Introduction to Logic and Critical Thinking Version 1.4 Matthew J. Van Cleave Lansing Community College Introduction to Logic and Critical Thinking by Matthew J. Van Cleave is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Table of contents Preface Chapter 1: Reconstructing and analyzing arguments 1.1 What is an argument? 1.2 Identifying arguments 1.3 Arguments vs. explanations 1.4 More complex argument structures 1.5 Using your own paraphrases of premises and conclusions to reconstruct arguments in standard form 1.6 Validity 1.7 Soundness 1.8 Deductive vs. inductive arguments 1.9 Arguments with missing premises 1.10 Assuring, guarding, and discounting 1.11 Evaluative language 1.12 Evaluating a real-life argument Chapter 2: Formal methods of evaluating arguments 2.1 What is a formal method of evaluation and why do we need them? 2.2 Propositional logic and the four basic truth functional connectives 2.3 Negation and disjunction 2.4 Using parentheses to translate complex sentences 2.5 “Not both” and “neither nor” 2.6 The truth table test of validity 2.7 Conditionals 2.8 “Unless” 2.9 Material equivalence 2.10 Tautologies, contradictions, and contingent statements 2.11 Proofs and the 8 valid forms of inference 2.12 How to construct proofs 2.13 Short review of propositional logic 2.14 Categorical logic 2.15 The Venn test of validity for immediate categorical inferences 2.16 Universal statements and existential commitment 2.17 Venn validity for categorical syllogisms Chapter 3: Evaluating inductive arguments and probabilistic and statistical fallacies 3.1 Inductive arguments and statistical generalizations 3.2 Inference to the best explanation and the seven explanatory virtues 3.3 Analogical arguments 3.4 Causal arguments 3.5 Probability 3.6 The conjunction fallacy 3.7 The base rate fallacy 3.8 The small numbers fallacy 3.9 Regression to the mean fallacy 3.10 Gambler’s fallacy Chapter 4: Informal fallacies 4.1 Formal vs. informal fallacies 4.1.1 Composition fallacy 4.1.2 Division fallacy 4.1.3 Begging the question fallacy 4.1.4 False dichotomy 4.1.5 Equivocation 4.2 Slippery slope fallacies 4.2.1 Conceptual slippery slope 4.2.2 Causal slippery slope 4.3 Fallacies of relevance 4.3.1 Ad hominem 4.3.2 Straw man 4.3.3 Tu quoque 4.3.4 Genetic 4.3.5 Appeal to consequences 4.3.6 Appeal to authority Answers to exercises Glossary/Index Preface Preface This is an introductory textbook in logic and critical thinking. The goal of the textbook is to provide the reader with a set of tools and skills that will enable them to identify and evaluate arguments. The book is intended for an introductory course that covers both formal and informal logic. As such, it is not a formal logic textbook, but is closer to what one would find marketed as a “critical thinking textbook.” The formal logic in chapter 2 is intended to give an elementary introduction to formal logic. Specifically, chapter 2 introduces several different formal methods for determining whether an argument is valid or invalid (truth tables, proofs, Venn diagrams). I contrast these formal methods with the informal method of determining validity introduced in chapter 1. What I take to be the central theoretical lesson with respect to the formal logic is simply that of understanding the difference between formal and informal methods of evaluating an argument’s validity. I believe there are also practical benefits of learning the formal logic. First and foremost, once one has internalized some of the valid forms of argument, it is easy to impose these structures on arguments one encounters. The ability to do this can be of use in evaluating an argumentative passage, especially when the argument concerns a topic with which one is not very familiar (such as on the GRE or LSAT). However, what I take to be of far more practical importance is the skill of being able to reconstruct and evaluate arguments. This skill is addressed in chapter 1, where the central ideas are that of using the principle of charity to put arguments into standard form and of using the informal test of validity to evaluate those arguments. Since the ability to reconstruct and evaluate arguments is a skill, one must practice in order to acquire it. The exercises in each section are intended to give students some practice, but in order to really master the skill, one must practice much, much more than simply completing the exercises in the text. It makes about as much sense to say that one could become a critical thinker by reading a critical thinking textbook as that one could become fluent in French by reading a French textbook. Logic and critical thinking, like learning a foreign language, takes practice because it is a skill. While chapters 1 and 2 mainly concern deductive arguments, chapter 3 addresses inductive arguments, including probabilistic and statistical fallacies. In a world in which information is commonly couched within probabilistic and statistical frameworks, understanding these basic concepts, as well as some of the common mistakes is essential for understanding our world. I have tried to i Preface write chapter 3 with an eye towards this understanding. As with all the chapters, I have tried to walk the fine line between being succinct without sacrificing depth. Chapter 4 picks out what I take to be some of the most common fallacies, both formal and informal. In my experience, many critical thinking textbooks end up making the fallacies sound obvious; one is often left wondering how anyone could commit such a fallacy. In my discussion of the fallacies I have tried to correct this not only in the particular examples I use in the text and exercises, but also by discussing what makes a particular fallacy seductive. I have used numerous different textbooks over the years that I have been teaching logic and critical thinking courses. Some of them were very good; others were not. Although this textbook is my attempt to improve on what I’ve encountered, I am indebted to a number of textbooks that have shaped how I teach logic and critical thinking. In particular, Sinnott-Armstrong and Fogelin’s Understanding Arguments: An Introduction to Informal Logic and Copi and Cohen’s Introduction to Logic have influenced how I present the material here (although this may not be obvious). My interest in better motivating the seductiveness of the fallacies is influenced by Daniel Kahneman’s work in psychology (for which he won the Nobel Prize in economics in 2002). This textbook is an “open textbook” that is licensed under the Creative Commons Attribution 4.0 license (CC BY 4.0). Anyone can take this work and alter it for their own purposes as long as they give appropriate credit to me, noting whether or not you have altered the text. (If you would like to alter the text but have come across this textbook in PDF format, please do not hesitate to email me at [email protected] and I will send you the text in a file format that is easier to manipulate.) At Lansing Community College, my place of employment, we have undertaken an initiative to reduce the cost of textbooks. I see this as an issue of access to education and even an issue of justice. Some studies have shown that without access to the textbook, a student’s performance in the class will suffer. Many students lack access to a textbook simply because they do not buy it in the first place since there are more pressing things to pay for (rent, food, child care, etc.) and because the cost of some textbooks is prohibitive. Moreover, both professors and students are beholden to publishers who profit from selling textbooks (professors, because the content of the course is set by the author of the textbook, and perhaps market forces, rather than by the professor herself; students, because they must buy the newest ii Preface editions of increasingly expensive textbooks). If education is necessary for securing certain basic human rights (as philosophers like Martha Nussbaum have argued), then lack of access to education is itself an issue of justice. Providing high quality, low-cost textbooks is one, small part of making higher education more affordable and thus more equitable and just. This open textbook is a contribution towards that end. Matthew J. Van Cleave January 4, 2016 iii Chapter 1: Reconstructing and analyzing arguments 1.1 What is an argument? This is an introductory textbook in logic and critical thinking. Both logic and critical thinking centrally involve the analysis and assessment of arguments. “Argument” is a word that has multiple distinct meanings, so it is important to be clear from the start about the sense of the word that is relevant to the study of logic. In one sense of the word, an argument is a heated exchange of differing views as in the following: Sally: Abortion is morally wrong and those who think otherwise are seeking to justify murder! Bob: Abortion is not morally wrong and those who think so are right-wing bigots who are seeking to impose their narrow-minded views on all the rest of us! Sally and Bob are having an argument in this exchange. That is, they are each expressing conflicting views in a heated manner. However, that is not the sense of “argument” with which logic is concerned. Logic concerns a different sense of the word “argument.” An argument, in this sense, is a reason for thinking that a statement, claim or idea is true.