Open Philosophy 1:360-379 (2018)

John Bova
University of New Mexico
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 value-ideal, 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 diagonalization  Sartre  reflection  incompleteness  self-reference  Badiou  mathematical existentialism  metalogic  metamathematics  Cantor's theorem  negative foundations
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DOI 10.1515/opphil-2018-0026
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L'Être et le Néant : essai d'ontologie phénoménologique.J. P. Sartre - 1942 - Revue Philosophique de la France Et de l'Etranger 133 (10):177-179.

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