Cover not available
Article published In:
Historiographia Linguistica
Vol. 47:2/3 (2020) ► pp.303–321

A letter from Zellig Harris to André Lentin

Explanatory notes

Toward the end of his life, Zellig Harris (1909–1992) wrote a brief account of the origins and development of his work to establish the foundations of a science of language on mathematical principles. A French translation was published in 1990, and in the same publication appeared a parallel appraisal from a mathematical point of view by André Lentin (1913–2015). Early the following year, having reread Lentin’s essay several times, Harris wrote him the letter which is presented here. More than a gesture of thanks and appreciation, this letter further illuminates the comprehensive overview afforded by the two essays, both of which appeared in English in 2002.
Article outline
  • 1.Introduction
  • 2.Foundations of mathematics and of empirical science
    • 2.1Background
    • 2.2Constructivism, intuitionism, and tertium non datur
    • 2.3Finitism and recursive mathematics
    • 2.4On the homology with empirical science
  • 3.Grammar and its formalizations: Realism vs description
    • 3.1Properties of language, analytical methods, and formal descriptions
    • 3.2From abstract algebraic system to applicative calculus
    • 3.3Typed lambda calculus
    • 3.4Inconsistency as a challenge to finitism
  • 4.Formalization and finding further regularities in the data
    • 4.1Testing an axiomatization of grammar
    • 4.2Resolution of exception cases
    • 4.3Cryptomorphisms subject to “pertinence and linguistic transparency”
  • 5.Beyond operator grammar
  • 6.Conclusion
  • Notes
  • References
Published online: 2 April 2021
DOI logo
https://doi.org/10.1075/hl.00077.nev
References
Alama, Jesse & Johannes Korbmacher
2019 “The Lambda Calculus”. The Stanford Encyclopedia of Philosophy ed. by Edward N. Zalta. Stanford: Metaphysics Research Lab. URL =[URL]
Bahdanau, Dzmitry, Kyunghyun Cho & Yoshua Bengio
2015 “Neural Machine Translation by Jointly Learning to Align and Translate”. 3rd International Conference on Learning Representations (ICLR 2015). San Diego, CA [arXiv:1409.0473].Google Scholar
Barendregt, Henk
1997 “The Impact of the Lambda Calculus in Logic and Computer Science”. The Bulletin of Symbolic Logic 3:2.181–215. DOI logoGoogle Scholar
Birkhoff, Garrett
1967 3 [1940]1 Lattice Theory. American Mathematical Society Colloquium Publications, 251 (3rd ed.). Providence, R.I.: American Mathematical Society.Google Scholar
Bishop, Errett
1967 Foundations of Constructive Analysis. New York: Academic Press.Google Scholar
Bloomfield, Leonard
1935 “Linguistic Aspects of Science”. Philosophy of Science 21.499–517. DOI logoGoogle Scholar
1939 Linguistic aspects of science. [Monograph.] International Encyclopedia of Unified Science 1.4. Chicago: University of Chicago Press.Google Scholar
Bridges, Douglas & Erik Palmgren
2018 “Constructive Mathematics”. The Stanford Encyclopedia of Philosophy ed. by Edward N. Zalta. Stanford: Metaphysics Research Lab. URL = [URL]
Daladier, Anne
1990a “Aspects constructifs des grammaires de Zellig Harris”. Langages 991.57–84. DOI logoGoogle Scholar
1990b “Une représentation applicative des énoncés et de leurs dérivations”. Langages 991.92–127. DOI logoGoogle Scholar
2016 “L’inconsistance de la théorie des opérateurs de Harris : de la fin des grammaires finitistes à une typologie inductive”. Perspectives harrissiennes ed. by Claire Martinot, Christiane Marque-Pucheu & Sonia Gerolimich, 13–35. Paris: Cellule de recherche en linguistique, (CRL).Google Scholar
Dybjer, Peter & Erik Palmgren
2020 “Intuitionistic Type Theory. The Stanford Encyclopedia of Philosophy ed. by Edward N. Zalta. Stanford: Metaphysics Research Lab. URL = [URL]
Gleitman, Lila
2002 “Verbs of a feather flock together II: The child’s discovery of words and their meanings”. The Legacy of Zellig Harris: Language and information into the 21st Century, Vol. 1: Philosophy of science, syntax, and semantics ed. by Bruce Nevin, 209–229. Amsterdam: John Benjamins. DOI logoGoogle Scholar
Gross, Maurice
1979 “On the Failure of Generative Grammar”. Language 55:4.859–885. DOI logoGoogle Scholar
1984 “Lexicon-grammar and the Syntactic Analysis of French”. Proceedings of the 10th International Conference on Computational Linguistics (COLING ‘84), 275–282. Stanford (Cal.): Association for Computational Linguistics. DOI logoGoogle Scholar
2002 “Consequences of the Metalanguage Being Included in the Language”. The Legacy of Zellig Harris: Language and information into the 21st Century, Vol. 1: Philosophy of science, syntax, and semantics ed. by Bruce Nevin, 57–67. Amsterdam: John Benjamins. DOI logoGoogle Scholar
Harris, Zellig S.
1946 “From Morpheme to Utterance”. Language 22:3.161–183. DOI logoGoogle Scholar
1957 “Co-occurrence and Transformation in Linguistic Structure”. Language 33:3(1).283–340. DOI logoGoogle Scholar
1965 “Transformational Theory”. Language 41:3.363–401. DOI logoGoogle Scholar
1968 Mathematical Structures of Language. (=Interscience Tracts in Pure and Applied Mathematics, 21.) New York: Interscience Publishers John Wiley & Sons.Google Scholar
1969 The Two Systems of Grammar: Report and paraphrase. (=Transformations and Discourse Analysis Papers, 79.) Philadelphia: University of Pennsylvania. [Repr. in Papers in Structural and Transformational Linguistics ed. by in Henry Hiż, 612–692. Dordrecht/ Holland: D. Reidel 1970; repr. and revised in Transformationelle Analyse: Die Transformationstheorie von Zellig Harris und ihre Entwicklung / Transformational Analysis: The transformational theory of Zellig Harris and its development ed. by Senta Plötz (=Linguistische Forschungen, 8.), 58–240. Frankfurt/Main: Athenäum-Verlag 1972; repr. in a shortened version in Papers on Syntax ed. by Henry Hiż (=Synthese Language Library, 14.), 293–351. Dordrecht/Holland: D. Reidel 1981.]Google Scholar
1982 A Grammar of English on Mathematical Principles. New York: Wiley/Interscience.Google Scholar
1988 Language and Information. (=Bampton Lectures in America, 28.) New York: Columbia University Press. [Revised version of the Bampton Lectures given at Columbia University, New York City, in Oct. 1986, URL= [URL].]
2002 [1990] “The background of transformational and metalanguage analysis”. The Legacy of Zellig Harris: Language and information into the 21st Century, Vol. 1: Philosophy of science, syntax, and semantics ed. by Bruce Nevin, 1–15. Amsterdam: John Benjamins. (Translated by Anne Daladier as “La genèse de l’analyse des transformations et de la métalangue”, Langages 991.9–19 1990.) Available at [URL]
1991 A Theory of Language and Information: A mathematical approach. Oxford & New York: Clarendon Press.Google Scholar
Harris, Zellig S. & Paul Mattick, Jr.
1988 “Science Sublanguages and the Prospects for a Global Language of Science”. Annals of the American Academy of Political and Social Science 4951.73–83 [Vol. Telescience: Scientific Communication in the Information Age.] DOI logoGoogle Scholar
Harris, Zellig S., Michael Gottfried, Thomas Ryckman, Paul Mattick, Jr., Anne Daladier, Tzvee N. Harris & Suzanna Harris
1989 “The Form of Information in Science: Analysis of an immunology sublanguage”. Preface by Hilary Putnam. (=Boston Studies in the Philosophy of Science, 104.) Dordrecht/Holland & Boston: Kluwer Academic Publishers.Google Scholar
Heijenoort, Jean van
2002 From Frege to Gödel: A source book in mathematical logic, 1879–1931. Cambridge: Harvard University Press.Google Scholar
Hiż, Henry M.
1983 Review: Logico-Linguistic Papers by Richard M. Martin, Language and Society 12:2.286–287.Google Scholar
Iemhoff, Rosalie
2019 “Intuitionism in the Philosophy of Mathematics”. The Stanford Encyclopedia of Philosophy ed. by Edward N. Zalta. Stanford: Metaphysics Research Lab. URL = [URL]
Johnson, Stephen B.
2002 “The Computability of Operator Grammar”. The Legacy of Zellig Harris: Language and information into the 21st Century, Vol. 2: Mathematics and computability of language ed. by Bruce Nevin & Stephen B. Johnson, 143–160. Amsterdam: John Benjamins. DOI logoGoogle Scholar
Joshi, Aravind K.
2002 “Hierarchical Structure and Sentence Description”. The Legacy of Zellig Harris: Language and information into the 21st Century, Vol. 2: Mathematics and computability of language ed. by Bruce Nevin & Stephen B. Johnson, 121–141. Amsterdam: John Benjamins. DOI logoGoogle Scholar
Lentin, André.
1990 “Quelques réflexions sur les références mathématiques dans l’œuvre de Zellig Harris”. Langages 991.85–91. Available at [URL]. DOI logo
2002 “Reflections on References to Mathematics in the Work of Zellig Harris”. The Legacy of Zellig Harris: Language and information into the 21st Century, Vol. 2: Mathematics and computability of language ed. by Bruce Nevin & Stephen B. Johnson, 1–9. Amsterdam: John Benjamins. DOI logoGoogle Scholar
Mancosu, Paolo
1998 From Brouwer to Hilbert: The Debate on the foundations of mathematics in the 1920s. Oxford: Clarendon Press.Google Scholar
Martin-Löf, Per
1968 Notes on Constructive Analysis. Stockholm: Almquist & Wiksell.Google Scholar
1975 “An Intuitionistic Theory of Types: predicative part”. Logic Colloquium 1973 ed. by Harvey E. Rose and John C. Shepherdson, 73–118. Amsterdam: North-Holland. DOI logoGoogle Scholar
Miller, Jim & Regina Weinert
1998 Spontaneous Spoken Language: Syntax and discourse. Oxford: Oxford University Press.Google Scholar
Moot, Richard & Christian Retoré
2019 “Natural Language Semantics and Computability”. Journal of Logic, Language and Information 28:2.287–307. DOI logoGoogle Scholar
Russell, Bertrand
1903 Principles of Mathematics. Cambridge: Cambridge University Press.Google Scholar
Sager, Naomi
1981 Natural Language Information Processing: A computer grammar of English and its applications. Reading (Mass.): Addison-Wesley.Google Scholar
Wells, Joe Brian
1999 “Typability and Type Checking in System F are Equivalent and Undecidable”. Annals of Pure and Applied Logic 98:1–3.111–156. DOI logoGoogle Scholar
Weyl, Hermann
1998 [1921] “Über die neue Grundlagenkrise der Mathematik”. Mathematische Zeitschrift 101.39–79. (Translated as “On the New Foundational Crisis in Mathematics”, in From Brouwer to Hilbert: The Debate on the foundations of mathematics in the 1920s by Paolo Mancosu, 86–122. Oxford: Clarendon Press 1998.)Google Scholar
1946 “Mathematics and Logic”. American Mathematical Monthly 53:1.2–13.Google Scholar