Assignment 1. Assessing Paradoxes

For submission

Consider the following paradoxes.

• Use the summary diagnosis at the end of the chapter Paradoxes: Their Diagnosis, Treatment and Cure to assign a tag to each of them.

• Explain why the tag is the appropriate diagnosis.

• Resolve each paradox.

1. Why is it that when I lose my keys, they are always in the last place that I look? Why does the cosmos hate me?

2. A Jeep is better than nothing.
Nothing is better than a Cadillac.
Therefore, a Jeep is better than a Cadillac.

3. In an ancient city, by law, new visitors had to state the reason for their visit. If they told the truth, they were not imprisoned. If they told a falsehood, there were imprisoned. A mischief maker declares "You will imprison me!"

For discussion

Not for submission

A. Consider any number. Say 1,000,023. We can always find a bigger number just by adding one. 1,000,024 > 1,000,023. This is true of any number. Use this fact to provide a reductio ad absurdum proof that there is an infinity of numbers.

B. Pick some of the paradoxes in the chapter, A Budget of Paradoxes, or elsewhere that have NOT been resolved in the chapter, Paradoxes: Their Diagnosis, Treatment and Cure. How can they be resolved? Some suggestions:

• Irresistible force
• The infinite past
• Another paradox not in the budget

C. Consider the recipe for curing paradoxes in the chapter Paradoxes: Their Diagnosis, Treatment and Cure. Is it exhaustive? Are all paradoxes dependent on an apparent absurdity, contradictory assumptions or fallacies of reasoning? Are there other cases?