Wittgenstein's Reductio


  • Gilad Nir University of Potsdam




By means of a reductio argument, Wittgenstein’s Tractatus calls into question the very idea that we can represent logical form. My paper addresses three interrelated questions: first, what conception of logical form is at issue in this argument? Second, whose conception of logic is this argument intended to undermine? And third, what could count as an adequate response to it? I show that the argument construes logical form as the universal, underlying correlation of any representation and the reality it represents. I further show that the argument seeks to undermine core commitments of Frege’s and Russell’s. But the reductio, as I read it, is not intended to establish the falsity of any of their specific assumptions. Rather, its aim is to make manifest the indeterminacies that underlie the language in which these assumptions are framed, and establish the need for a transformation of that language. So understood, Wittgenstein’s argument exemplifies his idea that philosophy is not a theory, but an activity of elucidation. The interpretation I propose bears on one of the central debates in the literature, namely how we should understand Wittgenstein’s contention that his elucidations succeed despite being nonsensical.


Anscombe, G. E. M., 1959. An Introduction to Wittgenstein’s Tractatus. London: Hutchinson.

Black, Max, 1964. A Companion to Wittgenstein’s Tractatus. Ithaca: Cornell University Press.

Blanchette, Patricia A., 2013. “From Logicism to Metatheory.” In The Palgrave Centenary Companion to Principia Mathematica, edited by Bernard Linsky and Nicholas Griffin, pp. 59–78. Basingstoke: Palgrave Macmillan Press.

Bronzo, Silver, 2012. “The Resolute Reading and Its Critics: An Introduction to the Literature.” Wittgenstein-Studien 3(1): 45–80.

Carnap, Rudolph, 2000. Logical Syntax of Language, edited by Amethe Smeaton. New York: Routledge.

Conant, James, 1992. “The Search for Logically Alien Thought: Descartes, Kant, Frege, and the Tractatus.” Philosophical Topics 20(1): 115–80.

———, 2007. “Mild-Mono Wittgensteinianism.” In , Wittgenstein and the Moral Life: Essays in Honor of Cora Diamond, edited by Alice Crary, pp. 174–217. Cambridge, MA: MIT Press.

Conant, James and Cora Diamond, 2004. “On Reading the Tractatus Resolutely.” In Wittgenstein’s Lasting Significance, edited by Max Kölbel and Bernhard Weiss, pp. 42–97. London: Routledge.

Davidson, Donald, 1974. “On the Very Idea of a Conceptual Scheme.” Proceedings and Addresses of the American Philosophical Association 47: 5–20.

Diamond, Cora, 1991a. “What Nonsense Might Be.” In Diamond (1991d), pp. 95–114.

———, 1991b. In Diamond (1991b), pp. 179–204.

———, 1991c. “Riddles and Anselm’s Riddle.” In Diamond (1991d), pp. 267–89.

———, 1991d. The Realistic Spirit: Wittgenstein, Philosophy, and the Mind. Cambridge, MA: MIT Press.

———, 2000. “Ethics, Imagination and the Method of the Tractatus.” In The New Wittgenstein, edited by Alice Crary and Rupert J. Read, pp. 149–73. London: Routledge.

———, 2011. “The Tractatus and the Limits of Sense.” In The Oxford Handbook of Wittgenstein, edited by Oskari Kuusela and Marie McGinn, pp. 238–73. New York: Oxford University Press.

———, 2014. “Addressing Russell Resolutely.” Philosophical Topics 42(2): 13–43.

———, 2019. Reading Wittgenstein with Anscombe, Going On to Ethics. Cambridge, MA: Harvard University Press.

Floyd, Juliet, 1995. “On Saying What You Want to Say: Wittgenstein, Gödel and the Trisection of the Angle.” In From Dedekind to Gödel: The Foundations of Mathematics in the Early Twentieth Century, edited by Jaakko Hintikka, pp. 373–426. Dordrecht: Kluwer Academic Publishers.

Frege, Gottlob, 1960. The Foundations of Arithmetic, Second revised edition, edited by John L. Austin. New York: Harper Torchbooks.

———, 1979a. “Logic.” In Frege (1979d), pp. 1–8.

———, 1979b. “Boole’s Logical Calculus and the Concept Script.” In Frege (1979d), pp. 9–46.

———, 1979c. “Logic in Mathematics.” In Frege (1979d), pp. 203–50.

———, 1979d. Posthumous Writings, edited by Hans Hermes, Friedrich Kambartel and Friedrich Kaulbach. Chicago: University of Chicago Press.

———, 1980. Philosophical and Mathematical Correspondence, edited by Gottfried Gabriel, Hans Hermes, Friedrich Kambartel, Christian Thiel and Albert Veraart. Chicago: University of Chicago Press.

———, 1984a. “On Concept and Object.” In Frege (1984c), pp. 182–94.

———, 1984b. “Thoughts.” In Frege (1984c), pp. 351–72.

———, 1984c. Collected Papers on Mathematics, Logic, and Philosophy, edited by Peter Geach. Oxford: Blackwell.

———, 1997. “On Sinn and Bedeutung.” In The Frege Reader, edited by Michael Beaney, pp. 151–71. London: Blackwell.

———, 2013. Basic Laws of Arithmetic, edited by Philip. A. Ebert and Marcus Rossberg. Oxford: Oxford University Press.

Geach, Peter T., 1976. “Saying and Showing in Frege and Wittgenstein.” Acta Philosophica Fennica 28: 54–70.

Goldfarb, Warren, 1982. “Logicism and Logical Truth.” Journal of Philosophy 79(1): 692–95.

Hacker, Peter M. S., 2001a. “Was He Trying to Whistle It?” In Hacker (2001c), pp. 98–140.

———, 2001b. “When the Whistling Had to Stop.” In Hacker (2001c), pp. 141–69.

———, 2001c. Wittgenstein: Connections and Controversies. Oxford: Clarendon Press.

Heck, Richard Kimberly, 2007. “Frege and Semantics.” Grazer Philosophische Studien 75(1): 27–63. (originally published under the name “Richard G. Heck, Jr”).

Hylton, Peter, 1990. Russell, Idealism, and the Emergence of Analytic Philosophy. New York: Oxford University Press.

———, 2005. “Logic in Russell’s Logicism.” In Propositions, Functions and Analysis: Selected Essays on Russell’s Philosophy, pp. 49–82. Oxford: Oxford University Press.

Johnston, Colin, 2017. “The Picture Theory.” In A Companion to Wittgenstein, edited by Hans Johann Glock and John Hyman, pp. 141–58. Chichester: John Wiley & Sons.

Korhonen, Anssi, 2012. “Logic as a Science and Logic as a Theory: Remarks on Frege, Russell and the Logocentric Predicament.” Logica Universalis Logica Universalis: 597–613.

Kremer, Michael, 2001. “The Purpose of Tractarian Nonsense.” Noûs 35(1): 39–73.

———, 2002. “Mathematics and Meaning in the Tractatus.” Philosophical Investigations 25(3): 272–303.

Kuhn, Thomas, 1962. The Structure of Scientific Revolutions. Chicago: University of Chicago Press.

Kuusela, Oskari, 2019. Wittgenstein on Logic as the Method of Philosophy: Re-examining the Roots and Development of Analytic Philosophy. Oxford: Oxford University Press.

Lützen, Jesper, 2009. “Why was Wantzel overlooked for a century? The changing importance of an impossibility result.” Historia Mathematica 36: 374–94.

Narboux, Jean-Philippe, 2014. “Showing, the Medium Voice, and the Unity of the Tractatus.” Philosophical Topics 42(2): 201–62.

Nordmann, Alfred, 2005. Wittgenstein’s Tractatus: An Introduction. Cambridge: Cambridge University Press.

Proops, Ian, 2007. “Russell and the Universalist Conception of Logic.” Noûs 41(1): 1–32.

Ricketts, Thomas, 1985. “Frege, The Tractatus, and the Logocentric Predicament.” Noûs 19(1): 3–15.

Russell, Bertrand, 1903. The Principles of Mathematics. Cambridge: Cambridge University Press.

———, 1905. “On Denoting.” Mind 14(56): 479–93.

———, 1920. Introduction to Mathematical Philosophy. London: G. Allen & Unwin.

———, 1960. “Introduction.” In Wittgenstein (1960), pp. 7–23.

———, 1973. “Meinong’s Theory of Complexes and Assumptions.” In Essays in Analysis, edited by Douglas Lackey, pp. 21–76. London: Allen and Unwin.

———, 2013. Theory of Knowledge: The 1913 Manuscript, edited by Kenneth Blackwell and Elizabeth Ramsden Eames. London: Routledge.

Stanley, Jason, 1996. “Truth and Metatheory in Frege.” Pacific Philosophical Quarterly 77: 45–50.

Sullivan, Peter, 2001. “A Version of the Picture Theory.” In Ludwig Wittgenstein. Tractatus logico-philosophicus, edited by Wilhelm Vossenkuhl, p. 89–110. Berlin: Akademie Verlag.

———, 2004. “What is the Tractatus about?” In Wittgenstein’s Lasting Significance, edited by Max Kölbel and Bernhard Weiss, pp. 28–41. London: Routledge.

Tappenden, Jamie, 1997. “Metatheory and Mathematical Practice in Frege.” Philosophical Topics 25(2): 213–63.

———, 2000. “Frege on Axioms, Indirect Proofs, and Independence Arguments in Geometry: Did Frege Reject Independence Arguments?” Notre Dame Journal of Formal Logic 41(3): 271–315.

Tarski, Alfred, 1944. “The Semantic Conception of Truth: And the Foundations of Semantics.” Philosophy and Phenomenological Research 4(3): 341–76.

van Heijenoort, Jean, 1967. “Logic as Calculus and Logic as Language.” Synthese 17(1): 324–30.

Weiner, Joan, 2005. “Semantic Descent.” Mind 114: 324–54.

White, Roger, 2006. Wittgenstein’s Tractatus Logico-Philosophicus: A Reader’s Guide. London: Continuum.

Williams, Meredith, 2004. “Nonsense and Cosmic Exile.” In Wittgenstein’s Lasting Significance, edited by Max Kölbel and Bernhard Weiss, pp. 1–27. London: Routledge.

Wittgenstein, Ludwig, 1960. Tractatus Logico-Philosophicus, edited by C. K. Ogden and F. P. Ramsey. London: Routledge & Kegan Paul.

———, 1974. Philosophical Grammar, edited by Rush Rhees, translated by Anthony Kenny. Oxford: Blackwell.

———, 1975. Philosophical Remarks, edited by Rush Rhees, translated by Roy Hargreaves and Roger White. Oxford: Blackwell.

———, 1976. Lectures on the Foundations of Mathematics, Cambridge 1939, edited by Cora Diamond. Ithaca, NY: Cornell University Press.

———, 1978. Wittgenstein, Ludwig, Third edition, edited by Georg H. Von Wright, Rush Rhees and G. E. M. Anscombe. Oxford: Blackwell.

———, 1984. 1984 Notebooks, 1914-1916, edited by Georg H. Von Wright and G. E. M. Anscombe. Chicago: University of Chicago Press.

———, 2009. Philosophical Investigations, Fourth edition, edited by Peter M. S. Hacker and Joachim Schulte, translated by G. E. M. Anscombe, P. M. S. Hacker and Joachim Schulte. Oxford: Blackwell.

Zalabardo, Jose, 2015. Zalabardo, Jose. Oxford: Oxford University Press.