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## Overview

In Paradox and Infinity, you will be introduced to highlights from the technical side of philosophy--from the higher infinite to Gödel's Theorem.

The class is divided into three modules:

• Time Travel and Free Will: Learn about whether time travel is logically possible, and whether it is compatible with free will.
• Infinity: Learn about how some infinities are bigger than others, and explore the mind-boggling hierarchy of bigger and bigger infinities.
• 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 both the MITx Philosophy Award and 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

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

Agustin Rayo

## Reviews for edX's Paradox and Infinity 4.0 Based on 4 reviews

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• 1
Monica G
2.0 2 years ago
is taking this course right now, spending 20 hours a week on it and found the course difficulty to be very hard.
There are not enough exercises to thoroughly learn the material. The exams are extremely tricky and more difficult than the exercises provided.
Jacob R
5.0 3 years ago
by completed this course.
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Steven X
5.0 2 years ago
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4.0 3 years ago
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