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Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method pp 227–236Cite as

Logic, Method and Psychology of Discovery

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Part of the book series: Logic, Argumentation & Reasoning ((LARI,volume 1))

Abstract

Frege’s view, that there cannot be a logic of discovery but only a logic of justification based on deduction, and that the goal of logic is the study of deduction, has had a deep impact on the relation of logic to method. Such relation was a very strict one at the origin of logic and from the sixteenth to the first half of the nineteenth century. But, with Frege, it ended up in a divorce, and the subsequent developments of mathematical logic consolidated the divorce.

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Notes

  1. 1.

    Tarski (1994, xiii).

  2. 2.

    Hempel (2000, 200).

  3. 3.

    Ibid.

  4. 4.

    Popper (2000, 6).

  5. 5.

    Popper (2002, 7).

  6. 6.

    Ibid., 8.

  7. 7.

    Ibid.

  8. 8.

    Ibid., 7.

  9. 9.

    Ibid., 9.

  10. 10.

    Ibid.

  11. 11.

    Ibid., 7.

  12. 12.

    Popper (2000, xxxv).

  13. 13.

    Ibid., 5.

  14. 14.

    Popper (1972, 90).

  15. 15.

    Ibid., 95.

  16. 16.

    Ibid., 23.

  17. 17.

    Popper (1945, II, 218).

  18. 18.

    Pólya (1990, 181).

  19. 19.

    Poincaré (1914, 50–51).

  20. 20.

    Ibid., 61.

  21. 21.

    Ibid.

  22. 22.

    Ibid., 62.

  23. 23.

    Ibid., 61.

  24. 24.

    Ibid., 62.

  25. 25.

    Ibid., 59.

  26. 26.

    Ibid.

  27. 27.

    Ibid., 56.

  28. 28.

    The names ‘preparation’, ‘incubation’, ‘illumination’, ‘verification’ for the four stages were introduced in (Wallas 1926).

  29. 29.

    Poincaré (1958, 23).

  30. 30.

    Poincaré (1914, 163).

  31. 31.

    Poincaré (1958, 22).

  32. 32.

    Poincaré (1914, 129).

  33. 33.

    Poincaré (1958, 23).

  34. 34.

    Ibid., 22.

  35. 35.

    Galilei (1968, VII, 56).

  36. 36.

    Dirac (1951, 291).

  37. 37.

    Peirce (1931–1958, 5.265).

  38. 38.

    Poincaré (1914, 52).

  39. 39.

    Ibid., 52–53.

  40. 40.

    Ibid., 53.

  41. 41.

    Ibid., 54.

  42. 42.

    Ibid.

  43. 43.

    For other critical remarks on Poincaré views, see Weisberg (2006), Chapter 8.

  44. 44.

    Novalis (2007, 28).

  45. 45.

    Ibid., 205.

  46. 46.

    Poincaré (1914, 50).

  47. 47.

    Ibid.

  48. 48.

    Byers (2007, 16).

  49. 49.

    Ibid.

  50. 50.

    Ibid., 329.

  51. 51.

    Ibid., 26.

  52. 52.

    Hilbert (1998, 233).

  53. 53.

    Newton (1959–1977, I, 416).

  54. 54.

    Reid (1863, II, 537).

  55. 55.

    Byers (2007, 329).

References

  • Byers, William. 2007. How mathematicians think. Using ambiguity, contradiction, and paradox to create mathematics. Princeton: Princeton University Press.

    Google Scholar 

  • Dirac, Paul Adrien Maurice. 1951. A new classical theory of electrons. Proceedings of the Royal Society of London, Series A 209: 291–296.

    Article  Google Scholar 

  • Galilei, Galileo. 1968. Opere, ed. Antonio Favaro. Florence: Barbera.

    Google Scholar 

  • Grosholz, Emily Rolfe. 2000. The partial unification of domains, hybrids, and the growth of mathematical knowledge. In The growth pf mathematical knowledge, ed. Emily Rolfe Grosholz and Herbert Breger, 81–91. Dordrecht: Kluwer.

    Chapter  Google Scholar 

  • Hilbert, David. 1998. Problems of the grounding of mathematics. In From Brouwer to Hilbert. The debate on the foundations of mathematics in the 1920s, ed. Paolo Mancosu, 227–233. Oxford: Oxford University Press.

    Google Scholar 

  • Newton, Isaac. 1959–1977. Correspondence, ed. Alfred Rupert Hall and Laura Tilling. Cambridge: Cambridge University Press.

    Google Scholar 

  • Novalis (von Hardenberg, Friedrich). 2007. Notes for a romantic encyclopedia. Das Allgemeine Brouillon. Albany: State University of New York Press.

    Google Scholar 

  • Peirce, Charles Sanders. 1931–1958. Collected papers, ed. Charles Hartshorne, Paul Weiss, and Arthur W. Burks. Cambridge: Harvard University Press.

    Google Scholar 

  • Poincaré, Henri. 1914. Science and method. London: Nelson.

    Google Scholar 

  • Poincaré, Henri. 1958. The value of science. Mineola: Dover.

    Google Scholar 

  • Pólya, George. 1990. How to solve it. A new aspect of mathematical method. London: Penguin.

    Google Scholar 

  • Popper, Karl Raimund. 1945. The open society and its enemies. London: Routledge.

    Google Scholar 

  • Popper, Karl Raimund. 1972. Objective knowledge. An evolutionary approach. Oxford: Oxford University Press.

    Google Scholar 

  • Popper, Karl Raimund. 2000. Realism and the aim of science, ed. William Warren Bartley III. London: Routledge.

    Google Scholar 

  • Popper, Karl Raimund. 2002. The logic of scientific discovery. London: Routledge.

    Google Scholar 

  • Reid, Thomas. 1863. Works, ed. William Hamilton and Dugald Stewart. Edinburgh: MacLachlan and Stewart.

    Google Scholar 

  • Tarski, Alfred. 1994. Introduction to logic and to the methodology of deductive sciences, ed. Jan Tarski. Oxford: Oxford University Press.

    Google Scholar 

  • Wallas, Graham. 1926. The art of thought. London: Cape.

    Google Scholar 

  • Weisberg, Robert W. 2006. Creativity. Understanding innovation in problem solving, science, invention, and the arts. New York: Wiley.

    Google Scholar 

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  1. Sapienza University of Rome, Rome, Italy

    Carlo Cellucci

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Cellucci, C. (2013). Logic, Method and Psychology of Discovery. In: Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method. Logic, Argumentation & Reasoning, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6091-2_13

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