creators_name: Casares, Ramón
creators_id: papa@ramoncasares.com
type: preprint
datestamp: 2014-05-10 00:08:42
lastmod: 2014-05-10 00:08:42
metadata_visibility: show
title: Universal Grammar Is a Universal Grammar
subjects: bio-evo
subjects: comp-sci-lang
subjects: ling-syntax
full_text_status: public
keywords: Universal Grammar, Turing completeness, language evolution
abstract: Is Universal Grammar a universal grammar? From Chomsky's hierarchy we deduce that for each grammar there is a Turing machine, and conversely. Following this equivalence, it is immediate to conclude that a universal Turing machine is equivalent to a universal grammar. Meanwhile, in linguistics, Universal Grammar is the human brain circuitry that implements the faculty of language. So the definitive answer is achieved only when we show that the human brain is Turing complete, and that language uses this capability. So yes: Universal Grammar is a universal grammar, because the human brain circuitry that implements the faculty of language is Turing complete.
date: 2014-04-11
date_type: completed
refereed: FALSE
referencetext: [Arbib 1987] Michael Arbib, "Brains, Machines, and Mathematics", Second Edition; Springer-Verlag, New York, 1987, ISBN 978-0-387-96539-0.

[Casares 2014] Ramón Casares, "Resolution Machinery"; http://cogprints.org/9209/.

[Chomsky 1959] Noam Chomsky, "On Certain Formal Properties of Grammars"; in Information and Control, Volume 2, Issue 2, pp. 137-167, June 1959.

[Chomsky 2005] Noam Chomsky, "Three Factors in Language Design"; in Linguistic Inquiry, Volume 36, Number 1, pp. 1-22, Winter 2005.

[Turing 1936] Alan Turing, "On Computable Numbers, with an Application to the Entscheidungsproblem"; in Proceedings of the London Mathematical Society, Volume s2-42, Issue 1, pp. 230-265, 1937. Received 28 May, 1936. Read 12 November, 1936.

citation:   Casares, Ramón  (2014) Universal Grammar Is a Universal Grammar.  [Preprint]     
document_url: http://cogprints.org/9229/1/UGisug-20140411.pdf