Welcome to the Course
Welcome to Think Again: How to Reason Inductively! This course is the third in a series of four courses jointly titled Think Again: How to Reason and Argue. We are excited that you are taking this course, and we hope that you will take all four courses in the series, because there is a great deal of important material to learn.
In the series as a whole, you learn how to analyze and evaluate arguments and how to avoid common mistakes in reasoning. These important skills will be useful to you in deciding what to believe and what to do in all areas of your life.
The first part of this course introduces the series and the course. It also clarifies some peculiarities you may find with this course. We encourage you to watch the "Introduction to the Course" video first as it will help you learn more from the materials that come later.
CONTENT: 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.
LEARNING OUTCOMES: By the end of this week's material you will be able to do:
- distinguish inductive from deductive arguments
- classify inductive arguments into five kinds
- identify and evaluate arguments that generalize from samples
- identify and evaluate arguments that apply generalizations to cases
- identify and evaluate inferences to the best explanation by applying standards that good explanations must meet
- identify and evaluate arguments from analogy
OPTIONAL READING: If you want more examples or more detailed discussions of these kinds of inductive arguments, we recommend Understanding Arguments, Ninth Edition, Chapters 8 and 9.
CONTENT: 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.
LEARNING OUTCOMES: By the end of this week’s material you will be able to do:
- analyze causal reasoning
- distinguish necessary from sufficient conditions
- determine what is necessary or sufficient for what
- separate causation from correlation
OPTIONAL READING: If you want more examples or more detailed discussions of these topics, we recommend Understanding Arguments, Ninth Edition, Chapter 10.
Chance and Choice
CONTENT: 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.
LEARNING OUTCOMES: By the end of this week’s material, you will be able to do:
- solve some classic paradoxes of probability
- apply simple rules of probability
- use Bayes’ theorem to calculate conditional probabilities
- avoid fallacies of probability
- apply probabilities to calculate expected financial values
- distinguish financial value from overall value
- use simple rules to aid decisions under uncertainty
OPTIONAL READING: If you want more examples or more detailed discussions of these topics, we recommend Understanding Arguments, Ninth Edition, Chapters 11 and 12
Catch-Up and Final Quiz
This week gives you time to catch up and review, because we realize that the previous weeks include a great deal of challenging material. It will also be provide enough time to take the final quiz as often as you want, with different questions each time.
We explain the answers in each exam so that you can learn more and do better when you try the exam again. You may take the quiz as many times as you want in order to learn more and do better, with different questions each time. You will be able to retake the quiz three times every eight hours. You might not need to take more than one version of the exam if you do well enough on your first try. That is up to you. However many versions you take, we hope that all of the exams will provide additional learning experiences.