Article published In: Historiographia Linguistica
Vol. 31:1 (2004) ► pp.105–136
Leonard Bloomfield
Linguistics and mathematics
Published online: 30 July 2004
https://doi.org/10.1075/hl.31.1.06tom
https://doi.org/10.1075/hl.31.1.06tom
Summary
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.
Résumé
Cet article discute divers aspects de l’intérêt que portait Leonard Bloomfield (1887–1949) pour les mathématiques de son époque. Plus précisément, on y traitera de certaines des sources d’où il obtint ses connaissances en mathématiques. On y traitera également de ses propres propositions (tirées de la linguistique) visant à résoudre la crise des fondations qui préoccupait nombre d’illustres mathématiciens au cours de la première moitié du XXe siècle. De plus, on reverra son point de vue quant au rôle du sens en linguistique théorique à la lumière de sa connaissance du formalisme d’Hilbert.
Zusammenfassung
Der vorliegende Beitrag untersucht verschiedenen Aspeckte von Leonard Bloomfields (1887–1949) Interesse an der zeitgenössischen Mathematik. Insbesonders werden einige Quellen diskutiert, von denen er mathematische Kenntnisse erworben hatte, aber auch seine eigenen Vorschläge zur einer auf der Linguistik basierenden Lösung der Krise der Grundlagen der Mathematik, die führende Wissenschaftler in der ersten Hälfte des 20. Jahrhunderts vornehmlich beschäftigte. Darüber hinaus wird Bloomfields Haltung gegenüber der Rolle der Bedeutung in der Sprachtheorie im Lichte seiner Kenntnis des hilbertischen Formalismus neu bewertet.
References (57)
Bar-Hillel, Yehoshua. 1953. “On Recursive Definitions in Empirical Science”. Eleventh International Congress of Philosophy, vol. V1, 160–165. Amsterdam: North-Holland.
. 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.)
. 1935. “Linguistic Aspects of Science”. Philosophy of Science 21.499–517. (Repr. in Bloomfield 1970.307–321.)
. 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.)
. 1943. “Meaning”. Monatshefte für deutschen Unterricht 351.101–106. (Repr. in Bloomfield 1970.400–405.)
. 1970 [1937]. The Language of Science. An unpublished manuscript, fragments of which are collected in Bloomfield 1970.333–338.
. 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.
. 1937 [1934]. The Logical Syntax of Language. Transl. by Atheme Smeaton. London: Kegan Paul, Trench, Trübner & Co.
. 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.
Ewald, William B. 1996. From Kant to Hilbert: A source book in the foundations of mathematics. 21 vols. Oxford: Clarendon Press.
Fought, John G. 1999. “Leonard Bloomfield’s Linguistic Legacy: Later uses of some technical features”. Historiographia Linguistica 261.313–332.
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.
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.
. 1918. “Axiomatisches Denken”. Mathematische Annalen 781.405–415. (Repr. in Hilbert, Gesammelte Abhandlungen, vol. III1, 146–156. Berlin: Springer, 1970.)
. 1925. “Über das Unendliche” Mathematische Annalen 951.161–190. [English transl. by S. Bauer-Mengelberg in Heijenoort 1967.367–392.]
. 1967 [1904]. “On the Foundations of Logic and Arithmetic”. Transl. by B. Woodward in van Heijenoort 1967.130–138.
. 1967 [1927]. “The Foundations of Mathematics”. Transl. by S. Bauer-Mengelberg and D. Føllesdal, in Heijenoort 1967. 464–479.
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.)
Kline, Morris. 1980. Mathematics: The loss of certainty. Oxford & New York: Oxford University Press.
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.
Murray, Stephen O. 1994. Theory Groups and the Study of Language in North America. Amsterdam & Philadelphia: John Benjamins.
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.)
. 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.
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