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Ideas of B Russell/AN Whitehead, by Text

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

1913 Principia Mathematica
p.5 Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Linsky,B]
p.17 The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Hughes/Cresswell]
p.47 The ramified theory of types used propositional functions, and covered bound variables [George/Velleman]
p.50 Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Friend]
p.51 Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Friend]
p.70 The Russell/Whitehead type theory was limited, and was not really logic [Friend]
p.101 Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B]
p.122 A real number is the class of rationals less than the number [Shapiro]
p.125 The multiple relations theory says assertions about propositions are about their ingredients [Linsky,B]
p.127 To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Shapiro]
p.148 Russell and Whitehead took arithmetic to be higher-order logic [Hodes]
p.177 Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine]
p.285 Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Bostock]
p.366 Russell's implication means that random sentences imply one another [Lewis,CI]
p.448 In 'Principia' a new abstract theory of relations appeared, and was applied [Gödel]
p.448 'Principia' lacks a precise statement of the syntax [Gödel]
p.452 Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Gödel]
p.459 Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Shapiro]
I p.57 p.175 An object is identical with itself, and no different indiscernible object can share that [Adams,RM]
p.267 p.267 In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays]
p.44 p.83 A judgement is a complex entity, of mind and various objects
p.44 p.84 The meaning of 'Socrates is human' is completed by a judgement
p.44 p.84 Propositions as objects of judgement don't exist, because we judge several objects, not one
p.44 p.117 The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M]
p.44 p.145 Only the act of judging completes the meaning of a statement
p.72 p.172 We regard classes as mere symbolic or linguistic conveniences