11.5: Review of Major Points

This chapter introduced the concept of a sentence's logical form and the concept of logical equivalence between sentences. Arguments have logical forms composed of the forms of their component sentences. Logical form in turn is the key to assessing whether a deductive argument is valid. Once you have identified the logical form of a deductive argument, the hardest part of assessing validity or invalidity is over, because with the form you can spot logical analogies, and you can use the method of truth tables to determine whether the argument is valid, that is, has no counterexample. In this chapter we concentrated on logical forms in Sentential Logic: forms involving and, or, not, and if-then that connect smaller sentences to form bigger sentences. We also examined three terms that are likely to cause logical confusion: only, only if and unless. The chapter ended with an excursion into 3-valued logic and then into the history of the field of logic. You have now developed an arsenal of powerful logical tools to use in attacking some cases of complex reasoning. Unfortunately, there is no single tool that works for all kinds of reasoning.