ABSTRACT
In the last chapter a technique was given for rigorously determining the validity of arguments of our propositional language. The reader is unlikely to have encountered anything even remotely like this technique outside of the study of logic. One is more likely to be familiar with attempts to show that a certain conclusion follows validly from a set of premises by deriving that conclusion from the premises. For instance, in Euclidean geometry one seeks to establish that certain results (the theorems) follow validly from certain premises (Euclid’s axioms) by manipulating the premises in various ways to obtain the conclusion. In this chapter we will develop this sort of procedure for rigorously establishing the validity of arguments by deriving the conclusion of the argument from the premises using a system of rules. We introduce the symbol ‘⊢’ called the syntactic turnstile writing, for instance, ‘P v Q, ⅂P ⅂ Q’ to express the claim that ‘Q’ can be derived from the premises using the system of rules to be introduced.
