Paradox and Infinity

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

Paradox and Infinity

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

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

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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.

Verified learners will be eligible for the MITx Philosophy Award and (for learners in high school) the MITx High School Philosophy Award. The awards will be given by the MIT Philosophy Department for outstanding written work. Award winners will be profiled on theMIT Philosophy Department website. See there for additional information and profiles of winners from previous years.

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

  • Featured image for Agustín Rayo
    Professor of Philosophy

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.