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Paradox and Infinity

This is a class about awe-inspiring issues at the intersection between philosophy and mathematics.

Paradox and Infinity
length
12 weeks
effort
5-6 per week
price
Free

About this course

In Paradox and Infinity, you will be introduced to highlights from the intersection of philosophy and mathematics.

The class is divided into three modules:

  • Infinity: Learn about how some infinities are bigger than others, and explore the mind-boggling hierarchy of bigger and bigger infinities.
  • Time Travel and Free Will : Learn about whether time travel is logically possible, and whether it is compatible with free will.
  • Computability and Gödel's Theorem : Learn about how some mathematical functions are so complex, that no computer could possibly compute them. Use this result to prove Gödel's famous Incompleteness Theorem.

Paradox and Infinity is a math-heavy class, which presupposes that you feel comfortable with college-level mathematics and that you are familiar with mathematical proofs.

Learners who display exceptional performance in the class are eligible to win the MITx Philosophy Award. High School students are eligible for that award and, in addition, the MITx High School Philosophy award. Please see the FAQ section below for additional information.

Note: learners who do well in Paradox will have typically taken at least a couple of college-level classes in mathematics or computer science. On the other hand, Paradox does not presuppose familiarity with any particular branch of mathematics or computer science. You just need to feel comfortable in a mathematical setting.

What you’ll learn

  • You will learn how to prove a number of beautiful theorems, including Cantor's Theorem, the Banach-Tarski Theorem, and Gödel's Theorem.
  • You will acquire the ability to think rigorously about paradoxes and other open-ended problems.
  • You will learn about phenomena at the boundaries of our theorizing, where our standard mathematical tools are not always effective.

Prerequisites

Experience in college-level mathematics or computer-science maybe helpful.

Meet your instructors

  • Agustín Rayo

    Agustín is a professor of philosophy at MIT, and a professorial fellow at the University of Oslo. His research lies in the intersection of the philosophy of language and the philosophy of logic and mathematics. He is the author of The Construction of Logical Space.

  • David Balcarras

    David Balcarras is a Lecturer in philosophy and a Digital Learning Lab Fellow at MIT. He got his PhD in philosophy from MIT, and his MA and BA in philosophy from the University of Toronto. His research focuses on the philosophy of mind and language.

Who can take this course?

Because of U.S. Office of Foreign Assets Control (OFAC) restrictions and other U.S. federal regulations, learners residing in one or more of the following countries or regions will not be able to register for this course: Iran, Cuba, Syria, North Korea and the Crimea, Donetsk People's Republic and Luhansk People's Republic regions of Ukraine.