User:Wvbailey/PM

Sandbox for the article Principia Mathematica: ⊃ Ɔ ≡ ⊂ ∪ ∩ ∨ ∧ ∨ ∩ ∪ ⊂ ⊃ Ɔ ≡ ε Λ ℩ ⊓ ⊔ ▪■︰✸ ✹ ✱

Organization

Three volumnes

Second edition (1927) with an important "Introduction To the Second Edition" that introduces the Sheffer stroke, a new chapter ✸8 to replace chapter ✸9 (and thereby remove the distincition between "real" and "apparent" variables).

A 1962 abridged single-volume version to ✸56.

Organization of abridged single-volume version to ✸56

PREFACE

Preface to first edition (dated 1910)

INTRODUCTION TO THE SECOND EDITION

Introduces the Sheffer stroke, a new chapter ✸8 to replace chapter ✸9 (and thereby remove the distinction between "real" and "apparent" variables), responds to criticisms of Wittgenstein and advances made by Hilbert et. al., discusses the "fully-extensional" notion of a function ("A function can only appear in a matrix through its values* [* This assumption is fundamental in the following theory. It has its difficulties, but for the moment we ignore them. It takes the place (not quite adequately) of the axiom of reducibility. It is discussed in Appendix C]".

INTRODUCTION

Chapter I. Preliminary Explanations of Ideas and Notations

Chapter II. The theory of Logical Types

This must be read together with the "Introduction to the Second Edition" and Appendix A (new section ✸8 replacing ✸9 of the first edition). Begins with a discussion of the "Vicious-Circle Principle", introduces the notion of the extension of a function (i.e. its values) and "matrix" (contemporary truth table), predicative functions ("it is of the next order above that of its arguments, i.e. of the lowest order compatible with its having that argument", introduces the Axiom of Reducibility.

Chapter III. Incomplete Symbols

PART I. MATHEMATICAL LOGIC

6 sections A - E from ✸1 to ✸43

PART II. PROLEGOMENA TO CARDINAL ARITHMETIC

1 section A from ✸50 to ✸56

APPENDIX A

New section ✸8 to replace ✸9 (but ✸9 is left in place)

APPENDIX C: Truth-Functions and others

LIST of DEFINITIONS

Approximately 100 symbols and their usage in an example formula, but without definition nor the location of their first occurrence.