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Gödel's Theorem and Postmodern Theory

Published online by Cambridge University Press:  23 October 2020

David Wayne Thomas
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Abstract

In 1931 the mathematician Kurt Gödel published a treatise establishing the inherent incompleteness and inconsistency of that order of logical system used in Alfred North Whitehead and Bertrand Russell's Principia Mathematica. Gödel's work has proved an attractive reference in diverse fields, particularly in postmodern literary-critical theory, which often seems intent on logical impasse and which sees a protodeconstructive corroboration in Gödel's theorem. Such analogizing is not without informative substance, but a closer look at the philosophical and mathematical theory surrounding Gödel's practice reveals that Gödelian undecidability emerges from a theoretical framework—a mathematical Platonism—with extensive metaphysical commitments regarding subject position and the objects of thought. Gödel's explorations of logical undecidability do not so much undermine logocentric suppositions as exploit them all the more consequentially. The analogy between Gödel's theorem and postmodern theory underscores the metaphysical operations of any criticism that finds in Gödel a “postmetaphysical” ally. (DWT)

Type
Research Article
Information
PMLA , Volume 110 , Issue 2: Special Millennium issue , March 1995 , pp. 248 - 261
Copyright
Copyright © Modern Language Association of America, 1995

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References

Works Cited

Barker, Stephen Philosophy of Mathematics. Englewood Cliffs: Prentice, 1969.Google Scholar
Benacerraf, Paul, and Putnam, Hilary, eds Philosophy of Mathematics: Selected Readings. 2nd ed. Cambridge: Cambridge UP, 1983.Google Scholar
Benveniste, Emile “Subjectivity in Language.” Problems in General Linguistics. Trans. Meek, Mary Elizabeth. Coral Gables: U of Miami P, 1971. 223–22.Google Scholar
Brouwer, Luitzen Egbertus Jan “On the Significance of the Principle of Excluded Middle in Mathematics, Especially in Function Theory.” Trans. Stephan Bauer-Mengelberg et al. Van Heijenoort 334–33.Google Scholar
Chihara, Charles Ontology of the Vicious-Circle Principle. Ithaca: Cornell UP, 1973.Google Scholar
Coleridge, Samuel Taylor Biographia Literaria. Everyman's Library 11. New York: Dutton, 1906.Google Scholar
DeLong, Howard A Profile of Mathematical Logic. Reading: Addison, 1970.Google Scholar
de Man, Paul Blindness and Insight: Essays in the Rhetoric of Contemporary Criticism. 2nd ed. Minneapolis: U of Minnesota P, 1983.Google Scholar
de Man, Paul “Semiology and Rhetoric.” Diacritics 3.3 (1973): 27–33. Rpt. in Allegories of Reading. New Haven: Yale UP, 1979. 3–19.10.2307/464524CrossRefGoogle Scholar
Derrida, Jacques “Differance.” “Speech and Phenomena” and Other Essays on Husserl's Theory of Signs. Trans. Allison, David B. Evanston: Northwestern UP, 1973. 129–12.Google Scholar
Derrida, Jacques Dissemination. Trans. Johnson, Barbara. Chicago: U of Chicago P, 1981.Google Scholar
Derrida, Jacques La dissemination. Paris: Seuil, 1972.Google Scholar
Derrida, Jacques Edmund Husserl's Origin of Geometry: An Introduction. Trans. Leavy, John P. Jr. Lincoln: U of Nebraska P, 1989.Google Scholar
Derrida, Jacques “How to Avoid Speaking: Denials.” Trans. Ken Frieden. Languages of the Unsayable: The Play of Negativity in Literature and Literary Theory. Ed. Burdick, Sanford and Iser, Wolfgang. New York: Columbia UP, 1989. 3–70.Google Scholar
Derrida, Jacques “Signature Event Context.” Trans. Samuel Weber and Jeffrey Mehlman. 1977. Limited Inc. Ed. Graff, Gerald. Evanston: Northwestern UP, 1988. 1–23.Google Scholar
Dummett, Michael The Logical Basis of Metaphysics. Cambridge: Harvard UP, 1991.Google Scholar
Emerson, Ralph Waldo “Experience.” Emerson, Emerson 216–21.Google Scholar
Emerson, Ralph Waldo “Fate.” Emerson, Emerson 345–34.Google Scholar
Emerson, Ralph Waldo Ralph Waldo Emerson. Ed. Poirer, Richard. Oxford Authors. Oxford: Oxford UP, 1990.Google Scholar
Foucault, Michel An Introduction. Trans. Hurley, Robert. New York: Vintage, 1980. Vol. 1 of A History of Sexuality.Google Scholar
Gasché, Rodolphe The Tain of the Mirror: Derrida and the Philosophy of Reflection. Cambridge: Harvard UP, 1986.Google Scholar
Gödel, Kurt On Formally Undecidable Propositions of Principia Mathematica and Related Systems I. Trans. Melzer, B. Edinburgh: Oliver, 1962. Trans. of “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I.” Monatshefte für Mathematik und Physik 38 (1931): 349-60.Google Scholar
Gödel, Kurt “Russell's Mathematical Logic.” Benacerraf and Putnam 447–44.10.1017/CBO9781139171519.024CrossRefGoogle Scholar
Gödel, Kurt “What Is Cantor's Continuum Problem?” Benacerraf and Putnam 470–47.Google Scholar
Goethe, Goethe Johann Wolfgang Conversations with Eckermann (1823-32). Trans. John Oxenford. 1850. San Francisco: North Point, 1984.Google Scholar
Heyting, Arend “Disputation.” Benacerraf and Putnam 66–76.Google Scholar
Hofstadter, Douglas Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basic, 1979.Google Scholar
Iser, Wolfgang The Fictive and the Imaginary: Charting Literary Anthropology. Baltimore: Johns Hopkins UP, 1993.Google Scholar
Jameson, Fredric Postmodernism; or, The Cultural Logic of Late Capitalism. Durham: Duke UP, 1991.Google Scholar
Jeffrey, Richard Formal Logic: Its Scope and Limits. 2nd ed. New York: McGraw, 1981.Google Scholar
Kadvany, John. “Reflections on the Legacy of Kurt Gödel: Mathematics, Skepticism, Postmodernism.” Philosophical Forum 20.3 (1989): 161–16.Google Scholar
Kant, Immanuel Critique of Pure Reason. Trans. Smith, Norman Kemp. London: Macmillan, 1950.Google Scholar
Kermode, Frank The Sense of an Ending: Studies in the Theory of Fiction. Oxford: Oxford UP, 1967.Google Scholar
Kristeva, Julia “D'une identité l'autre.” Polylogue. Paris: Seuil, 1977. 149–14.Google Scholar
Kristeva, Julia “From One Identity to an Other.” Desire and Language: A Semiotic Approach to Language and Art. Trans. Gora, Thomas et al. New York: Columbia UP, 1980. 124–12.Google Scholar
Lucas, J. R “Minds, Machines, and Gödel.” Philosophy 36 (1961): 112–11.Google Scholar
Lyotard, Jean-François The Postmodern Condition: A Report on Knowledge. Trans. Bennington, Geoff and Massumi, Brian. Minneapolis: U of Minnesota P, 1984.Google Scholar
Myhill, John “Some Philosophical Implications of Mathematical Logic.” Review of Metaphysics 6.2 (1952): 165–16.Google Scholar
Nagel, Ernest, and Newman, James Gödel's Proof. New York: New York UP, 1958.Google Scholar
Penrose, Roger The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. New York: Oxford UP, 1989.Google Scholar
Rorty, Richard “Philosophy as a Kind of Writing: An Essay on Derrida.” Consequences of Pragmatism. Minneapolis: U of Minnesota P, 1982. 90–109.Google Scholar
Sedgwick, Eve Kosofsky Epistemology of the Closet. Berkeley: U of California P, 1990.Google Scholar
Smullyan, Raymond Gödel's Incompleteness Theorems. Oxford Logic Guides 19. New York: Oxford UP, 1992.Google Scholar
Steiner, George Real Presences. Chicago: U of Chicago P, 1989.Google Scholar
Vaihinger, Hans The Philosophy of As-If. Trans. Ogden, C. K. 2nd ed. London: Routledge, 1935.Google Scholar
van Heijenoort, Jean, ed From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931. Cambridge: Harvard UP, 1967.Google Scholar
Whitehead, Alfred North, and Russell, Bertrand Principia Mathematica. 2nd ed. 1925. Cambridge: Cambridge UP, 1950.Google Scholar