Foundations of Science

, Volume 19, Issue 1, pp 1–10 | Cite as

Script and Symbolic Writing in Mathematics and Natural Philosophy

Article

Abstract

We introduce the question whether there are specific kinds of writing modalities and practices that facilitated the development of modern science and mathematics. We point out the importance and uniqueness of symbolic writing, which allowed early modern thinkers to formulate a new kind of questions about mathematical structure, rather than to merely exploit this structure for solving particular problems. In a very similar vein, the novel focus on abstract structural relations allowed for creative conceptual extensions in natural philosophy during the scientific revolution. These preliminary reflections are meant to set the stage for the following contributions in this volume.

Keywords

Symbolic writing Algebra Scientific revolution 

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References

  1. Abdeljapoud M. (2002) Le manuscrit mathématique de Jerba: Une pratique des symboles algébriques maghrébins en pleine maturité. Quaderni de Ricerca in Didattica del Guppo di Ricerca Sull’Insegnamento/Apprendimento delle Matematiche 11: 110–173Google Scholar
  2. Bartholomew J. R. (1976) Why was there no scientific revolution in Tokugawa Japan?. Japanese Studies in the History of Science 15: 111–126Google Scholar
  3. Bartholomew J. R. (1993) The Formation of Science in Japan: Building a Research Tradition. Yale University Press, New Haven and LondonGoogle Scholar
  4. Boyer C. (1949) The Concepts of the Calculus. A Critical and Historical Discussion of the Derivative and the Integral. Hafner Pub. Co, New YorkGoogle Scholar
  5. Cajori F. (1925) Leibniz, the master-builder of mathematical notations. Isis 23: 412–429CrossRefGoogle Scholar
  6. Cajori, F. (1928-9). A History of Mathematical Notations (2 vols.), Open Court Publishing, La Salle, Il. (reprinted by Dover, 1993).Google Scholar
  7. De Cruz, H. & De Smedt, J. (2012). Mathematical symbols as epistemic actions. Synthese, (Online first) doi:10.1007/s11229-010-9837-9.
  8. Damerow P. (2006) The origins of writing as a problem of historical epistemology. Cuneiform Digital Library Journal 1: 1–10Google Scholar
  9. Ferrari M. (2000) Sources for the history of the concept of symbol from leibniz to cassirer. In: Ferrari M., Stamatescu I. O. (eds) Symbol and Physical Knowledge. On the Conceptual Structure of Physics. Springer, Heidelberg, pp 3–32Google Scholar
  10. Galileo G. (1957) Discoveries and Opinions of Galileo. Translated with an Introduction and Notes by Stillman Drake. Anchor Books, New YorkGoogle Scholar
  11. Galileo G. (2001) Dialogue Concerning the Two Chief World Systems. Translated and with revised notes by Stillman Drake. The Modern Library, New YorkGoogle Scholar
  12. Gelb I. J. (1952) A Study of Writing: The Foundations of Grammatology. University of Chicago Press, ChicagoGoogle Scholar
  13. Goody J., Watt I. (1963) The consequences of literacy. Comparative Studies in Society and History 5: 304–345CrossRefGoogle Scholar
  14. Heeffer A. (2007) The Tacit Appropriation of Hindu Algebra in Renaissance Practical Arithmetic. Gaņita Bhārāti 29(1-2): 1–60Google Scholar
  15. Heeffer, A., Van Dyck, M. (eds) (2010) Philosophical Aspects of Symbolic Reasoning in Early-modern Mathematics Studies in Logic 26. College Publications, LondonGoogle Scholar
  16. Høyrup J. (2002) Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and its Kin. Springer, HeidelbergCrossRefGoogle Scholar
  17. Høyrup, J. (2010). Hesitating progress: The slow development toward algebraic symbolization in abbacus-and related manuscripts, c. 1300 to c. 1550, In Heeffer and Van Dyck (2010) (Eds.) pp. 3–56.Google Scholar
  18. Kearney H. F. (1964) Origins of the Scientific Revolution. Longmans Green and Co, LondonGoogle Scholar
  19. Knobloch, E. (2010). Leibniz between ars characteristica and ars inveniendi: Unknown news about Cajori’s ‘master-builder of mathematical notations. In Heeffer and Van Dyck (Eds.) pp. 289–302.Google Scholar
  20. Landy, D. (2010). Toward a physics of equations. In Diagrams 2010: The Sixth International Conference the Theory and Application of Diagrams. Portland, Oregon.Google Scholar
  21. Landy D., Goldstone R. L. (2007) Formal notations are diagrams: Evidence from a production task. Memory and Cognition 35(8): 2033–2040CrossRefGoogle Scholar
  22. Mahoney M. S. (1998) The Mathematical Realm of Nature. In: Garber D., Ayers M. (eds) The Cambridge History of Seventeenth-Century Philosophy. Cambridge University Press, Cambridge, pp 702–755Google Scholar
  23. Netz R. (1999) The Shaping of Deduction in Greek Mathematics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  24. Olson D. R. (1996) Towards a psychology of literacy: On the relations between speech and writing. Cognition 60: 83–104CrossRefGoogle Scholar
  25. Osamu, T., Mitsuo, M. (eds) (2003) Selected Mathematical Works of Takebe Katahiro (1664 1739). Wasan Institute, TokyoGoogle Scholar
  26. Ravina M. (1993) Wasan and the physics that wasn’t. Mathematics in the Tokugawa period. Monumenta Nipponica 48(2): 205–224CrossRefGoogle Scholar
  27. Rossi P. (1983) Logic and the Art of Memory. Continuum, LondonGoogle Scholar
  28. Rotman B. (2000) Mathematics as Sign: Writing, Imagining, Counting. Stanford University Press, StanfordGoogle Scholar
  29. Seki, T. (Eds.) (1974). Akira Hirayama, Kazuo Shimodaira and Hideo Hirose Takakazu Seki’s Collected Works, Edited with Explanations. Osaka: Kyoiku Tosho.Google Scholar
  30. Schuster, J. (2000). Descartes opticien: the construction of the law of refraction and the manufacture of its physical reationales 1618–1629. In S. Gaukgroger & J. Schuster (Eds.) Descartes’ Natural Philosophy (pp. 258–312). London: Routledge.Google Scholar
  31. Schuster, J. (2011). Physico-mathematics and the search for causes in Descartes’ optics—1619-1637. Synthese Published online first: 7 December 2011. doi:10.1007/s11229-011-9979-4.
  32. Serfati, M. (2005). La révolution symbolique—La constitution de l’écriture symbolique mathématique. Paris: Pétra.Google Scholar
  33. Stifel, M. (1553). Die Coss C. Rudolff’s mit schönen Exempeln der Coss durch M. Stifel gebessert und sehr gemehrt. Königsperg in Preussen, durch Alexandrum Behm von Luthomisl.Google Scholar
  34. Stifel, M. (1545). Arithmetica Integra a cum præfatione P. Melanchthoni. Nürnberg: Johann Petreius.Google Scholar
  35. Tropfke, J. (1930–40). Geschichte der Elementar-Mathematik in systematischer Darstellung mit besonderer Berücksichtigung der Fachwörter, 4 vols. 3 ed., 1930-40, Vol. I (1930): Rechnen, Vol. II (1933): Allgemeine Arithmetik, Vol. III (1937): Proportionen, Gleichungen, Vol. IV (1940): Ebene Geometrie, Leipzig.Google Scholar
  36. Van Dyck M. (2006) Gravitating towards stability: Guidobaldo’s Aristotelian-Archimedean synthesis. History of Science 54: 373–407Google Scholar
  37. Van Dyck, M. (forthcoming) ‘Argumentandi modus huius scientiae maximè proprius...’ Guidobaldo’s mechanics and the question of mathematical principles. In Gamba, E., Becchi, A. & Bertoloni Meli, D. (Eds.) Mathematiche e tecnica da Urbino all’Europa. Berlin: Edition Open Access Max Planck Research Library for the History and Development of Knowledge.Google Scholar
  38. Yates F. A. (1966) The Art of Memory. Routledge and Kegan Paul, Pimlico LondonGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of Philosophy and Moral ScienceGhent UniversityGhentBelgium

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