Symbolic Logic

Catalog description

This course is an introduction to symbolic logic. Logic is the science of correct reasoning, and symbolic logic is a particular branch of logic that studies correct reasoning using a formal or arti¿cial language. In this course, students will first learn basic vocabulary for argument analysis, standards for evaluating arguments that are expressed in English, and basic methods for testing these arguments along with the shortcomings of said methods. The deficiencies of the more natural approach to evaluating and testing arguments motivates a turn to learning symbolic logic as it purports to provide a more precise way of evaluating arguments. To this end, students will learn the symbols, syntax, and semantics of two different logical (formal, symbolic) languages (propositional and first-order predicate logic) and how to translate sentences from English into these formal languages. Once the languages are formulated, students will learn how to make use of mechanical tests (truth tables and/or truth trees) that allow for evaluating arguments for validity as well as testing propositions and sets of propositions for other logical properties (e.g. consistency, tautology, etc.). In addition to mechanical tests, students will learn how to solve proofs in two different languages. That is, they will learn a set of inference, derivation, or "proof" rules and use these rules to show that a conclusion follows from a set of premises.