Overview
What makes an argument good? How do you show that someone has reasoned invalidly? In this course we will study arguments and reasoning both informally as well as with the tools and techniques of formal deductive logic. We learn the syntax and semantics of propositional and first-order logic (polyadic with identity), and we will use them to explicate the notion of a valid argument. We then apply our formal logical techniques to a variety of domains, such as the domain of sets (abstract collections of objects). Topics include syntax, semantics, pragmatics, consistency, proof, logical consequence, logical equivalence, logical truth, logical form, set theory, infinity, paradoxes, truth functionality, binary numbers, logic gates, truth tables, quantification, relations, functions, interpretations, models, soundness, and completeness. We will also discuss connections between formal logic and computability theory, philosophy of language, cognitive science, foundations of mathematics, and metalogic (theorems about logical systems themselves).
Course Structure
For Winter 2021, lectures will be asynchronous, so you do not need to be available during lecture time. Lectures will be pre-recorded and uploaded to Canvas, so you can watch them any time. Quiz sections will meet live twice per week in the times assigned in the UW time schedule. Both lecture and quiz sections are remote. No part of this course is in person.
Warning
This is a difficult and fast-paced course. We have a problem set due every week. Furthermore, all the material is cumulative, so you must keep up with the work all quarter in order to succeed. That does not mean that this class will be all work and no fun. This is the most fun class on campus! (In my biased opinion.) But you must know what you are getting into if you take this course.
The final exam for this course is required. It will be a timed Canvas quiz available on Weds. March 17 (our day assigned during finals week). You will have several hours to take the exam once you start it. You do not need to take it at the exact time-slot assigned to us by the university, but you do have to take it on that day. Do not enroll in this course unless you can commit to taking the exam on that day!