Homework 3: Conditionals

Yesterday in class we talked about the truth conditions of complex sentences formed by taking basic sentences and making new ones using the sentential connectives 'not', 'and' and 'or.' We said that sentences denote propositions, which in our model correspond to functions from possible worlds to truth values, or to sets of possible worlds. These two conceptions are equivalent, and the set-way of thinking about things turned out to give us an easy way to formulate the meanings of the complex sentences with connectives.

YOUR JOB: Consider sentences formed with 'if ... then':

1. • If it is sunny, then it is warm..
   • If Jane ate oatmeal, then she is happy.
   • If Marco goes to the party, Maria will stay home.

Can you characterize the meanings of conditional sentences in a way that is similar to the way that we characterized sentences with 'not', 'and' and 'or', i.e., where the meaning of "if S1 then S2" is stated in terms of the meaning of S1 and S2, and the meanings of S1 and S2 are sets of possible worlds?

NOTE: You do not need to present a formal analysis; an informal statement of the truth conditions is fine!!