| The strengths of a formal grammar in describing language should be clear to the reader of some of the other works on this website. The effects of formalism on grammatical description are not unlike its effects in the study of logic (cf. The Languages of Science). The logician cannot consider an expression to be valid until demonstrated by means of a proof. Each step in a proof is built on previously defined concepts. At the base of a logical proof are the premises and axioms — certain undefined terms, simple concepts that we are obliged to accept without proof. It is possible to apply this approach to a grammar that is built with formal elements in a logical way. Suppose an expression in English is to be taken as grammatical. The student ought to be able to use logic to determine that the expression is describable by the rules of the grammar. Just as formal logic has concepts underlying it at its base, a formal grammar would also be expected to have simple elements that the student would accept without proof and be able to build on logically. |