PHIL 120

 PHIL 120: Symbolic Logic
Instructor: Paolo Verdini

Course Description

We can think of logic as the study of consistent sets of assertions, as the collection of all valid inferences, or even, albeit less thematically, as the rules that govern our reasoning. In this course, we will take all these definitions into account, with the fundamental premise that our inquiry will aim at formal logic, that is, a mathematically precise method of framing those concepts. It is what "symbolic" stands for: a rigorous translation of English into a formal language through unambiguous mathematical symbols. Accordingly, our first goal will be to formalize sentences with an increasing degree of complexity by dealing first with the syntax of propositional logic and then predicate or first-order logic. Secondarily, we will investigate the semantics of these two systems by effectively using truth tables and Tarski's interpretations. This part will tackle notions of "satisfiability" and "logical truth" of a sentence, as well as "validity" and "soundness" of an argument. We will then proceed to define and put to practical use a proof system for first-order logic. A proof system is a rigorous method to demonstrate results (theorems) given premises (sometimes axioms) and deduction rules. The course will culminate with an overview of some fundamental theorems (soundness, completeness) about the connection between syntax and semantics in first-order logic.