Conceptual and Historiographical Foundations—Natural Philosophy, Mixed Mathematics, Physico-mathematics, Method

  • John SchusterEmail author
Part of the Studies in History and Philosophy of Science book series (AUST, volume 27)


This chapter examines a number of conceptual and historiographical issues which frame the entire project. First of all, a model is constructed for how the increasingly competitive and turbulent culture of natural philosophizing worked in the era of Descartes. This model also addresses the question of the place of the subordinate mixed mathematical sciences, and the meaning Descartes, and others, attached to the idea of a physico-mathematics, that would render those mixed sciences more properly ‘natural philosophical’. Also presented are the generic rules of construction and contestation which governed natural philosophizing; a model for dealing with the problem of ‘external or contextual’ drivers of natural philosophical utterance; an heuristic model for assessing the nature and degree of ‘systematicity’ of a natural philosophy; and an outline of the main phases in the trajectory of natural philosophizing in the period of the Scientific Revolution, so that Descartes’ location and role can be better identified. Additionally, the basis is set down for the deconstruction of Descartes’ method, which takes place in  Chap. 6.


Seventeenth Century Sixteenth Century Geometrical Optic Scientific Revolution Scientific Tradition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Works of Descartes and Their Abbreviations

  1. AT  =  Oeuvres de Descartes (revised edition, 12 vols.), edited by C. Adam and P. Tannery (Paris, 1964–76). References are by volume number (in roman) and page number (in Arabic).Google Scholar
  2. SG  =  The World and Other Writings, edited and translated by Stephen Gaukroger (Cambridge,1998).Google Scholar
  3. MM  =  René Descartes, The Principles of Philosophy, translated by V. R. Miller and R. P. Miller (Dordrecht, 1991)Google Scholar
  4. MSM  =  Rene Descartes, Le Monde, ou Traité de la lumière, translated by Michael S. Mahoney (New York, 1979).Google Scholar
  5. CSM(K)  =  The Philosophical Writings Of Descartes, 3 vols., translated by John Cottingham, Robert Stoothoff, and Dugald Murdoch, and (for vol. 3) Anthony Kenny, (Cambridge, 1988) References are by volume number (in roman) and page number (in arabic).Google Scholar
  6. HR  =  The Philosophical Works of Descartes, vol I translated by E.S. Haldane and G.R.T. Ross (Cambridge, 1968 [1st ed. 1911])Google Scholar


  1. Aldridge, Larissa. 2009. ‘Kaleidoscopic natural theology: The dynamics of natural theological discourse in seventeenth and early eighteenth century-England,’ Unpublished Ph.D. dissertation. University of New South Wales.Google Scholar
  2. Anstey, Peter. 2000. Descartes’ cardiology and its reception in english physiology. In Descartes’ natural philosophy, ed. S. Gaukroger, J.A. Schuster, and J. Sutton, 420–444. London: Routledge.Google Scholar
  3. Anstey, Peter. 2005. Experimental versus speculative natural philosophy. In The science of nature in the seventeenth century: Changing patterns of early modern natural philosophy, ed. Peter Anstey and John Schuster, 215–242. Dordrecht: Springer.Google Scholar
  4. Anstey, Peter, and John Schuster. 2005. Introduction. In The science of nature in the seventeenth century: Patterns of change in early modern natural philosophy, ed. P. Anstey and J.A. Schuster, 1–7. Dordrecht: Springer.Google Scholar
  5. Arieu, R. 1999. Descartes and the late scholastics. Ithaca: Cornell Universiety Press.Google Scholar
  6. Bachelard, Gaston. 1949. Le rationalisme appliqué. Paris: Presses Universitaires de France.Google Scholar
  7. Bachelard, G. 1975a. Le Nouvel Esprit Scientifique, 13th ed. Paris: Presses Universitaires de France.Google Scholar
  8. Bachelard, G. 1975b. La Formation de l’Esprit Scientifique, 9th ed. Paris: Vrin.Google Scholar
  9. Barnes, Barry. 1982. T.S.Kuhn and social science. London: MacMillan.Google Scholar
  10. Boschiero, Luciano. 2007. Experiment and natural philosophy in seventeenth century Tuscany: The history of the Accademia del Cimento. Dordrecht: Springer.Google Scholar
  11. Bourdieu, Pierre. 1971. Intellectual field and creative project. In Knowledge and control: New directions for the sociology of education, ed. M.F.D. Young, 161–188. London: Collier-MacMillan.Google Scholar
  12. Bourdieu, Pierre. 1971a. Systems of education and systems of thought. In Knowledge and control: New directions for the sociology of education, ed. M.F.D. Young, 189–207. London: Collier-MacMillan.Google Scholar
  13. Bourdieu, Pierre. 1975b. The specificity of the scientific field and the social conditions of the progress of reason. Social Science Information 14: 19–47.Google Scholar
  14. Brannigan, Augustine. 1980. Naturalistic and sociological models of the problem of scientific discovery. The British Journal of Sociology 31: 559–573.Google Scholar
  15. Brannigan, Augustine. 1981. The social basis of scientific discoveries. Cambridge: Cambridge University Press.Google Scholar
  16. Brundell, Barry. 1987. Pierre Gassendi. Dordrecht: Reidel.Google Scholar
  17. Clark, William. 1992. The scientific revolution in the German nations. In The scientific revolution in national context, ed. Roy Porter and Mikulas Teich, 90–114. Cambridge: CUP.Google Scholar
  18. Clarke, Desmond. 1989. Occult powers and hypotheses: Cartesian natural philosophy under Louis XIV. Oxford: Clarendon.Google Scholar
  19. Clarke, Desmond. 2006. Descartes, a biography. Cambridge: CUP.Google Scholar
  20. Cohen, H.Floris. 1994. The scientific revolution: A historiographical inquiry. Chicago: University of Chicago Press.Google Scholar
  21. Cohen, H.Floris. 2005. The onset of the scientific revolution: Three near–simultaneous transformations. In The science of nature in the seventeenth century: Changing patterns of early modern natural philosophy, ed. Peter Anstey and John Schuster, 1–33. Dordrecht: Springer.Google Scholar
  22. Cohen, H.Floris. 2010. How modern science came into the world: Four civilizations, One 17th–century breakthrough. Amsterdam: Amsterdam University Press.Google Scholar
  23. Collins, Harry. 1985. Changing order. London: Sage.Google Scholar
  24. Crombie, A.C. 1953. Robert Grosseteste and the origins of experimental science, 1100–1700. Oxford: Clarendon.Google Scholar
  25. Cunningham, A. 1985. Fabricius and the “Aristotle project” in anatomical teaching and research at Padua. In The medical renaissance of the sixteenth century, ed. A. Wear et al., 195–222. Cambridge: CUP.Google Scholar
  26. Cunningham, Andrew. 1988. Getting the game right: Some plain words on the identity and invention of science. Studies in History and Philosophy of Science 19: 365–389.Google Scholar
  27. Cunningham, Andrew. 1991. How the Principia got its name; or, taking natural philosophy seriously. History of Science 24: 377–392.Google Scholar
  28. Cunningham, Andrew, and Perry Williams. 1993. De-centring the ‘big picture’: The Origins of Modern Science and the modern origins of science. British Journal for the History of Science 26: 407–432.Google Scholar
  29. de Dainville, F. 1954. Enseignement des mathématiques dans les Collèges Jesuites de France au XVIIe et XVIIIe siècles. Révue d’Histoire des Sciences 7: 6–21.Google Scholar
  30. Dear, Peter. 1991. The church and the new philosophy. In Science, culture and popular belief in renaissance Europe, ed. S. Pumfrey, P.L. Rossi, and M. Slawinski, 119–139. Manchester: Manchester University Press.Google Scholar
  31. Dear, Peter. 1995. Discipline and experience: The mathematical way in the scientific revolution. Chicago: Chicago University Press.Google Scholar
  32. Dear, Peter. 2001a. Revolutionizing the sciences: European knowledge and its ambitions, 1500–1700. Princeton: Princeton University Press.Google Scholar
  33. Dear, Peter. 2001b. Religion, science and natural philosophy: Thoughts on Cunningham’s thesis. Studies in History and Philosophy of Science 32: 377–386.Google Scholar
  34. Debus, A.G. 1970. Harvey and Fludd: The irrational factor in the rational science of the seventeenth century. Journal of the History of Biology 3: 81–105.Google Scholar
  35. Debus, A.G. 1977. The chemical philosophy, vol. I. New York: Dover.Google Scholar
  36. Des Chene, D. 1996. Physiologia: Natural philosophy in late Aristotelian and Cartesian thought. Ithaca: Cornell University Press.Google Scholar
  37. Desmond, A. 1982. Archetypes and ancestors: Paleontology in Victorian London, 1850–1875. London: Blond & Briggs.Google Scholar
  38. Dibon, Paul. 1954. La Philosophie neérlandaise au siècle d’or. Vol I, L’enseignement philosophique dans les universités a l’époque précartesienne, 1575–1650. Paris: Elsevier.Google Scholar
  39. Easlea, Brian. 1980. Witch-hunting, magic and the new philosophy: An introduction to the debates of the scientific revolution 1450–1750. Sussex: Harvester Press.Google Scholar
  40. Feyerabend, P.K. 1975. Against method. London: New Left Books.Google Scholar
  41. Foucault, Michel. 1972. The archaeology of knowledge. Trans. Alan Sheridan. London: Tavistock.Google Scholar
  42. Frank, Robert G. 1980. Harvey and the english physiologists: Scientific ideas and social interaction. Berkeley: University of California Press.Google Scholar
  43. Friedrich, Carl. 1962. The age of the baroque: 1610–1660. (1st ed 1952). New York: Harper & Row.Google Scholar
  44. Garber, Daniel. 1992. Descartes’ metaphysical physics. Chicago: University of Chicago Press.Google Scholar
  45. Gascoigne, John. 1990. A reappraisal of the role of universities in the scientific revolution. In Reappraisals of the scientific revolution, ed. D.C. Lindberg and R.S. Westman, 207–260. Cambridge: Cambridge University Press.Google Scholar
  46. Gaukroger, S. 1976. Bachelard and the problem of epistemological analysis. Studies in History and Philosophy of Science 7: 189–244.Google Scholar
  47. Gaukroger, Stephen. 1995. Descartes: An intellectual biography. Oxford: OUP.Google Scholar
  48. Gaukroger, Stephen. 2006. The emergence of a scientific culture. Oxford: Clarendon.Google Scholar
  49. Gaukroger, S., and J.A. Schuster. 2002. The hydrostatic paradox and the origins of Cartesian dynamics. Studies in History and Philosophy of Science 33: 535–572.Google Scholar
  50. Gieryn, Thomas. 1983. Boundary-work and the demarcation of science from non-science: Strains and interests in professional ideologies of scientists. American Sociological Review 48: 781–795.Google Scholar
  51. Gilson, E. (ed.). 1947. René Descartes, Discours de la Méthode: Texte et Commentaire. Paris: Vrin.Google Scholar
  52. Gouhier, H. 1958. Les Premières Pensées de Descartes. Paris: Vrin.Google Scholar
  53. Grayling, A.C. 2005. Descartes: The life of René Descartes and its place in his times. London: Free Press.Google Scholar
  54. Hannaway, O. 1975. The chemists and the word: The didactic origins of chemistry. Baltimore: Johns Hopkins University Press.Google Scholar
  55. Harrison, Peter. 2000. The influence of Cartesian cosmology in England. In Descartes’ natural philosophy, ed. S. Gaukroger, J.A. Schuster, and J. Sutton, 168–192. London: Routledge.Google Scholar
  56. Harrison, Peter. 2002. Voluntarism and early modern science. History of Science 40: 63–89.Google Scholar
  57. Harrison, Peter. 2005. Physico-theology and the mixed sciences: The role of theology in early modern natural philosophy. In Early modern natural philosophy: Patterns of change in the culture of natural philosophy in the seventeenth century, ed. Peter Anstey and J.A. Schuster, 165–184. Dordrecht: Springer.Google Scholar
  58. Hattab, Helen. 2005. From mechanics to mechanism: The Quaestiones Mechanicae and Descartes’ physics. In The science of nature in the seventeenth century: Changing patterns of early modern natural philosophy, ed. Peter Anstey and John Schuster, 99–129. Dordrecht: Springer.Google Scholar
  59. Henry, John. 2002. The scientific revolution and the origins of modern science, 2nd ed. MacMillan: London.Google Scholar
  60. Hessen, Boris. 1931. The social and economic roots of Newton’s “Principia”. In Science at the crossroads, papers presented to the international congress of the history of science and technology held in London from June 29th to July 3rd, 1931, by the delegates of the USSR, 149–212. London: Kniga (England) Ltd.Google Scholar
  61. Knorr-Cetina, Karin. 1981. The manufacture of knowledge: An essay on the constructivist and conventional character of knowledge and cognition. Oxford: Pergamon.Google Scholar
  62. Koyré, A. 1939, Eng. Trans. 1978. Etudes Galiléenes. Paris: Hermann & Cie. English trans. Galileo Studies. Trans. J. Mepham. Hassocks, Sussex: Harvester.Google Scholar
  63. Koyré, Alexandre. 1956. The origins of modern science. Diogenes 16: 1–22.Google Scholar
  64. Koyré, A. 1969. Metaphysics and measurement: Essays in scientific revolution. London: Chapman & Hall.Google Scholar
  65. Kuhn, Thomas S. 1970. The structure of scientific revolutions, 2nd ed. Chicago: University of Chicago Press.Google Scholar
  66. Kuhn, Thomas S. 1977. The essential tension: Selected studies in scientific tradition and change. Chicago: University of Chicago Press.Google Scholar
  67. Laird, W.R. 1986. The scope of renaissance mechanics. Osiris 2: 43–68.Google Scholar
  68. Lakatos, I. 1978. Falsification and the methodology of scientific research programmes. In Imre Lakatos: Philosophical papers, vol. I, ed. J. Worrall and G. Currie, 8–101. Cambridge: C.U.P.Google Scholar
  69. Latour, Bruno, and Steve Woolgar. 1979. Laboratory life, the social construction of scientific facts. London: Sage.Google Scholar
  70. Lecourt, D. 1975. Marxism and epistemology: Bachelard, Canguilhem, Foucault. Trans. B. Brewster. London: New Left Books.Google Scholar
  71. Lenoble, Robert. 1943. Mersenne ou la naissance du mécanisme. Paris: J.Vrin.Google Scholar
  72. Lindberg, David. 1992. The beginnings of Western science. Chicago: University of Chicago Press.Google Scholar
  73. Maclean, I. Ed. and Trans. 2006. René Descartes: A discourse on method. Oxford: OUP.Google Scholar
  74. Maclean, I. 2007. Logic, signs and nature in the renaissance. Cambridge: CUP.Google Scholar
  75. Maravall, José Antonio. 1973. The culture of the baroque: Analysis of a historical structure. English Trans, 1986. Minneapolis: University of Minnesota Press.Google Scholar
  76. Mulkay, Michael. 1979. Science and the sociology of knowledge. London: George Allen & Unwin.Google Scholar
  77. Pagel, W. 1982. Joan Baptista Van Helmont. Cambridge: CUP.Google Scholar
  78. Pickering, Andrew. 1995. The mangle of practice: Time, agency and science. Chicago: University of Chicago Press.Google Scholar
  79. Popkin, Richard. 1964. The history of scepticism from Erasmus to Spinoza. Berkeley: University of California.Google Scholar
  80. Popper, K.R. 1959. The logic of scientific discovery. London: Hutchinson.Google Scholar
  81. Priestley, J. 1767. The history and present state of electricity with original experiments. London: J. Dodsley et al.Google Scholar
  82. Randall, J.H. 1961. The school of Padua and the emergence of modern science. Padua: Editrice Antenore.Google Scholar
  83. Rattansi, P.M. 1963. Paracelsus and the Puritan revolution. Ambix 11: 24–34.Google Scholar
  84. Rattansi, P.M. 1964. The Helmontian-Galenist controversy in seventeenth century England. Ambix 12: 1–23.Google Scholar
  85. Ravetz, J.R. 1971. Scientific knowledge and its social problems. Oxford: OUP.Google Scholar
  86. Ravetz, J.R. 1975. ‘Science, history of’, Encyclopedia Britannica. 16: 366–372Google Scholar
  87. Rief, Patricia. 1969. The textbook tradition in natural philosophy, 1600–1650. Journal of the History of Ideas 30: 17–32.Google Scholar
  88. Rix, Mark. 1997. Discipline and threatened punishment: The theory of nuclear deterrence and the discipline of strategic studies, 1946–1960’. Unpublished Ph.D. dissertation, University of Wollongong, Department of Science and Technology Studies.Google Scholar
  89. Rodis-Lewis, G. 1992. Descartes’ life and the development of his philosophy. In The Cambridge companion to Descartes, ed. J. Cottingham, 21–57. Cambridge: CUP.Google Scholar
  90. Rose, Paul Lawrence, and Stillman Drake. 1971. The Pseudo-Aristotelian Questions of mechanics in renaissance culture. Studies in the Renaissance 18: 65–104.Google Scholar
  91. Rossi, Paolo. 1970. Philosophy, technology and the arts in the early modern era. New York: Harper and Row.Google Scholar
  92. Rudwick, M.J.S. 1985. The great Devonian Controversy: The shaping of scientific knowledge among gentlemanly specialists. Chicago: University of Chicago Press.Google Scholar
  93. Sahlins, Marshall. 1993. Goodbye to tristes tropes: Ethnography in the context of modern world history. The Journal of Modern History 65: 1–25.Google Scholar
  94. Sarton, G. 1921-22. Introduction to the history and philosophy of science. Isis 4: 23–31.Google Scholar
  95. Sarton, G. 1924. The new humanism. Isis 6: 9–34.Google Scholar
  96. Schaffer, Simon. 1986. Scientific discoveries and the end of natural philosophy. Social Studies of Science 16: 387–420.Google Scholar
  97. Schmitt, Charles. 1973. Towards a reassessment of renaissance Aristotelianism. History of Science 11: 159–193.Google Scholar
  98. Schuster, John. 1979. Kuhn and Lakatos revisited. British Journal for the History of Science 12: 301–317.Google Scholar
  99. Schuster, J.A. 1986. Cartesian method as mythic speech: A diachronic and structural analysis. In The politics and rhetoric of scientific method, ed. J.A. Schuster and R.R. Yeo, 33–95. Dordrecht: D. Reidel.Google Scholar
  100. Schuster, J.A. 1990. The scientific revolution. In The companion to the history of modern science, ed. R.C. Olby, G.N. Cantor, J.R.R. Christie, and M.J.S. Hodge, 217–242. London: Routledge.Google Scholar
  101. Schuster, J.A. 1993. Whatever should we do with Cartesian method: Reclaiming Descartes for the history of science. In Essays on the philosophy and science of René Descartes, ed. S. Voss, 195–223. Oxford: OUP.Google Scholar
  102. Schuster, John. 1995. Descartes Agonistes: New tales of Cartesian mechanism. Perspectives on Science 3: 99–145.Google Scholar
  103. Schuster, J.A. 1995a. An introduction to the history and social studies of science Open Learning Australia. This work may be found on my website
  104. Schuster, J.A. 2000. Descartes Opticien: The construction of the law of refraction and the manufacture of its physical rationales, 1618–1629. In Descartes’ natural philosophy, ed. S. Gaukroger, J.A. Schuster, and J. Sutton, 258–312. London: Routledge.Google Scholar
  105. Schuster, John. 2000a. Internalist and externalist historiographies of the scientific revolution. In Encyclopedia of the scientific revolution, ed. W. Applebaum. New York: Garland Publishing.Google Scholar
  106. Schuster, J.A. 2002. L’Aristotelismo e le sue Alternative’. In La Rivoluzione Scientifica, ed. D. Garber, 337–357. Rome: Instituto della Enciclopedia Italiana.Google Scholar
  107. Schuster, J.A. 2005. “Waterworld”: Descartes’ vortical celestial mechanics: A Gambit in the natural philosophical contest of the early seventeenth century. In The science of nature in the seventeenth century: Changing patterns of early modern natural philosophy, ed. Peter Anstey and John Schuster, 35–79. Dordrecht: Springer.Google Scholar
  108. Schuster, J.A. 2012. ‘Physico-mathematics and the search for causes in Descartes’ Optics—1619–1637’, Synthèse 185:467–499. [published online Dec. 2011 DOI  10.1007/s11229-011-9979-4].
  109. Schuster, J.A. 2012a. What was the relation of Baroque culture to the trajectory of Early Modern Natural Philosophy? In O.Gal and R. Chen-Morris eds. Science in the Age of the Baroque, Archives internationales d’histoire des ideés 209: 1–35.Google Scholar
  110. Schuster, J.A., and R.R. Yeo (eds.). 1986a. The politics and rhetoric of scientific method. Dordrecht: D. Reidel.Google Scholar
  111. Schuster, J.A., and Graeme Watchirs. 1990. Natural philosophy, experiment and discourse: Beyond the Kuhn/Bachelard problematic. In Experimental inquiries: historical, philosophical and social studies of experimentation in science, ed. H.E. Le Grande, 1–47. Dordrecht: Kluwer.Google Scholar
  112. Schuster, John, and Alan B.H. Taylor. 1996. Seized by the spirit of modern science. Metascience 9: 9–26.Google Scholar
  113. Schuster, John, and Alan B.H. Taylor. 1997. Blind trust: The gentlemanly origins of experimental science. Social Studies of Science 27: 503–536.Google Scholar
  114. Shapin, Steven. 1992. Discipline and bounding: The history and sociology of science as seen through the externalism-internalism debate. History of Science 30: 333–369.Google Scholar
  115. Shapin, S., and S. Schaffer. 1985. Leviathan and the air-pump: Hobbes, Boyle and the experimental life. Princeton: Princeton University Press.Google Scholar
  116. Singer, C. (ed.). 1917–21. Studies in the history and method of science. Oxford: Clarendon Press.Google Scholar
  117. Sirven, J. 1928. Les années d’apprentissage de Descartes. Albi: Imprimerie Coopérative du Sud-Ouest.Google Scholar
  118. Smith, Russell. 2008. Optical reflection and mechanical rebound: The shift from analogy to axiomatization in the seventeenth century, Part 1. British Journal for the History of Science 41: 1–18.Google Scholar
  119. Toulmin, Stephen. 1990. Cosmopolis, the hidden agenda of modernity. New York: The Free Press.Google Scholar
  120. Watson, Richard. 2007. Cogito, Ergo Sum, the life of René Descartes. Boston: Godine.Google Scholar
  121. Wear, Andrew. 1983. William Harvey and the “way of the anatomists”. History of Science 53: 223–249.Google Scholar
  122. Wear, A. 1990. The heart and the blood from Vesalius to Harvey. In The companion to the history of modern science, ed. R.C. Olby, G.N. Cantor, J.R.R. Christie, and M.J.S. Hodge, 571–574. London: Routledge.Google Scholar
  123. Whewell, W. 1837. History of the inductive sciences, vol. I. London: John W. Parker.Google Scholar
  124. Whewell, W. 1980. The philosophy of the inductive sciences. London: J. W. Parker.Google Scholar
  125. Zilsel, Edgar. 1942a. The sociological roots of science. The American Journal of Sociology 47: 544–562.Google Scholar
  126. Zilsel, Edgar. 1942b. The genesis of the concept of physical law. Philosophical Review 51: 245–279.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht. 2012

Authors and Affiliations

  1. 1.Campion CollegeSydneyAustralia
  2. 2.Unit for History and Philosophy of ScienceUniversity of SydneySydneyAustralia

Personalised recommendations