Universal Grammar Is a universal grammar

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DOI: 10.6084/m9.figshare.4956764

Opening question

The word ‘universal’ is used differently in computing, as in ‘universal Turing machine’, and in linguistics, as in ‘Universal Grammar’. But: Could it be that both ‘universals’ are nevertheless the same?

Comment

This paper is a continuation of Sintax Evolution, and it is founded on the same two bases:

• from Chomsky (1959), that the best point of view to explain syntax and language is computing, and
• from Turing (1936), that from the point of view of computing, we humans are Turing complete.

Computing is a point of view that defines decidability and Turing completeness, and that distinguishes program from data and hardware from software. These concepts are needed to explain the cognitive gap between our species, Homo sapiens, and all others: we are the first and only species that achieved Turing completeness. Being Turing complete means that we can do by software whatever hardware does, so we can imagine anything that evolution could build, thus speeding up problem solving enormously. Turing completeness needs a complete language in which programs are treated as data, and any complete language has to fulfill two requirements:

• its syntax has to be an infinite set, which can be decidable, and
• it has to implement a functional semantics, where functional semantics is the semantics of syntax, and then its place is the core syntax.

This way we reach our thesis: Universal Grammar is Turing complete. Or, in other words, the human brain circuitry that implements language is Turing complete.

Our thesis that Universal Grammar is Turing complete implies that there are not unlearnable languages. This, together with the fact that natural languages are neither one nor any, demands a distinction between

• native language, which is developed,
• first language, which is acquired, and
• later languages, which are learned,

where all natural languages are first languages, and our native language is not accessible. Two consequences follow:

• Not every language can be acquired, but we can learn any language.
• Instruction is a way of learning, once we have acquired a first complete language.

Computing is a problem solving point of view from which language is a tool to translate problems to the hardware that resolves them. Two consequences follow:

• Language influences thinking, but a complete language does not limit thinking.
• Turing completeness is a fixed point in the evolution of Universal Grammar.

Universal Grammar evolved as a compromise that took into account its various functions and its implementation. Universal Grammar functions include, at least, language, mathematics, and problem solving, and its implementation had to resolve its interaction with other brain modules while still satisfying other engineering conditions.

Last paragraph

This is the theory I am proposing here for your consideration. The theory is firmly founded on two bases: firstly, that the best point of view to explain syntax and language is computing, which is the essence of Chomsky (1959), and secondly, that from the point of view of computing, we humans are Turing complete, which is the essence of Turing (1936). Then there are some assumptions that you will have to assess, but they are very few, and the only important thesis is that Universal Grammar is Turing complete.

References

Link to my paper on the thesis that "the human brain circuitry that implements language is Turing complete", in figshare, with its pdf file.

The papers cited in this web page are:

• Chomsky (1959): On Certain Formal Properties of Grammars
• Turing (1936): On Computable Numbers, with an Application to the Entscheidungsproblem

Versions:

• c1 20140411
• t1 20170406
• f1 20170501: also in SSRN.
• f2 20220831