Wittgenstein’s Philosophy of Mathematics: Felix Mühlhölzer in Conversation with Sebastian Grève

Authors

  • Sebastian Grève University of Oxford
  • Felix Mühlhölzer University of Göttingen

Keywords:

mathematics, Wittgenstein Ludwig, Mühlhölzer Felix

Abstract

Sebastian Grève interviews Felix Mühlhölzer on his work on the philosophy of mathematics.

Author Biographies

Sebastian Grève, University of Oxford

Sebastian Grève is currently reading for a DPhil in Philosophy at Queen’s College, University of Oxford. He previously studied philosophy and German language/literature at the universities of Göttingen, Bergen and London. He has written papers on J. L. Austin, Nietzsche, Plato, Wittgenstein and Socrates as well as on topics in epistemology, metaphysics, philosophical methodology and philosophy of mathematics. He is the co-editor of Wittgenstein and the Creativity of Language (forthcoming, Palgrave Macmillan 2015) and Variations on Wittgenstein (forthcoming).

Felix Mühlhölzer, University of Göttingen

Felix Mühlhölzer has been Professor of Philosophy at the University of Göttingen since 1997. He completed his habilitation treatise in 1989 at the University of Munich and was a member of a research group on "Semantic aspects of space-time theories" at the Center for Interdisciplinary Research, Bielefeld, in 1992/93 and Professor of Philosophy of Science and Logic at Dresden University of Technology from 1993 to 1997. He has published articles on topics in philosophy of science and philosophy of language, and since 2001 has written primarily on later Wittgenstein’s philosophy of mathematics. His recent works include Braucht die Mathematik eine Grundlegung? Ein Kommentar des Teils III von Wittgensteins Bemerkungen über die Grundlagen der Mathematik (2010) and Wissenschaft (2011).

References

Dummett, M., 1959. “Wittgenstein’s philosophy of mathematics”. In: P. Benacerraf and H. Putnam, eds. 1964. Philosophy of Mathematics. Selected Readings. Upper Saddle River, NJ: Prentice Hall, pp. 491–509.

Floyd, J./Mühlhölzer, F.: forthcoming. Wittgenstein’s Annotations to Hardy’s A Course of Pure Mathematics.

Fogelin, R. J., 2009. Taking Wittgenstein at His Word: A Textual Study. Princeton, NJ: Princeton University Press.

Halbach, V./Horsten, L., 2005. “Computational Structuralism”. Philosophia Mathematica (III) 13, 174–186.

Mühlhölzer, F., 1998. “Braucht die Mathematik eine philosophische Basis?”. Ethik und Sozialwis¬senschaften 9 (3), pp. 472–474.

Mühlhölzer, F., 1999. “Mathematik ohne Metaphysik”. In: J. Nida-Rümelin, ed. 1999. Rationalität, Realismus, Revision. Berlin: Verlag Walter de Gruyter, pp. 416–423.

Mühlhölzer, F., 2001. “Wittgenstein and the Regular Heptagon”. Grazer Philosophische Studien 62, pp. 215–247.

Mühlhölzer, F., 2002a. “Wittgenstein and Surprises in Mathematics”. In: R. Haller and K. Puhl, eds. 2002. Wittgenstein and the Future of Philosophy: A Reassessment after 50 Years (Proceedings of the 24th International Wittgenstein Symposium, Kirchberg am Wechsel, 2001). Vienna: öbv&hpt Verlagsgesellschaft, pp. 306–315.

Mühlhölzer, F., 2002b. “Regelfolgen und die Identität von Begriffen”. In: U. Baltzer and G. Schönrich, eds. 2002. Institutionalität und Regelfolgen. Münster: mentis Verlag, pp. 137–156.

Mühlhölzer, F., 2006. “›A mathematical proof must be surveyable‹ – What Wittgenstein meant by this and what it implies”. Grazer Philosophische Studien 71, pp. 57–86.

Mühlhölzer, F., 2008. “Wittgenstein und der Formalismus”. In: M. Kroß, ed. 2008. »Ein Netz von Normen«: Wittgenstein und die Mathematik. Parerga Verlag, pp. 107–148.

Mühlhölzer, F., 2010a. Braucht die Mathematik eine Grundlegung? Ein Kommentar des Teils III von Wittgen¬steins Bemerkungen über die Grundlagen der Mathematik. Frankfurt: Vittorio Klostermann.

Mühlhölzer, F., 2010b. “Mathematical Intuition and Natural Numbers”. Erkenntnis 73, pp. 265–292.

Mühlhölzer, F., 2011. Wissenschaft. Stuttgart: Reclam.

Mühlhölzer, F., 2012a. “Wittgenstein and Metamathematics”. In: P. Stekeler-Weithofer, ed. 2012. Wittgenstein: Zu Philosophie und Wissenschaft. Hamburg: Verlag Felix Meiner, pp. 103–128.

Mühlhölzer, F., 2012b. “Teil III der Bemerkungen über die Grundlagen der Mathematik und die zugrunde liegenden Manuskripte (122 und 117): ein Vergleich”. Wittgenstein Studien Vol. 3. Berlin: Verlag Walter de Gruyter, pp. 19–44.

Mühlhölzer, F., 2014. “On Live and Dead Signs in Mathematics”. In: G. Link, ed. Formalism and Beyond. On the Nature of Mathematical Discourse. Verlag Walter De Gruyter, pp. 183-208.

Mühlhölzer, F., forthcoming (a). “Putnam, Wittgenstein and the Objectivity of Mathematics”. In: R. E. Auxier, ed. forthcoming. The Philosophy of Hilary Putnam. Library of Living Philosophers. Chicago, IL: Open Court.

Mühlhölzer, F., forthcoming (b). “How Arithmetic Is About Numbers: A Wittgensteinian Perspective”. In: H.-J. Glock, ed. forthcoming. Perspectives on Wittgenstein’s Philosophy of Mathematics.

Mühlhölzer, F., forthcoming (c). “Wittgenstein’s Philosophy of Mathematics: Beyond Logicism, Intuitionism and Formalism”. In: J. Conant and S. Grève, eds. forthcoming. Variations on Wittgenstein.

Parsons, Charles, 2008. Mathematical Thought and Its Objects. Cambridge: Cambridge University Press.

Putnam, H., 2007. “Wittgenstein and the Real Numbers”. In: A. Crary, ed. 2007. Wittgenstein and the Moral Life. Essays in Honor of Cora Diamond. Cambridge, MA: MIT Press, pp. 235–250.

Wittgenstein, L., 2000. Wittgenstein’s Nachlass: The Bergen Electronic Edition, ed. Wittgenstein Archives at the University of Bergen. Oxford: Oxford University Press.

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Published

2014-12-16