Assignment 1. Assessing Paradoxes

For submission

Consider the following paradoxes. Reconstruct each as an argument and show how each is resolved, using the methods of the chapter Paradoxes: Their Diagnosis, Treatment and Cure

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. 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?