### Ideas of B Russell/AN Whitehead, by Theme

#### [British, fl. 1912, Professors at Cambridge. Collaborators during 1910-1913.]

green numbers give full details    |    back to list of philosophers    |     expand these 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 [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]
###### 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 [Shapiro]
 18208 We regard classes as mere symbolic or linguistic conveniences
###### 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]
 9359 Russell's implication means that random sentences imply one another [Lewis,CI]
###### 5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
 21707 Russell unusually saw logic as 'interpreted' (though very general, and neutral) [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 [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 [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 [Bostock]
###### 6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
 10025 Russell and Whitehead took arithmetic to be higher-order logic [Hodes]
 8683 Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Friend]
 10037 'Principia' lacks a precise statement of the syntax [Gödel]
###### 6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
 10093 The ramified theory of types used propositional functions, and covered bound variables [George/Velleman]
 8691 The Russell/Whitehead type theory was limited, and was not really logic [Friend]
###### 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]
###### 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
 8684 Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [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 [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 [Adams,RM]
###### 12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
 10040 Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [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 [Linsky,B]
 18275 Only the act of judging completes the meaning of a statement