Abstract
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.
Similar content being viewed by others
References
Bever T. G., Fodor J. A., Garrett M. (1968) A formal limitation of associationism. In: Dixon T. R., Horton D. L. (eds) Verbal behavior and general behavior theory. Prentice-Hall, Englewood Cliffs, NJ, pp 582–585
Borsley R. D. (2003) Against ConjP. Lingua 115: 461–482
Brainerd W. S., Landweber L. H. (1974) Theory of computation. John Wiley, New York
Carnap, R. (1934). Logische Syntax der Sprache. Julius Springer, Vienna, translated as The Logical Syntax of Language, Kegan Paul, 1937.
Chomsky, N. (1956a). The logical structure of linguistic theory. MIT Library, Cambridge, MA, microfilmed; revised version of a 1955 unpublished manuscript.
Chomsky, N. (1956b). Three models for the description of language. IRE Transactions on Information Theory IT-2, 113–123, reprinted with substantive revisions in Luce, Bush & Galanter (1965), 105–124.
Chomsky N. (1957) Syntactic structures. Mouton, The Hague
Chomsky, N. (1959). On certain formal properties of grammars. Information and Control 2, 137–167, reprinted in Luce, Bush & Galanter (1965, 125–155; citation to original is incorrect).
Chomsky, N. (1961). On the notion ‘rule of grammar’. In: Proceedings of the Twelfth Symposium in Applied Mathematics (pp. 6–24). American Mathematical Society, Providence, RI, reprinted with slight revision in Jerry A. Fodor and Jerrold J. Katz (Eds.), The Structure of Language: Readings in the Philosophy of Language, 155–210 (Englewood Cliffs, NJ: Prentice-Hall).
Chomsky, N. (1962). Explanatory models in linguistics. In: E. Nagel, P. Suppes & A. Tarski (Eds.) Logic, Methodology and philosophy of science: Proceedings of the 1960 International Congress (pp. 528–550), Stanford University Press, Stanford, CA.
Chomsky N. (1965) Aspects of the theory of syntax. MIT Press, Cambridge
Chomsky, N. (1975). The logical structure of linguistic theory. Plenum, New York, published version of Chomsky (1956).
Chomsky N., Miller G.A. (1963) Introduction to the formal analysis of natural languages. In: Luce R.D., Bush R.R., Galanter E. (eds) Handbook of Mathematical Psychology (Vol. II). John Wiley and Sons, New York, pp 269–321
Daly R. T. (1974) Applications of the mathematical theory of linguistics. Mouton, The Hague
Davis, M. (1994a). Emil L. Post: His life and work. In Davis 1994b, xi–xxviii.
Davis, M. (Ed.) (1994b). Solvability, provability, definability: The collected works of Emil L. Post. Birkhäuser, Boston.
Firth J. R. (1957) Papers in linguistics 1934–1951. Oxford University Press, London
Fitch W. T., Hauser M. D. (2004) Computational constraints on syntactic processing in nonhuman primates. Science 303: 377–380
Gazdar G. (1981) Unbounded dependencies and coordinate structure. Linguistic Inquiry 12: 155–184
Gazdar G. (1982) Phrase structure grammar. In: Jacobson P., Pullum G.K. (eds) The nature of syntactic representation. D. Reidel, Dordrecht, Netherlands, pp 131–186
Gazdar G., Pullum G. K., Sag I. A. (1982) Auxiliaries and related phenomena in a restrictive theory of grammar. Language 58: 591–638
Harman G. (1963) Generative grammars without transformation rules. Language 39: 597–616
Harris Z. S. (1951) Methods in structural linguistics. Oxford University Press, New York
Harrison M. (1978) Introduction to formal language theory. Addison-Wesley, Reading, MA
Huddleston R., Pullum G. K. (2002) The Cambridge grammar of the English language. Cambridge University Press, Cambridge
Joos, M. (eds) (1957) Readings in linguistics I: The development of descriptive linguistics in America since 1925. (1st ed.). American Council of Learned Societies, Washington, DC
Lasnik H. (2000) Syntactic structures revisited: Contemporary lectures on classic transformational theory. MIT Press, Cambridge
Lees R. B. (1957) Review of Noam Chomsky, Syntactic Structures. Language 33: 375–408
Lightfoot, D. (2002). Introduction. In Noam Chomsky, syntactic structures, 2nd edn., v–xviii. Mouton de Gruyter, Berlin.
Luce R.D., Bush R.R., Galanter E. (1965) Readings in mathematical psychology, Vol. II. Wiley, New York
Lyons J. (1970) Chomsky. Fontana, London
Newmeyer F. J. (1986) Has there been a ‘Chomskyan revolution’ in linguistics?. Language 62(1): 1–18
Partee, B. H., ter Meulen, A., Wall, R. E. (1993). Mathematical methods in linguistics, corrected first edn. Kluwer Academic, Dordrecht.
Pelletier F. J. (1980) The generative power of rule orderings in formal grammars. Linguistics 18(1/2 (227/228)): 17–72
Pereira F. (2000) Formal grammar and information theory: Together again?. Philosophical Transactions of the Royal Society 358(1769): 1239–1253
Peters P. S., Ritchie R. W. (1971) On restricting the base component of transformational grammars. Information and Control 18: 483–501
Peters P. S., Ritchie R. W. (1973) On the generative power of transformational grammars. Information Sciences 6: 49–83
Philological Society (1957). Studies in linguistic analysis. Philological Society, Oxford.
Post, E. (1921). Introduction to a general theory of elementary propositions. American Journal of Mathematics 43, 163–185, reprinted in Jan van Heijenoort, Ed., From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, Harvard University Press, Cambridge MA, 1967, 264–283.
Post, E., (1943). Formal reductions of the general combinatory decision problem. American Journal of Mathematics 65, 197–215, reprinted in Davis 1994b, 442–460.
Post, E., (1944). Recursively enumerable sets of positive integers and their decision problems. Bulletin of the American Mathematical Society 50, 284–316, reprinted in Davis 1994b, 461–494.
Post, E., (1947). Recursive unsolvability of a problem of Thue. Journal of Symbolic Logic 12, 1–11, reprinted in Davis 1994b, 503–513.
Postal P. M. (1971) Crossover phenomena. Holt Rinehart and Winston, New York
Pullum G. K., Scholz B. C. (2007) Systematicity and natural language syntax. Croatian Journal of Philosophy 7: 375–402
Pullum G. K., Scholz B. C. (2009) For universals (but not finite-state learning), visit the zoo. Behavioral and Brain Sciences 32(5): 466–467
Putnam, H. (1961). Some issues in the theory of grammar. In: R. Jakobson (Ed.) Structure of language and its mathematical aspects, no. 12 in Proceedings of symposia in applied mathematics (pp. 25–42). American Mathematical Society, Providence, RI.
Rogers, J. (1999). The descriptive complexity of generalized local sets. In: H. P. Kolb, U. Mönnich (Eds.) The mathematics of syntactic structure: Trees and their logics, no. 44 in studies in generative grammar (pp. 21–40). Mouton de Gruyter, Berlin.
Rogers, J., Pullum, G. K. (2010). Aural pattern recognition experiments and the subregular hierarchy. In this issue.
Rogers, Jr. H. (1967) The theory of recursive functions and effective computability. McGraw-Hill, New York
Rosenbloom P. (1950) The Elements of Mathematical Logic. Dover, New York
Ross, J. R. (1967). Constraints on variables in syntax. PhD thesis, MIT, Cambridge, MA, duplicated version published in 1968 by Indiana University Linguistics Club, Bloomington, IN. Later published in book form as Infinite Syntax! (Norwood, NJ: Ablex, 1986).
Sampson, G. (1979). What was transformational grammar? Lingua 48, 355–378, reprinted in Empirical linguistics, Continuum, 2001.
Scholz B. C., Pullum G. K. (2007) Tracking the origins of transformational generative grammar. Journal of Linguistics 43: 701–723
Seuren P. (2009) Concerning the roots of transformational generative grammar. Historiographia Linguistica 36(1): 97–115
Skinner B. F. (1957) Verbal behavior. Appleton-Century-Crofts, New York
Svenonius L. (1957) Review of ‘Three models for the description of language’ by Noam Chomsky. Journal of Symbolic Logic 23: 71–72
Thue, A. (1914). Probleme über Veränderungen von Zeichenreihen nach gegebenen Regeln. In: Skrifter utgit av Videnskapsselskapet i Kristiana, I, no. 10 in Matematisk-naturvidenskabelig klasse, Norske Videnskaps-Akademi, Oslo.
Tomalin M. (2006) Linguistics and the formal sciences. Cambridge University Press, Cambridge
Urquhart A. (2009) Emil Post. In: Gabbay D.M., Woods J. (eds) Handbook of the history of logic, Volume 5: Logic from Russell to Church. North-Holland, Amsterdam, pp 617–666
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pullum, G.K. On the Mathematical Foundations of Syntactic Structures . J of Log Lang and Inf 20, 277–296 (2011). https://doi.org/10.1007/s10849-011-9139-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10849-011-9139-8