Journal of Logic, Language and Information

, Volume 20, Issue 3, pp 277–296 | Cite as

On the Mathematical Foundations of Syntactic Structures

  • Geoffrey K. PullumEmail author


Chomsky’s highly influential Syntactic Structures (SS) has been much praised its originality, explicitness, and relevance for subsequent cognitive science. Such claims are greatly overstated. SS contains no proof that English is beyond the power of finite state description (it is not clear that Chomsky ever gave a sound mathematical argument for that claim). The approach advocated by SS springs directly out of the work of the mathematical logician Emil Post on formalizing proof, but few linguists are aware of this, because Post’s papers are not cited. Chomsky’s extensions to Post’s systems are not clearly defined, and the arguments for their necessity are weak. Linguists have also overlooked Post’s proofs of the first two theorems about effects of rule format restrictions on generative capacity, published more than ten years before SS was published.


Generative grammar Transformations Emil Post Formalization Proof theory Mathematical logic 


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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.School of Philosophy, Psychology and Language SciencesUniversity of EdinburghEdinburghUK

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