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All the ideas for 'fragments/reports', 'Principia Mathematica' and 'Ideas'

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48 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Because of Darwin, wisdom as a definite attainable state has faded [Watson]
1. Philosophy / B. History of Ideas / 1. History of Ideas
The three key ideas are the soul, Europe, and the experiment [Watson]
The big idea: imitation, the soul, experiments, God, heliocentric universe, evolution? [Watson]
2. Reason / E. Argument / 3. Analogy
Babylonian thinking used analogy, rather than deduction or induction [Watson]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro]
We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead]
5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead]
Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Mesopotamian numbers applied to specific things, and then became abstract [Watson]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / a. Defining numbers
Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes]
Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend]
'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman]
The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
By nature people are close to one another, but culture drives them apart [Hippias]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B]
A judgement is a complex entity, of mind and various objects [Russell/Whitehead]
The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead]
The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead]
Only the act of judging completes the meaning of a statement [Russell/Whitehead]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
Modern democracy is actually elective oligarchy [Watson]
26. Natural Theory / A. Speculations on Nature / 1. Nature
Greek philosophers invented the concept of 'nature' as their special subject [Watson]
27. Natural Reality / G. Biology / 3. Evolution
DNA mutation suggests humans and chimpanzees diverged 6.6 million years ago [Watson]
28. God / C. Attitudes to God / 4. God Reflects Humanity
During the rise of civilizations, the main gods changed from female to male [Watson]
29. Religion / A. Polytheistic Religion / 3. Hinduism
Hinduism has no founder, or prophet, or creed, or ecclesiastical structure [Watson]
29. Religion / B. Monotheistic Religion / 2. Judaism
Modern Judaism became stabilised in 200 CE [Watson]
The Israelites may have asserted the uniqueness of Yahweh to justify land claims [Watson]
Monotheism was a uniquely Israelite creation within the Middle East [Watson]
29. Religion / B. Monotheistic Religion / 3. Zoroastrianism
The Gathas (hymns) of Zoroastrianism date from about 1000 BCE [Watson]
Zoroaster conceived the afterlife, judgement, heaven and hell, and the devil [Watson]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Paul's early writings mention few striking episodes from Jesus' life [Watson]
Jesus never intended to start a new religion [Watson]
29. Religion / C. Spiritual Disciplines / 1. Confucianism
Confucius revered the spiritual world, but not the supernatural, or a personal god, or the afterlife [Watson]
29. Religion / C. Spiritual Disciplines / 2. Taoism
Taoism aims at freedom from the world, the body, the mind, and nature [Watson]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
The three basic ingredients of religion are: the soul, seers or priests, and ritual [Watson]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
In ancient Athens the souls of the dead are received by the 'upper air' [Watson]