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Actuality of transcendental æsthetics for modern physics

  • Part 5 Some Insights About Modern Physics
  • Conference paper
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1830–1930: A Century of Geometry

Part of the book series: Lecture Notes in Physics ((LNP,volume 402))

Abstract

  1. 1.

    The more mathematics and physics unify themselves in the physico-mathematical modern theories, the more an objective epistemology becomes necessary. Only such a transcendental epistemology is able to thematize correctly the status of the mathematical determination of physical reality.

  2. 2.

    There exists a transcendental history of the synthetic a priori and of the construction of physical categories.

  3. 3.

    The transcendental approach allows to supersed Wittgenstein's and Carnap's antiplatonist thesis according to which pure mathematics are physically applicable only if they lack any descriptive, cognitive or objective, content and reduce to mere prescriptive and normative devices. In fact, pure mathematics are prescriptive-normative in physics because:

    1. (i)

      the categories of physical objectivity are prescriptive-normative, and

    2. (ii)

      their categorial content is mathematically “constructed” through a Transcendental Aesthetics. Only a transcendental approach make compatible, in the one hand, a grammatical conventionalism of Wittgensteinian or Carnapian type and, on the other hand, a platonist realism of Gödelian type. Mathematics are not a grammar of the world but a mathematical hermeneutics of the intuitive forms and of the categorial grammar of the world.

  4. 4.

    The transcendental approach allows also to reconcile the objective validity and the historical value of scientific theories. It allows to go beyond the epistemological antinomy opposing dogmatic positivism (there exists an absolute value of objective truth) and sceptic post-positivism (there exists an historico-anthropological relativity of truth). As we have seen, truth, reality, necessity are moments of the procedures of constitution and determination. They are relative to them, and therefore relative to an historical (non cognitive) synthetic a priori.

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References

  • Abraham, R., Marsden, J. 1978. Foundations of Mechanics, Benjamin Cummings, New-York, Reading.

    Google Scholar 

  • Allison, H.E., 1981.“Transcendental Schematism and the Problem of the Synthetic a priori”, Dialectica, 35, 1-2, 57–83.

    Google Scholar 

  • Allison, H.E., 1983. Kant's Transcendental Idealism. An Interpretation and Defense, New-Haven, Yale University Press.

    Google Scholar 

  • Ameriks, K., 1982. “Current German Epistemology: The Significance of Gerold Prauss”, Inquiry, 25, 1, 125–138.

    Google Scholar 

  • Arnold, V., 1976, Méthodes mathématiques de la mécanique classique, Moscou, Mir.

    Google Scholar 

  • Bohr, N., 1935. Physical Review, 48, 696.

    Article  Google Scholar 

  • Boi, L., 1989. “Idéalisation et objectivation, ou des rapports entre géométrie et physique”, Fundamenta Scientiae, 10, 1, 85–114.

    Google Scholar 

  • Bouveresse, J., 1987. La Force de la Règle, Paris, Editions de Minuit.

    Google Scholar 

  • Brittan, G., 1978. Kant's Theory of Science, Princeton University Press.

    Google Scholar 

  • Brittan, G., 1991. Algebra and Intuition, Department of Philosophy, Montana Sate University, (to appear).

    Google Scholar 

  • Cassirer, E., 1910. Substanzbegrif und Funktionbegriff, Berlin. Substance et Fonction (trans. P. Caussat), Paris, Editions de Minuit, 1977.

    Google Scholar 

  • Châtelet, G., 1985. “Le retour de la monade”, Fundamenta Scientiae, 6, 327–345.

    Google Scholar 

  • Cohen-Tannoudji, G., Spiro, M., 1986. La Matière — Espace — Temps, Paris, Fayard.

    Google Scholar 

  • Connes, A., 1990. Géométrie non commutative, Paris, InterEditions.

    Google Scholar 

  • d'Espagnat, B. 1985. Une incertaine réalité, Paris, Gauthier-Villars.

    Google Scholar 

  • Duncan, H., 1984. “Inertia, the Communication of Motion, and Kant's Third Law of Mechanics”, Philosophy of Science, 51, 93–119.

    Article  Google Scholar 

  • Ehlers, J., 1973. “The Nature and Structure of Spacetime”, The Physicist's Conception of Nature, (J. Mehra ed.), 71–91, Dordrecht, Reidel.

    Google Scholar 

  • Folse, H.J., 1978. “Kantian Aspects of Complementarity”, Kant-Studien, 69, 58–66.

    Google Scholar 

  • Friedman, M., 1985. “Kant's Theory of Geometry”, The Philosophical Review, XCIV, 4, 455–506.

    Google Scholar 

  • Gomez, R.J., 1986. “Beltrami's Kantian View of Non-Euclidean Geometry”, Kant-Studien, 77, 1, 102–107.

    Google Scholar 

  • Green, M. B., Schwarz, J. H., Witten, E., 1987. Superstring Theory, Cambridge University Press.

    Google Scholar 

  • Grünbaum, A., 1973. Philosophical Problems of Space and Time, Dordrecht-Boston, Reidel.

    Google Scholar 

  • Honner, J. 1982. “The Transcendental Philosophy of Niels Bohr”, Studies in History and Philosophy of Science, 13, 1, 1–29.

    Article  Google Scholar 

  • Itzykson, C., Zuber, J.B., 1985. Quantum Field Theory, Singapour, McGraw-Hill.

    Google Scholar 

  • Jammer, M., 1974. The Philosophy of Quantum Mechanics, New-York, John Wiley and Sons.

    Google Scholar 

  • Kaku, M., 1988. Introduction to Superstrings, New-York, Springer.

    Google Scholar 

  • Kant, E, 1980-1986. Oeuvres philosophiques (F. Alquié ed.), Paris, Bibliothèque de la Pléiade, Gallimard.

    Google Scholar 

  • Kant, E., 1781-1787. Critique de la Raison pure, (trans. A.J.L. Delamarre et F. Marty), Paris, Pléïade, Gallimard, 1980.

    Google Scholar 

  • Kant, E., 1786. Premiers Principes métaphysiques de la Science de la Nature, (trans. J. Gibelin), Paris, Vrin, 1971.

    Google Scholar 

  • Kant, E., 1790. Critique de la Faculté de Juger, (trans. A. Philonenko), Paris, Vrin, 1979.

    Google Scholar 

  • Kant, E., 1796-1803. Opus Postumum, (trans. F. Marty), Paris, Presses Universitaires de France, 1986.

    Google Scholar 

  • Kant, I., 1781-1787. Kritik der reinen Vernunft, Kants gesammelte Schriften, Band III, Preussische Akademie der Wissenschaften, Berlin, Georg Reimer, 1911.

    Google Scholar 

  • Kant, I., 1786. Metaphysische Anfangsgründe der Naturwissenschaft, Kants gesammelte Schriften, Band IV, Preussische Akademie der Wissenschaften, Berlin, Georg Reimer, 1911.

    Google Scholar 

  • Kant, I., 1790. Kritik der Urtheilskraft, Kants gesammelte Schriften, Band V, Preussische Akademie der Wissenschaften, Berlin, Georg Reimer, 1913.

    Google Scholar 

  • Lautman, A., 1937-1939. Essai sur l'unité des mathématiques et divers écrits, Paris, Bourgois, 1977.

    Google Scholar 

  • Le Bellac, M., 1988. Des phénomènes critiques aux champs de jauge, Paris, InterEditions-C.N.R.S.

    Google Scholar 

  • Manin, Y. I., 1988. Gauge Field Theory and Complex Geometry, Berlin, New-York, Springer.

    Google Scholar 

  • Marsden, J., 1974. Applications of Global Analysis in mathematical Physics, Berkeley, Publish or Perish.

    Google Scholar 

  • Mc Goldrick, P.M., 1985. “The Metaphysical Exposition: An Analysis of the Concept of Space”, Kant-Studien, 76, 3, 257–275.

    Google Scholar 

  • Misner, C.W., Thorne, K.S., Wheeler, J.A., 1973. Gravitation, San Francisco, Freeman.

    Google Scholar 

  • MNS, 1989. La Mathématique non standard, (H. Barreau, J. Harthong, eds.), Paris, Editions du CNRS.

    Google Scholar 

  • Paty, M., 1988. La Matière dérobée, Paris, Editions des Archives Contemporaines.

    Google Scholar 

  • Petitot, J., 1979-1982. “infinitesimale”, “Locale/Globale”, “Unità delle matematiche”, Enciclopedia Einaudi, VII, 443–521; VIII, 429–490; XV, 341–352; XV, 1034–1085, Turin, Einaudi.

    Google Scholar 

  • Petitot, J., 1987a. “Refaire le Timée. Introduction à la philosophie mathématique d'Albert Lautman”, Revue d'Histoire des Sciences, XL, 1, 79–115.

    Google Scholar 

  • Petitot, J., 1987b. “Mathématique et Ontologie”, La scienza tra filosofia e storia in Italia net Novecento, (F. Minazzi, L. Zanzi, eds.), 191–211, Rome, Edizione della Presidenza del Consiglio dei Ministri.

    Google Scholar 

  • Petitot, J., 1988. “Logique transcendantale et ontologies régionales”, Colloque de Cerisy: Rationalité et Objectivités, (to appear, Editions Patiño).

    Google Scholar 

  • Petitot, J., 1989. “Rappels sur l'analyse non standard”, MNS [1989],187–209.

    Google Scholar 

  • Petitot, J., 1990. “Premiers principes métaphysiques d'une Science de la Forme”, Colloque de Cerisy autour de la Critique de la Faculté de Juger, (to appear).

    Google Scholar 

  • Petitot, J., 1990a. “Logique transcendantale, Synthétique a priori et Herméneutique mathématique des objectivités”, Fundamenta Scientiae, 10, 1, 57–84.

    Google Scholar 

  • Petitot, J., 1990b. “Logique transcendantale et Herméneutique mathématique: le problème de l'unité formelle et de la dynamique historique des objectivités scientifiques”, Il pensiero di Giulio Preti nella cultura filosofica del novecento, (F. Minazzi ed.), 155–172, Milano, Franco Angeli.

    Google Scholar 

  • Petitot, J., 1990c. “Note sur la querelle du déterminisme”, La Querelle du Déterminisme, (K. Pomian ed.), 202–227, Paris, Le Débat, Gallimard.

    Google Scholar 

  • Petitot, J., 1991a. “Idéalités mathématiques et Réalité objective. Approche transcendantale”, Hommage à Jean-Toussaint Desanti, (G. Granel ed.), 213–282, Mauvezin, Editions TER.

    Google Scholar 

  • Petitot, J., 1991b. “Continu et Objectivité”, Le Continu mathématique, (J.M.Salanskis, H. Sinaceur eds.), Colloque de Cerisy (to appear).

    Google Scholar 

  • PQG, 1988. Physique quantique et géométrie (Colloque André Lichnerowicz,, D. Bernard, Y. Choquet-Bruhat eds.), Paris, Hermann.

    Google Scholar 

  • Prauss, G., 1980. Einführung in die Erkenntnistheorie, Darmstadt, Wissenschaftliche Buchgesellschaft.

    Google Scholar 

  • Prauss, G., 1981a. “Time, Space and Schematisation”, The Philosophical Forum, XIII, 1, 1–11.

    Google Scholar 

  • Prauss, G., 1981b. “Kants Theorie der ästhetischen Einstellung”, Dialectica, 35, 1-2, 265–281.

    Google Scholar 

  • Quigg, C., 1983. Gauge Theories of the Strong, Weak, and Electromagnetic Interactions, Reading, Benjamin-Cummings.

    Google Scholar 

  • Salanskis, J.M., 1989. “Le potentiel et le virtuel”, MNS [1989], 275-303.

    Google Scholar 

  • Salanskis, J.M., 1991. L'Herméneutique formelle, Paris, Éditions du CNRS.

    Google Scholar 

  • Scheibe, E., 1981. “Invariance and Covariance”, (J. Agassi, R. S. Cohen, eds.), Scientific Philosophy Today, 311–331, Dordrecht, Reidel.

    Google Scholar 

  • Souriau, J.M., 1975. Géométrie symplectique et physique mathématique, Coll. Internat. du C.N.R.S., 237, Paris.

    Google Scholar 

  • Stegmüller, W., 1979. The Structuralist Vieras of Theories, Berlin, New-York, Springer.

    Google Scholar 

  • Vuillemin, J., 1955. Physique et Métaphysique kantiennes, Paris, Presses Universitaires de France.

    Google Scholar 

  • Wang, H., 1987. Reflections on Kurt Gödel, Cambridge, M.I.T Press.

    Google Scholar 

  • Weinstein, A., 1977. Lectures on Symplectic Manifolds, C.B.M.S., Conf. Series, Am. Math. Soc., 29, Providence.

    Google Scholar 

  • Weizsäcker, C.F. von, 1979. Die Einheit der Natur, Munich, Hauser.

    Google Scholar 

  • Weyl, H., 1922. Space — Time — Matter, New-York, Dover.

    Google Scholar 

  • Wiredu, J.E., 1970. “Kants Synthetic A Priori in Geometry and the Rise of Non-Euclidean Geometries”, Kant-Studien, 61, 1, 5–27.

    Google Scholar 

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  1. Séminaire d'Epistémologie des Mathématiques, Ecole des Hautes Etudes en Sciences Sociales, 54, Bd Raspail, 75006, Paris

    Jean Petitot

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  1. Jean Petitot
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Luciano Boi Dominique Flament Jean-Michel Salanskis

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Petitot, J. (1992). Actuality of transcendental æsthetics for modern physics. In: Boi, L., Flament, D., Salanskis, JM. (eds) 1830–1930: A Century of Geometry. Lecture Notes in Physics, vol 402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55408-4_72

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  • DOI: https://doi.org/10.1007/3-540-55408-4_72

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