Formalism, grammatical rules, and normativity

Formalism within logic and mathematics has indirect connections to modern formal linguistics in that the earliest attempt at realizing the formalist program for logic had the side effect of leading to the development of what today we call generative grammars. Syntactic theory has been dominated by the generative conception for six decades. Despite reference in the literature to ``rules'', generative grammars do not contain rules in the usual sense (under which a rule can be followed or disobeyed). It is not clear how work on generative grammars could make sense of the idea of normative principles of grammar. But the subject matter of grammar is indeed best taken to be normative: a grammar expresses statements about what is correct or incorrect, not claims directly about phenomena in the empirical world. Grammatical rules with normative force can nonetheless be rendered mathematically precise through a type of formalization that does not involve generative grammars, and normativity can be understood in a way that does not imply anything about obligations or duties. Thus there is some hope of reconciling the normativity of grammar with the enterprise of formalizing grammars for human languages and the view that linguistics is an empirical science.