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All the ideas for 'Posthumous notes', 'The Principles of Mathematics' and '21: Book of Ecclesiastes'

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97 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
In much wisdom is much grief [Anon (Ecc)]
1. Philosophy / D. Nature of Philosophy / 8. Humour
Laughter is mad; of mirth, what doeth it? [Anon (Ecc)]
Sorrow is better than laughter [Anon (Ecc)]
1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
Analysis gives us nothing but the truth - but never the whole truth [Russell]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
The study of grammar is underestimated in philosophy [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]
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]
3. Truth / A. Truth Problems / 5. Truth Bearers
What is true or false is not mental, and is best called 'propositions' [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 / 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 / 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 / G. Formal Mereology / 1. Mereology
The part-whole relation is ultimate and indefinable [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
The only classes are things, predicates and relations [Russell]
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]
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
Variables don't stand alone, but exist as parts of propositional functions [Russell]
5. Theory of Logic / G. Quantification / 1. Quantification
'Any' is better than 'all' where infinite classes are concerned [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]
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]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Geometry throws no light on the nature of actual space [Russell]
In geometry, Kant and idealists aimed at the certainty of the premisses [Russell]
Pure geometry is deductive, and neutral over what exists [Russell]
In geometry, empiricists aimed at premisses consistent with experience [Russell]
Two points have a line joining them (descriptive), a distance (metrical), and a whole line (projective) [Russell, by PG]
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]
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]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Ordinals are defined through mathematical induction [Russell]
Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic [Russell]
Ordinals are types of series of terms in a row, rather than the 'nth' instance [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 / 4. Using Numbers / b. Quantity
Some quantities can't be measured, and some non-quantities are measurable [Russell]
Quantity is not part of mathematics, where it is replaced by order [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]
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 / 5. The Infinite / a. The Infinite
We do not currently know whether, of two infinite numbers, one must be greater than the other [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
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 / 4. Axioms for Number / a. Axioms for numbers
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
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]
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 / 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 / 6. Logicism / a. Early logicism
Pure mathematics is the class of propositions of the form 'p implies q' [Russell]
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]
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 / E. Categories / 3. Proposed Categories
Four classes of terms: instants, points, terms at instants only, and terms at instants and points [Russell]
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]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness [Russell]
8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation
Symmetrical and transitive relations are formally like equality [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]
9. Objects / A. Existence of Objects / 5. Simples
Unities are only in propositions or concepts, and nothing that exists has unity [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 / 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
Terms are identical if they belong to all the same classes [Russell]
It at least makes sense to say two objects have all their properties in common [Wittgenstein on Russell]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
Transcendental philosophy is the subject becoming the originator of unified reality [Kant]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
The principle of Abstraction says a symmetrical, transitive relation analyses into an identity [Russell]
Abstraction principles identify a common property, which is some third term with the right relation [Russell]
A certain type of property occurs if and only if there is an equivalence relation [Russell]
19. Language / D. Propositions / 1. Propositions
Proposition contain entities indicated by words, rather than the words themselves [Russell]
19. Language / D. Propositions / 3. Concrete Propositions
If propositions are facts, then false and true propositions are indistinguishable [Davidson on 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]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
All is vanity, saith the Preacher [Anon (Ecc)]
25. Society / E. State Functions / 4. Education / a. Education principles
Books are endless, and study is wearisome [Anon (Ecc)]
26. Natural Theory / C. Causation / 7. Eliminating causation
We can drop 'cause', and just make inferences between facts [Russell]
Moments and points seem to imply other moments and points, but don't cause them [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]
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]
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 / 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 / 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]