## Argument and Inference

by Johnson

### Instructor Requests

This textbook offers a thorough and practical introduction to inductive logic. The book covers a range of different types of inferences with an emphasis throughout on representing them as arguments. This allows the reader to see that, although the rules and guidelines for making each type of inference differ, the purpose is always to generate a probable conclusion.

After explaining the basic features of an argument and the different standards for evaluating arguments, the book covers inferences that do not require precise probabilities or the probability calculus: the induction by confirmation, inference to the best explanation, and Mill’s methods. The second half of the book presents arguments that do require the probability calculus, first explaining the rules of probability, and then the proportional syllogism, inductive generalization, and Bayes’ rule. Each chapter ends with practice problems and their solutions. Appendixes offer additional material on deductive logic, odds, expected value, and (very briefly) the foundations of probability.

Argument and Inference can be used in critical thinking courses. It provides these courses with a coherent theme while covering the type of reasoning that is most often used in day-to-day life and in the natural, social, and medical sciences. Argument and Inference is also suitable for inductive logic and informal logic courses, as well as philosophy of sciences courses that need an introductory text on scientific and inductive methods.

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Contents (pg. v)
Preface (pg. ix)
1 An Introduction to Arguments (pg. 1)
1.1 Premises and a Conclusion (pg. 1)
1.2 Deductively Valid and Inductively Strong (pg. 4)
1.3 Soundness and Reliability (pg. 9)
1.4 Some Argument Forms (pg. 11)
1.6 Exercises (pg. 23)
2 The Induction by Confirmation (pg. 35)
2.1 Halley’s Comet (pg. 35)
2.2 The Hypothesis, Prediction, and Data (pg. 36)
2.3 The Induction by Confirmation (pg. 41)
2.4 Other Conclusions (pg. 44)
2.5 The Inference (pg. 49)
2.6 Exercises (pg. 53)
3 More on the Induction by Confirmation (pg. 67)
3.1 The Crucial Experiment (pg. 67)
3.2 The Inference to the Best Explanation (pg. 71)
3.3 Exercises (pg. 78)
4 Mill’s Methods (pg. 99)
4.1 Necessary and Sufficient Conditions (pg. 100)
4.2 Mill’s First Three Methods (pg. 104)
4.3 Typhoid Mary (pg. 110)
4.4 Mill’s Fourth and Fifth Methods (pg. 114)
4.5 Exercises (pg. 118)
5 Describing Populations (pg. 131)
5.1 Variables and Their Values (pg. 132)
5.2 Describing a Population with Two Variables (pg. 133)
5.3 Difference in Proportions, Independence, and Association (pg. 134)
5.4 The Strengths of Positive and Negative Associations (pg. 136)
5.5 Information about a Population (pg. 138)
5.6 Measuring the Strength of an Association (Again) (pg. 140)
5.7 Exercises (pg. 141)
6 The Proportional Syllogism (pg. 151)
6.1 Probability and Proportion (pg. 151)
6.2 The Theory of Probability (pg. 152)
6.3 Relative Risk (pg. 159)
6.4 Calculating the Probability for Multiple Individuals (pg. 161)
6.5 The Proportional Syllogism (pg. 164)
6.6 Exercises (pg. 169)
7 The Inductive Generalization (pg. 189)
7.1 Introduction (pg. 189)
7.2 Calculating the Probability of an Interval (pg. 191)
7.3 The 95 Percent Interval (pg. 193)
7.4 An Example of an Inductive Generalization (pg. 196)
7.5 The Conclusion of an Inductive Generalization (pg. 200)
7.6 Inductive Strength (pg. 202)
7.7 Exercises (pg. 203)
8 Bayes’ Rule (pg. 213)
8.1 Bayes’ Rule (pg. 213)
8.2 Example 1: Two Jars of Marbles (pg. 214)
8.3 Example 2: The Stolen \$1.3 Million (pg. 215)
8.4 The Argument Using Bayes’ Rule (pg. 218)
8.5 Example 3: A Match Made with Bayes’ Rule (pg. 220)
8.6 Example 4: A Positive Mammogram (pg. 222)
8.7 Exercises (pg. 223)
A A Brief Introduction to Deductive Logic (pg. 235)
A.1 Some Rules of Deductive Logic (pg. 235)
A.2 Categorical Syllogisms (pg. 239)
A.3 Exercises (pg. 240)
B Some Further Topics on Probability (pg. 247)
B.1 Odds (pg. 247)
B.2 Expected Value (pg. 250)
B.3 Where Do Probabilities Come From? (pg. 254)
B.4 Exercises (pg. 257)