Combining Texts

All the ideas for 'The Central Questions of Philosophy', 'Moral Consciousness and Communicative Action' and 'Principia Mathematica'

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41 ideas

2. Reason / E. Argument / 3. Analogy
5331 You can't infer that because you have a hidden birth-mark, everybody else does [Ayer]
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 / 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]
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
10037 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead]
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]
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 / 11. Ontological Commitment / b. Commitment of quantifiers
2611 It is currently held that quantifying over something implies belief in its existence [Ayer]
9. Objects / D. Essence of Objects / 3. Individual Essences
16520 We see properties necessary for a kind (in the definition), but not for an individual [Ayer]
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]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
2613 The theory of other minds has no rival [Ayer]
5328 Originally I combined a mentalistic view of introspection with a behaviouristic view of other minds [Ayer]
5330 Physicalism undercuts the other mind problem, by equating experience with 'public' brain events [Ayer]
16. Persons / B. Nature of the Self / 5. Self as Associations
5326 Qualia must be united by a subject, because they lead to concepts and judgements [Ayer]
5325 Is something an 'experience' because it relates to other experiences, or because it relates to a subject? [Ayer]
16. Persons / B. Nature of the Self / 7. Self and Body / a. Self needs body
5324 Bodily identity and memory work together to establish personal identity [Ayer]
16. Persons / C. Self-Awareness / 2. Knowing the Self
5322 Self-consciousness is not basic, because experiences are not instrinsically marked with ownership [Ayer]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / c. Inadequacy of mental continuity
5327 Temporal gaps in the consciousness of a spirit could not be bridged by memories [Ayer]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
5329 Why shouldn't we say brain depends on mind? Better explanation! [Ayer]
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 / D. Propositions / 3. Concrete Propositions
23453 Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead]
19. Language / D. Propositions / 6. Propositions Critique
2610 Talk of propositions is just shorthand for talking about equivalent sentences [Ayer]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
15677 Moral right is linked to validity and truth, so morality is a matter of knowledge, not an expression of values [Habermas, by Finlayson]
23. Ethics / B. Contract Ethics / 9. Contractualism
15671 Move from individual willing of a general law, to willing norms agreed with other people [Habermas]