Ideas from 'Principia Mathematica' by B Russell/AN Whitehead [1913], by Theme Structure
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
9542

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

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
18208

We regard classes as mere symbolic or linguistic conveniences

10044

Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element

5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
10036

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

6. Mathematics / A. Nature of Mathematics / 3. Numbers / i. Reals from cuts
18248

A real number is the class of rationals less than the number

6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / a. Defining numbers
18152

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

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
10025

Russell and Whitehead took arithmetic to be higherorder logic

8683

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

10037

'Principia' lacks a precise statement of the syntax

6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10093

The ramified theory of types used propositional functions, and covered bound variables

8691

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

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
10305

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

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
8684

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

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
8746

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

9. Objects / F. Identity among Objects / 7. Indiscernible Objects
12033

An object is identical with itself, and no different indiscernible object can share that

12. Knowledge Sources / E. Direct Knowledge / 1. Intuition
10040

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

19. Language / B. Meaning / 8. Meaning through Sentences
18275

Only the act of judging completes the meaning of a statement
