Homework for Philosophy 270, Fall 2011

(i)

Give your own example of four non-equivalent sentences that make up a “square of opposition”—i.e., two mutually exclusive sentences each of implies one of a pair of jointly exhaustive sentences and is contradictory to the other member of that pair. (Hint: it is enough to find a pair of mutually exclusive sentence that are not also jointly exhaustive; sentences that are contradictory to each of the two will then provide two more non-equivalent sentences for the diametrically opposite vertices of the square.)

(ii)

Pick one of the pairs of sentences from your square that are not equivalent but related by entailment and briefly describe a possible world in which they have different truth values (i.e., describe a possible world that shows they are not equivalent).