Logic & Argumentation

It is a common experience to hear someone argue for a position, and sense that something is wrong with the argument. Perhaps the reasoning is somehow flawed or there are hidden assumptions that are questionable. We think the argument should not be persuasive but perhaps we are not sure just why. We can criticize such arguments as bad or weak, or even use stronger terms of abuse like fallacious or illogical, but that is not enough. We want to be able to say more. Why does the argument fail? What makes it fallacious? What are its strengths and weaknesses? What could be done to strengthen it? For our purposes — argumentation theory — the fundamental question is always this:

Is the argument a good one?

There are several senses for the word "argument," so there are several ways for arguments to succeed or fail. In one sense, an argument is just an abstract structure of statement, some of which are premises and one of which is the conclusion. But that leaves out the arguer — or arguers. One person can present an argument, but it takes two to have an argument.

Three common models are helpful for thinking about arguments: mathematicians’ proofs, lawyers’ presentations, and formal debates. A mathematical proof is good if the conclusion really does follow from the premises. A lawyer’s case is good when it cites the relevant legal precedents and uses the available evidence in the best possible way. One way to judge a debater’s case is by whether it successfully responds to objections, answers questions, and offers persuasive reasons — in short, by whether it wins. These criteria are separable. A proof can be valid, even if no one is persuaded; a lawyer may have done her job well even though she lost her case; and a debater might win although his reasoning was flawed — or he might lose despite very good argumentation. These correspond, roughly, to three areas of argumentation theory: logic, rhetoric, and dialectics.

Logic is the study of inferences, the links that constitute the chains of reasoning in arguments. Rhetoric is the art of rational persuasion — not just persuasion itself. Dialectics, as the term will be used here, refers to the communicative exchanges, the give and take that make up dialogical arguments. The techniques we will bring to bear on argument analysis all have that same end: to enable us to say something intelligent about arguments. If an argument fails, we want to know what went wrong in order to avoid such failures in our reasoning and, more important, not be taken in by similarly fraudulent arguments in the future. If the argument succeeds, we want to be able to identify its particular virtues so they may be used again.

Two main approaches will be developed in this course. First comes critical thinking. This includes argument diagramming and fallacy identification. Diagramming is largely a descriptive exercise involving the abstraction of form from content to isolate the logical structure of ordinary arguments. Accordingly, we develop and deploy conventions for representing the internal relationships of the parts of arguments — premises, inferences, conclusions, etc. Identifying an argument as fallacious is a more evaluative task. Content and "extra-logical" knowledge must be taken into account. The second approach uses the powerful techniques of symbolic logic. The first formal logic was Aristotle’s syllogistic logic, but we will begin with the more general propositional logic. The syntax of a symbolic language is developed, along with a formal semantics to provide the means for evaluating argument validity. This section culminates with proofs, the most rigorous logical exercise. Finally, with the time remaining, we will turn to the richly expressive language and inferential powerful system of first-order predicate logic.

The overall grade for the course will be calculated from the hour exams* (100 points each), the comprehensive final exam (200 points), several quizzes* (10 points each to a total 50 points), and regular home-work assignments* (50 points).

Office Hours: MWF: 8:30-11:00, & by appointment.

* Notes: The optional make-up for test three is for those who do poorly the first time. Quizzes are unannounced. There are no make-ups, but the lowest quiz grades are dropped. Late homework assignments are accepted for partial credit until that unit’s exam.