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Synthese

pp 1–24 | Cite as

Structure-preserving representations, constitution, and the relative a priori

  • Thomas Mormann
S.I.: Modeling and Representation
  • 67 Downloads

Abstract

The aim of this paper is to show that a comprehensive account of the role of representations in science should reconsider some neglected theses of the classical philosophy of science proposed in the first decades of the twentieth century. More precisely, it is argued that the representational accounts of Helmholtz and Hertz, in which the concept of structure-preservation plays an essential role, still deserve attention for contemporary debates. Following Reichenbach, structure-preserving representations provide a useful device for formulating an up-to-date version of a (relativized) Kantian a priori. An essential feature of modern scientific representations is their mathematical character. That is, representations can be conceived as (partially) structure-preserving maps or functions. This observation suggests an interesting but neglected perspective on the history and philosophy of this concept, namely, that structure-preserving representations are closely related to a priori elements of scientific knowledge. Reichenbach’s early theory of a relativized constitutive but non-apodictic a priori component of scientific knowledge provides a further elaboration of Kantian aspects of scientific representation. To cope with the dynamic aspects of the evolution of scientific knowledge, Cassirer proposed a re-interpretation of the concept of representation that conceived of a particular representation as only one phase in a continuous process determined by pragmatic considerations. Pragmatic aspects of representations are further elaborated in the classical account of C.I. Lewis and the more modern of Hasok Chang who characterized in certain relativized representational a priori assumptions as pragmatically justified metaphysical arguments.

Keywords

Representation Relative a priori Structure preservation Ernst Cassirer Hasok Chang Hans Reichenbach Clarence Irving Lewis 

References

  1. Awodey, S. (2006). Category theory. Oxford: Oxford University Press.CrossRefGoogle Scholar
  2. Baldwin, T. (2007). C.I. Lewis: Pragmatism and analysis. In M. Beaney (Ed.), The analytic turn: Analysis in early analytic philosophy and phenomenology (pp. 178–195). London: Routledge.Google Scholar
  3. Bell, J. L. (1986). From absolute to local mathematics. Synthese, 69, 409–426.CrossRefGoogle Scholar
  4. Boniolo, G. (2007). On scientific representations: From Kant to a new philosophy of science. Basingstoke: Palgrave-MacMillan.CrossRefGoogle Scholar
  5. Carnap, R. (1928). Der logische Aufbau der Welt, Berlin, Weltkreis Verlag. Second edition Hamburg, Meiner (R. George as The Logical Structure of the World, Trans.). Berkeley and Los Angeles: University of California Press (Aufbau).Google Scholar
  6. Cassirer, E. (1907). Kant und die moderne Mathematik. Kant-Studien, 12, 1–49.CrossRefGoogle Scholar
  7. Cassirer, E. 1910 (1953). Substance and function. New York: Dover.Google Scholar
  8. Cassirer, E. 1956 (1937). Determinism and indeterminism in modern physics. Historical and Systematic Studies. New Haven: Yale University Press.Google Scholar
  9. Chang, H. (2008). Contingent transcendental arguments for metaphysical principles. In M. Massimi (Ed.), Kant and philosophy of science today (pp. 113–133). London: Royal Institute of Philosophy. (Supplement 63).Google Scholar
  10. Coffa, A. (1991). The semantic tradition from Kant to Carnap. In L. Wessels (Ed.), To the Vienna Station. Cambridge: Cambridge University Press.Google Scholar
  11. Duhem, P. 1954 (1906). The aim and structure of physical theory. Princeton: Princeton University Press.Google Scholar
  12. French, S. (2014). The structure of the world, metaphysics and representation. Oxford: Oxford University Press.CrossRefGoogle Scholar
  13. Friedman, M. (1997). Helmholtz’ Zeichentheorie and Schlick’s Allgemeine Erkenntnislehre: Early logical empiricism and its Nineteenth-Century background. Philosophical Topics, 25, 19–50.CrossRefGoogle Scholar
  14. Friedman, M. (1999a). Reconsidering logical positivism. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  15. Friedman, M. (1999b). Geometry, convention, and the relativized a priori: Reichenbach, Schlick, and Carnap. In M. Friedman (Ed.), Reconsidering logical positivism (pp. 59–71). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  16. Friedman, M. (2001). Dynamics of reason. Stanford, CA: CSLI Publications.Google Scholar
  17. Giere, R. (2004). How models are used to represent reality. Philosophy of Science, 71(5), 742–752.CrossRefGoogle Scholar
  18. Giere, R. N. (2006). Scientific perspectivism. Chicago: Chicago University Press.CrossRefGoogle Scholar
  19. Gierz, G., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislove, M. W., & Scott, D. S. (2005). Continuous lattices and domains. Cambridge: Cambridge University Press.Google Scholar
  20. Hacking, I. (1983). Representing and intervening. Introductory Topics in the Philosophy of Natural Science. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  21. Hacking, I. (2007). On not being a pragmatist. In C. Misak (Ed.), New pragmatists (pp. 32–49). Oxford: Clarendon Press.Google Scholar
  22. Heidelberger, M. (1998). From Helmholtz’s philosophy of science to Hertz’s picture theory. In D. Baird, R. I. G. Hughes, & A. Nordmann (Eds.), Heinrich Hertz classical physicist, modern philosopher, Boston studies in the philosophy of science (Vol. 198, pp. 9–24). Boston: Springer.Google Scholar
  23. Hertz, H. (1894). Die Prinzipien der Mechanik in neuem Zusammenhange dargestellt. Leipzig: Barth. Gesammelte Werke 3 (1910). Translated as The principles of mechanics presented in a new form. London: Macmillan.Google Scholar
  24. Johnstone, P. (1982). Stone spaces. Cambridge: Cambridge University Press.Google Scholar
  25. Kant, I. 1998 (1787). Critique of pure reason. Cambridge: Cambridge University Press.Google Scholar
  26. Kuhn, T. (1962). The structure of scientific revolutions (2nd ed.). Chicago: University of Chicago Press, 1970.Google Scholar
  27. Lakoff, G. (1987). Women, fire, and dangerous things: What categories reveal about the mind. Chicago: The University of Chicago Press.CrossRefGoogle Scholar
  28. Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.Google Scholar
  29. Lewis, C. I. (1922). A pragmatic conception of the a priori. Journal of Philosophy, 20, 169–177. (Reprinted in Lewis 1970, 231–239).CrossRefGoogle Scholar
  30. Lewis, C. I. (1926). The pragmatic element in knowledge. Publications in philosophy (Vol. 6, pp. 205–227). California: University of California. (reprinted in Lewis 1970, 240–257).Google Scholar
  31. Lewis, C. I. 1929 (1956). Mind and the world order: Outline of a theory of knowledge. New York: Dover.Google Scholar
  32. Lewis, C. I. (1929). Mind and the world order: Outline of a theory of knowledge. New York: Dover.Google Scholar
  33. Lewis, C. I. (1946). An analysis of knowledge and valuation. Chicago: Open Court.Google Scholar
  34. Lewis, C. I. (1970). In J. D. Goheen, & J. L. Motherhead (Eds.), Collected papers of clarence Irving Lewis. Stanford: Stanford University Press.Google Scholar
  35. Lützen, J. (2005). Mechanistic images in geometric form, Heinrich Hertz’ Principles of Mechanics. Oxford: Oxford University Press.CrossRefGoogle Scholar
  36. Mac Lane, S. (1986). Mathematics: Form and function. Berlin: Springer.CrossRefGoogle Scholar
  37. Majer, U. (1998). Heinrich Hertz’s picture-conception of theories: Its elaboration by Hilbert, Weyl, and Ramsey. In D. Baird, R. I. G. Hughes, & A. Nordmann (Eds.), Heinrich Hertz. Classical physicist, modern philosopher, Boston studies in the philosophy of science (Vol. 198, pp. 225–245). Berlin: Springer.Google Scholar
  38. Misak, C. (2013). The American pragmatists. Oxford: Oxford University Press.Google Scholar
  39. Mormann, T. (2012a). Toward a theory of the pragmatic a priori. In R. Creath (Ed.), Rudolf Carnap and the legacy of logical empiricism, Vienna circle Institute yearbook (Vol. 16, pp. 11–132). Berlin: Springer.Google Scholar
  40. Mormann, T. (2012b). A place for pragmatism in the dynamics of reason? Studies in History and Philosophy of Science Part A, 43(1), 27–37.CrossRefGoogle Scholar
  41. Murphey, G. M. (2005). C.I. Lewis. The last great pragmatist. New York: State University Press of New York.Google Scholar
  42. Oberdan, T. (2015). From Helmholtz to Schlick: The evolution of the sign-theory of perception. Studies in History and Philosophy of Science, 50, 35–43.CrossRefGoogle Scholar
  43. Padovani, F. (2011). Relativizing the relativized a priori: Reichenbach’s axioms of coordination divided. Synthese, 181, 41–62.CrossRefGoogle Scholar
  44. Redhead, M. (1975). Symmetry in intertheory relations. Synthese, 32, 77–112.CrossRefGoogle Scholar
  45. Reichenbach, H. (1920). Relativitätstheorie und Erkenntnis A priori. Berlin: Springer. (Maria Reichenbach as The theory of relativity and a priori knowledge, 1965, Trans.). Berkeley: University of California Press.Google Scholar
  46. Reichenbach, H. (1924). Axiomatik der relativistischen Raum-Zeit-Lehre. Braunschweig: Vieweg. (M. Reichenbach as Axiomatization of the theory of relativity, 1969, Trans.). Los Angeles: University of California Press.Google Scholar
  47. Reichenbach, H. (1928). Philosophie der Raum-Zeit-Lehre. Berlin: de Gruyter. (M. Reichenbach & J. Freund as The philosophy of space and time, 1969, Trans). New York: Dover.Google Scholar
  48. Rheinberger, H.-J. (2010). On historicizing epistemology. An essay. Stanford: Stanford University Press.Google Scholar
  49. Rorty, R. (1991). Objectivity, relativism, and truth. Philosophical papers (Vol. 1). Cambridge: Cambridge University Press.Google Scholar
  50. Rorty, R. (1993). An antirepresentationalist view: Comments on Richard Miller, van Fraassen/Sigman, and Churchland. In G. Levine (Ed.), Realism and representation (pp. 124–133). Madison, WI: The University of Wisconsin Press.Google Scholar
  51. Rosenthal, S. B. (2007). CI Lewis in focus. The pulse of pragmatism. Bloomington, IN: Indiana University Press.Google Scholar
  52. Ryckman, T. (2005). The reign of relativity. Philosophy in physics 1915–1925. New York: Oxford University Press.CrossRefGoogle Scholar
  53. Sciortino, L. (2017). On Ian Hacking’s Notion of Style of Reasoning. Erkenntnis, 82, 243–264.CrossRefGoogle Scholar
  54. van Fraassen, B. (2006). Scientific representation. Paradoxes of perspectives. Oxford: Clarendon Press.Google Scholar
  55. Von Helmholtz, H. (1878). Über die Tatsachen, die der Geometrie zugrunde liegen (On the facts underlying geometry). In Helmholtz (1977), pp. 39–58.Google Scholar
  56. Von Helmholtz, H. (1977). Epistemological writings. The Paul Hertz/Moritz Schlick centenary edition of 1921, with notes and commentary by the editors (Malcolm F. Lowe, Trans.), Boston Studies in the Philosophy of Science, (Vol. 37). Dordrecht: Reidel.Google Scholar
  57. Whitehead, A. N. 1929 (1985). In D. R. Griffin & D. W. Sherburne (Eds.), Process and reality, corrected edition. New York: The Free Press.Google Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Logic and Philosophy of ScienceUniversity of the Basque Country UPV/EHUDonostia-San SebastianSpain

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