Book contents
- Frontmatter
- PREFACE
- Contents
- Note
- ALPHABETICAL LIST OF PROPOSITIONS REFERRED TO BY NAMES
- INTRODUCTION TO THE SECOND EDITION
- INTRODUCTION
- CHAPTER I PRELIMINARY EXPLANATIONS OF IDEAS AND NOTATIONS
- CHAPTER II THE THEORY OF LOGICAL TYPES
- CHAPTER III INCOMPLETE SYMBOLS
- PART I MATHEMATICAL LOGIC
- PART II PROLEGOMENA TO CARDINAL ARITHMETIC
- APPENDIX A The Theory of Deduction for Propositions containing Apparent Variables
- APPENDIX C Truth-Functions and others
- LIST OF DEFINITIONS
CHAPTER I - PRELIMINARY EXPLANATIONS OF IDEAS AND NOTATIONS
Published online by Cambridge University Press: 25 February 2010
- Frontmatter
- PREFACE
- Contents
- Note
- ALPHABETICAL LIST OF PROPOSITIONS REFERRED TO BY NAMES
- INTRODUCTION TO THE SECOND EDITION
- INTRODUCTION
- CHAPTER I PRELIMINARY EXPLANATIONS OF IDEAS AND NOTATIONS
- CHAPTER II THE THEORY OF LOGICAL TYPES
- CHAPTER III INCOMPLETE SYMBOLS
- PART I MATHEMATICAL LOGIC
- PART II PROLEGOMENA TO CARDINAL ARITHMETIC
- APPENDIX A The Theory of Deduction for Propositions containing Apparent Variables
- APPENDIX C Truth-Functions and others
- LIST OF DEFINITIONS
Summary
The notation adopted in the present work is based upon that of Peano, and the following explanations are to some extent modelled on those which he prefixes to his Formulario Mathematico. His use of dots as brackets is adopted, and so are many of his symbols.
Variables. The idea of a variable, as it occurs in the present work, is more general than that which is explicitly used in ordinary mathematics. In ordinary mathematics, a variable generally stands for an undetermined number or quantity. In mathematical logic, any symbol whose meaning is not determinate is called a variable, and the various determinations of which its meaning is susceptible are called the values of the variable. The values may be any set of entities, propositions, functions, classes or relations, according to circumstances. If a statement is made about “Mr A and Mr B,” “Mr A” and “Mr B” are variables whose values are confined to men. A variable may either have a conventionally-assigned range of values, or may (in the absence of any indication of the range of values) have as the range of its values all determinations which render the statement in which it occurs significant. Thus when a text-book of logic asserts that “A is A,” without any indication as to what A may be, what is meant is that any statement of the form “A is A” is true.
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- Information
- Principia Mathematica to *56 , pp. 4 - 36Publisher: Cambridge University PressPrint publication year: 1997
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