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.
- 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.
Agustin 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.
Cosmo Grant is an Instructor / Digital Learning Lab Fellow in philosophy at MIT. He got his PhD in philosophy, also at MIT, in September 2019. He works on epistemology, decision and game theory, and philosophy of science. Before coming to MIT, he studied Mathematics & Philosophy at Merton College, Oxford, gaining his BA in 2012 and MMathPhil in 2013.
David Balcarras is a fifth-year graduate student in philosophy at MIT. He works on language, mind, and metaphysics. His thesis is about metasemantics and the nature of natural language. Before coming to MIT, he studied at the University of Toronto, getting his BA in 2013 and MA in 2014.