Empirical and Mathematical Reasoning

After they graduate, students will be making important decisions, for themselves and others, under conditions of uncertainty. They will have to decide, for example, what medical treatments to undergo, when a defendant in court has been proven guilty, whether to support a policy proposal, and how to manage their personal finances. They also will be called upon, as individuals and as citizens, to evaluate empirical claims made by others. Courses in empirical reasoning help students learn how to make decisions and draw inferences in matters like these that involve the evaluation of empirical data. They teach students how to gather and assess information, weigh evidence, understand estimates of probabilities, solve problems, draw inferences from the data available, and also how to recognize when an issue cannot be settled on the basis of the available evidence. To develop these abilities, students need to learn how to apply the abstract principles and concepts of probability theory, statistics, decision theory, logic, and mathematics to concrete problems. Ordinarily, they will learn to do this in the form of hands-on exercises. Just as one doesn’t become a marathon runner by reading about the Boston Marathon, so, too, one doesn’t become a good problem solver by listening to lectures or reading about statistics. Students should learn empirical reasoning by practicing it.

Empirical reasoning is not a discrete body of knowledge. It is a set of related conceptual skills that guide valid reasoning and decision-making. To take just a few examples, students might learn the statistical principle that exceptional cases will regress to the mean; that relaxing the standards for reporting an uncertain event will increase both hits and false alarms; that a person with the typical symptoms of a rare condition probably does not have that condition; that in certain interactions the best option for each individual can bring about the worst outcome for all of them. It is also helpful for students to become aware of the many mistakes that human beings are prone to making in their reasoning, such as mistaking correlation for causation, ignoring base rates in estimating probabilities, overinterpreting coincidences, and the like. Knowing common pitfalls in inference-making can help students avoid them.

Empirical reasoning should be taught in the context of a variety of subjects so that students can work on topics of intrinsic interest to them, such as medicine and disease, public policy and political behavior, and legal or economic decision-making. We expect that many students will fulfill the requirement with courses in the statistical and analytical methods of their field. Mathematics and logic courses that demonstrate the applicability of their methods to concrete problems should also count toward this requirement.

Courses in Empirical and Mathematical Reasoning should:

  • teach the conceptual and theoretical tools used in reasoning and problem solving, such as statistics, probability, mathematics, logic, and decision theory;
  • provide exercises in which students apply these tools to concrete problems of wide concern; and
  • where practicable, familiarize students with some of the mistakes human beings typically make in reasoning and problem solving.

See my.harvard for a list of courses that satisfy this category.  Using the Advanced Search function, select Empirical and Mathematical Reasoning from the drop-down menu found under FAS – Additional Attributes.

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