Paradox & Infinity

A wise older being floats above two boxes, Box A and Box B.

Newcomb's Paradox, aka Newcomb's Problem. Box A contains $1000, and Box B contains either nothing or $1 million. You can choose only Box B or choose both Box A and Box B. However, several days ago, a predictor with an excellent track record made a prediction of what your choice will be. If the predictor predicted that you will choose both boxes, he put nothing in box B. If the predictor predicted that you will choose only Box B, he filled the box with $1 million. Box B was then sealed, and its contents will remain fixed regardless of what you choose. What should you do? (Image by MIT OpenCourseWare.)


MIT Course Number


As Taught In

Spring 2013



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Course Description

Course Features

Course Description

This course explores different kinds of infinity; the paradoxes of set theory; the reduction of arithmetic to logic; formal systems; paradoxes involving the concept of truth; Gödel’s incompleteness theorems; the nonformalizable nature of mathematical truth; and Turing machines.

Related Content

Agustín Rayo, and Owain Evans. 24.118 Paradox & Infinity. Spring 2013. Massachusetts Institute of Technology: MIT OpenCourseWare, License: Creative Commons BY-NC-SA.

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