ABSTRACT
Chapter 1 emphasised a clear distinction between the syntactic forms of propositions and the semantic functions that provide interpretations for the propositional symbols. Syntactic forms are decided by the order in which symbols appear in a string of symbols whereas the semantics of that string of symbols is decided by the interpretation, meaning or denotation given to the symbols. Many different interpretations may be given to strings defining formulas and we have to be sure that the denotations given are consistent with the syntactic form. This distinction between syntactic and semantic forms might at first seem unfamiliar, but it has been with us since our earliest days in primary school. If a child were asked whether 6 × 7 is equal to 42, he might reasonably reply that it is not. The symbols 6, × and 7 on the left are quite clearly different from the 4 and the 2 on the right, so the two expressions are not the same. Two expressions are syntactically the same if they consist of the same symbols in the same order. Later the child will learn that, although the expressions are syntactically different, they denote the same value and are interpreted as equivalents.
