Philosophy 0540: Course Description

What Is Deductive Logic?

Logic is the study of what makes an inference, in a certain limited sense, "good", "valid", or "correct". Logic, as the great logician (and founder of modern logic) Gottlob Frege convincingly argued, is not a branch of psychology: It does not concern itself with how people do in fact reason, with what sorts of argument they find compelling, nor even with whether a given argument in fact shows its conclusion to be true. Logic is, instead, a normative discipline: It is about one important constraint on what it is to reason or argue correctly. Logic is concerned with how people ought to reason, that is, with what rules they ought to follow when they do reason; it concerns itself with whether, if one accepts the assumptions someone is making, one must also (on pain of irrationality) either accept the conclusion for which she is arguing or else give up one of those assumptions.

One should not, however, expect this to be a course in reasoning or argument. Logic studies the principles of valid argument abstractly: While the course should teach you something about distinguishing valid from invalid arguments—and, like any good course, should teach you something beyond its specific subject-matter, something which will help you with other courses (and in your life after all the courses are over)—this course is not designed to help you write or reason better. What the course will do is introduce you to the fundamental concepts of modern mathematical logic.

We shall seek to characterize valid arguments of two different types. In order to do so, however, we shall have to introduce a great deal of special symbolism: We wish to consider, not specific arguments, but kinds of arguments; and we want to see, for example, what is common to the good, or 'valid', arguments, "John is at home; so either he is at home or at the zoo" and "Tom is a professor; so he is either a professor or a fireman".

As part of our study of logic, we will develop a `formal system' in which to prove that various arguments are, indeed, valid. Much of this middle part of the course will be something like a high school geometry class, as we shall be learning to do proofs in this system, just as one learns, in high school, to do proofs in axiomatic geometry.

Finally, we shall turn our attention upon the formal system itself and study it. We shall ask such questions as: Is it possible to prove, in this system, that any given valid argument really is valid? Or are there some valid arguments whose validity can not be demonstrated in this system? Is there some kind of way to decide or to calculate whether an argument is valid?

Course Information

The course will consist of lectures, held at 10am in 220 Sidney Frank Hall on Monday, Wednesday, and Friday. Class meetings will consist primarily of lectures. This course website will always contain the most up-to-date information about the schedule.

There are three `Q&A' sessions held each week:

These are group-oriented opportunities to ask questions and typically will involve the instuctor working through examples. You can attend any one you wish and as many as you wish. Specifically, you do not have to attend the session that is led by the person who grades your problem sets.

Please note that the Q&A sessions will begin on Monday, 11 September.

There are five hours of office hours each week:

Generally speaking, these function as opportunities to ask questions individually, though if several people arrive at once, they can become group-oriented, since different people often have similar questions. You can go to office hours to ask questions of any of the instructors.

The text for the course is Deductive Logic, by Warren Goldfarb. List price is $39.00. Copies are available at the Brown bookstore. Students should plan to read the relevant material from the book before each lecture. Lectures will not cover all material for which students will be responsible.

Please see this page for details on course requirements.

Prerequisites

There are no formal prerequisites for this course. In particular, the course presupposes no college-level mathematical knowledge. However, much of the course is mathematical in content: Some familiarity, experience, and comfort with proofs, such as those in a high-school geometry course, is extremely useful. Anyone uncertain of their background in this area is encouraged to speak with the instructor.

Richard Heck Department of Philosophy Brown University