Infinity and the foundations of linguistics

Abstract

The concept of linguistic infinity has had a central role to play in foundational debates within theoretical linguistics since its more formal inception in the mid-twentieth century. The Conceptualist tradition, marshalled in by Chomsky and others, holds that infinity is a core explanandum and a link to the formal sciences. Realism/Platonism takes this further to argue that linguistics is in fact a formal science with an abstract ontology. In this paper, I argue that a central misconstrual of formal apparatus of recursive operations such as the set-theoretic operation merge has led to a mathematisation of the object of inquiry, producing a strong analogy with discrete mathematics and especially arithmetic. The main product of this error has been the assumption that natural, like some formal, languages are discretely infinite. I will offer an alternative means of capturing the insights and observations related to this posit in terms of scientific modelling. My chief aim will be to draw from the larger philosophy of science literature in order to offer a position of grammars as models compatible with various foundational interpretations of linguistics while being informed by contemporary ideas on scientific modelling for the natural and social sciences.

Scientific Models and Political Theory: The Ideal Theory Debate Revisited

“…Unfortunately, like the other claims, this claim of 'precisely specifiable outcomes' ignores the literature on exploratory models such as cellular automata in biology (Weisberg, 2013) or formal models in linguistics (Nefdt, 2019) in which the modelling is more exploratory in nature. Thus, the present interpretation of ideal theory in political philosophy is indeed compatible with the role, nature, and structure of modelling in sciences considered under non-ideal circumstances themselves.…”

Why is Generative Grammar Recursive?

“…In large part as a result of the papers in van der(Hulst, 2010), particularly,Pullum and Scholz, 2010 andTiede andStout, 2010. A recent discussion can be found in(Nefdt, 2019) 5 This dual-status as both idealisation and desideratum can be found throughout generative writing. Cedric Boeckx in Language in Cognition, acknowledges that 'the property of infinity is a simplifying assumption.…”