Mathematical logic and biological foundations

Last week, we considered generative linguistics as a theory of the faculty of language, and identified four distinct scopes that can be encompassed by the term faculty of language. In order to be clear about these different meanings, I adopted the notations FLB and FLN which were proposed by Chomsky, Fitch, and Hauser in a pair of articles, and I introduced FLC and FLG to represent a similar division independently of the evolutionary history of the faculty of language. All of this presupposes a biolinguistic perspective, in which language is treated as a biologically-founded cognitive phenomenon rather than as a collection of observable sentences. This view is essentially synchronic, considering only the current state of generative theory. It is also instructive to look at the historical development of the theoretical framework in order to understand why there is a distinction between FLC and FLG within the theory.

The origins of generative linguistics are often traced to Chomsky’s Syntactic Structures (1957/2002) and The Logical Structure of Linguistic Theory (1975, written ca. 1956). The fundamental idea of generation, however, has a longer history in algebra and in symbolic logic, dating as far back as the end of the 19th century; Moore (1894), for example, defines a particular abstract group in terms of generators and generating relations; these relations generate all of the elements of the group from the generators . A more direct antecedent to Chomsky’s initial work on generative grammar was Emil Post’s work from ca. 1921, by way of Rosenbloom’s The Elements of Mathematical Logic (Chomsky 1975 p. 105 fn 1; Post 1943, p. 215 fn 18; Rosenbloom 1950, p. 206). Rosenbloom even proposed that “one might also expect that many concepts in linguistics which have resisted all attempts up to now at clear and general formulation may now be treated with the same lucidity and rigor which has made mathematics a model for other sciences. The wealth of detail and the manifold irregularities of natural languages have often obfuscated the simple general principles underlying linguistic phenomena” (1950, p. 163). Chomsky’s early works pursued precisely this direction.

Some recent claims notwithstanding, the original literature suggests that generative linguistics was not originally conceived as a theory of the faculty of language, but rather just as a theory of language as an abstract corpus of sentences. (I’ll have more to say on this point in a later post.) The initial steps towards a treatment of generative theory as a theory of the faculty of language were evidently taken within a decade of the publication of Syntactic Structures. By the mid-1960s, Chomsky was writing an appendix to Lenneberg’s The Biological Foundations of Language (1967), and had already formulated the separation between competence and performance. A clearer distinction was drawn between the notions of I-language and E-language by the mid-1980s, where E-language treats language “independently of the mind/brain” (Chomsky 1986, p. 20), and I-language “is some element of the mind of the person who knows the language, acquired by the learner, and used by the speaker-hearer” (Chomsky 1986, p. 22). Taking generative grammar then to be the study of this I-language, we have a clear claim that it is a theory of the faculty of language.

Copyright © 2008 Michael L. McCliment.


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