Logic is typically understood as the systematic and rigorous study of inference and argument — the science of figuring out what follows from what, and why. Formal logic does this by thinking carefully about systems of inference: what are they good for; what choices we confront when devising them; how, if at all, can we show that we've made the right choices and that our systems of inference really accomplish their aims. We will study two of the most central and important logical systems, propositional logic and predicate logic. Each of these will be examined from several points of view (syntax/grammar, semantics/truth, truth tables, truth trees, natural deduction). We will practice the use of these systems and their application to garden-variety arguments. We will also establish some meta-theoretic results about our systems of logic (e.g., concerning the relation between what’s true and what we can use our systems to prove to be true).