Chapter Summaries Part One: The Basics of Good Reasoning Chapter 1: The Basic Tools of Reasoning The most basic concepts in good reasoning are claims and arguments. In this chapter, we define “claim,” explain how claims can be used to support beliefs, and then explain how various types of evidence can be organized into arguments so we can evaluate the strength of this support for the claims that we make. Chapter Sections: 1.1. Claims 1.2. Evidence 1.3. Arguments 1.4. Identifying arguments 1.5. More exercises Real-Life Example: Reasoning through a Crime Scene © Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum. Chapter 2: Evaluating Arguments Arguments are usually found embedded in books and articles that are intended to convey information in addition to the argument. In this chapter, we explain how to extract an argument from extraneous material, clarify ambiguous or vague words and phrases, and organize the argument, so that it is clear and pre- cise. In addition, we explain two broad categories of argument (deductive and inductive), identify the distinctive features of these arguments, and then explain what makes a deductive or inductive “good” or “bad.” Chapter Sections: 2.1. Reconstructing arguments 2.1.1. Extraneous material 2.1.2. Implicit claims 2.1.3. Ambiguity and vagueness 2.1.4. Argument form 2.2. Two types of arguments 2.3. Good and bad arguments 2.3.1. Good deductive arguments 2.3.2. Good inductive arguments 2.4. Complex arguments 2.5. More exercises Real-Life Example: A Logic Problem © Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum. Part Two: Deductive Reasoning Chapter 3: Categorical Logic An intuitive way of understanding reality is to categorize it (big, red, species, dog, alligator, etc.). We can then use these categories to compare and contrast objects. We can also use them to reason about objects. In this chapter, we explain the basic concepts used in categorical logic, including members, categories, the quantifiers “all,” “some,” and “none,” Venn diagrams, the Venn Diagram Method of testing for validity, and the limitations of categorical logic. Chapter Sections: 3.1. Categories of things 3.2. Relating categories to one another 3.3. Standard-form categorical claims 3.4. Translation tips 3.4.1. Most? 3.4.2. Four parts of categorical claims 3.4.3. Singular expressions and proper nouns 3.4.4. Time and place 3.4.5. Conditional claims 3.5. Syllogisms and testing for validity with Venn Diagrams 3.6. The limitations of categorical logic 3.7. More exercises Real-Life Example: Mexican Holy Week © Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum. Chapter 4: Basic Propositional Logic A more powerful logical system than categorical logic is called “propositional logic.” In this chapter, we explain basic logical operators “and,” “or,” “not,” “if . ., then . .,” and “if and only if,” how to translate English claims into the language of propositional logic and vice versa, and explain how propositional logic helps us evaluate arguments. Chapter Sections: 4.1. A new language 4.2. Translating English claims into claims of propositional logic 4.3. Translating claims with operators 4.4. Translation examples 4.5. Basic translation exercises 4.6. Tips for translating 4.7. More difficult translation exercises 4.8. Rules of inference and their value 4.9. More exercises Real-Life Example: Translating a Legal Document © Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum. Chapter 5: Truth Tables Logical operators have specific implications for interpreting claims and evaluat- ing arguments. The clearest way to understand these implications is to construct truth tables for them. In this chapter, we explain how to construct a truth table, the truth tables for each logical operator, and how to evaluate the validity of an argument using two different truth table methods. Chapter Sections: 5.1. Constructing truth tables 5.2. Using truth tables to express relationships among claims 5.3. Using truth tables to evaluate short arguments 5.4. Using truth tables to evaluate long arguments 5.5. More exercises Real-Life Example 1: Former Illinois Governor Rob Blagojevich Real-Life Example 2: Political Pundit Rush Limbaugh © Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum. Chapter 6: Rules of Inference With a firm grasp of the truth tables of the operators in propositional logic, we can begin to see how to draw inferences from claims of propositional logic. Some of these inferences are so clear and precise that they can be used as rules for all inferences in propositional logic. In this chapter, we explain nine rules of infer- ence, how to use them to derive conclusions from complicated arguments, and three common mistakes associated with these rules. Chapter Sections: 6.1. Deductive inference 6.2. Four basic rules 6.2.1. Simplification 6.2.2. Conjunction 6.2.3. modus ponens 6.2.4. modus tollens 6.3. Basic inference exercises 1 6.4. Three more rules 6.4.1. Disjunctive syllogism 6.4.2. Addition 6.4.3. Hypothetical syllogism 6.5. Basic inference exercises 2 6.6. Two special rules 6.6.1. Conditional proof 6.6.2. reductio ad absurdum / indirect proof 6.7. More complicated inference exercises 6.8. Mistakes to avoid 6.8.1. Affirming the consequent 6.8.2. Denying the antecedent 6.8.3. Affirming the disjunct 6.9. Formal fallacy exercises Real-Life Example: Blagojevich’s Resignation Speech © Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum. Part Three: Inductive Reasoning Chapter 7: Probability and Induction In arguments where conclusions do not follow with certainty from premises, we must turn to a different set of rules to evaluate them. In these inductive arguments, the conclusions follow with some degree of probability. In this chapter, we distinguish probability from statistics, explain three common types of probability, explain how statistics and probability are used in inductive reason- ing, and explain the most difficult obstacle to inductive reasoning, “the problem of induction.” Chapter Sections: 7.1. Inductive strength 7.2. Types of probability 7.3. Conditional probabilities 7.4. Using probability in argument: Cost/benefit analysis 7.5. The problem of induction 7.6. Exercises Real-Life Example: The Teleological Argument for God’s Existence © Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum. Chapter 8: Inductive Arguments Inductive arguments take a variety of forms and each of these forms must meet a specific set of conditions in order to be considered a “good” argument. In this chapter, we explain four types of inductive argument: inductive enumeration, inductive generalization, argument from analogy, and causal argument, and their strengths and weaknesses. This chapter ends by highlighting some specific wor- ries about evaluating causal arguments. These worries are addressed in the next chapter. Chapter Sections: 8.1. Types of inductive argument 8.2. Enumerative induction 8.3. Exercises with enumerative inductions 8.4. Inductive generalization, or reasoning from a sample 8.5. Statistical errors 8.6. Exercises with inductive generalizations 8.7. Argument from analogy 8.8. Strengths and weaknesses of analogies 8.9. Exercises for arguments from analogy 8.10. Causal arguments 8.11. Exercises with causal arguments Real-Life Example 1: The Ouija Board Real-Life Example 2: Horoscopes © Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum. Chapter 9: Experiment and Inference to the Best Explanation Though there are numerous ways that a causal inference can be drawn inappro- priately, philosophers and scientists have devised clever ways of mitigating these worries through various types of experiments. In this chapter, we explain the most common formal and informal experiments, their strengths and limitations, and a method of choosing among theories for which there is conflicting evi- dence, called “inference to the best explanation.” Chapter Sections: 9.1. Testing causal claims 9.2. The structure of an experiment 9.3. Formal experiments 9.4. Exercises with formal experiments 9.5. Informal experiments 9.6. Exercises with informal experiments 9.7. A problem for causal tests: Underdetermination 9.8. A new type of argument: Inference to the best explanation 9.9. Explanatory virtues 9.10. Applying the virtues 9.11. Exercises with inference to the best explanation Real-Life Example: A Murder Mystery © Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum. Chapter 10: Informal Fallacies There are probably innumerable ways that inductive inferences can go wrong, but some are so common they have been given names. In this chapter we explain eleven of the most common informal fallacies, including: Argumentum ad Hom- inem, Abusive (appeal to the man/person); Argumentum ad Hominem, Circum- stantial; Tu Quoque (you, too; “hypocrite” fallacy); Argumentum ad Populum (appeal to the people); Appeal to Snobbery/Vanity; Argumentum ad Verecun- diam (appeal to [inappropriate] authority); Argumentum ad Baculum (appeal to force); Argumentum ad Misericordiam (appeal to pity); Argumentum ad Igno- rantiam (appeal to ignorance); Petitio Principii (begging the question); and Straw Man. Chapter Sections: 10.1. Argumentum ad Hominem, Abusive (appeal to the man/person) 10.2. Argumentum ad Hominem, Circumstantial 10.3. Tu Quoque (you, too; “hypocrite” fallacy) 10.4. Argumentum ad Populum (appeal to the people) 10.5. Appeal to snobbery/vanity 10.6. Argumentum ad Verecundiam (appeal to [inappropriate] authority) 10.7. Argumentum ad Baculum (appeal to force) 10.8. Argumentum ad Misericordiam (appeal to pity) 10.9.