Paradox and Infinity
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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
- Learn about how some infinities are bigger than others, and explore the mind-boggling hierarchy of bigger and bigger infinities.
- : Learn about whether time travel is logically possible, and whether it is compatible with free will.
- : 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.
- 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.
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| Rating | 4.4★ based on 7 ratings |
|---|---|
| Length | 12 weeks |
| Effort | 5 - 6 hours per week |
| Starts | On Demand (Start anytime) |
| Cost | $99 |
| From | Massachusetts Institute of Technology, MITx via edX |
| Instructors | Agustin Rayo, Damien Rochford, David Balcarras, Cosmo Grant |
| Download Videos | On all desktop and mobile devices |
| Language | English |
| Subjects | Programming Mathematics Humanities |
| Tags | Computer Science Math Philosophy & Ethics |
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What people are saying
penchant for abstract thinking
If you have a penchant for abstract thinking and contemplating the complexities and puzzles of life - whether or not you enjoy mathematics - this course has a world of pleasures to offer.
even what seems obvious
The paradoxes available in the course urge me to be puzzled about even what seems obvious.
many other stimulating things
If you really hate math, then I would suggest skipping a couple of the weeks - but there's so many other stimulating things to learn that it's still worth it.
which looks nearly similar
And the most interesting to me one is Yablo's paradox (The liar paradox) which looks nearly similar to Russell's paradox but in a different way about "Set theory".
exams are extremely tricky
The exams are extremely tricky and more difficult than the exercises provided.
life - whether or
not understand every topic
I do not understand every topic in this course when I first see it.
professor rayo does
Professor Rayo does an amazing job teaching and explaining this subject, and the material itself is incredibly interesting.
materials like having
I enjoy reading the materials like having a very tasteful meal which my mom makes.
very tasteful meal
instructor was solid
The instructor was solid, but the content of the course is what makes this such a unique experience.
other mathematical subjects
Before I began, I knew only the basics of Set Theory and other mathematical subjects that are covered and used in this course.
Careers
An overview of related careers and their average salaries in the US. Bars indicate income percentile.
Professor of Philosophy Fellow $20k
Lecturer, Philosophy $44k
Mathematics $50k
Professor of Philosophy 2 $54k
Adjunct Lecturer in Philosophy $59k
Philosophy $64k
Professor of Theology/Philosophy $86k
Professor of Philosophy & Mathematics $103k
Professor of Philosophy Consultant $116k
Assitant Professor of Philosophy $121k
Associate Instructor of Philosophy $151k
President Professor of Philosophy $264k
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| Rating | 4.4★ based on 7 ratings |
|---|---|
| Length | 12 weeks |
| Effort | 5 - 6 hours per week |
| Starts | On Demand (Start anytime) |
| Cost | $99 |
| From | Massachusetts Institute of Technology, MITx via edX |
| Instructors | Agustin Rayo, Damien Rochford, David Balcarras, Cosmo Grant |
| Download Videos | On all desktop and mobile devices |
| Language | English |
| Subjects | Programming Mathematics Humanities |
| Tags | Computer Science Math Philosophy & Ethics |
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