Typeset your answers neatly and submit a hardcopy solution at the beginning of class on 2012-01-31. You are strongly urged to use LaTeX, but I will not force you to do so.

Please note that many of these questions are not answerable solely from the course notes and textbooks. You may actually need to do some research—the web is fine. Remember to cite your sources. Also note that just because you pull data from a reputable source doesn't mean your answer will be good enough for full credit, let alone correct. Make sure your response answers the question, and answers it thoroughly. But be brief!

1. What are the easy and hard problems of consciousness? Why do many people think the hard problem may not be solvable?
2. What does Dan Dennett say about the hard problem of consciousness? What does John Searle say about it?
3. Why were Gödel's incompleteness theorems such a big deal in the 1930s?
4. Give five examples of self-swallowing sets, five examples of autological words, and five examples of heterological words (other than those used in GEB or in class).
5. Translate the following sentences into logical notation. Use smart abbreviations.
   1. If you don't leave now, you will not win the prize.
   2. Ani or her sisters might have been late.
   3. Some dogs like cats who live in the capital of Turkey.
   4. The person who won the race prefers orange juice to tea.
   5. 3 will never be greater be 7.
   6. Not every odd number is greater than its own square.
   7. Something evil caused all evil things except itself.
   8. Some day, it will be possible that all players will have the same score.
   9. War is peace, freedom is slavery, and ignorance is strength.
   10. All that was once true will someday necessarily be forever false.
6. Give an ambiguous English sentence, other than the ones in Logic: A Very Short Introduction that could be interpreted as either A→◻B or ◻(A→B), such that one of the formulae is false in our world and the other true. Then give renderings of each formula in English that would not be ambiguous.
7. How do you resolve the issue put forward at the end of Chapter 4 in Logic: A Very Short Introduction? Recall that the claim was that sentences referring to non-existent objects are false, but many ancient Greeks did worship Zeus, and for that matter, Pegasus was a horse, Santa Claus lives at the North Pole, Harry Potter wore (wears?) glasses, and Noah survived a rather nasty flood. Describe two ways to make these kinds of statements be true despite the non-existence (in our world) of the subjects or events.
8. Continue the sketch on page 60 in Logic: A Very Short Introduction, adding the next four temporal logic formulas to their proper positions in the diagram.
9. There is a test for a rare disease that affects 0.003% of the population. The test is 98% accurate, meaning that it gives the correct result (positive or negative) 98 times out of 100. You've just tested positive. What is the probability you have the disease?
10. In classical logic, ∃ and ∀ are duals of each other, because (~∃x.P) ≡ ∀x.~P and (~∀x.P) ≡ ∃x.~P. Are the temporal operators F and G duals of each other? Why or why not?