“The Philosophers and the Machine”: Philosophy of Mathematics and History of Science in Alexandre Koyré

  • Mauro L. Condé


This study examines the influence of Koyré’s philosophy of mathematics on his later history of science. This chapter focuses on a topic that has been almost unexamined by Koyré’s commentators, his first papers on the foundations of mathematics (which present his criticism of Bertrand Russell’s paradox), to establish a link between Koyré’s mathematical realism – present in his preoccupation with the foundations of mathematics – and his later history of science. Based on this link, I reassess an old controversy: “the philosophers and the machine”, as it is called by Koyré, or the problem of theoria versus praxis. Finally, I attempt to understand the extent to which Koyré’s internalism, which originates in this controversy, continues to raise important issues, such as the autonomy of science, in the face of sociological interpretations of science.


Koyré Philosophy of mathematics History of science Internalism Theoria Praxis 


  1. Bar–Hillel J (1947) The revival of the liar. Philosophy and Phenomenological Research 8:245–253.CrossRefGoogle Scholar
  2. Black M (1948) Review of Koyré, Epimenide le menteur. The Journal of Symbolic Logic 8:146–147.CrossRefGoogle Scholar
  3. Elkana Y (1987) Alexandre Koyré: between the history of ideas and sociology of disembodied knowledge. History and Technology 4:115-148.CrossRefGoogle Scholar
  4. Frege G ([1967] 1902) Letter to Russell. In Heijenoort 1967, p.128.Google Scholar
  5. Haddock G (2006) Husserl’s philosophy of mathematics: its origin and relevance. Husserl Studies 22:193-222.CrossRefGoogle Scholar
  6. Heijenoort J (1967) From Frege to Gödel: a source book in mathematical logic, 1879–1931. Harvard University Press, Cambridge.Google Scholar
  7. Koyré A (1912) Sur les nombres de M. Russell. Revue de Métaphysique et de Morale 20:722–4. English Translation in Russell 1992, pp. 451–452.Google Scholar
  8. Koyré A (1922) Bemerkungen zu den Zenonischen Paradoxen. Jahrbuch für Philosophie und Phänomenologische Forschung 5:603–628. French Translation in Koyré, 1971, pp. 09–35.Google Scholar
  9. Koyré A (1946) The Liar. Philosophy and Phenomenological Research 6:344–362.CrossRefGoogle Scholar
  10. Koyré A (1947) Epimenide le menteur (Ensemble et catégories). Hermann, Paris.Google Scholar
  11. Koyré A (1948) Manifold and categories. Philosophy and Phenomenological Research 9:1–20.CrossRefGoogle Scholar
  12. Koyré A (1965) Newtonian studies. Harvard University Press, Cambridge.CrossRefGoogle Scholar
  13. Koyré A ([1966] 1939) Études galileennes. Hermann, Paris.Google Scholar
  14. Koyré A ([1971] 1961) Études d’histoire de la pensée philosophique. Gallimard, Paris.Google Scholar
  15. Koyré A ([1973] 1966) Étude d’histoire de la pensée scientifique. Gallimard, Paris.Google Scholar
  16. Russell, B ([1967] 1902) Letter to Frege. In Heijenoort 1967, p. 125.Google Scholar
  17. Russell, B ([1967] 1908) Mathematical logic as based on the theory of types. In Heijenoort pp. 150–182.Google Scholar
  18. Russell, B (1912) Réponse à M. Koyré. Revue de Métaphysique et de Morale 20:725–6. English Translation in Russell 1992, pp. 57–59.Google Scholar
  19. Russell, B (1992) Logical and philosophical papers, 1909–1913. Routledge, London.Google Scholar
  20. Shapin S (1992) Discipline and bounding: the history and sociology of science as seen through the externalism-internalism debate. History of Science 30: 333-369.CrossRefGoogle Scholar
  21. Stump J (2001) History of science through Koyré’s lenses. Studies in History and Philosophy of Science 32: 243-263.CrossRefGoogle Scholar
  22. Wiener P, Noland, A (1957) Roots of scientific thought: a cultural perspective. Basic Book Publish, New York.Google Scholar
  23. Zambelli P (1999) Alexandre Koyré im der mekka der mathematik. NTM International Journal of History and Ethics of Natural Sciences, Technology and Medicine 7:208-230.Google Scholar

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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of HistoryFederal University of Minas Gerais – UFMGBelo HorizonteBrazil

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