1887
image of The prehistory of generative grammar and Chomsky’s debt to Emil
Post

Abstract

Summary

Generative linguistics has a longer prehistory than most linguists realize. The rewriting systems that Chomsky brought into linguistics as generative grammars were explicitly defined more than a century ago, as part of a project to formalize inference rules in logic, and were later applied to studying mathematical properties of certain kinds of infinite sets. Their developer was the mathematician and logician Emil Leon Post, whose work was inspired by Clarence Irving Lewis and Cassius Jackson Keyser. Post also proved the first two theorems about what linguists now call generative capacity. The idea of deploying Post’s systems within linguistics was first suggested in 1950 by the logician Paul Rosenbloom. I review the relevant pre-1950 work, and explore the reasons for its having remained so little known among linguists.

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2025-10-23
2025-11-14
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References

  1. Anellis, Irving H.
    2012 “Peirce’s Truth-functional Analysis and the Origin of the Truth Table”. History and Philosophy of Logic:.–. 10.1080/01445340.2011.621702
    https://doi.org/10.1080/01445340.2011.621702 [Google Scholar]
  2. Bar-Hillel, Yehoshua
    1953 “A Quasi-arithmetical Notation for Syntactic Description”. Language:.–. Reprinted with revisions inBar-Hillel (1964), –. 10.2307/410452
    https://doi.org/10.2307/410452 [Google Scholar]
  3. 1964Language and Information: Selected essays on their theory and application. Reading, MA: Addison-Wesley.
    [Google Scholar]
  4. Bar-Hillel, Yehoshua, Micha Perles & Eliyahu Shamir
    1961 “On Formal Properties of Simple Phrase Structure Grammars”. Zeitschrift für Phonetik, Sprachwissenschaft, und Kommunikationsforschung.–. Reprinted with revisions inBar-Hillel (1964), –.
    [Google Scholar]
  5. Berwick, Robert & Noam Chomsky
    2016Why Only Us? Language and evolution. Cambridge, MA: MIT Press. 10.7551/mitpress/9780262034241.001.0001
    https://doi.org/10.7551/mitpress/9780262034241.001.0001 [Google Scholar]
  6. Beth, Evert W.
    1963 “Konstanten van het wiskundige denken [constants in mathematical thinking]”. Mededelingen der Koninklijke Nederlandse Akademie van Wetenschappen: Afdeling Letterkunde, Nieuwe Reeks:.–.
    [Google Scholar]
  7. Brainerd, Walter S. & Lawrence H. Landweber
    1974Theory of Computation. New York: John Wiley.
    [Google Scholar]
  8. Brodda, Benny
    1992 “Comments [on Geoffrey Sampson’s paper ‘Probabilistic parsing’]”. Directions in Corpus Linguistics: Proceedings of Nobel Symposium 82, Stockholm, 4–8 August 1991ed. byJan Svartvik, number 65 in Trends in Linguistics Studies and Monographs, –. Berlin: Mouton de Gruyter.
    [Google Scholar]
  9. Chomsky, Noam
    1951a Morphophonemics of Modern Hebrew. Master’s thesis, University of Pennsylvania, Philadelphia, PA.
    [Google Scholar]
  10. 1951b Morphophonemics of Modern Hebrew. Typescript of a radical revision of Chomsky’s MA thesis, datedDecember 1951; retyped and published byGarland, New York 1979.
    [Google Scholar]
  11. 1955 Transformational Analysis. Ph.D. thesis, University of Pennsylvania, Philadelphia, PA. URL: https://search.proquest.com/docview/89172813
    [Google Scholar]
  12. 1955–1956Manuscript, mimeographed 1955; revised 1956 and distributed on microfilm by MIT Library, Cambridge, MA; ultimately published (with some omissions and a new introduction) as Chomsky 1975.
    [Google Scholar]
  13. 1956 “Three Models for the Description of Language”. I.R.E. Transactions on Information Theory.–. Substantially revised version published inReadings in Mathematical Psychology, Volume IIed. byR. Duncan Luce, Robert R. Bush & Eugene Galanter, –. New York: John Wiley & Sons 1965 10.1109/TIT.1956.1056813
    https://doi.org/10.1109/TIT.1956.1056813 [Google Scholar]
  14. 1957Syntactic Structures. The Hague: Mouton. 10.1515/9783112316009
    https://doi.org/10.1515/9783112316009 [Google Scholar]
  15. 1959 “On Certain Formal Properties of Grammars”. Information and Control():–. Reprinted inReadings in Mathematical Psychology, Volume, ed. byR. Duncan Luce, Robert R. Bush & Eugene Galanter, –. New York: John Wiley & Sons 1965 (citation to the original on p. 125 of this reprinting is incorrect). 10.1016/S0019‑9958(59)90362‑6
    https://doi.org/10.1016/S0019-9958(59)90362-6 [Google Scholar]
  16. 1961 “On the notion ‘rule of grammar’.” Proceedings of the Twelfth Symposium in Applied Mathematics, –. Providence, RI: American Mathematical Society. Reprinted inThe Structure of Language: Readings in the philosophy of languageed. byJerry A. Fodor & Jerrold J. Katz, –. Englewood Cliffs, NJ: Prentice-Hall. 10.1090/psapm/012/9985
    https://doi.org/10.1090/psapm/012/9985 [Google Scholar]
  17. 1962 “Explanatory Models in Linguistics”. Logic, Methodology and Philosophy of Science: Proceedings of the 1960 International Congressed. byErnest Nagel, Patrick Suppes & Alfred Tarski, –. Stanford, CA: Stanford University Press.
    [Google Scholar]
  18. 1963 “Formal Properties of Grammars”. Handbook of Mathematical Psychology, Volume, ed. byR. Duncan Luce, Robert R. Bush & Eugene Galanter–. New York: Wiley.
    [Google Scholar]
  19. 1965Aspects of the Theory of Syntax. Cambridge, MA: MIT Press.
    [Google Scholar]
  20. 1966Topics in the Theory of Generative Grammar. The Hague: Mouton.
    [Google Scholar]
  21. 1975The Logical Structure of Linguistic Theory. New York: Plenum. Revision ofChomsky (1955–1956).
    [Google Scholar]
  22. 1986Knowledge of Language. Its origins, nature, and use. New York: Praeger.
    [Google Scholar]
  23. 1991 “Linguistics and Adjacent Fields: A personal view”. The Chomskyan Turned. byAsa Kasher, –. Oxford: Blackwell.
    [Google Scholar]
  24. Chomsky, Noam & George A. Miller
    1963 “Introduction to the Formal Analysis of Natural Languages”. eds., Handbook of Mathematical Psychology, Volume, ed. byR. Duncan Luce, Robert R. Bush & Eugene Galanter, –. New York: Wiley.
    [Google Scholar]
  25. Church, Alonzo
    1936 “An Unsolvable Problem of Elementary Number Theory”. American Journal of Mathematics:.–. 10.2307/2371045
    https://doi.org/10.2307/2371045 [Google Scholar]
  26. Cormen, Thomas H., Charles E. Leiserson & Ronald L. Rivest
    2000Introduction to Algorithms. Cambridge MA / New York: MIT Press / McGraw Hill.
    [Google Scholar]
  27. Davis, Martin
    ed. 1958Computability and Unsolvability. New York: McGraw-Hill.
    [Google Scholar]
  28. ed. 1965The Undecidable: Basic papers on undecidable propositions, unsolvable problems and computable functions. New York: Raven Press. Reissued 2004 by Dover Publications with a different version of the final paper by Post.
    [Google Scholar]
  29. 1982 “Why Gödel didn’t Have Church’s Thesis”. Information and Control:.–. 10.1016/S0019‑9958(82)91226‑8
    https://doi.org/10.1016/S0019-9958(82)91226-8 [Google Scholar]
  30. 1994a “Emil L. Post: His life and work”. InDavis 1994b, –.
    [Google Scholar]
  31. ed. 1994bSolvability, Provability, Definability: The collected works of Emil L. Post. Boston, MA: Birkhäuser.
    [Google Scholar]
  32. De Mol, Liesbeth
    2006 “Closing the Circle: An analysis of Emil Post’s early work”. Bulletin of Symbolic Logic:.–. 10.2178/bsl/1146620062
    https://doi.org/10.2178/bsl/1146620062 [Google Scholar]
  33. 2009 “On the Boundaries of Solvability and Unsolvability in Tag Systems: Theoretical and experimental results. The Complexity of Simple Programs 2008, number 1 in Electronic Proceedings in Theoretical Computer Science, ed. byT. Neary, D. Woods, A. K. Seda & N. Murphy, –. Waterloo, NSW, Australia: Open Publishing Association. Https://arxiv.org/abs/0906.3329. 10.4204/EPTCS.1.5
    https://doi.org/10.4204/EPTCS.1.5 [Google Scholar]
  34. Epstein, Richard L. & Walter A. Carnielli
    2000Computability: Computable functions, logic, and the foundations of mathematics. Belmont, CA: Wadsworth, 2nd ed.
    [Google Scholar]
  35. George, Alexander
    1989 “How not to Become Confused about Linguistics”. Reflections on Chomskyed. byAlexander George, –. Oxford: Basil Blackwell.
    [Google Scholar]
  36. Ginsburg, Seymour & Barbara Hall-Partee
    1969 “A Mathematical Model of Transformational Grammar”. Information and Control:.–. 10.1016/S0019‑9958(69)90464‑1
    https://doi.org/10.1016/S0019-9958(69)90464-1 [Google Scholar]
  37. Gödel, Kurt
    1931 “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I”. Monatshefte für Mathematik und Physik:.–. Translated as “On Formally Undecidable Propositions of Principia Mathematica and Related Systems, I”. Invan Heijenoort, –.
    [Google Scholar]
  38. Gross, Maurice & André Lentin
    1970Introduction to Formal Grammars. London: George Allen & Unwin. Translated byMorris Salkoff. 10.1007/978‑3‑642‑87129‑0
    https://doi.org/10.1007/978-3-642-87129-0 [Google Scholar]
  39. Harris, Randy Allen
    2021The Linguistics Wars: Chomsky, Lakoff, and the battle over deep structure. New York: Oxford University Press, second ed.. 10.1093/oso/9780199740338.001.0001
    https://doi.org/10.1093/oso/9780199740338.001.0001 [Google Scholar]
  40. Harris, Zellig S.
    1951Methods in Structural Linguistics. Chicago, IL: University of Chicago Press. Republished asStructural Linguistics 1960 Preface datedJanuary 1947.
    [Google Scholar]
  41. 1954 “Transfer Grammar”. International Journal of American Linguistics:.–. 10.1086/464289
    https://doi.org/10.1086/464289 [Google Scholar]
  42. 1991A Theory of Language and Information: A mathematical approach. Oxford: Clarendon Press. 10.1093/oso/9780198242246.001.0001
    https://doi.org/10.1093/oso/9780198242246.001.0001 [Google Scholar]
  43. Hockett, Charles F.
    1954 “Two Models of Grammatical Description”. Word:.–. Page references are to the reprinting inJoos (ed.) , –. 10.1080/00437956.1954.11659524
    https://doi.org/10.1080/00437956.1954.11659524 [Google Scholar]
  44. 1966 “Language, Mathematics and Linguistics. Current Trends in Linguistics: Volume 3, theoretical foundations, –. The Hague: Mouton. Republished as a monograph byMouton, The Hague 1967.
    [Google Scholar]
  45. Humberstone, Lloyd
    2008 “Replacing Modus Ponens with One-premiss Rules”. Logic Journal of the IGPL:.–. 10.1093/jigpal/jzn017
    https://doi.org/10.1093/jigpal/jzn017 [Google Scholar]
  46. Jackson, Allyn
    2018 “Emil Post: Psychological fidelity”. Inference: International Review of Science:. Online athttps://inference-review.com/article/psychological-fidelity
    [Google Scholar]
  47. Jakobson, Roman
    1969 “Linguistics in its Relation to Other Sciences. Proceedings of the 10th International Congress of Linguists, –. Bucharest: Éditions de l’Académie de la République Socialiste de Roumanie. Page reference is to the reprinting in Jakobson’s, Selected Writings, II: Word and Language (The Hague: Mouton 1971), –.
    [Google Scholar]
  48. Joseph, John E.
    1990 “Ideologizing Saussure: Bloomfield’s and Chomsky’s readings of the Cours de linquistique générale”. Ideologies of Languageed. byJohn E. Joseph & Talbot J. Taylor, –. London: Routledge.
    [Google Scholar]
  49. 2002From Whitney to Chomsky. Amsterdam: John Benjamins. 10.1075/sihols.103
    https://doi.org/10.1075/sihols.103 [Google Scholar]
  50. Joshi, Aravind K.
    1985 “Tree Adjoining Grammars: How much context-sensitivity is required to provide reasonable structural descriptions?” Natural Language Parsing: Psychological, Computational and Theoretical Perspectivesed. byDavid Dowty, Lauri Karttunen & Arnold Zwicky, –. Cambridge: Cambridge University Press. 10.1017/CBO9780511597855.007
    https://doi.org/10.1017/CBO9780511597855.007 [Google Scholar]
  51. Katz, Jerrold J. & Paul M. Postal
    1964An Integrated Theory of Linguistic Descriptions. Cambridge, MA: MIT Press.
    [Google Scholar]
  52. Kimball, John
    1967 “Predicates Definable over Transformational Derivations by Intersection with Regular Languages”. Information and Control:.–. 10.1016/S0019‑9958(67)90497‑4
    https://doi.org/10.1016/S0019-9958(67)90497-4 [Google Scholar]
  53. 1973The Formal Theory of Grammar. Englewood Cliffs, NJ: Prentice-Hall.
    [Google Scholar]
  54. Kracht, Marcus
    2003The Mathematics of Language. NumberinStudies in Generative Grammar. Berlin: Mouton de Gruyter. 10.1515/9783110895667
    https://doi.org/10.1515/9783110895667 [Google Scholar]
  55. Levelt, W. J. M.
    1974Formal Grammars in Linguistics and Psycholinguistics. The Hague: Mouton. volumes; republished in one volume asLevelt (2008).
    [Google Scholar]
  56. 2008Formal Grammars in Linguistics and Psycholinguistics. Amsterdam: John Benjamins. 10.1075/z.144
    https://doi.org/10.1075/z.144 [Google Scholar]
  57. Lewis, C. I.
    1918A Survey of Symbolic Logic. Berkeley, CA: University of California Press, first ed.. 10.1525/9780520398252
    https://doi.org/10.1525/9780520398252 [Google Scholar]
  58. Markov, Andrey A.
    1947 “Névozmožnost’ nékotoryh algorifmov v téorii associativnyh sistém” (‘Impossibility of certain algorithms in the theory of associative systems’). Doklady Akadémii Nauk SSSR:–. Abstracted byAndrzej MostowskiinJournal of Symbolic Logic:.– 1948.
    [Google Scholar]
  59. Minsky, Marvin L.
    1967Computation: Finite and infinite machines. Englwood Cliffs, NJ: Prentice-Hall.
    [Google Scholar]
  60. Nevin, Bruce E.
    2009 “More concerning the Roots of Transformational Generative Grammar”. Historiographia Linguistica:.–. 10.1075/hl.36.2.21nev
    https://doi.org/10.1075/hl.36.2.21nev [Google Scholar]
  61. 2010 “Noam and Zellig”. Chomskyan (R)evolutionsed. byDouglas A. Kibbee, –. Amsterdam: John Benjamins. 10.1075/z.154.05nev
    https://doi.org/10.1075/z.154.05nev [Google Scholar]
  62. Newmeyer, Frederick J.
    1980Linguistic Theory in America. New York, NY: Academic Press. First edition 1980; second edition 1986.
    [Google Scholar]
  63. Ney, James
    1993 “On Generativity: The history of a notion that never was”. Historiographia Linguistica:.–. 10.1075/hl.20.2‑3.08ney
    https://doi.org/10.1075/hl.20.2-3.08ney [Google Scholar]
  64. Partee, Barbara Hall
    1978Fundamentals of Mathematics for Linguistics. Dordrecht: D. Reidel.
    [Google Scholar]
  65. Partee, Barbara Hall, Alice ter Meulen & Robert E. Wall
    1993Mathematical Methods in Linguistics. Dordrecht: Kluwer. 10.1007/978‑94‑009‑2213‑6
    https://doi.org/10.1007/978-94-009-2213-6 [Google Scholar]
  66. Peters, P. Stanley & Robert W. Ritchie
    1971 “On Restricting the Base Component of Transformational Grammars”. Information and Control:.–. Republished inMathematical Systems Theory, – 1973 10.1016/S0019‑9958(71)90510‑9
    https://doi.org/10.1016/S0019-9958(71)90510-9 [Google Scholar]
  67. 1973 “On the Generative Power of Transformational Grammars”. Information Sciences.–. 10.1016/0020‑0255(73)90027‑3
    https://doi.org/10.1016/0020-0255(73)90027-3 [Google Scholar]
  68. Piattelli-Palmarini, Massimo, Juan Uriagereka & Pello Salaburu
    eds. 2009Of Minds and Language: A dialogue with Noam Chomsky in the Basque country. Oxford: Oxford University Press. 10.1093/oso/9780199544660.001.0001
    https://doi.org/10.1093/oso/9780199544660.001.0001 [Google Scholar]
  69. Post, Emil L.
    1921 “Introduction to a General Theory of Elementary Propositions”. American Journal of Mathematics:.–. Reprinted invan Heijenoort (: –) and reproduced inDavis (1994b: –). 10.2307/2370324
    https://doi.org/10.2307/2370324 [Google Scholar]
  70. 1936 “Finite Combinatory Processes — Formulation 1”. Journal of Symbolic Logic:.–. Reproduced inDavis (1965: –) and inDavis (1994b: –). 10.2307/2269031
    https://doi.org/10.2307/2269031 [Google Scholar]
  71. 1941The Two-Valued Iterative Systems of Mathematical Logic. Princeton NJ: Princeton University Press.
    [Google Scholar]
  72. 1941[1965] “Absolutely Undecidable Problems and Relatively Undecidable Propositions — Account of an Anticipation”. Rejected byAmerican Journal of Mathematicsin 1941; posthumously published inDavis (1965: –); reprinted inDavis (1994: –).
    [Google Scholar]
  73. 1943 “Formal Reductions of the General Combinatory Decision Problem”. American Journal of Mathematics:.–. Reproduced inDavis (1994b: –). 10.2307/2371809
    https://doi.org/10.2307/2371809 [Google Scholar]
  74. 1944 “Recursively Enumerable Sets of Positive Integers and their Decision Problems”. Bulletin of the American Mathematical Society:.–. Reproduced inDavis (1965: –) and inDavis (1994b: –). 10.1090/S0002‑9904‑1944‑08111‑1
    https://doi.org/10.1090/S0002-9904-1944-08111-1 [Google Scholar]
  75. 1946 “A Variant of a Recursively Unsolvable Problem”. Bulletin of the American Mathematical Society.–. Reproduced inDavis (1994b: –). 10.1090/S0002‑9904‑1946‑08555‑9
    https://doi.org/10.1090/S0002-9904-1946-08555-9 [Google Scholar]
  76. 1947 “Recursive Unsolvability of a Problem of Thue”. Journal of Symbolic Logic:.–. Reproduced inDavis (1965: –) and inDavis (1994b: –). 10.2307/2267170
    https://doi.org/10.2307/2267170 [Google Scholar]
  77. Postal, Paul M.
    1971Crossover Phenomena. New York: Holt, Rinehart and Winston.
    [Google Scholar]
  78. Pullum, Geoffrey K.
    1989 “Prospects for Generative Grammar in the 1990s”. Proceedings of the Western Conference on Linguistics [WECOL 89], Volume 2, ed.byFrederick H. Brengelman, Vida Samiian & Wendy Wilkins, –. California State University, Fresno: Department of Linguistics.
    [Google Scholar]
  79. 2011 “On the Mathematics of Syntactic Structures”. Journal of Logic, Language and Information:.–. 10.1007/s10849‑011‑9139‑8
    https://doi.org/10.1007/s10849-011-9139-8 [Google Scholar]
  80. Pullum, Geoffrey K. & Barbara C. Scholz
    2001 “On the Distinction between Model-Theoretic and Generative-Enumerative Syntactic Frameworks”. Logical Aspects of Computational Linguistics: 4th International Conference, number 2099 in Lecture Notes in Artificial Intelligence, ed. byPhilippe de Groote, Glyn Morrill & Christian Retoré, –. Berlin / New York: Springer. 10.1007/3‑540‑48199‑0_2
    https://doi.org/10.1007/3-540-48199-0_2 [Google Scholar]
  81. 2005 “Contrasting Applications of Logic in Natural Language Syntactic Description”. Proceedings of the 13th International Congress of Logic, Methodology and Philosophy of Scienceed. byPetr Hájek, Luis Valdés-Villanueva & Dag Westerståhl, –. London: KCL Publications.
    [Google Scholar]
  82. Putnam, Hilary
    1961 “Some Issues in the Theory of Grammar”. Structure of Language and Its Mathematical Aspects, number XII inProceedings of Symposia in Applied Mathematicsed. byRoman Jakobson, –. Providence, RI: American Mathematical Society. 10.1090/psapm/012/9984
    https://doi.org/10.1090/psapm/012/9984 [Google Scholar]
  83. Quine, Willard Van Orman
    1940Mathematical Logic. New York, NY: W. W. Norton.
    [Google Scholar]
  84. Rogers, Hartley
    1967Theory of Recursive Functions and Effective Computability. Cambridge, MA: MIT Press.
    [Google Scholar]
  85. Rosenbloom, Paul
    1950The Elements of Mathematical Logic. New York: Dover.
    [Google Scholar]
  86. Rosner, Michael
    1983 “Production Systems”. Parsing Natural Languageed. byMargaret King, –. London: Academic Press.
    [Google Scholar]
  87. Salomaa, Arto
    1971 “The Generative Capacity of Transformational Grammars of Ginsburg and Partee”. Information and Control:.–. 10.1016/S0019‑9958(71)90364‑0
    https://doi.org/10.1016/S0019-9958(71)90364-0 [Google Scholar]
  88. Scholz, Barbara C. & Geoffrey K. Pullum
    2007 “Tracking the Origins of Generative Grammar”. Journal of Linguistics.–. 10.1017/S0022226707004823
    https://doi.org/10.1017/S0022226707004823 [Google Scholar]
  89. Seuren, Pieter A. M.
    1969Operators and Nucleus: A contribution to the theory of grammar. Cambridge: Cambridge University Press.
    [Google Scholar]
  90. 1998Western Linguistics: An historical introduction. Oxford: Basil Blackwell. 10.1002/9781444307467
    https://doi.org/10.1002/9781444307467 [Google Scholar]
  91. 2009 “Concerning the Roots of Transformational Generative Grammar”. Historiographia Linguistica:.–. 10.1075/hl.36.1.05seu
    https://doi.org/10.1075/hl.36.1.05seu [Google Scholar]
  92. Soare, Scott
    1996 “Computability and Recursion”. Bulletin of Symbolic Logic.–. 10.2307/420992
    https://doi.org/10.2307/420992 [Google Scholar]
  93. Stillwell, John
    2004 “Emil Post and his Anticipation of Gödel and Turing”. Mathematics Magazine:.–. 10.1080/0025570X.2004.11953222
    https://doi.org/10.1080/0025570X.2004.11953222 [Google Scholar]
  94. Thue, Axel
    1914 “Probleme über Veränderungen von Zeichenreihen nach gegebenen Regeln”. Skrifter utgit av Videnskapsselskapet i Kristiana, I, number 10 inMatematisk-naturvidenskabelig klasse 1914 Oslo: Norske Videnskaps-Akademi.
    [Google Scholar]
  95. Tomalin, Marcus
    2006Linguistics and the Formal Sciences: The origins of generative grammar. Cambridge: Cambridge University Press. 10.1017/CBO9780511486340
    https://doi.org/10.1017/CBO9780511486340 [Google Scholar]
  96. 2007 “Reconsidering Recursion in Syntactic Theory”. Lingua.–. 10.1016/j.lingua.2006.11.001
    https://doi.org/10.1016/j.lingua.2006.11.001 [Google Scholar]
  97. Turing, Alan M.
    1936 “On Computable Numbers, with an Application to the Entscheidungsproblem”. Proceedings of the London Mathematical SocietySeries 2, :.–. Received28 May 1936; read12 November 1936. Correction published in PAMS series 2, .– 1937.
    [Google Scholar]
  98. Urquhart, Alasdair
    2009 “Emil Post”. The Handbook of the History of Logic, Volume 5ed. byDov Gabbay & John Woods. –. Amsterdam: Elsevier.
    [Google Scholar]
  99. Van Heijenoort, Jean
    1967From Frege to Gödel: A source book in mathematical logic, 1879–1931. Cambridge, MA: Harvard University Press.
    [Google Scholar]
  100. Wall, Robert
    1972Introduction to Mathematical Linguistics. Englewood Cliffs, NJ: Prentice-Hall.
    [Google Scholar]
  101. Whitehead, Alfred North and Bertrand Russell
    1910–1913Principia Mathematica. Cambridge: Cambridge University Press.
    [Google Scholar]
  102. Zwicky, Arnold M.
    1963 “Grammars of Number Theory: Some examples”. Working Paper W-6671, MITRE Corporation, Bedford, MA. Online at: https://web.stanford.edu/∼zwicky/grammars-of-number-theory.pdf
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