Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Open Philosophy

Editor-in-Chief: Harman, Graham

Covered by:
DOAJ - Directory of Open Access Journals

Open Access
See all formats and pricing
More options …

Minimal Sartre: Diagonalization and Pure Reflection

John Bova
Published Online: 2018-12-05 | DOI: https://doi.org/10.1515/opphil-2018-0026


These remarks take up the reflexive problematics of Being and Nothingness and related texts from a metalogical perspective. A mutually illuminating translation is posited between, on the one hand, Sartre’s theory of pure reflection, the linchpin of the works of Sartre’s early period and the site of their greatest difficulties, and, on the other hand, the quasi-formalism of diagonalization, the engine of the classical theorems of Cantor, Godel, Tarski, Turing, etc. Surprisingly, the dialectic of mathematical logic from its inception through the discovery of the diagonal theorems can be recognized as a particularly clear instance of the drama of reflection according to Sartre, especially in the positing and overcoming of its proper valueideal, viz. the synthesis of consistency and completeness. Conversely, this translation solves a number of systematic problems about pure reflection’s relations to accessory reflection, phenomenological reflection, pre-reflective self-consciousness, conversion, and value. Negative foundations, the metaphysical position emerging from this translation between existential philosophy and metalogic, concurs by different paths with Badiou’s Being and Event in rejecting both ontotheological foundationalisms and constructivist antifoundationalisms.

Keywords: Badiou; Mathematical Existentialism; Metalogic; Negative Foundations; Reflexivity; Self- Reference; Tetradic Dialectic; Value


  • Badiou, Alain. Being and Event. Translated by Oliver Feltham. London; New York: Continuum, 2005.Google Scholar

  • Badiou, Alain. L’Immanence des vérités: L’être et l’événement, 3. Fayard, 2018.Google Scholar

  • Badiou, Alain. Logics of Worlds: Being and Event, 2. Translated by Alberto Toscano. London; New York: Continuum, 2013.Google Scholar

  • Badiou, Alain. Theory of the Subject. Translated by Bruno Bosteels. London: Bloomsbury, 2013.Google Scholar

  • Beauvoir, Simone de. The Ethics of Ambiguity. Translated by Bernard Frechtman. New York: Philosophical Library, 1949.Google Scholar

  • Boolos, George, and Richard C. Jeffrey. Computability and Logic. Edited by John P. Burgess. 5th ed. Cambridge University Press, 2007.Google Scholar

  • Bova, J. A Metalogical Approach to the Problem of Reflexivity in Platonic Dialectic. Unpublished dissertation. 2016.Google Scholar

  • Cannon, Betty. “Psychoanalysis and Existential Psychoanalysis,” Ch. 7 in Sartre: Key Concepts. Edited by Stephen Churchill and Jack Reynolds. Routledge; New York: 2013.Google Scholar

  • Cantor, Georg. “On an Elementary Question in the Theory of Manifolds (1891).” In From Kant to Hilbert a Source Book in the Foundations of Mathematics. Volume 2, translated by William Bragg Ewald. Oxford; New York: Oxford University Press, 2005.Google Scholar

  • Chaitin, Gregory J. Thinking about Gödel and Turing: Essays on Complexity 1970-2007. Hackensack, N.J.: World Scientific, 2007.Google Scholar

  • Davis, Martin. The Undecidable; Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions. Hewlett, N.Y.: Raven Press, 1965.Google Scholar

  • DeLong, Howard. A Profile of Mathematical Logic. Reading, Mass.: Addison-Wesley Pub. Co., 1970.Google Scholar

  • Fitting, Melvin. Incompleteness in the Land of Sets. Studies in Logic vol. 5. College Publications, 2007.Google Scholar

  • Fraser, Olivia Lucca. “Nothingness & Event” 2009 (Unpublished manuscript).Google Scholar

  • Fraser, Olivia Lucca. This Infinite, Unanimous Dissonance: A Study in Mathematical Existentialism Through the Works of Jean-Paul Sartre and Alain Badiou Unpublished manuscript)Google Scholar

  • Gödel, Kurt. On Formally Undecidable Propositions of Principia Mathematica and Related Systems. New York: Dover Publications, 1992.Google Scholar

  • Grim, Patrick. The Incomplete Universe : Totality, Knowledge, and Truth. Cambridge, Mass.: MIT Press, 1991.Google Scholar

  • Hofstadter, Douglas R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basic Books, 1979.Google Scholar

  • Hofstadter, Douglas R. “What Is It like to Be a Strange Loop?” In Self-Representational Approaches to Consciousness, edited by Uriah Kriegel and Kenneth Williford. Cambridge, Mass.: MIT Press, 2006.Google Scholar

  • Hunter, Geoffrey. Metalogic: An Introduction to the Metatheory of Standard First Order Logic. Berkeley: University of California Press, 1971.Google Scholar

  • Kleene, Stephen Cole. Introduction to Metamathematics. New York: Van Nostrand, 1952.Google Scholar

  • Miguens, Sofia, Gerhard Preyer, & Clara Bravo Morando eds. Pre-Reflective Consciousness: Sartre and Contemporary Philosophy of Mind. Routledge. 2016.Google Scholar

  • Petersen, Uwe. Diagonal Method and Dialectical Logic: Tools, Materials, and Groundworks for a Logical Foundation of Dialectic and Speculative Philosophy. Osnabrück: Der Andere Verlag, 2002.Google Scholar

  • Plato. Charmides, Translated by Rosamond Kent Sprague. In Complete Works, edited by John M Cooper and D. S Hutchinson. Indianapolis, Ind.: Hackett Pub., 1997.Google Scholar

  • Priest, Graham. Beyond the Limits of Thought. Cambridge; New York, NY, USA: Cambridge University Press, 1995.Google Scholar

  • Priest, Graham. The Nature of Philosophy and its Place in the University. University of Queensland Press, 1991.Google Scholar

  • Putnam, Hilary. Representation and Reality. Cambridge, Mass.: MIT Press, 1988.Google Scholar

  • Sartre, Jean-Paul. Being and Nothingness: An Essay on Phenomenological Ontology. Translated by Hazel Barnes. New York: Washington Square Press, 1992.Google Scholar

  • Sartre, Jean-Paul. “Intentionality: A fundamental idea of Husserl’s phenomenology.” Translated by Joseph Fell. Journal of the British Society for Phenomenology 1 (2): 4-5, 1970Google Scholar

  • Sartre, Jean-Paul. L’être et le néant: essai d’ontologie phénoménologique. Gallimard, 2016.Google Scholar

  • Sartre, Jean-Paul.. Notebooks for an Ethics. Translated by David Pellauer. Chicago: University of Chicago Press, 1992.Google Scholar

  • Sartre, Jean-Paul. The Transcendence of the Ego: A Sketch for a Phenomenological Description. Translated by Andrew Brown. London; New York: Routledge, 2004.Google Scholar

  • Sartre, Jean-Paul. What Is Literature? New York: Harper & Row, 1965.Google Scholar

  • Smullyan, Raymond M. Gödel’s Incompleteness Theorems. New York: Oxford University Press, 1992.Google Scholar

  • Smullyan, Raymond M. Recursion Theory for Metamathematics. New York: Oxford University Press, 1993.Google Scholar

  • Yanofsky, Noson S. “A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points.” arXiv:math/0305282, May 19, 2003.Google Scholar

About the article

Received: 2018-10-12

Accepted: 2018-10-18

Published Online: 2018-12-05

Published in Print: 2018-11-01

Citation Information: Open Philosophy, Volume 1, Issue 1, Pages 360–379, ISSN (Online) 2543-8875, DOI: https://doi.org/10.1515/opphil-2018-0026.

Export Citation

© by John Bova, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

Comments (0)

Please log in or register to comment.
Log in