## Beginning LogicThe aim of this book is to provide an exposition of elementary formal logic. The course, which is primarily intended for first-year students who have no previous knowledge of the subject, forms a working basis for more advanced reading and is presented in such a way as to be intelligible to the layman. The nature of logic is examined with the gradual introduction of worked samples showing how to distinguish the sound statement from the unsound. Arguments whose soundness cannot be proved by propositional calculus are discussed, and it is shown how formalization can reveal the logical form of arguments. The final section of the book deals with the application of the predicate calculus as applied in various other fields of logic. |

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### Contents

THE PROPOSITIONAL CALCULUS 2 | 42 |

THE PREDICATE CALCULUS 1 | 92 |

THE PREDICATE CALCULUS 2 | 138 |

Appendix A Normal forms | 189 |

Appendix B The elementary theory of classes | 201 |

211 | |

217 | |

### Common terms and phrases

affirms antecedent application arbitrarily selected object arbitrary name argument assignment of truth-values assume assumptions atomic sentence brackets called Chapter clusion complex conclusion conjunction consequent contradiction define definition derivable sequents derived rules equivalent example existential proposition existential quantifier expression F F F F has G F T F false following sequents formula Hence identity inconsistent irreflexive lemma logical form Metatheorem natural numbers normal form obtain occurrence ostensive definition patterns predicate calculus predicate-letter premiss primitive rules proof proper names propositional calculus propositional function propositional variable prove relation replacing rests rules of derivation scope sequent-expression sitional sound substitution substitution-instance Suppose syllogism symbols symmetric takes the value tautologous sequents theorem things with F true truth-table test typical disjunct universal proposition universal quantifier universe of discourse valid value F well-formed well-formed formula x)Fx x)Gx