Combining Philosophers

All the ideas for Wilson,G/Schpall,S, Archelaus and B Russell/AN Whitehead

expand these ideas     |    start again     |     specify just one area for these philosophers

43 ideas

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
8683 Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend]
10025 Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes]
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]
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 / 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
20014 Actions include: the involuntary, the purposeful, the intentional, and the self-consciously autonomous [Wilson/Schpall]
20. Action / A. Definition of Action / 4. Action as Movement
20019 Maybe bodily movements are not actions, but only part of an agent's action of moving [Wilson/Schpall]
20021 Is the action the arm movement, the whole causal process, or just the trying to do it? [Wilson/Schpall]
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
20022 To be intentional, an action must succeed in the manner in which it was planned [Wilson/Schpall]
20023 If someone believes they can control the lottery, and then wins, the relevant skill is missing [Wilson/Schpall]
20025 We might intend two ways to acting, knowing only one of them can succeed [Wilson/Schpall]
20. Action / B. Preliminaries of Action / 1. Intention to Act / c. Reducing intentions
20031 On one model, an intention is belief-desire states, and intentional actions relate to beliefs and desires [Wilson/Schpall]
20. Action / B. Preliminaries of Action / 1. Intention to Act / d. Group intentions
20028 Groups may act for reasons held by none of the members, so maybe groups are agents [Wilson/Schpall]
20027 If there are shared obligations and intentions, we may need a primitive notion of 'joint commitment' [Wilson/Schpall]
20. Action / C. Motives for Action / 2. Acting on Beliefs / b. Action cognitivism
20016 Strong Cognitivism identifies an intention to act with a belief [Wilson/Schpall]
20017 Weak Cognitivism says intentions are only partly constituted by a belief [Wilson/Schpall]
20018 Strong Cognitivism implies a mode of 'practical' knowledge, not based on observation [Wilson/Schpall]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
20012 Maybe the explanation of an action is in the reasons that make it intelligible to the agent [Wilson/Schpall]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
20013 It is generally assumed that reason explanations are causal [Wilson/Schpall]
20029 Causalists allow purposive explanations, but then reduce the purpose to the action's cause [Wilson/Schpall]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]