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.
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 the fundamental concepts of modern matheamatical 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?
The course will consist of lectures, held in 119 Gerard House on Monday, Wednesday, and Friday. The text for the course is Deductive Logic, by Warren Goldfarb. Copies are available at the Brown bookstore.
There will be an open `Q&A' session held each week, at times that will alternate from week to week. The first will be on Monday, 21 September, from 4-5pm in room G18, Smith-Buananno Hall. The second will be on Thursday, 1 October, again from 4-5, and in the same place; then Monday, Thursday, etc. See the syllabus for a proper schedule.
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.
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.
Let me emphasize, however, that, while the course is fairly easy at the beginning, it starts to get more difficult after the mid-term, and it then quickly becomes very difficult. And the 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. It is therefore absolutely impossible to learn this material in the two weeks before the final exam, and, if you try to learn it that way, I can pretty much guarantee that you will fail the course. Several people do regularly fail the course each time it is offered for this very reason.