## Introduction to Deductive Logic |

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### Contents

Inferability | 1 |

Propositions | 5 |

Logical truth | 11 |

Entailment | 19 |

Truthfunctions | 23 |

Axiomatic deduction | 45 |

Natural deduction | 51 |

Metatheory | 77 |

Quantifiers | 107 |

Predicate calculus | 119 |

Categorical propositions | 139 |

Other notations | 158 |

Summary of systems | 160 |

177 | |

180 | |

Modalities | 91 |

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### Common terms and phrases

antecedent appear apply assertion Axfx axiom schema borrowing Brutus killed Caesar categorical propositions claim concepts conditional propositions cp's deductive system defined derived rule developed discussion elimination rules entailment equivalent by definition example existential quantifier expressions fact follows formation rules formulas free occurrences given HP(AE HP(CI HP(EI HP(NI hypothesis inductive inferability relationships introduced involving Iseminger 21 kind knowledge-claims logical constants logical truth logician major premise metatheory metavariables modal mortal name variable natural deduction negation NKpq notion occur paraphrased philosophical possible predicate calculus predicate stand-ins proposition stand-ins propositional calculus propositional connective propositional logic provable prove quasi-proof question Quine 37 reader regard replacing represent the forms sense sentence-types sentences simply Socrates square of opposition step subordinate proof syllogism syllogistic forms symbols theorems things tions truth table truth-functional truth-values ttt's universal quantifier valid wff's