A Turing Program for Linguistic Theory

ness it subsumes and thereby relates all computational primitives; in principle therefore it renders commensurable the computational ontologies of linguistics and neuroscience — or so I would endeavor to prove in the TPLT. A Turing machine is a mathematical abstraction, not a physical device, but my theory is that the information it specifies in the form of I-language must be encoded in the human genetic program — and/or derived from the mathematical laws of nature (‘third factors’ in the sense of Chomsky 2005) — and expressed in the brain. Central to the machine is a generative procedure for dinfinity; however, “[a]lthough the characterizations of what might be the most basic linguistic operations must be considered one of the deepest and most pressing in experimental language research, we know virtually nothing about the neuronal implementation of the putative primitives of linguistic computation” (Poeppel & Omaki 2008: 246). So is presented the great challenge for the TPLT: To precisify (formalize) the definitions of linguistic primitives in order that ‘linking hypotheses’ (not mere correlations) to as yet undiscovered neurobiological primitives can be formed. 4. Generative Systems It was in the theory of computability and its equivalent formalisms that the infinite generative capacity of a finite system was formalized and abstracted and thereby made available to theories of natural language (see Chomsky 1955 for a discussion of the intellectual zeitgeist and the influence of mathematical logic, computability theory, etc. at the time generative linguistics emerged in the 1950s). In particular, a generative grammar15 was defined as a set of rules that recursively generate (enumerate/specify) the sentences of a language in the form of a production system as defined by Post (1944) and exapted by Chomsky (1951): (1) φ1, ..., φn → φn+1 15 Linguists use the term with systematic ambiguity to refer to the explananda of linguistic theory (i.e. I-languages) and to the explanantia (i.e. theories of I-languages). Biolinguistics  Forum  228 “[E]ach of the φi is a structure of some sort and [...] the relation → is to be interpreted as expressing the fact that if our process of recursive specification generates the structures φ1, ..., φn then it also generates the structure φn+1” (Chomsky & Miller 1963: 284); the inductive (recursive) definition derives infinite sets of structures. The objective of this formalization was analogous to “[t]he objective of formalizing a mathematical theory a la Hilbert, [i.e.] to remove all uncertainty about what constitutes a proof in the theory, [...] to establish an algorithm for the notion of proof” (Kleene 1981: 47) (see Davis 2012 on Hilbert’s program). Chomsky (1956: 117) observed that a derivation as in (1) is analogous to a proof with φ1, ..., φn as the set of axioms, the rewrite rule (production) → as the rule of inference, and the derived structure φn+1 as the lemma/theorem. For a toy model, let (2) be a simplified phrase structure grammar with S = Start symbol Sentence, ⌒ = concatenation, # = boundary symbol, N[P] = Noun [Phrase], V[P] =