Think Again III: How to Reason Inductively

<p><b>CONTENT</b>: This week begins by distinguishing inductive arguments from deductive arguments. Then we discuss four common forms of inductive argument: generalizations from samples (such as in political polls), applications of generalizations to particular cases (such as in predicting weather on a certain day), inferences to the best explanation (such as in using evidence to determine who committed a crime), and arguments from analogy (such as in identifying the use of one archaeological artifact by comparing it to other artifacts). We will expose the most common mistakes in these kinds of reasoning. Some of the "lectures" this week are a bit experimental (and perhaps weird!), as you will see. We hope that you enjoy them.<p><b>LEARNING OUTCOMES</b>: By the end of this week's material you will be able to do:<ul> <li>distinguish inductive from deductive arguments</li> <li>classify inductive arguments into five kinds</li> <li>identify and evaluate arguments that generalize from samples</li><li>identify and evaluate arguments that apply generalizations to cases</li><li>identify and evaluate inferences to the best explanation by applying standards that good explanations must meet</li><li>identify and evaluate arguments from analogy</li></ul></p><p><b>OPTIONAL READING</b>: If you want more examples or more detailed discussions of these kinds of inductive arguments, we recommend <em>Understanding Arguments, Ninth Edition</em>, Chapters 8 and 9.</p>

<p><b>CONTENT</b>: This module will focus on how to decide what causes what. Students will learn how to distinguish necessary conditions from sufficient conditions and how to use data to test hypotheses about what is and what is not a necessary condition or a sufficient condition. Then we will distinguish causation from correlation (or concomitant variation) and explain the fallacy of post hoc ergo propter hoc. It is sad that some diners had to die to make this lesson possible, as you will see.</p>

<p><b>LEARNING OUTCOMES</b>: By the end of this week’s material you will be able to do: <ul> <li> analyze causal reasoning</li> <li>distinguish necessary from sufficient conditions</li> <li>determine what is necessary or sufficient for what</li> <li>separate causation from correlation</li> </ul> </p> <p><b>OPTIONAL READING</b>: If you want more examples or more detailed discussions of these topics, we recommend <em>Understanding Arguments, Ninth Edition</em>, Chapter 10.</p>

<p><b>CONTENT</b>: This week will cover chance and choice—in other words, probability and decision making. Probability is useful for measuring the strength of inductive arguments and also for deciding what to believe and what to do. You will learn about the nature and kinds of probability along with four simple rules for calculating probabilities. An optional honors lecture will then explain Bayes’ theorem and the common mistake of overlooking the base rate. Next we will use probabilities to evaluate decisions by figuring their expected financial value and contrasting financial value with overall value. </p><p><b>LEARNING OUTCOMES</b>: By the end of this week’s material, you will be able to do: <ul><li> solve some classic paradoxes of probability</li><li>apply simple rules of probability</li><li>use Bayes’ theorem to calculate conditional probabilities</li><li>avoid fallacies of probability</li><li>apply probabilities to calculate expected financial values</li><li>distinguish financial value from overall value</li><li>use simple rules to aid decisions under uncertainty</li></ul></p><p><b>OPTIONAL READING</b>: If you want more examples or more detailed discussions of these topics, we recommend<em> Understanding Arguments, Ninth Edition</em>, Chapters 11 and 12