The goal of this course is to provide students with a basic understanding of the proof theory and semantics of classical propositional and first-order logic; we prove fundamental metatheoretic results, including equivalences between different proof-theoretic systems, soundness, and completeness. By the end of the term, students should have a good understanding of these results, as well as the techniques involved in establishing them and in constructing
proofs about formal systems more generally. Although the subject of symbolic logic was developed by mathematicians and philosophers for their own special purposes (which we may discuss), logical concepts and techniques have found applications in a variety of disciplines including computer science, economics, law, linguistics, and psychology. Students in any of these subjects can benefit from the ideas studied in this course.

WARNING: Although this course builds on material from PHIL 170, it is very different in character. In this course, we prove theorems about logical systems (and not in logical systems). Doing well in PHIL 170 is no guarantee that this will come easy to you.