## An Introduction to Formal LogicFormal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He 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. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book 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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### Contents

The counterexample | |

Proofs 6 Validityand arguments InterludeLogic formal andinformal | |

The semantics of | |

AsandBs Ps andQs | |

Tautologies | |

Interlude Propositionallogic 14 PLC and thematerial conditional | |

PLC trees 19 PLtrees vindicated | |

Quantifiers | |

QL introduced | |

The syntaxof QL 27 Qvaluations 28 Qvalidity 29 MoreonQLtrees 30 QLtreesvindicated Interlude Developing | |

Extensionality | |

Identity | |

The language | |

Trees for identity | |

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### Common terms and phrases

andthe Angharad apply argument assigns atomic wff brackets Bryn chapter Clark Kent closed complex wffs conclusion false conjunction connectives consider constant construction tree contradiction counterexample deductively deductively valid definition disjunction domain domain of discourse English equivalence relation equivalent evaluating example existential quantifier expressions extension function Hence Here’s inference step inferential instantiate interpretation inthe introduced invalid involving isn’t istrue itis Jack Jill language let’s logic logicians loves material conditional means negation Nerys nonprimitive ofthe open branch pattern philosopher Plato possible predicate premisses and conclusion proof propositions qvalid qvaluation restricted quantifications righthand saturated set schematic variables semantics sentences Socrates someone Superman Suppose symbols tautological entailment tautologically valid thatthe thereis thesame thetree things tothe translation truth truthfunctional truthtable test truthvalue universal quantifier unpack valuation q variables we’ll wecan x(Fx Gx x(Gx y(Fy