The paper presents an interpretation of Platonism, the seeds of which can be found in the writings of Gödel and Wittgenstein. Although it is widely accepted that Wittgenstein is an anti-Platonist the author points to some striking affinities between Gödel’s and Wittgenstein’s accounts of mathematical concepts and the role of feeling and intuition in mathematics. A version of Platonism emerging from these considerations combines realism with respect to concepts with a view of concepts as accessible to feeling and able to guide our behavior through feeling.
concepts, Gödel, intuition, mathematics, Platonism, realism, rule-following, Wittgenstein
How to cite:
Poręba, Marcin. “Gödel, Wittgenstein and the Sensibility of Platonism.” Eidos. A Journal for Philosophy of Culture 5, no. 1 (2021): 108-125. https://doi.org/10.14394/eidos.jpc.2021.0007.
Faculty of Philosophy, University of Warsaw
Krakowskie Przedmieście 3, 00-927 Warsaw, Poland
Cohen, Paul J. Set Theory and the Continuum Hypothesis. New York: W. A. Benjamin, 1966.
Frege, Gottlob. “Function and Concept.” In Translations from the Philosophical Writings of Gottlob Frege, edited by Peter Geach and Max Black. Oxford: Basil Blackwell, 1960.
Gödel, Kurt. “Is mathematics syntax of language?” In vol. 3 of the Collected Works, edited by Solomon Feferman, John W. Dawson, Jr., Warren Goldfarb, Charles Parsons, and Robert M. Solovay. Oxford: Oxford University Press, 1995.
Gödel, Kurt. “Some Basic Theorems on the Foundations of Mathematics and their Implications.” In vol. 3 of the Collected Works, edited by Solomon Feferman, John W. Dawson, Jr., Warren Goldfarb, Charles Parsons, and Robert M. Solovay. Oxford: Oxford University Press, 1995.
Gödel, Kurt. “What is Cantor’s Continuum Problem?” In vol. 3 of the Collected Works, edited by Solomon Feferman, John W. Dawson, Jr., Warren Goldfarb, Charles Parsons, and Robert M. Solovay. Oxford: Oxford University Press, 1995.
Kant, Immanuel. Critique of Pure Reason (1787). Translated by N. Kemp Smith. London: Macmillan 1929.
Natorp, Paul. Plato’s Theory of Ideas: An Introduction to Idealism. Sankt Augustin: Academia Verlag, 2004.
Wittgenstein, Ludwig. Bemerkungen über die Grundlagen der Mathematik. Frankfurt a. M.: Suhrkamp, 1994.
Wittgenstein, Ludwig. Philosophical Investigations. Translated by G.E.M. Anscombe. New York: Macmillan, 1968.
Wittgenstein, Ludwig. Tractatus Logico-Philosophicus. Translated by Charles K. Ogden. London: Kegan Paul, 1933.
Youschkevitch, Adolph P. “The Concept of Function up to the Middle of the 19th Century.” Archive for History of Exact Sciences 16, no. 1 (1976): 55-60.
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