Chapter 4: Validity and Other Semantic Properties

In Chapter 3 we introduced the semantics of PL, that is, we showed how, for any wff of PL, its truth-value is completely determined by the truth-values of its simple parts.  In this chapter, we show how the rules of truth for PL can be applied to determine important properties of wffs, sets of wffs, and arguments. 

First we'll demonstrate that some wffs are always true, no matter what truth-values are assigned to their sentence letter components, that other wffs are always false, and that the rest are sometimes true and sometimes false. 

We'll also look at what happens when we evaluate the truth values of wffs taken together.  Some sets of wffs are inconsistent, that is, they can't all be true at the same time. Happily, many sets of wffs are consistent.

Finally, we will turn to arguments, which consist of premises and a conclusion, and we'll be able to use the truth-table method as a test for the validity of argumets. Remember that a valid argument is one where it is not possible for the premises to be true and the conclusion false.  It's very straightfoward to determine validity and all the other semantic properties using the truth-table method and other methods based on it.