## An Introduction to Formal LogicThis is a highly accessible guide to the fundamental aims and basic elements of formal logic. Peter Smith introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises, and also provides provides illuminating philosophical commentary. It will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic. |

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#### LibraryThing Review

User Review - Foretopman - LibraryThingI love this book. It is written in an easy, almost conversational, style, and yet lacks nothing in formal rigor. I especially appreciate the many places where Smith points out how things could be done differently, and gives the arguments for and against each approach. Highly recommended. Read full review

Some explanations are drawn out, but this drawn out approach gives Smith the opportunity to repeat himself - thus making the material easier to retain. It may take me longer than other works to cover a subject, but I feel like my ability to recall the material is far better than other Formal Logic book's i've attempted to read. Also, unlike most Formal Logic texts, solutions to the many exercises are provided online.

### Contents

What is logic? | 1 |

Validity and soundness | 9 |

Patterns of inference | 18 |

The counterexample technique | 29 |

Proofs | 36 |

Validity and arguments | 44 |

Logic formal and informal | 51 |

Three prepositional connectives | 53 |

After prepositional logic | 192 |

Quantifiers | 194 |

QL introduced | 202 |

QL explored | 210 |

More QL translations | 219 |

Introducing QL trees | 228 |

The syntax of QL | 242 |

Qvaluations | 250 |

The syntax of PL | 63 |

The semantics of PL | 72 |

As and Bs Ps and Qs | 82 |

Truth functions | 88 |

Tautologies | 101 |

Tautological entailment | 107 |

Propositional logic | 123 |

PLC and the material conditional | 125 |

More on the material conditional | 137 |

Introducing PL trees | 145 |

Rules for PL trees | 157 |

PLC trees | 171 |

PL trees vindicated | 179 |

Trees and proofs | 185 |