green numbers give full details.     |    back to list of philosophers     |     expand these ideas

Ideas of B Russell/AN Whitehead, by Text

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

1913 Principia Mathematica
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.122 A real number is the class of rationals less than the number [Korsgaard]
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.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