Inclusive and Exclusive 'or'

In the section 6.4, Lepore introduces the concept of inclusive "or" and exclusive "or" in the disjunction. The inclusive "or" is the case that both disjuncts can be chose, performed, or existed at the same time; while in sentences with exclusive "or", to choose one disjunct prevent us from choosing the other one. We can look at an example for better analysis: John will go to school or he will go to the shopping mall. In this example, the two disjuncts are "John will go to school" and "John will go to the shopping mall." Now the question is: is it possible that John will both go to school and to the shopping mall. If it is possible, this sentences has an inclusive "or"; if not, it has an exclusive "or." In this case, the answer is yes, because the fact that John will go to school does not prevent John from going to the shopping mall. He can go to one place after another one. Lepore also clarifies the logical implication and conversational implication of "or" in another example.

In Lepore's point of view, in order for a disjunction to have an exclusive "or", it must be possible that when the two disjuncts are both true, yet the whole sentence is false. There are some examples that seem like exclusive "or", but they are not. One of them will be "Today is the Labor Day or the Valentine's Day." People may think that it is not possible for today to be both Labor Day and Valentine's Day, so that it is an exclusive "or." However, they are wrong. These sentences cannot satisfy the first column of the truth table, that is, they are not even able to be true at the same time. In fact, this kind of sentences should not be translated into PL as disjunction.

Lepore says that logicians have not yet come up with a strong example of exclusive "or" so far, but we cannot conclude that there is only one "or", the inclusive one. As long as we are not able to prove, there is still some possibilities that an exclusive "or" will exist.