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Ideas of B Russell/AN Whitehead, by Text
[British, fl. 1912, Professors at Cambridge. Collaborators during 1910-1913.]
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1913
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Principia Mathematica
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p.5
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21707
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Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Linsky,B]
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p.17
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9542
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The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Hughes/Cresswell]
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p.47
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10093
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The ramified theory of types used propositional functions, and covered bound variables [George/Velleman]
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p.50
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8683
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Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Friend]
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p.51
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8684
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Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Friend]
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p.70
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8691
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The Russell/Whitehead type theory was limited, and was not really logic [Friend]
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p.101
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21720
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Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B]
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p.122
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18248
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A real number is the class of rationals less than the number [Shapiro]
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p.125
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21725
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The multiple relations theory says assertions about propositions are about their ingredients [Linsky,B]
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p.127
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8746
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To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Shapiro]
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p.148
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10025
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Russell and Whitehead took arithmetic to be higher-order logic [Hodes]
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p.177
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8204
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Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine]
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p.285
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18152
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Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Bostock]
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p.366
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9359
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Russell's implication means that random sentences imply one another [Lewis,CI]
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p.448
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10036
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In 'Principia' a new abstract theory of relations appeared, and was applied [Gödel]
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p.448
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10037
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'Principia' lacks a precise statement of the syntax [Gödel]
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p.452
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10040
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Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Gödel]
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p.459
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10044
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Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Shapiro]
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I p.57
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p.175
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12033
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An object is identical with itself, and no different indiscernible object can share that [Adams,RM]
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p.267
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p.267
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10305
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In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays]
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p.44
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p.83
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23474
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A judgement is a complex entity, of mind and various objects
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p.44
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p.84
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23455
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The meaning of 'Socrates is human' is completed by a judgement
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p.44
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p.84
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23453
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Propositions as objects of judgement don't exist, because we judge several objects, not one
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p.44
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p.117
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23480
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The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M]
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p.44
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p.145
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18275
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Only the act of judging completes the meaning of a statement
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p.72
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p.172
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18208
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We regard classes as mere symbolic or linguistic conveniences
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