Summary of Semantic Methods

We have seen that we can characterize the semantic status of individual wffs, the consistency/inconsistency of sets of wffs, and the validity/invalidity of arguments.  The methods we've used, full truth-tables, gappy truth-tables, and truth-trees, are all variations on a theme. If you know the rules of truth for the operators of PL, then you can determine the truth-value of any wff when you know the truth value of its individual sentence letters. When you know the truth value of wffs in all possible cases, (all rows of the truth-table) you can determine their semantic status.  

We now turn to the third branch of logic, now that we've mastered the syntax and semantics of PL, namely proof theory.