Intrinsic functionality of mathematics, metafunctions in Systemic Functional Semiotics

Mathematics and language appear from one angle very alike. They seem to have similar structures and maintain similar grammars. However, they are regularly used in different situations to achieve different goals. This suggests that they have quite distinct functionalities. This paper explores this tension between the similarity and difference of language and mathematics by focusing on mathematics' intrinsic functionality as conceptualzsed through metafunction in Systemic Functional Semiotics and Social Semiotics. Unlike many studies in these traditions, however, it does not assume the metafunctions developed for language will unproblematically transfer over to mathematics. Rather, it derives the metafunctional organization of mathematics from its paradigmatic and syntagmatic organization. This method illustrates that although metafunction is a productive category for understanding mathematics, its metafunctional organization is not the same as that for language. In particular, mathematics displays an expanded logical component, while giving no evidence for an autonomous interpersonal component. In addition to allowing a principled comparison of mathematics and language in terms of their intrinsic functionality, this method suggests that if Systemic Functional and Social Semiotic studies wish to understand the functions of various semiotic resources, they cannot unquestioningly assume metafunctions will occur across all semiosis.