Remarks Concerning the Phenomenological Foundations of Mathematics
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03.03.2016
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In this paper I investigate the phenomenological approach to foundations of mathematics. Phenomenological reflection plays the certain role in extension of mathematical knowledge by clarification of meanings. The phenomenological technique pays our attention to our own acts in the use of the abstract concepts. Mathematical constructions must not be considered as passive objects, but as categories are given in theoretical acts, in categorical experiences and in our senses. Phenomenology moves like a category theory from formal components of knowledge to the dynamics of constitutive process.
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Седов Ю. Remarks Concerning the Phenomenological Foundations of Mathematics // Логические исследования / Logical Investigations. 2016. Т. 22. № 1. C. 136-144.
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Литература
Conway, J.H. The sensual (quadratic) form. Washington: Mathematical association of America, 1997. 228 pp.
Godel, K. Collected Works, Vol. 3: Unpublished Essays and Lectures, ed. by S. Feferman. New York: Oxford University Press, 1995. 560 pp.
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Lurie, J. Higher topos theory. Princeton: Princeton University Press, 2009. 944 pp.
McLarty, C. “Recent debate over categorical foundations”, in: Foundational theories of classical and constructive mathematics. Dordrecht: Springer, 2011, pp. 145–154.
Novikov, N.Y. Teoriya shkal. Printsipy postroeniya etalonnykh protsedur izmereniya, kodirovaniya i upravleniya [The theory of scale. Principles of building etalon procedures of measuring, coding and control]. Moscow: FIZMATLIT, 2012. 536 pp. (In Russian)
Patras, F. “Phenomenologie et theorie des categories”, in: Geometries of nature, living systems and human cognition, ed. by L. Boi. World Scientific, 2005, pp. 401–419.
Tieszen, R. After Godel. Platonism and rationalism in mathematics and logic. New York: Oxford University Press, 2011. 245 pp.
Godel, K. Collected Works, Vol. 3: Unpublished Essays and Lectures, ed. by S. Feferman. New York: Oxford University Press, 1995. 560 pp.
Hintikka, J. “How can phenomenologist have a philosophy of mathematics?”, in: Phenomenology and Mathematics. Phenomenologica 195, ed. by M. Hartimo. Springer, 2010, pp. 91–105.
Husserl, E. Formale und transzendentale Logik. Versuch einer Kritik der logischen Vernunft. 2, Auflage, Tubingen: Max Niemeyer Verlag, 1981. § 31, § 74.
Husserl, E. Ideen zu einer reinen Phaenomenologie und phaenomenologischen Philosophie. Erster Buch: Allgemeine Einf_uhrung in die reine Phanomenologie. Husserliana. Bd. III. Den Haag: Nijhoff, 1976. § 72.
Lurie, J. Higher topos theory. Princeton: Princeton University Press, 2009. 944 pp.
McLarty, C. “Recent debate over categorical foundations”, in: Foundational theories of classical and constructive mathematics. Dordrecht: Springer, 2011, pp. 145–154.
Novikov, N.Y. Teoriya shkal. Printsipy postroeniya etalonnykh protsedur izmereniya, kodirovaniya i upravleniya [The theory of scale. Principles of building etalon procedures of measuring, coding and control]. Moscow: FIZMATLIT, 2012. 536 pp. (In Russian)
Patras, F. “Phenomenologie et theorie des categories”, in: Geometries of nature, living systems and human cognition, ed. by L. Boi. World Scientific, 2005, pp. 401–419.
Tieszen, R. After Godel. Platonism and rationalism in mathematics and logic. New York: Oxford University Press, 2011. 245 pp.