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Ideas of B Russell/AN Whitehead, by Text
[British, fl. 1912, Professors at Cambridge. Collaborators during 19101913.]
1913

Principia Mathematica


p.5

21707

Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Linsky,B]


p.17

9542

The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Hughes/Cresswell]


p.47

10093

The ramified theory of types used propositional functions, and covered bound variables [George/Velleman]


p.50

8683

Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Friend]


p.51

8684

Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Friend]


p.70

8691

The Russell/Whitehead type theory was limited, and was not really logic [Friend]


p.101

21720

Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B]


p.122

18248

A real number is the class of rationals less than the number [Shapiro]


p.125

21725

The multiple relations theory says assertions about propositions are about their ingredients [Linsky,B]


p.127

8746

To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Shapiro]


p.148

10025

Russell and Whitehead took arithmetic to be higherorder logic [Hodes]


p.177

8204

Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine]


p.285

18152

Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Bostock]


p.366

9359

Russell's implication means that random sentences imply one another [Lewis,CI]


p.448

10037

'Principia' lacks a precise statement of the syntax [Gödel]


p.448

10036

In 'Principia' a new abstract theory of relations appeared, and was applied [Gödel]


p.452

10040

Russell showed, through the paradoxes, that our basic logical intuitions are selfcontradictory [Gödel]


p.459

10044

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

12033

An object is identical with itself, and no different indiscernible object can share that [Adams,RM]

p.267

p.267

10305

In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays]

p.44

p.145

18275

Only the act of judging completes the meaning of a statement

p.72

p.172

18208

We regard classes as mere symbolic or linguistic conveniences
