History and Grammar of Recursión: Clarifications from Wittgenstein's Work

Abstract

The main goal of this paper is to introduce the concept of recursion, its history, and its evolution within Computability Theory and Mathematical Logic. In this analysis I will stress the remarkable neglect of Wittgenstein's contribution to the development of this notion, and will argue that such neglect is totally unjustified. In fact, I will show that recursion is a central property in Wittgenstein's work, from the Tractatus to his emphasis on the notion of grammatical rule. Finally, I will focus on a number of applications stemming from Wittgenstein's thoughtful reflections on the concept of recursion. Such applications will be restricted to the domain of the Cognitive Science of Language.