ABSTRACT
This chapter extends the tableau system of Chapter 6 to cover the language of first-order logic with identity.
As in Chapter 6, tableaux offer a mechanical procedure for finding out the different ways a case might serve as a counterexample to an argument. Tableaux rules are given entirely in terms of the shape or form of sentences; they are silent on semantics. But the rules are nonetheless built to respect – and serve as a supplement to – the semantic account of validity. We use tableaux to determine whether particular arguments (or argument forms) are valid. We can use them to do this by checking whether any of the possible ways a case could serve as a counterexample to a given argument is actually possible (as a case).1
