A Complete Hierarchy of Languages

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doi: 10.6084/m9.figshare.6126917


The thesis is that human language is best characterized as a Turing complete language. A hiearachy of languages is presented where languages are ordered by their expressiveness. That hierarchy of languages has also some value by itself, discriminating precisely several kinds of languages, and giving us a preliminary explanation for the evolution of language.

Hierarchy figure

This paper was written as a constructive critique to Watumull et al. (2014). I had already written a first critique in On "On Recursion", so this paper is a constructive continuation of that first one.

Four steps


A complete hierarchy of languages is introduced to defend the thesis that 'human language is a Turing complete language'. This complete hierarchy discriminates languages on computability, meaning mixability, generativity, decidability, and expressiveness. We show that our thesis is true and, using the complete hierarchy, that our thesis is more specific and then more significant than other truths about human language. The complete hierarchy explains the evolution of language on the assumption that it was driven by expressiveness, and consequently it explains that our language is complete because complete languages are the most expressive languages.

Four steps

Last paragraph

Nevertheless, the complete hierarchy can explain why our language is syntactic, generative, non-decidable, and complete, since it provides a framework to locate some phases of the evolution of human language that the classical hierarchy by Chomsky (1959) does not provide. Explaining language evolution using the complete hierarchy requires us to assume that evolutionary fitness has a direct relationship with expressiveness.


Link to the page of my paper on the complete hierarchy of languages in figshare, and direct link to the pdf file.

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Última actualización: 2019-09-11.

© Ramón Casares 2019