## An Introduction to Symbolic LogicThis is probably the clearest book ever written on symbolic logic for the philosopher, the general scientist, and the layman. For years it has received the appreciation of those who have been rebuffed by other introductory works because of insufficient mathematical training. No special knowledge of mathematics is required here; even if you have forgotten most of your high school algebra, you can learn to use mathematical logic by following the directions in this book. Now revised and corrected, the book allows you to start with the simplest symbols and conventions and end up with a remarkable grasp of the Boole-Schroeder and Russell-Whitehead systems. It covers the study of forms, essentials of logical structure, generalization, classes, and the principal relations among them, universe of classes, the deductive system of classes, the algebra of logic, abstraction and interpretation, calculus of propositions, the assumptions of Whitehead and Russell's Principia Mathematica, and logistics. Appendices cover symbolic logic and the logic of the syllogism, the construction and use of truth-tables, and proofs of two theorems."One of the clearest and simplest introductions to a subject which is very much alive." — Mathematics Gazette. |

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### Contents

INTRODUCTION | 17 |

THE ESSENTIALS OF LOGICAL STRUCTURE | 45 |

THE ESSENTIALS OF LOGICAL STRUCTURE continued | 64 |

CLASSES | 75 |

I | 83 |

CHAPTER V | 112 |

Deﬁning Forms of Classes | 119 |

The Notion of a Null Class | 137 |

Operations as Primitive Notions | 203 |

Further Discussion of the Postulates | 210 |

Consequences of the Deﬁnition of | 228 |

CHAPTER X | 240 |

CHAPTER | 254 |

Constituent Relations | 266 |

CHAPTER | 273 |

THE ASSUBIPTIONS OF PRINCIPIA MATHEMATICA | 287 |

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### Common terms and phrases

A X B abstract assertion assume Boolean algebra calculus of classes called chapter class-calculus classes in extension common commutative law complement concept constituent relation construct creatures deductive system deﬁning form deﬁnition denote diagram disjunction dots dyadic dyadic relation elementary propositions equivalent fact fellowman ﬁgure ﬁnd ﬁrst formal context function given holds houses North identical implies included indeﬁnite individuals instance interpretation King Arthur laws least logical conjunction logical form logical relations material implication mathematics matter means membership mutual inclusion namely notion null class operation positions possible predicates premises Principia Principia Mathematica principle proof properties propositional calculus propositional form q is true quantiﬁer sense set of postulates signiﬁcance speciﬁc propositions statement structure sub-class Suppose symbolic logic theorems thing tion true propositions truth truth-value unit class universe class universe of discourse values variable whole