Abstract
Few have entertained the idea that Georg Cantor, the creator of set theory, might have influenced Edmund Husserl, the founder of the phenomenological movement. Yet an exchange of ideas took place between them when Cantor was at the height of his creative powers and Husserl in the throes of an intellectual struggle during which his ideas were particularly malleable and changed considerably and definitively. Here their writings are examined to show how Husserl's and Cantor's ideas overlapped and crisscrossed in the areas of philosophy and mathematics, arithmetization, abstraction, consciousness and pure logic, psychologism, metaphysical idealism, new numbers, and sets and manifolds.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Becker, P.: 1930, ‘The Philosophy of E. Husserl', translated in The Phenomenology of Husserl: Selected Critical Readings, R. O. Elveton (ed.), Quadrangle Books, Chicago, 1970, 40–72 (originally published as ‘Die Philosophie Edmund Husserls', Kantstudien 35, (1930), 119–50).
Cantor, G.: 1883, Grundlagen einer allgemeinen Mannigfaltigkeitslehre. Ein mathematischphilosophischer Versuch in der Lehre des Unendlichen, Teubner, Leipzig, 1883. Cited as appears in Cantor 1932, pp165–246.
Cantor, G.: 1884, ‘Principien einer theorie der Ordnungstypen’ (dated November 6, 1884), first published by I. GrattanGuinness in Acta Mathematica 124, 1970, 65–107.
Cantor, G.: 1885, ‘Rezension von Freges Grundlagen', Deutsche Literaturzeitung 6, 728–29. Cited as appears in Cantor 1932, 440–41.
Cantor, G.: 1887/88, ‘Mitteilungen zur Lehre vom Transfinitum', Zeitschrift für Philosophie und philosophische Kritik, 91, 81–125, 92, 240–65. Cited as appears in Cantor 1932, 378–439. Also published as Cantor 1890.
Cantor G.: 1890, Gesammelte Abhandlungen zur Lehre vom Transfiniten, C.E.M. Pfeffer, Halle. See Cantor 1887/88.
Cantor, G.: 1895, Contributions to the Founding of the Theory of Transfinite Numbers, trans. P.E.B. Jourdain (1915), Dover, New York, 1955. Originally ‘Beiträge zur Begründung der transfiniten Mengenlehre', Mathematischen Annalen 46, 1895, 481–512.
Cantor, G.: 1932, Gesammelte Abhandlungen, E. Zermelo (ed.), Springer, Berlin.
Cantor, G.: 1991, Georg Cantor Briefe, H. Meschkowski and W. Nilson (eds.), Springer, New York.
Cavaillès, J.: 1962, Philosophie Mathématique, Hermann, Paris.
Couturat, L.: 1896, De l'infini mathématique, Blanchard, Paris, 1973.
Dauben, J.: 1979, Georg Cantor, His Mathematics and Philosophy of the Infinite, Princeton University Press, Princeton.
Eccarius, W.: 1985, ‘Georg Cantor und Kurd Lasswitz: Briefe zur Philosophie des Unendlichen', NTM Schriftenr. Gesch. Naturwiss., Technik., Med. 22, 7–28.
Fraenkel, A.: 1930, ‘Georg Cantor', Jahresbericht der deutschen Mathematiker Vereinigung 39 (appears abridged in Cantor 1932).
Frege, G.: 1884, Foundations of Arithmetic, Oxford, Blackwell, 1986.
Frege, G.: 1892, ‘Review of Georg Cantor, Zur Lehre vom Transfiniten: Gesammelte Abhandlungen aus der Zeitschrift für Philosophie und philosophische Kritik', Collected Papers on Mathematics, Logic and Philosophy, Oxford, Blackwell, 1984, pp. 178–81.
Frege, G.: 1979, Posthumous Writings, Blackwell, Oxford.
Frege, G.: 1980, Philosophical and Mathematical Correspondence, Blackwell, Oxford.
Grattan Guinness, I.: 1971, ‘Towards a Biography of Georg Cantor', Annals of Science 27(4), 345–91.
Grattan Guinness, I.: 1978, ‘How Russell Discovered His Paradox', Historia Mathematica 5, 127–37.
Grattan Guinness, I.: 1980, ‘Georg Cantor's Influence on Bertrand Russell', History and Philosophy of Logic 1 (1980), 61–93.
Grattan Guinness, I.: 1982, ‘Psychology in the Foundations of Logic and Mathematics: the Cases of Boole, Cantor and Brouwer', History and Philosophy of Logic 3, 33–53.
GrattanGuinness, I.: 1996, ‘Numbers, Magnitudes, Ratios, and Proportions in Euclid's Elements: How Did He Handle Them?', Historia Mathematica 23, 355–75.
Hallett, M.: 1984, Cantorian Set Theory and Limitation of Size, Oxford, Clarendon.
Hilbert, O.: 1925, ‘On the Infinite', in Van Heijenoort, 1967, pp. 367–92.
Hill, C.: 1991, Word and Object in Husserl, Frege and Russell, the Roots of Twentieth Century Philosophy, Ohio University Press, Athens.
Hill, C.: 1994a, ‘Frege Attacks Husserl and Cantor', The Monist 77(3), 347–57.
Hill, C.: 1994b, ‘Husserl and Frege on Substitutivity', in Mind, Meaning and Mathematics, L. Haaparanta (ed.), Kluwer, Dordrecht, pp. 113–140.
Hill, C.: 1995, ‘Husserl and Hilbert on Completeness', From Dedekind to Gödel, Essays on the Development of the Foundations of Mathematics, J. Hintikka (ed.), Kluwer, Dordrecht, pp. 143–63.
Hill, C.: Forthcoming a, ‘Abstraction and Idealization in Georg Cantor and Edmund Husserl', Abstraction and Idealization, R. Poli (ed.)
Hill, C.: Forthcoming b, ‘From Empirical Psychology to Phenomenology: Husserl on the Brentano Puzzle', The Brentano Puzzle, R. Poli (ed).
Husserl, E.: 1887, ‘On the Concept of Number', Husserl: Shorter Works, P. McCormick and F. Elliston (eds.), University of Notre Dame Press, Notre Dame 1981, pp. 92–120. Originally published as ‘Ueber den Begriff der Zahl', available in Husserl, 1970, pp. 289–339.
Husserl, E.: 1891, Philosophie der Arithmetik, Pfeffer, Halle Also Husserl, 1970.
Husserl, E.: 1900–01, Logical Investigations, New York: Humanities Press, 1970.
Husserl, E.: 1905, ‘Husserl an Brentano, 27. III. 1905', Briefwechsel, Die Brentanoschule, vol. I, Kluwer, Dordrecht, 1994.
Husserl, E.: 1913, Introduction to the Logical Investigations,M. Nijhoff, The Hague, 1975.
Husserl, E.: 1919, ‘Recollections of Franz Brentano', Husserl: Shorter Works, P. McCormick and F. Elliston (eds.), University of Notre Dame Press, Notre Dame, 1981, 342–49 (also translated by L. McAllister in her The Philosophy of Brentano, Duckworth, London, 1976, 47–55). Originally published as ‘Errinerungen an Franz Brentano', O. Kraus, (ed.), Franz Brentano: Zur Kenntnis seines Lebens und seiner Lehre, Beck'sche, Munich, 1919.
Husserl, E.: 1929, Formal and Transcendental Logic, M. Nijhoff, The Hague, 1969.
Husserl, E.: 1970, Philosophie der Arithmetik. Mit Ergänzenden Texten (1890–1901), M. Nijhoff, The Hague, 1970. Introduction by L. Eley.
Husserl, E.: 1983, Studien zur Arithmetik und Geometrie, Texte aus dem Nachlass (1886– 1901), M. Nijhoff, The Hague.
Husserl, E.: 1994, Early Writings in the Philosophy of Logic and Mathematics, Kluwer, Dordrecht.
Husserl, M.: 1988, ‘Skizze eines Lebensbildes von E.Husserl', Husserl Studies 5, 105–125.
Illemann, W.: 1932, Husserls vorphänomenologische Philosophie, Hirzel, Leipzig.
Jourdain, P.: 1910–14, ‘The Development of the Theory of Transfinite Numbers', Archiv der Mathematik und Physik 14 (1908–1909), 289–311, 16 (1910), 21–43, 22 (1913–1914), 1–21 (reprinted in Jourdain's works I. Grattan Guinness (ed.), CLUEB, Bologna 1991, pp. 33–99).
Klein, M.: 1972, Mathematical Thought from Ancient to Modern Times, Oxford University Press, New York.
Kreiser, L.: 1979, ‘W. Wundts Auffassung der Mathematik. – Briefe von G. Cantor an W. Wundt', Wissenschaftliche Zeitschrift, Karl Marx Universität, Ges. u. Sprachwissenschaft 28, 197–206.
Kusch, M.: 1989, Language as Calculus vs. Language as Universal Medium, Kluwer, Dordrecht.
Lotze, H.: 1880, Logic, Clarendon Press, Oxford, (1888).
Mahnke, O.: 1966, ‘From Hilbert to Husserl: First Introduction to Phenomenology, especially that of formal mathematics', Studies in the History and Philosophy of Science 8, 71–84. (First published as ‘Von Hilbert zu Husserl: Erste Einführung in die Phänomenologie, besonders der formalen Mathematik', Unterrichtsblä tter 29(3/4).
Miller, J.: 1982, Numbers in Presence and Absence, M. Nijhoff, The Hague.
Osborn, A.: 1934, Edmund Husserl and his Logical Investigations. Cambridge MA, 1949.
Picker, B.: 1962, ‘Die Bedeutung der Mathematik für die Philosophie Edmund Husserls', Philosophia Naturalis 7, 266–355.
Purkert, W. and H. Ilgauds: 1991, Georg Cantor 1845–1918, Birkhäuser, Basel.
Rosado Haddock, G.: 1973, Edmund Husserls Philosophie der Logik im Lichte der gegenwärtigen Logik und Grundlagenforschung, Doctoral Thesis Rheinische Friedrich Wilhelms Universit ät, Bonn.
Russell, B.: 1903, Principles of Mathematics, Norton, London.
Russell, B.: 1917, ‘Mathematics and Metaphysicians', Mysticism and Logic, Allen and Unwin, London (1963), pp. 75–95.
Russell, B.: 1959, My Philosophical Development, Unwin, London.
Schmit, R.: 1981, Husserls Philosophie der Mathematik: platonische und konstructivische Moment in Husserls Mathematik Begriff, Bouvier Verlag, Bonn.
Schuhmann, K.: 1977, Husserl Chronik, M. Nijhoff, The Hague.
Sepp, Hans Rainer, (ed.): 1994, Husserl in Halle, P. Lang, Berne.
Van Heijenoort, J. (ed.): 1967, From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, Harvard University Press, Cambridge MA.
Willard, O.: 1980, ‘Husserl on a Logic That Failed’, The Philosophical Review 89(1), 46–64.
Willard, D.: 1984, Logic and the Objectivity of Knowledge, Ohio University Press, Athens.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hill, C.O. Did Georg Cantor Influence Edmund Husserl?. Synthese 113, 145–170 (1997). https://doi.org/10.1023/A:1005099615326
Issue Date:
DOI: https://doi.org/10.1023/A:1005099615326