Take my Infinity final exam! - by Joel David Hamkins
My undergraduate students and I have been studying infinity and paradox all semester here at the University of Notre Dame, following The Book of Infinity, with all my favorite conundrums. The book will appear soon with MIT Press.
We just wrapped up the class with a final exam, and I thought it would be fun to share the exam questions here (some slightly edited), so that the rest of my readers here can have a chance to think about the questions as well.
Instructions. For each question, answer as fully and robustly as possible, with a brief essay explaining the main points and arguments at stake and bringing fully to light all the relevant philosophical issues. Incorporate diagrams or technical matters, if any, as a part of the narrative flow. Some questions are open-ended, and feel free to take any position on the matter, provided you can defend it well.
Defend or criticize the argument: “ The set of rational numbers cannot be countable, because between any two rational numbers there are more.” Give a full explanation of your position.
