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These problems appeared either in problem sets or in exams.
If you’re one of my current students: don’t expect these to show up on any of the exams!
Evaluate the following set of sentences for consistency.
- Some professors are liars.
- Every professor is either a liar or a walrus.
- If someone is a walrus, then they are blubbery.
- All blubbery things are delicious.
- Some professors are delicious.
Prof. Lee has been asked to teach a business course. It’s surprisingly popular: in fact, there are infinitely many students enrolled. During class, he pitches his “Sequential Cash Accumulation Model,” a business plan that he claims will allow everyone in the class to make some cash money.
Here’s the plan. We first assign each student who wants to join the business plan to a unique natural number, starting with 1 and ascending in order. Then we do business:
Then Student #2 gives $2 to Student #1.
Then Student #3 gives $3 to Student #2…
In general, Student #n gives $n but receives $(n + 1).
(Assume each student has unlimited credit, and that the bank allows interest-free overdrafts while these transfers are processed).
It sounds intriguing, but it also sounds kind of like a SCAM. Other students are similarly wary. In fact, you know that only about 1 in 100 students plan to do business with Prof. Lee.
Will this plan work? Why or why not?
The Tortoise is running an ultramarathon. The entire race is 100 kilometers long. The Tortoise is very slow. Initially, its speed is 1 meter per minute. Furthermore, the Tortoise gradually grows more tired: after each minute, its speed decreases. That is, for every n, the Tortoise’s speed at minute n + 1 is less than its speed at minute n, and its maximum speed during the whole race is its initial speed (1 meter per minute). Is it possible for the Tortoise to finish the race? Explain why or why not.
After living a very fun life of Vice!, you find yourself in Hell. Here’s the way Hell works: you do grueling work for 99 hours, then rest for 1 hour, then work for 99 hours, then rest for 1 hour, and so on, for eternity. While it initially sounds pretty bad, the Devil makes the following argument:
You aren’t convinced. Can you come up with a counterargument to the Devil’s remark?
Suppose Prof. Lee tells you the following:
You assign infinite utility to Eternity in Heaven. However, you seriously doubt that Prof. Lee is telling the truth—there’s a very, very high chance that he’s just lying (though you aren’t 100% certain). What does standard decision theory recommend that you answer in this case? (Justify your answer).
Define a claim as paradoxical iff it cannot be assigned a stable truth value. For example, the Liar Sentence—‘This sentence is false’—is paradoxical. But a claim that’s straightforwardly true or false is not paradoxical. Which amongst the following sentences are paradoxical?
PHLA10 is an introduction to philosophy. Which amongst the following statements is true?
Syllabi and course materials — coming soon.