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Elementary Logic: a Brief Introduction

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Elementary Logic: a Brief Introduction ELECTRONIC TEXT Elementary Logic: A Brief Introduction, Fourth Edition By Michael Pendlebury Published online by the Department of Philosophy, University of the Witwatersrand, Johannesburg in December 2013.1 Pp. vi, 151 © 1997–2013 Michael Pendlebury The copyright of this text is the property of the author. Without the written permission of the author, the text may not be used for commercial or fundraising purposes, or altered or edited in any way. Until further notice, the text may be used freely and without the author’s permission as follows: 1. Individuals may use, print, and copy the text for personal information, education, or entertainment. 2. Instructors in nonprofit educational and organizations and institutions may prescribe or recommend part or all of the text to their students. 3. Individuals and nonprofit organizations may supply printed copies of all or part of the text to anyone subject to the condition that they do not charge them more than the reasonable cost of printing it. 4. The text may be cited or quoted in other publications subject to the condition that it is clearly identified and attributed to the author. The Author Michael Pendlebury is Professor of Philosophy Head of the Department of Philosophy and Religious Studies at North Carolina State University. He studied at the University of the Witwatersrand, Johannesburg (BAHons, MA in Philosophy) and at Indiana University, Bloomington (MA, PhD in Philosophy, MA in Linguistics). He has taught philosophy at Illinois State University, the University of Natal, Pietermaritzburg, and for twenty years at the University of the Witwatersrand, where he was Professor and Head of Philosophy when he left to take up his current position at North Carolina State University in January 2004. He has published articles on a wide range of philosophical topics, and was editor of the journal Philosophical Papers from 1986 to 1998. 1 The URL of the Department’s home page at the time of publication was http://www.wits.ac.za/academic/humanities/socialsciences/8641/philosophy.html. [BLANK PAGE] ELEMENTARY LOGIC: A Brief Introduction Fourth Edition Michael Pendlebury Department of Philosophy University of the Witwatersrand, Johannesburg December 2013 Copyright © Michael Pendlebury 1997, 1998, 2002, 2013 Preface The first three editions of this text were published in booklet form by the Department of Philosophy at the University of the Witwatersrand, Johannesburg (“Wits”). I prepared these editions of the text for students in some of the courses that I taught at Wits between 1997 and 2003. The Department carried on using the third edition after I moved from Wits to North Carolina State University at the end of 2003. At the beginning of 2013, I was surprised and gratified to learn that during 2012 the Department had supplied over 1,500 copies of the text to students in various courses. This prompted me to offer to prepare a new edition and seek to get it published in a form that would make it unnecessary for the Department to print and distribute booklets. On the advice of Dr. David Martens, Head of the Department, I decided that it would be best to publish it as an online electronic text, because this would be the most effective way to make it accessible to students at Wits and elsewhere. I am grateful to Dr. Martens and the Wits Philosophy Department for agreeing to publish the fourth edition on the Department’s website. The biggest change I have made in the fourth edition is to add a fourteen-page section on analogical arguments (section 4.4) to the chapter on deductive validity and nondeductive strength (Chapter 4). The second biggest change I have made is to expand the material on formal validity that constituted the first section in the chapter on propositional operators in the third edition so that it also covers syllogistic logic (as it should) and give it a chapter of its own (Chapter 5) before the chapter on syllogistic logic. In addition to these two major changes, I have made numerous improvements in substance, clarity, and style throughout the text, and have changed or adjusted many examples to increase their shelf life. Although I believe it is possible for many readers to learn something worthwhile from this text on its own, it was designed primarily to serve as an aid to systematic teaching in the classroom. I do not believe that the text (or even a very effective course based on it) can produce robust critical thinkers, and it aims only to lay some foundations on which students can build by applying the basic concepts and skills that it covers to all their reading and thinking. I am grateful to Barbara Aarden, Rashad Bagus, Colin Hossack, Darrel Moellendorf, James Pendlebury, Brian Penrose, and Mary Tjiattas for useful assistance, advice, or ideas with respect to the first three editions; and to David Austin, Damien Bruneau, David Martens, Thomas Pendlebury, Ken Peters, and Mary Tjiattas for useful assistance, advice, iii or ideas with respect to the fourth edition. I am also grateful to the Wits students who took courses in which I prescribed the first three editions between 1997 and 2003 for exposing some of the limitations of those editions. MP Raleigh, North Carolina 18 November 2013 iv CONTENTS Preface page iii INTRODUCTION 1 Chapter 1 IDENTIFYING ARGUMENTS 1.1 Arguments, Premises, and Conclusions 2 1.2 Statements and Propositions 9 1.3 Recognizing Arguments 15 1.4 Compound Arguments 22 Chapter 2 EVALUATING ARGUMENTS 2.1 Logical Evaluation 29 2.2 Some Fallacies of Inadequate Support 36 2.3 Three Further Fallacies 41 Chapter 3 MEANING AND DEFINITION 3.1 Meaning versus Denotation 48 3.2 Types of Definitions 55 3.3 Evaluating Theoretical Definitions 61 Chapter 4 DEDUCTIVE VALIDITY AND NONDEDUCTIVE STRENGTH 4.1 Deductive Validity 66 4.2 Nondeductive Strength (I): Inductive Arguments 70 4.3 Nondeductive Strength (II): Abductive Arguments 76 4.4 Nondeductive Strength (III): Analogical Arguments 81 Chapter 5 FORMAL VALIDITY 95 Chapter 6 “ALL,” “SOME,” “SOME NOT,” AND “NO” 6.1 Categorical Propositions 103 6.2 Standard Form Syllogisms 112 6.3 Other Arguments 120 v Chapter 7 “NOT,” “IF,” “AND,” AND “OR” 7.1 Symbolization (I) 127 7.2 Symbolization (II) 133 7.3 Valid and Invalid Argument Forms (I) 138 7.4 Valid and Invalid Argument Forms (II) 143 Appendix on Truth 150 vi INTRODUCTION This text is an elementary introduction to applied logic. As such, it is centrally concerned with the identification, clarification, analysis and (most importantly) the assessment of arguments. The text has two main aims, which cannot be completely separated. One is to give readers a practical appreciation of some basic essentials of logical theory. The other, which is probably more important for most students, is to develop some key basic concepts and skills that should help them to improve their ability to understand and evaluate texts that involve significant reasoning, and to enhance their powers of clear, critical and constructive thinking. I have tried to write in clear and accessible English, but have also tried not to oversimplify. For, if a text in applied logic is too easy and does not encourage serious thought about the topics it covers, then it will inevitably fail to develop the student’s capacity for critical reading and thinking. You should therefore be warned that it is not possible to come to terms with the following material simply by reading it over once. It must be worked through and understood paragraph by paragraph, and page by page. It will also frequently be necessary to refer back to earlier passages in order to make sense of something under discussion. Except on an initial skimming of a section to get an overview of its contents, your goal should always be to understand as much as possible before proceeding to the next paragraph, page or section.1 This might require several re-readings, as well as serious attempts to work through problems and examples with the help of pencil and paper. It is always best to study material in the text in advance of classes covering that material. Finally, as an essential check on your understanding, you should attempt all the exercises at the end of each section before proceeding to the next section. You should also deal immediately with any shortcomings in your understanding which these exercises reveal by reviewing appropriate parts of the section concerned, and, if necessary, seeking assistance. A great deal of the material covered in the text is cumulative, and it is often difficult to follow later sections without an adequate grasp of earlier sections. 1 If you use a dictionary (which is a good thing to do), please note that ordinary dictionaries are often unreliable on technical concepts of specialized disciplines. This includes the basic concepts of logic. In the case of these concepts, you should not depend upon a dictionary, but on the definitions and explanations given in this text. 1 Chapter 1 IDENTIFYING ARGUMENTS 1.1 Arguments, Premises, and Conclusions An argument in the logical sense is a piece of reasoning in support of a conclusion. In order to keep things simple, let us restrict our attention to the central case of what may be described as propositional arguments1 that are expressed in language. This allows us to identify an argument with a group of two or more statements one of which — the conclusion — is advanced by the speaker or writer2 on the strength of the others, which are known as premises. Let us use the following pedestrian example of an argument to help clarify some of these terms. (A) Mary has got an A on all her work for the course other than the upcoming final exam.
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