Book:Alfred North Whitehead/Principia Mathematica

Subject Matter

 * Mathematical Logic

Contents

 * Preface


 * Introduction
 * Preliminary Explanations of Ideas and Notations
 * The Theory of Logical Types
 * Incomplete Symbols


 * Part 1: Mathematical Logic


 * Section A. The Theory of Deduction
 * $\S 1$ Primitive Ideas and Propositions
 * $\S 2$ Immediate Consequences of the Primitive Propositions
 * $\S 3$ The Logical Product of two Propositions
 * $\S 4$ Equivalence and Formal Rules
 * $\S 5$ Miscellaneous Propositions


 * Section B. Theory of Apparent Variables
 * $\S 10$ Theory of Propositions containing one Apparent Variable
 * $\S 11$ Theory of two Apparent Variables
 * $\S 12$ The Hierarchy of Types and the Axiom of Reducibility
 * $\S 13$ Identity
 * $\S 14$ Descriptions


 * Section C. Classes and Relations
 * $\S 20$ General Theory of Classes
 * $\S 21$ General Theory of Relations
 * $\S 22$ Calculus of Classes
 * $\S 23$ Calculus of Relations
 * $\S 24$ The Universal Class, the Null-Class, and the Existence of Classes
 * $\S 25$ The Universal Relation, the Null-Relation, and the Existence of Relations


 * Section D. Logic of Relations
 * $\S 30$ Descriptive Functions
 * $\S 31$ Converses of Relations
 * $\S 32$ Referents and Relata of a given Term with respect to a given Relation
 * $\S 33$ Domains, Converse Domains, and Fields of Relations
 * $\S 34$ The Relative Product of two Relations
 * $\S 35$ Relations with Limited Domains and Converse Domains
 * $\S 36$ Relations with Limited Fields
 * $\S 37$ Plural Descriptive Functions
 * $\S 38$ Relations and Classes derived from a Double Descriptive Function


 * Section E. Products and Sums of Classes
 * $\S 40$ Products and Sums of Classes of Classes
 * $\S 41$ The Product and Sum of a Class of Relations
 * $\S 42$ Miscellaneous Propositions
 * $\S 43$ The Relations of a Relative Product to its Factors


 * Part 2: Prolegomena to Cardinal Arithmetic
 * Section A. Unit Classes and Couples
 * $\S 50$ Identity and Diversity as Relations
 * $\S 51$ Unit Classes
 * $\S 52$ The Cardinal Number $1$
 * $\S 53$ Miscellaneous Propositions involving Unit Classes
 * $\S 54$ Cardinal Couples
 * $\S 55$ Ordinal Couples
 * $\S 56$ The Ordinal Number $2_r$