Wittgenstein's Diagonal Argument: A Variation on Cantor and Turing

Juliet Floyd; Kurt Wischin

doi:10.5281/zenodo.3568216

Juliet Floyd Boston University, United States of America
Kurt Wischin Universidad de Granada, Spain

DOI: https://doi.org/10.5281/zenodo.3568216

Keywords: Common Sense, Formal System, Turing Machine, Ordinary Language, Philosophical Discussion

Abstract

Turing was a philosopher of logic and mathematics, as well as a mathematician. His work throughout his life owed much to the Cambridge milieu in which he was educated and to which he returned throughout his life. A rich and distinctive tradition discussing how the notion of “common sense” relates to the foundations of logic was being developed during Turing’s undergraduate days, most intensively by Wittgenstein, whose exchanges with Russell, Ramsey, Sraffa, Hardy, Littlewood and others formed part of the backdrop which shaped Turing’s work. Beginning with a Moral Sciences Club talk in 1933, Turing developed an “anthropological” approach to the foundations of logic, influenced by Wittgenstein, in which “common sense” plays a foundational role. This may be seen not only in “On Computable Numbers” (1936/7) and Turing’s dissertation (written 1938, see (1939)), but in his exchanges with Wittgenstein in 1939 and in two later papers, “The Reform of Mathematical Phraseology and Notation” (1944/5) and “Solvable and Unsolvable Problems” (1954).

Author Biographies

Juliet Floyd, Boston University, United States of America

Juliet Floyd began her career in 1990 teaching at the City College of New York and CUNY (1992), where she became the assistant executive director of the graduate program. She moved to Boston University in 1995 as Visiting Assistant Professor, joining the Philosophy Department there as Associate Professor the following year. She is Professor of Philosophy in Boston since 2006. After obtaining a Philosophy B.A. at Wellesley College with Highest Honors and studying at the London School of Economics and Political Science (1978–1982), she earned her Philosophy MA (“Kant’s Sensus Communis: Regulative and Constitutive”, 1984) and PhD (“The Rule of the Mathematical: Wittgenstein’s Later Discussions”, 1990) at Harvard University. Her research revolves, among other topics, around the History and Development of Analytic and Twentieth Century Philosophy, Philosophy of Logic and Mathematics, Philosophy of Language, Formal and Traditional Epistemology, Theories of Truth, Modern Philosophy (Kant), Aesthetics, Wittgenstein, Pragmatism, History and Philosophy of Science, especially Logic and Mathematics and Philosophy of Emerging Computational Technologies. She was awarded numerous Fellowships and Major Grants. She edited together with S. Shieh the book Future Pasts: Perspectives on the Place of the Analytic Tradition in Twentieth–Century Philosophy (Oxford University Press, 2001), together with J. E. Katz Philosophy of Emerging Media: Understanding, Appreciation, Application (Oxford University Press, 2016), and with A. Bokulich Philosophical Explorations of the Legacy of Alan Turing – Turing 100, Boston Studies in the Philosophy and History of Science Vol. 324 (Springer Verlag, 2017). She contributed with chapters to more than fifty books and published numerous articles in a wide variety of philosophical Journals.

Kurt Wischin, Universidad de Granada, Spain

Kurt Wischin is currently CPhil at the University of Granada, Spain. He got in touch with philosophy first at the University of Vienna in the 1970s, obtained a BA in Philosophy from the University of Queretaro, Mexico and an MPhil at the National Autonomous University of Mexico, Mexico. His main interest centres in Philosophy of Language and early Analytical Philosophy, in particular, Frege and Wittgenstein. He has published articles and translations in some anthologies and academic reviews.

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Wittgenstein's Diagonal Argument: A Variation on Cantor and Turing

Abstract

Author Biographies

References

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