Synthese 196 (5):1671-1711 (2019)

Authors
Ryan Mark Nefdt
University of Cape Town
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.
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DOI 10.1007/s11229-017-1574-x
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References found in this work BETA

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Three Kinds of Idealization.Michael Weisberg - 2007 - Journal of Philosophy 104 (12):639-659.
The Strategy of Model-Based Science.Peter Godfrey-Smith - 2006 - Biology and Philosophy 21 (5):725-740.

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Citations of this work BETA

Formal Semantics and Applied Mathematics: An Inferential Account.Ryan M. Nefdt - 2020 - Journal of Logic, Language and Information 29 (2):221-253.
Chomsky in the Playground: Idealization in Generative Linguistics.Giulia Terzian - 2021 - Studies in History and Philosophy of Science Part A 87:1-12.

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