Compositionality from a “Use-Theoretic” Perspective

Abstract

What does it mean to say that language is a potential-infinite object, as opposed
to an actual-infinite one? I want to inquiry into the notion of the infinite
that could be attributed to language, in such a way that we move closer to an
inquiry into language-understanding. Philosophers have attributed to language
the property of actual-infinity. This has motivated the study of compositional
theories of meaning. Compositionality is also supposed to solve the problem of
productivity of language. I will argue that the assumption that languages are
actual-infinite objects leads to insurmountable obstacles to putting the notion
of understanding back into the picture –and therefore, that compositionality
doesn't do the job it was hired for. I will follow instead the idea that it is
fruitful to analyze the problem of productivity in a way parallel to
Wittgenstein’s discussion of the infinity of natural numbers.