parish makes it the same church [Hume]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
We accept the identity of a river through change, because it is the river's nature [Hume]
9. Objects / E. Objects over Time / 9. Ship of Theseus
The purpose of the ship makes it the same one through all variations [Hume]
9. Objects / F. Identity among Objects / 1. Concept of Identity
Multiple objects cannot convey identity, because we see them as different [Hume]
Both number and unity are incompatible with the relation of identity [Hume]
9. Objects / F. Identity among Objects / 5. Self-Identity
'An object is the same with itself' is meaningless; it expresses unity, not identity [Hume]
Saying an object is the same with itself is only meaningful over a period of time [Hume]
10. Modality / A. Necessity / 10. Impossibility
Nothing we clearly imagine is absolutely impossible [Hume]
10. Modality / A. Necessity / 11. Denial of Necessity
Necessity only exists in the mind, and not in objects [Hume]
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 / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
If something is true in all possible worlds then it is logically necessary [Russell]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / c. Representative realism
Hume says objects are not a construction, but an imaginative leap [Hume, by Robinson,H]
12. Knowledge Sources / D. Empiricism / 2. Associationism
Associationism results from having to explain intentionality just with sense-data [Robinson,H on Hume]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Even Hume didn't include mathematics in his empiricism [Hume, by Kant]
13. Knowledge Criteria / C. External Justification / 8. Social Justification
Mathematicians only accept their own proofs when everyone confims them [Hume]
13. Knowledge Criteria / D. Scepticism / 2. Types of Scepticism
Hume became a total sceptic, because he believed that reason was a deception [Hume, by Kant]
14. Science / B. Scientific Theories / 1. Scientific Theory
Mathematically expressed propositions are true of the world, but how to interpret them? [Russell]
14. Science / C. Induction / 1. Induction
The idea of inductive evidence, around 1660, made Hume's problem possible [Hume, by Hacking]
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
Memory, senses and understanding are all founded on the imagination [Hume]
16. Persons / B. Nature of the Self / 5. Self as Associations
Hume's 'bundle' won't distinguish one mind with ten experiences from ten minds [Searle on Hume]
A person is just a fast-moving bundle of perceptions [Hume]
The parts of a person are always linked together by causation [Hume]
Hume gives us an interesting sketchy causal theory of personal identity [Perry on Hume]
A person is simply a bundle of continually fluctuating perceptions [Hume]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
Introspection always discovers perceptions, and never a Self without perceptions [Hume]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / a. Memory is Self
Memory only reveals personal identity, by showing cause and effect [Hume]
We use memory to infer personal actions we have since forgotten [Hume]
Memory not only reveals identity, but creates it, by producing resemblances [Hume]
Who thinks that because you have forgotten an incident you are no longer that person? [Hume]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
Causation unites our perceptions, by producing, destroying and modifying each other [Hume]
16. Persons / E. Rejecting the Self / 4. Denial of the Self
A continuous lifelong self must be justified by a single sustained impression, which we don't have [Hume]
When I introspect I can only observe my perceptions, and never a self which has them [Hume]
We pretend our perceptions are continuous, and imagine a self to fill the gaps [Hume]
Identity in the mind is a fiction, like that fiction that plants and animals stay the same [Hume]
18. Thought / D. Concepts / 2. Origin of Concepts / a. Origin of concepts
The concept 'red' is tied to what actually individuates red things [Peacocke]
19. Language / D. Propositions / 1. Propositions
Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell]
20. Action / A. Definition of Action / 2. Duration of an Action
If one event causes another, the two events must be wholly distinct [Hume, by Wilson/Schpall]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
For Hume, practical reason has little force, because we can always modify our desires [Hume, by Graham]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
Reason alone can never be a motive to any action of the will [Hume]
20. Action / C. Motives for Action / 4. Responsibility for Actions
You can only hold people responsible for actions which arise out of their character [Hume]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
We cannot discover vice by studying a wilful murder; that only arises from our own feelings [Hume]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
Modern science has destroyed the Platonic synthesis of scientific explanation and morality [Hume, by Taylor,C]
The problem of getting to 'ought' from 'is' would also apply in getting to 'owes' or 'needs' [Anscombe on Hume]
You can't move from 'is' to 'ought' without giving some explanation or reason for the deduction [Hume]
22. Metaethics / B. Value / 2. Values / i. Self-interest
Total selfishness is not irrational [Hume]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / a. Early Modern matter
We have no good concept of solidity or matter, because accounts of them are all circular [Hume]
26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
For Hume a constant conjunction is both necessary and sufficient for causation [Hume, by Crane]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
Hume seems to presuppose necessary connections between mental events [Kripke on Hume]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
If all of my perceptions were removed by death, nothing more is needed for total annihilation [Hume]