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
10044

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

18208

We regard classes as mere symbolic or linguistic conveniences

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
10037

'Principia' lacks a precise statement of the syntax

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

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
