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All the ideas for 'Principia Mathematica', 'Intellectual Autobiography' and 'Works (refs to 8 vol Colli and Montinari)'

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61 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
7846 Nietzsche thinks philosophy makes us more profound, but not better [Nietzsche, by Ansell Pearson]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
20107 How many mediocre thinkers are occupied with influential problems! [Nietzsche]
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
20352 Nietzsche has a metaphysics, as well as perspectives - the ontology is the perspectives [Nietzsche, by Richardson]
2. Reason / A. Nature of Reason / 7. Status of Reason
20379 Reason is just another organic drive, developing late, and fighting for equality [Nietzsche]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
18901 Truthmakers are facts 'of' a domain, not something 'in' the domain [Sommers]
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
18904 'Predicable' terms come in charged pairs, with one the negation of the other [Sommers, by Engelbretsen]
18895 Logic which maps ordinary reasoning must be transparent, and free of variables [Sommers]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
9542 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
21720 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
10044 Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro]
18208 We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead]
5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
8204 Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead]
9359 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
21707 Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
18897 Predicate logic has to spell out that its identity relation '=' is an equivalent relation [Sommers]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18893 Translating into quantificational idiom offers no clues as to how ordinary thinkers reason [Sommers]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
18903 Sommers promotes the old idea that negation basically refers to terms [Sommers, by Engelbretsen]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
10036 In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel]
5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
18894 Predicates form a hierarchy, from the most general, down to names at the bottom [Sommers]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
18248 A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / a. Defining numbers
18152 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
10025 Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes]
8683 Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend]
10037 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10093 The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman]
8691 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
10305 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
8684 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
8746 To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro]
7. Existence / D. Theories of Reality / 2. Realism
18900 Unfortunately for realists, modern logic cannot say that some fact exists [Sommers]
7. Existence / D. Theories of Reality / 5. Naturalism
20123 First see nature as non-human, then fit ourselves into this view of nature [Nietzsche]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
20105 Storms are wonderful expressions of free powers! [Nietzsche]
9. Objects / D. Essence of Objects / 3. Individual Essences
20376 We begin with concepts of kinds, from individuals; but that is not the essence of individuals [Nietzsche]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
12033 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
10040 Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
21725 The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B]
23474 A judgement is a complex entity, of mind and various objects [Russell/Whitehead]
23455 The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead]
23480 The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead]
18275 Only the act of judging completes the meaning of a statement [Russell/Whitehead]
19. Language / B. Reference / 1. Reference theories
18898 In standard logic, names are the only way to refer [Sommers]
19. Language / D. Propositions / 3. Concrete Propositions
23453 Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead]
20. Action / A. Definition of Action / 1. Action Theory
22501 Nietzsche classified actions by the nature of the agent, not the nature of the act [Nietzsche, by Foot]
20. Action / C. Motives for Action / 4. Responsibility for Actions
22500 Nietzsche failed to see that moral actions can be voluntary without free will [Foot on Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
20128 Each person has a fixed constitution, which makes them a particular type of person [Nietzsche, by Leiter]
22503 Nietzsche could only revalue human values for a different species [Nietzsche, by Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / f. Übermensch
8041 The superman is a monstrous oddity, not a serious idea [MacIntyre on Nietzsche]
20135 Nietzsche's higher type of man is much more important than the idealised 'superman' [Nietzsche, by Leiter]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / g. Will to power
20353 The 'will to power' is basically applied to drives and forces, not to people [Nietzsche, by Richardson]
22. Metaethics / B. Value / 2. Values / g. Love
20113 Friendly chats undermine my philosophy; wanting to be right at the expense of love is folly [Nietzsche]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
22475 Moral generalisation is wrong, because we should evaluate individual acts [Nietzsche, by Foot]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
22476 Nietzsche thought our psychology means there can't be universal human virtues [Nietzsche, by Foot]
23. Ethics / F. Existentialism / 1. Existentialism
20104 Nietzsche tried to lead a thought-provoking life [Safranski on Nietzsche]
23. Ethics / F. Existentialism / 2. Nihilism
7847 Initially nihilism was cosmic, but later Nietzsche saw it as a cultural matter [Nietzsche, by Ansell Pearson]
9782 Nietzsche urges that nihilism be active, and will nothing itself [Nietzsche, by Zizek]
23. Ethics / F. Existentialism / 4. Boredom
20102 Flight from boredom leads to art [Nietzsche]
23. Ethics / F. Existentialism / 7. Existential Action
20106 Nietzsche was fascinated by a will that can turn against itself [Nietzsche, by Safranski]
23. Ethics / F. Existentialism / 8. Eternal Recurrence
20124 Reliving life countless times - this gives the value back to life which religion took away [Nietzsche]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
20367 Individual development is more important than the state, but a community is necessary [Nietzsche]
24. Political Theory / B. Nature of a State / 4. Citizenship
20371 Nietzsche thinks we should join a society, in order to criticise, heal and renew it [Nietzsche, by Richardson]
24. Political Theory / B. Nature of a State / 5. Culture
20108 Every culture loses its identity and power if it lacks a major myth [Nietzsche]