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".
The course will consist primarily of lectures, which will be presented online. At present, the plan is to do the lectures 'live' for the first four weeks at 10am on Monday, Wednesday, and Friday. (These lectures will be recorded and made available on Canvas as well.) During that period, all sections will also meet online, with times and other details still to be determined.
Beginning on Wednesday 7 October, and assuming we are able to have some in-person instruction at that time, we'll shift to recorded lectures and in-person sections, again held at 10am. Students who are not on campus, or who have other reasons not to wish to join in-person sections, should register for the online section, who meeting time (or times) is still to be determined.
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.
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.