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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

10036

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


p.448

10037

'Principia' lacks a precise statement of the syntax [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.83

23474

A judgement is a complex entity, of mind and various objects

p.44

p.84

23455

The meaning of 'Socrates is human' is completed by a judgement

p.44

p.84

23453

Propositions as objects of judgement don't exist, because we judge several objects, not one

p.44

p.117

23480

The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M]

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
