Pre-College Programs
Summer@Brown Courses

« Return to Course Catalog

Logic & Paradox

Two Sections Available to Choose From:

Course DatesWeeksMeeting TimesStatusInstructor(s)CRN
June 15, 2015 - June 26, 20152M-F 12:15-3:05POpenZachary Barnett10630
July 27, 2015 - August 07, 20152M-F 12:15-3:05POpenZachary Barnett10730

Course Description

Logic is a system of rules upon which human reasoning is based. It pervades every academic discipline, from mathematics to the sciences, to the humanities. It is a tool that we deploy in our everyday lives. To philosophers, logic is a deep and complex subject of study in its own right. This course is devoted in part to exploring this system of rules, which we will build from the ground up. Previous exposure to logic is not a prerequisite for the course.

A paradox is a chain of reasoning that starts from seemingly obvious premises and arrives at a conclusion we find unacceptable. Consider the famous Liar Paradox: “This sentence is false.” Is it true? Can’t be. Is it false? Can’t be. Perhaps it is neither true nor false? For reasons we will see, this option doesn't work either. Nothing works. Or at least, that’s how things seem. Paradoxes reveal inconsistencies in our everyday beliefs. They show us that our intuitions sometimes break down. Part of this course will be an opportunity to investigate some of the most mind-bending and perplexing paradoxes that have been discovered.

The logic part of the course will be similar to an accelerated math class. We will cover new material every day; there will be problem sets every night. In terms of content, we will cover much of the same material that a college-level introduction to logic course would cover. We will start by formally defining the core concepts (propositions, truth/falsity) as well as the logical operators (conjunction, disjunction, negation, the conditional). We will use truth tables examine how these operators affect the truth of sentences that contain them. We will work our way toward definitions of satisfiability, implication, and validity. In the second half of the course, we will introduce predicates and quantifiers into our system in order to study first-order logic in all of its depth and rigor.

The paradoxes part of the course will not be similar to any high-school course that I know of. Each day, we will explore a new paradox together. In the evening students will work in small groups trying to devise their own solutions to the paradox of the day. In class the following day students will have the opportunity to present their preferred solutions to their peers. In past instances of this course some student solutions have been so innovative and insightful that we have published them to the web. Paradoxes we will study include: Zeno’s paradoxes of motion, Newcomb’s Paradox, the Two-Envelope Paradox, the Problem of Moral Luck, the Ship of Theseus, the Trolley Problem, the Mere Addition Paradox, The Sleeping Beauty Paradox, the Monty Hall Problem, Hilbert’s Hotel, and many others.

he course has no prerequisites. Historically, students who have enjoyed this course the most either: (a) love math, (b) love puzzles, and/or (c) have very strong opinions. But all students are welcome!