Logic aims to clarify principles of good reasoning in a range of areas: ordinary day-to-day reasoning as well as more abstract investigations in mathematics and the physical sciences. A basic guiding idea is the idea that logically good reasoning is 'truth-preserving'. ('Truth-preserving' reasoning cannot fail to take you from true premises to true conclusions. If the premises of truth-preserving reasoning are true, the conclusions must be as well.) So one goal we have in the study of logic is to get a grip on which forms of argument are truth-preserving and which are not.
In this course, we study two simple yet powerful systems of formal logic — 'sentential' logic, and 'predicate' logic. In the course of learning these systems, we will have the chance to apply formal techniques in analyzing arguments, and to solve practical problems. After mastering these systems, we'll address some questions concerning their power and dependability. In order to answer our questions we will have to develop a 'meta-theory' for the systems we've studied: that is, we'll develop techniques for studying the systems themselves: what can be proven in these systems? How do we know that the systems are reliable? And along the way, we will learn to employ the extremely important tool of mathematical induction.
Weekly homework assignments, a midterm examination & a final examination
No previous training in logic is required.
2 hrs of lecture per week and 1 hour of problem-solving/discussion section