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 arguments 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 s'he is arguing or else give up one of one's assumption.
Logic can be studied from many different perspectives. In this course, we will study it from a mathematical perspective. This means, first, that we will be particularly interested in the role that logic plays in mathematical reasoning and argument, that is, in proof. We want to understand in what sense proof is "compelling": in what sense a correct proof really does prove its conclusion. But there is a second sense, too, in which our perspective will be mathematical: We will use mathematics itself as a tool with which to study logic. We will, that is to say, be formulating and proving a variety of theorems, in an effort to understand the role logical reasoning plays in proof.
The course will consist of lectures, held in 119 Gerard House on Monday, Wednesday, and Friday. The text for the course is Fundamentals of Mathematical Logic, by Peter Hinman. Copies are available at the Brown bookstore and at your favorite online outlets.
Students should plan to read the relevant material from the book before each lecture. Regular attendance at lecture is a good idea. Neither the book nor the lectures will cover all material for which students will be responsible.
There are no formal prerequisites for this course. In particular, the course presupposes no particular college-level mathematical knowledge, not even calculus. However, as has already been said, the course is mathematical in content. It is essential that students should be familiar with and comfortable with mathematical argument, that is, with the presentation and conduct of proofs. Anyone uncertain of their background in this area is encouraged to speak with the instructor. Students seeking an introduction to logic who do not have the preparation for this course are encouraged to enroll in Philosophy 0540, which is also being taught this semester.
Let me emphasize that this course is very cumulative: What we do later always depends heavily on what we've done earlier. If you get behind, it can be very difficult to catch up.