Abstract
In this paper I investigate the question whether mathematical realism is compatible with Husserl’s transcendental phenomenological idealism. The investigation leads to the conclusion that a unique kind of mathematical realism that I call “constituted realism” is compatible with and indeed entailed by transcendental phenomenological idealism. Constituted realism in mathematics is the view that the transcendental ego constitutes the meaning of being of mathematical objects in mathematical practice in a rationally motivated and non-arbitrary manner as abstract or ideal, non-causal, unchanging, non-spatial, and so on. The task is then to investigate which kinds of mathematical objects, e.g., natural numbers, real numbers, particular kinds of functions, transfinite sets, can be constituted in this manner. Various types of founded acts of consciousness are conditions for the possibility of this meaning constitution.
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I would like to thank participants in the Phenomenology and Mathematics conference at Tampere for questions and comments. Work on this paper was partially supported by a National Endowment for the Humanities (NEH) fellowship, which support I hereby gratefully acknowledge.
References
Gödel, K. [1954–59] 2003. Correspondence with Gotthard Günther. In Kurt Gödel: Collected Works, Volume IV, eds. S. Feferman et al., 476–535. Oxford: Oxford University Press.2003.
Gödel, K. [*1961/?] 1995. The Modern Development of the Foundations of Mathematics in the Light of Philosophy. In Kurt Gödel: Collected Works, Volume III, eds. S. Feferman et al., 374–387. Oxford: Oxford University Press.1995.
Gödel, K. [1964] 1990. What is Cantor’s Continuum Problem? In Kurt Gödel: Collected Works, Volume II, eds. S. Feferman et al., 254–270. Oxford: Oxford University Press, 1990.
Husserl, E. 1964. The Idea of Phenomenology, Translated by W.P. Alston and G. Nakhnikian. The Hague: Nijhoff.
Husserl, E. 1991. The Phenomenology of the Consciousness of Internal Time, Translation by J. Brough of Hua 10. Dordrecht: Kluwer.
Husserl, E. 1994. Edmund Husserl: Early Writings in the Philosophy of Logic and Mathematics, Dordrecht: Kluwer. Materials from the period 1890–1908.Translated by D. Willard.
Kant, I. 1973. Critique of Pure Reason, Translated by N.K. Smith. London: Macmillan.
Putnam, H. 1987. The Many Faces of Realism. Chicago and La Salle, Ill: Open Court Press.
Putnam, H. 1981. Reason, Truth, and History. Cambridge: Cambridge University Press.
Tieszen, R. 2004. Husserl’s Logic. In Handbook of the History of Logic, Volume 3, eds. D.Gabbay and J. Woods, 207–321, Amsterdam: Elsevier Press.
Tieszen, R. 2005a. Consciousness of Abstract Objects. In Phenomenology and the Philosophy of Mind, eds. D. Smith and A. Thomasson, 181–200, Oxford: Oxford University Press.
Tieszen, R. 2005b. Phenomenology, Logic, and the Philosophy of Mathematics. Cambridge: Cambridge University Press.
Tieszen, R. 2006. After Gödel: Mechanism, Reason and Realism in the Philosophy of Mathematics. Philosophia Mathematica 14: 229–254. In a special issue on Kurt Gödel.
Wang, H. 1974. From Mathematics to Philosophy. London: Routledge & Kegan Paul.
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Tieszen, R. (2010). Mathematical Realism And Transcendental Phenomenological Idealism. In: Hartimo, M. (eds) Phenomenology and Mathematics. Phaenomenologica, vol 195. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3729-9_1
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DOI: https://doi.org/10.1007/978-90-481-3729-9_1
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