Originally published in 1965. This is a textbook of modern deductive logic, designed for beginners but leading further into the heart of the subject than most other books of the kind. The fields covered are the Propositional Calculus, the more elementary parts of the Predicate Calculus, and Syllogistic Logic treated from a modern point of view. In each of the systems discussed the main emphases are on Decision Procedures and Axiomatisation, and the material is presented with as much formal rigour as is compatible with clarity of exposition. The techniques used are not only described but given a theoretical justification. Proofs of Consistency, Completeness and Independence are set out in detail. The fundamental characteristics of the various systems studies, and their relations to each other are established by meta-logical proofs, which are used freely in all sections of the book. Exercises are appended to most of the chapters, and answers are provided.
Formal 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.
"This book is intended for readers who, while mature mathematically, have no knowledge of mathematical logic. We attempt to introduce the reader to the most important approaches to the subject, and, wherever possible within the limitations of space which we have set for ourselves, to give at least a few nontrivial results illustrating each of the important methods for attacking logical problems"--Preface.
This accessible, SHORT introduction to symbolic logic includes coverage of sentential and predicate logic, translations, truth tables, and derivations. The author’s engaging style makes this the most informal of introductions to formal logic. Topics are explained in a conversational, easy-to-understand way for readers not familiar with mathematics or formal systems, and the author provides patient, reader-friendly explanations—even with the occasional bit of humour. The first half of the book deals with all the basic elements of Sentential Logic: the five truth-functional connectives, formation rules and translation into this language, truth-tables for validity, logical truth/falsity, equivalency, consistency and derivations. The second half deals with Quantifier Logic: the two quantifiers, formation rules and translation, demonstrating certain logical characteristics by “Finding an Interpretation” and derivations. There are plenty of exercises scattered throughout, more than in many texts, arranged in order of increasing difficulty and including separate answer keys.
Formal Logic is an undergraduate text suitable for introductory, intermediate, and advanced courses in symbolic logic. The book’s nine chapters offer thorough coverage of truth-functional and quantificational logic, as well as the basics of more advanced topics such as set theory and modal logic. Complex ideas are explained in plain language that doesn’t presuppose any background in logic or mathematics, and derivation strategies are illustrated with numerous examples. Translations, tables, trees, natural deduction, and simple meta-proofs are taught through over 400 exercises. A companion website offers supplemental practice software and tutorial videos.
Logic Works is a critical and extensive introduction to logic. It asks questions about why systems of logic are as they are, how they relate to ordinary language and ordinary reasoning, and what alternatives there might be to classical logical doctrines. The book covers classical first-order logic and alternatives, including intuitionistic, free, and many-valued logic. It also considers how logical analysis can be applied to carefully represent the reasoning employed in academic and scientific work, better understand that reasoning, and identify its hidden premises. Aiming to be as much a reference work and handbook for further, independent study as a course text, it covers more material than is typically covered in an introductory course. It also covers this material at greater length and in more depth with the purpose of making it accessible to those with no prior training in logic or formal systems. Online support material includes a detailed student solutions manual with a running commentary on all starred exercises, and a set of editable slide presentations for course lectures. Key Features Introduces an unusually broad range of topics, allowing instructors to craft courses to meet a range of various objectives Adopts a critical attitude to certain classical doctrines, exposing students to alternative ways to answer philosophical questions about logic Carefully considers the ways natural language both resists and lends itself to formalization Makes objectual semantics for quantified logic easy, with an incremental, rule-governed approach assisted by numerous simple exercises Makes important metatheoretical results accessible to introductory students through a discursive presentation of those results and by using simple case studies
With Imprimatur. Introduction 1. Definition of Logic. -- Logic is the systematic study of the order to be observed in judging, reasoning, and other processes of thought in order to arrive at the knowledge of truth. This definition shows us: (1) the materials (material cause) of the logical order; (2) their elaboration (formal cause) (3) the purpose of this elaboration (final cause). 2. Materials of Logical Order. -- In some sense, these materials are acts of the mind, like apprehension, judgment, ratiocination (reasoning); but strictly speaking, only apprehensions are the material object of logical order (3). (1) By apprehension the mind represents to itself one thing or many things, without either affirming or denying anything. Concepts; the product of apprehension, are expressed by names or terms. (2) To establish a relation of identity or non-identity, of agreement or non-agreement, between the objects of two concepts, in affirming or denying one object of another is to judge. A judgment is expressed in a proposition. (3) To reason is to combine two or more judgments so as to form a new one. The complete ordinary expression of this simplest exercise of reasoning is the syllogism. 3. The Formal Cause of the Logical Order. -- The formal object of logic, or the point of view from which logic regards the acts of the mind, is their adaptability to certain processes of thought which are called either particular sciences or philosophy. These processes imply stages. The mind must grasp the numerous aspects of reality one after another before coordinating the fragmentary explications. Judgment is the first step in combining ideas; judgments in their turn become the materials of reasoning; an isolated piece of reasoning does not suffice to produce adequate knowledge of things, but several reasonings become materials of a scientific system. This rational arrangement of ideas constitutes the logical order properly so called: "the order which reason constitutes for its own acts". 4. Difference between Psychology and Logic. -- Many different sciences may be concerned with one and the same subject, if they study different properties in it, and, consequently, consider it from different points of view. They are then said to have a common (that is, undetermined) object, but each has its own formal (or determined) object. Psychology, too, has in part for its (material) object the act of human reason, but it does not study them under the same aspect (formal object) as logic does. Psychology sees in them vital acts, of which it seeks the nature and origin. Logic considers them in so far as they are cognitions of objects, objective representations, abstract and universal, furnishing the matter of the relations which reason formulates in judgments and reasonings, and arranges in a scientific system. In psychology, as in all the sciences of the real, order is the necessary condition of science; but logic has this order for its object. Its proper object is the form itself of this scientific construction.
