Paradox and Infinity

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Overview

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.

Syllabus

Module 1: INFINITY

Week 1 Infinite Cardinalities

Week 2 The Higher Infinite

Week 3 Omega-Sequence Paradoxes

Module 2: DECISIONS, PROBABILITIES AND MEASURES

Week 4 Time Travel

Week 5 Newcomb's Problem

Week 6 Probability

Week 7 Non-Measurable Sets

Week 8 The Banach-Tarski Theorem

Module 3: COMPUTABILITY AND GÖDEL'S THEOREM

Week 9 Computability

Week 10 Gödel's Theorem

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