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All the ideas for 'fragments/reports', 'Problems of Philosophy' and 'Intermediate Logic'

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160 ideas

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]
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
Metaphysics cannot give knowledge of the universe as a whole [Russell]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
Philosophy is similar to science, and has no special source of wisdom [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]
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]
3. Truth / A. Truth Problems / 7. Falsehood
A good theory of truth must make falsehood possible [Russell]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
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]
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]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
The mortality of Socrates is more certain from induction than it is from deduction [Russell]
Venn Diagrams map three predicates into eight compartments, then look for the conclusion [Bostock]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
'Disjunctive Normal Form' is ensuring that no conjunction has a disjunction within its scope [Bostock]
'Conjunctive Normal Form' is ensuring that no disjunction has a conjunction within its scope [Bostock]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
'Cutting' allows that if x is proved, and adding y then proves z, you can go straight to z [Bostock]
'Negation' says that Γ,¬φ|= iff Γ|=φ [Bostock]
'Conjunction' says that Γ|=φ∧ψ iff Γ|=φ and Γ|=ψ [Bostock]
'Assumptions' says that a formula entails itself (φ|=φ) [Bostock]
'Thinning' allows that if premisses entail a conclusion, then adding further premisses makes no difference [Bostock]
The 'conditional' is that Γ|=φ→ψ iff Γ,φ|=ψ [Bostock]
'Disjunction' says that Γ,φ∨ψ|= iff Γ,φ|= and Γ,ψ|= [Bostock]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
A logic with ¬ and → needs three axiom-schemas and one rule as foundation [Bostock]
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
A 'free' logic can have empty names, and a 'universally free' logic can have empty domains [Bostock]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Truth is the basic notion in classical logic [Bostock]
Elementary logic cannot distinguish clearly between the finite and the infinite [Bostock]
Fictional characters wreck elementary logic, as they have contradictions and no excluded middle [Bostock]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem' [Bostock]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Γ|=φ is 'entails'; Γ|= is 'is inconsistent'; |=φ is 'valid' [Bostock]
Validity is a conclusion following for premises, even if there is no proof [Bostock]
It seems more natural to express |= as 'therefore', rather than 'entails' [Bostock]
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]
MPP is a converse of Deduction: If Γ |- φ→ψ then Γ,φ|-ψ [Bostock]
MPP: 'If Γ|=φ and Γ|=φ→ψ then Γ|=ψ' (omit Γs for Detachment) [Bostock]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
|= α=α and α=β |= φ(α/ξ ↔ φ(β/ξ) fix identity [Bostock]
The sign '=' is a two-place predicate expressing that 'a is the same thing as b' (a=b) [Bostock]
If we are to express that there at least two things, we need identity [Bostock]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Truth-functors are usually held to be defined by their truth-tables [Bostock]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
A 'zero-place' function just has a single value, so it is a name [Bostock]
A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs [Bostock]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
In logic, a name is just any expression which refers to a particular single object [Bostock]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
Proper names are really descriptions, and can be replaced by a description in a person's mind [Russell]
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
An expression is only a name if it succeeds in referring to a real object [Bostock]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Definite descriptions don't always pick out one thing, as in denials of existence, or errors [Bostock]
We are only obliged to treat definite descriptions as non-names if only the former have scope [Bostock]
The phrase 'a so-and-so' is an 'ambiguous' description'; 'the so-and-so' (singular) is a 'definite' description [Russell]
Definite desciptions resemble names, but can't actually be names, if they don't always refer [Bostock]
Because of scope problems, definite descriptions are best treated as quantifiers [Bostock]
Definite descriptions are usually treated like names, and are just like them if they uniquely refer [Bostock]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
Names do not have scope problems (e.g. in placing negation), but Russell's account does have that problem [Bostock]
5. Theory of Logic / G. Quantification / 1. Quantification
'Prenex normal form' is all quantifiers at the beginning, out of the scope of truth-functors [Bostock]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
If we allow empty domains, we must allow empty names [Bostock]
5. Theory of Logic / H. Proof Systems / 1. Proof Systems
An 'informal proof' is in no particular system, and uses obvious steps and some ordinary English [Bostock]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
Quantification adds two axiom-schemas and a new rule [Bostock]
Axiom systems from Frege, Russell, Church, Lukasiewicz, Tarski, Nicod, Kleene, Quine... [Bostock]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
'Conditonalised' inferences point to the Deduction Theorem: If Γ,φ|-ψ then Γ|-φ→ψ [Bostock]
The Deduction Theorem greatly simplifies the search for proof [Bostock]
Proof by Assumptions can always be reduced to Proof by Axioms, using the Deduction Theorem [Bostock]
The Deduction Theorem and Reductio can 'discharge' assumptions - they aren't needed for the new truth [Bostock]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
Natural deduction takes proof from assumptions (with its rules) as basic, and axioms play no part [Bostock]
Excluded middle is an introduction rule for negation, and ex falso quodlibet will eliminate it [Bostock]
In natural deduction we work from the premisses and the conclusion, hoping to meet in the middle [Bostock]
Natural deduction rules for → are the Deduction Theorem (→I) and Modus Ponens (→E) [Bostock]
5. Theory of Logic / H. Proof Systems / 5. Tableau Proof
Tableau proofs use reduction - seeking an impossible consequence from an assumption [Bostock]
Non-branching rules add lines, and branching rules need a split; a branch with a contradiction is 'closed' [Bostock]
A completed open branch gives an interpretation which verifies those formulae [Bostock]
In a tableau proof no sequence is established until the final branch is closed; hypotheses are explored [Bostock]
Tableau rules are all elimination rules, gradually shortening formulae [Bostock]
A tree proof becomes too broad if its only rule is Modus Ponens [Bostock]
Unlike natural deduction, semantic tableaux have recipes for proving things [Bostock]
5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
Each line of a sequent calculus is a conclusion of previous lines, each one explicitly recorded [Bostock]
A sequent calculus is good for comparing proof systems [Bostock]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Interpretation by assigning objects to names, or assigning them to variables first [Bostock, by PG]
5. Theory of Logic / I. Semantics of Logic / 5. Extensionalism
Extensionality is built into ordinary logic semantics; names have objects, predicates have sets of objects [Bostock]
If an object has two names, truth is undisturbed if the names are swapped; this is Extensionality [Bostock]
5. Theory of Logic / K. Features of Logics / 2. Consistency
A set of formulae is 'inconsistent' when there is no interpretation which can make them all true [Bostock]
A proof-system is 'absolutely consistent' iff we don't have |-(S)φ for every formula [Bostock]
For 'negation-consistent', there is never |-(S)φ and |-(S)¬φ [Bostock]
5. Theory of Logic / K. Features of Logics / 6. Compactness
Inconsistency or entailment just from functors and quantifiers is finitely based, if compact [Bostock]
Compactness means an infinity of sequents on the left will add nothing new [Bostock]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
Ordinary or mathematical induction assumes for the first, then always for the next, and hence for all [Bostock]
Complete induction assumes for all numbers less than n, then also for n, and hence for all numbers [Bostock]
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]
7. Existence / D. Theories of Reality / 3. Reality
Space is neutral between touch and sight, so it cannot really be either of them [Russell]
7. Existence / D. Theories of Reality / 8. Facts / c. Facts and truths
In a world of mere matter there might be 'facts', but no truths [Russell]
8. Modes of Existence / A. Relations / 1. Nature of Relations
Because we depend on correspondence, we know relations better than we know the items that relate [Russell]
That Edinburgh is north of London is a non-mental fact, so relations are independent universals [Russell]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
A relation is not reflexive, just because it is transitive and symmetrical [Bostock]
Relations can be one-many (at most one on the left) or many-one (at most one on the right) [Bostock]
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
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 / 4. Concept Nominalism
If we consider whiteness to be merely a mental 'idea', we rob it of its universality [Russell]
9. Objects / F. Identity among Objects / 5. Self-Identity
If non-existent things are self-identical, they are just one thing - so call it the 'null object' [Bostock]
10. Modality / A. Necessity / 6. Logical Necessity
The idea that anything which can be proved is necessary has a problem with empty names [Bostock]
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]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Knowledge cannot be precisely defined, as it merges into 'probable opinion' [Russell]
11. Knowledge Aims / A. Knowledge / 4. Belief / b. Elements of beliefs
Belief relates a mind to several things other than itself [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 / 4. The Cogito
Descartes showed that subjective things are the most certain [Russell]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
'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]
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 / 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
Some propositions are self-evident, but their implications may also be self-evident [Russell]
Particular instances are more clearly self-evident than any general principles [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]
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]
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]
Knowledge by descriptions enables us to transcend private experience [Russell]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
I can know the existence of something with which nobody is acquainted [Russell]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
Images are not memory, because they are present, and memories are of the past [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]
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 / D. Scepticism / 5. Dream Scepticism
Dreams can be explained fairly scientifically if we assume a physical world [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 / 3. Limits of Induction
Chickens are not very good at induction, and are surprised when their feeder wrings their neck [Russell]
We can't prove induction from experience without begging the question [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]
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 / 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]
18. Thought / A. Modes of Thought / 5. Rationality / a. 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
In order to explain falsehood, a belief must involve several terms, not two [Russell]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
A universal of which we are aware is called a 'concept' [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]
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 / C. Assigning Meanings / 3. Predicates
A (modern) predicate is the result of leaving a gap for the name in a sentence [Bostock]
19. Language / D. Propositions / 6. Propositions Critique
The main aim of the multiple relations theory of judgement was to dispense with propositions [Russell, by Linsky,B]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
23. Ethics / E. Utilitarianism / 2. Ideal of Pleasure
Judgements of usefulness depend on judgements of value [Russell]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
We can't know that our laws are exceptionless, or even that there are any laws [Russell]