Philosophy 251: Handout #5

VIII. Translate each of the following sentences into formulas of SL.

1. If any of the French, Dutch, or Germans win a gold medal, so will the other two nations.
   
   
2. If the French are plagued with injuries, they will win a gold medal if either of the other two teams wins or it rains during most of the competition or the star German runner is disqualified.
   
   
3. Provided that both their star runner not being disqualified and its not raining during most of the competition is sufficient for the Germans winning a gold medal, then the Germans will win a gold medal only if neither of the other two nations wins one.
   
   
4. If the Dutch will win a gold medal except when the Germans do and the Germans win provided that either the French do not or it rains during most of the competition, then at most one of the three countries will win a gold medal.
   
   
5. The Germans will win a gold medal unless their star runner is disqualified; in which case the French will win unless it rains during most of the competition, in which case the Dutch will win.

IX. Extract the argument(s) from each of the following passages, put the arguments into standard form, and then translate the premises and conclusion of each argument into formulas of SL.

1. The club's social prestige will rise if Adams joins, but the club's financial position will become more secure, if Baker joins. If the club's social prestige rises, then Baker will join unless Wilson joins. Wilson will join only if the club's financial position becomes more secure. Hence, either Baker or Wilson will join, but not both.
   
   
2. The river will rise only if the rain continues and if both the rain continues and the river rises, then the bridge will wash out. If the continuation of rain is sufficient for the bridge to wash out, then a single road is not sufficient for the town to prosper. Hence a single road is not sufficient for the town to prosper. In addition, either a single road is sufficient for the town to prosper or the traffic engineers have made a mistake. So, the traffic engineers have made a mistake.
   
   
3. Assuming Betty is the judge, if Peter gets a sentence, it will not be suspended. Peter will not be found guilty only if Fred is not his defense lawyer. The trial will be long unless the D.A. is brief. Unfortunately, neither the D.A. is brief nor is Fred not Peter's defense lawyer. If Peter is found guilty he will be given a sentence. Consequently, after a long trial Peter will be given a sentence which will not be suspended.
   
   
4. Physical states of brains are not identical with mental states of minds. For if they are identical, then two creatures are in the same mental state only if they are in the same physical brain state. But having similar brains is a necessary condition for two creatures being in the same physical brain state, and frogs and humans do not have similar brains even though they share mental states such as pain.
   
   
5. Either the universe is 20 billion years old or 15 billion or less than 10 billion. If the universe is 20 billion years old, then there would be more older stars than there are unless hyper-expansion is necessary for slow star formation. But hyper-expansion is not necessary for slow star formation. Hence, the universe is 15 billion years old, for some class K stars have gone supernova and the universe is less than 10 billion years old only if no class K stars have gone supernova.