Homework 2: Truth Conditions

Today in class we talked about the truth conditions of sentences: the way the world must be if the sentence is true. Truth conditions can also be viewed as a certain kind of inference that can be drawn from a sentence, called "entailments." Definitionally, we say that a particular inference I is an entailment of a sentence S just in case whenever S is true, I must also be true. Stating the set of entailments of a sentence therefore is a way of stating its truth conditions.

YOUR JOB: Consider the following pairs of sentences and for each, say whether the first entails the second, and justify your answers as well as you can. Where proper names or pronouns or similar expressions are repeated, assume that the same individual is referred to in each case. Assume also that temporal expression (like today and the present tense) receive a constant interpretation.

1. • Today is sunny.
   • Today is warm
2. • Jane ate oatmeal for breakfast this morning.
   • Jane ate breakfast this morning.
3. • Jane ate oatmeal for breakfast this morning.
   • Jane ate something hot this morning.
4. • Juan is not aware that Mindy is pregnant.
   • Mindy is pregnant.
5. • Every second year student who knows Latin will get credit for it.
   • If John is a second year student and knows Latin, he will get credit for it.
6. • If Alice wins a fellowship, she can finish her thesis.
   • If Alice doesn't win a fellowship, she can't finish her thesis.
7. • Maria and Marco are married.
   • Maria and Marco are married to each other.
8. • Only Amy knows the answer.
   • Amy knows the answer.
9. • Some student will not go to the party.
   • Not every student will go to the party.
10. • Not every student will go to the party.
    • Some student will go to the party.