Leonard Bloomfield
Linguistics and mathematics
This paper considers various aspects of Leonard Bloomfield’s (1887–1949) interest in contemporaneous mathematics. Specifically, some of the sources from which he obtained his mathematical knowledge are discussed, as are his own proposals for a linguistics-based solution to the foundations crisis which preoccupied leading mathematicians during the first half of the 20th century. In addition, his attitude towards the role of meaning in linguistic theory is reassessed in the light of his knowledge of Hilbertian Formalism.
References (57)
References
Bar-Hillel, Yehoshua. 1953. “On Recursive Definitions in Empirical Science”. Eleventh International Congress of Philosophy, vol. V1, 160–165. Amsterdam: North-Holland.
Bar-Hillel, Yehoshua. 1964. Language and Information: Selected essays on their theory and application. Reading, Mass.: Addison-Wesley.
Belyi, Vilen V[iktorovič]. 1967. “Some Facts about Weiss’ Influence on Bloomfield”. Zeitschrift für Anglistik und Amerikanistik 151.409–412. (Repr. in Fought 1999, ed. II1, 115–118.)
Bloomfield, Leonard. 1926. “A Set of Postulates for the Science of Language”. Language 21.153–164. (Repr. in Bloomfield 1970.128–140.)


Bloomfield, Leonard. 1933. Language. New York: Henry Holt & Co.
Bloomfield, Leonard. 1935. “Linguistic Aspects of Science”. Philosophy of Science 21.499–517. (Repr. in Bloomfield 1970.307–321.)


Bloomfield, Leonard. 1936. “Language or Ideas?”. Language 121.89–95. (Repr. in Bloomfield 1970.322–328.) 

Bloomfield, Leonard. 1939. “Linguistic Aspects of Science”. International Encyclopedia of Unified Science 1:1/5.258–301. (Also published separately, Chicago: University of Chicago Press, iv1, 1–59 pp.)
Bloomfield, Leonard. 1943. “Meaning”. Monatshefte für deutschen Unterricht 351.101–106. (Repr. in Bloomfield 1970.400–405.)
Bloomfield, Leonard. 1970 [1937]. The Language of Science. An unpublished manuscript, fragments of which are collected in Bloomfield 1970.333–338.
Bloomfield, Leonard. 1970. A Leonard Bloomfield Anthology. Ed. by Charles F. Hockett. Bloomington & London: Indiana University Press.
Carnap, Rudolf. 1928. Der logische Aufbau der Welt: Versuch einer Konstitutionstheorie der Begriffe. Berlin: Welt-Kreis.
Carnap, Rudolf. 1934. Logische Syntax der Sprache. Vienna: Julius Springer. 

Carnap, Rudolf. 1937 [1934]. The Logical Syntax of Language. Transl. by Atheme Smeaton. London: Kegan Paul, Trench, Trübner & Co.
Carnap, Rudolf. 1967 [1928]. The Logical Structure of the World: Pseudoproblems in philosophy. Transl. by R. A. George. London: Routledge & Kegan Paul.
Church, Alonzo. 1944. Introduction to Mathematical Logic. Vol. I1. Princeton, N. J.: Princeton University Press.
Copi, Irving, M. 1971. The Theory of Logical Types. London: Routledge & Kegan Paul.
Detlefsen, Michael. 1993. “Hilbert’s Formalism”. Revue Internationale de Philosophie 471.285–304.
Ewald, William B. 1996. From Kant to Hilbert: A source book in the foundations of mathematics. 21 vols. Oxford: Clarendon Press.
Fought, John G., ed. 1999. Leonard Bloomfield: Critical assessments. 31 vols. London & New York: Routledge.
Friedman, Michael. 1999. Reconsidering Logical Positivism. Cambridge: Cambridge University Press. 

Fries, Charles C. 1954. “Meaning and Linguistic Analysis”. Language 301.57–68.


Grattan-Guinness, Ivor. 2000. The Search for Mathematical Roots, 1870–1940: Logics, set theories and the foundations of mathematics from Cantor through Russell to Gödel. Princeton, N. J.: Princeton University Press.
Grelling, Kurt. 1936. “The Logical Paradoxes”. Mind 451.481–486. 

Harris, Zellig S. 1991. The Theory of Language and Information. Oxford: Clarendon Press.
Harwood, F. W. 1955. “Axiomatic Syntax: The construction and evaluation of syntactic calculus”. Language 311.409–413. 

Heijenoort, Jean van, ed. 1967. From Frege to Gödel: A source book in mathematical logic, 1879–1931. Cambridge, Mass. & London: Harvard University Press.
Hilbert, David. 1899. Grundlagen der Geometrie. Leipzig: B. G. Teubner.
Hilbert, David. 1900. “Über den Zahlbegriff”. Jahresbericht der Deutschen Mathematiker-Vereinigung 81.180–184.
Hilbert, David. 1918. “Axiomatisches Denken”. Mathematische Annalen 781.405–415. (Repr. in Hilbert, Gesammelte Abhandlungen, vol. III1, 146–156. Berlin: Springer, 1970.)
Hilbert, David. 1925. “Über das Unendliche” Mathematische Annalen 951.161–190. [English transl. by S. Bauer-Mengelberg in Heijenoort 1967.367–392.] 

Hilbert, David. 1967 [1904]. “On the Foundations of Logic and Arithmetic”. Transl. by B. Woodward in van Heijenoort 1967.130–138.
Hilbert, David. 1967 [1927]. “The Foundations of Mathematics”. Transl. by S. Bauer-Mengelberg and D. Føllesdal, in Heijenoort 1967. 464–479.
Hilbert, David. 1998 [1922]. “The New Grounding of Mathematics”. Transl. by W. Ewald in Mancosu 1998.198–214.
Hintikka, Jaakko ed. 1995. From Dedekind to Gödel: Essays on the development of the foundations of mathematics. London & New York: Kluwer Academic Publisher. 

Hiż, Henry & Pierre Swiggers. 1990. “Bloomfield, the Logical Positivist”. Semiotica 791.257–270. (Repr. in Fought, ed. 1999 II1, 224–236.) 

Hockett, Charles F., ed. 1970. See Bloomfield 1970.
Kleene, Stephen. 1952. Introduction to Metamathematics. Amsterdam: North-Holland.
Kline, Morris. 1980. Mathematics: The loss of certainty. Oxford & New York: Oxford University Press.
Koerner, E. F. K[onrad]. 2002. Towards a History of American Linguistics. London: Routledge.
Kreisel, Georg. 1958. “Hilbert’s Programme”. Dialectica 121.346–372. 

Luschei, Eugene C. 1962. The Logical Systems of Lésniewski. Amsterdam: North-Holland.
Mancosu, Paolo. 1998. From Brouwer to Hilbert: The debate on the foundations of mathematics in the 1920s. Oxford: Oxford University Press.
Matthews, Peter H. 1993. Grammatical Theory in the United States from Bloomfield to Chomsky. Cambridge: Cambridge University Press. 

Quine, Willard V. O. 1985. The Time of My Life: An autobiography. Cambridge, Mass.: MIT Press.
Reid, Constance. 1996. Hilbert. New York – Heidelberg – Berlin: Springer. 

Richardson, Alan W. 1998. Carnap’s Construction of the World: The Aufbau and the emergence of logical positivism, Cambridge: Cambridge University Press.
Robins, Robert H. 1988. “Leonard Bloomfield: The man and the man of science”. Transactions of the Philological Society 86:1.63–87. (Repr. in Fought, ed. 1999 I1, 231–250.)


Russell, Bertrand. 1903. Principles of Mathematics. London: Allen & Unwin.
Tomalin, Marcus. 2002. “The Formal Origins of Syntactic Theory”. Lingua 1121.805–826. 

Tomalin, Marcus. 2003. The Mathematical Origins of Transformational Generative Grammar. Ph.D. thesis, University of Cambridge.
Weiss, Albert P. 1925. “One Set of Postulates for a Behaviourist Psychology”. Psychological Review 321.83–87.


Whitehead, Alfred N. & Bertrand Russell. 1925 [1910]. Principia Mathematica. 2nd ed. 31 vols. Cambridge: Cambridge University Press.
Young, John W. 1911. Fundamental Concepts of Algebra and Geometry. New York: Macmillan.
Young, John W. & Oswald Veblen. 1918. Projective Geometry. Boston: Ginn & Co.
Cited by (1)
Cited by one other publication
Passos, Maria de Lourdes R. da F. & Maria Amelia Matos
2007.
The influence of Bloomfield’s linguistics on Skinner.
The Behavior Analyst 30:2
► pp. 133 ff.

This list is based on CrossRef data as of 3 august 2024. Please note that it may not be complete. Sources presented here have been supplied by the respective publishers.
Any errors therein should be reported to them.