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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.17 The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules
p.47 The ramified theory of types used propositional functions, and covered bound variables
p.50 Russell and Whitehead were not realists, but embraced nearly all of maths in logic
p.51 Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality
p.70 The Russell/Whitehead type theory was limited, and was not really logic
p.122 A real number is the class of rationals less than the number
p.127 To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it
p.148 Russell and Whitehead took arithmetic to be higher-order logic
p.285 Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers
p.448 'Principia' lacks a precise statement of the syntax
p.448 In 'Principia' a new abstract theory of relations appeared, and was applied
p.452 Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory
p.459 Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element
I p.57 p.175 An object is identical with itself, and no different indiscernible object can share that
p.267 p.267 In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains
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