Abstract
In this final part of the book several rules of discovery are considered, that is, non-deductive rules for finding hypotheses to solve problems. Of course, finding hypotheses is not a sufficient condition for discovery. The latter requires hypotheses to be plausible, and the plausibility test procedure of Chapter 4 involves operations beyond simple hypothesis formation. Nevertheless, finding hypotheses is a necessary condition for discovery and, in that sense, one may speak of rules of discovery. The latter are not a closed set, given once for all, but rather an open set which can always be extended as research develops. Each such extension is a development of the analytic method, which grows as new non-deductive rules are added. As Bacon says, “the art of discovery may grow with discoveries.”
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Notes
- 1.
Bacon (1961–1986, I, 223).
- 2.
Pólya (1954, I, vi–vii).
- 3.
Swetz and Kao (1977, 14).
- 4.
Ibid.
- 5.
Ibid.
- 6.
Fuss (1843, I, 127 footnote).
- 7.
Popper (2002, 18).
- 8.
Popper (1972, 30).
- 9.
Popper (2002, 20).
- 10.
Ibid., 66.
- 11.
Ibid., 67.
- 12.
Ibid., 86.
- 13.
Ibid., 85.
- 14.
Ibid., 87.
- 15.
Ibid., 88.
- 16.
Carnap (1962, v).
- 17.
Ibid., 206.
- 18.
Ibid., v.
- 19.
Carnap (1966, 34).
- 20.
Salmon (1965b, 280).
- 21.
Aristotle, Topica, A 18, 108 b 13–14.
- 22.
See Archimedes (1880–81, I, 258.2–4).
- 23.
Simplicius, In Aristotelis Physicorum Libros Quattuor Priores Commentaria (Diels), 54.20–22.
- 24.
Ibid., 55.7–8.
- 25.
Leibniz (1971, V, 181).
- 26.
Proclus, In Primum Euclidis Elementorum Librum Commentarii (Friedlein), 157.20.
- 27.
Ibid., 157.22–158.1.
- 28.
Ibid., 158.1–2.
- 29.
Herschel (2008, 73).
- 30.
Aristotle, Poetica, 1457 b 22–23.
- 31.
Ibid., 1457 b 23–24.
- 32.
See Leibniz (1971, V, 182).
- 33.
Rutherford (1911, 671).
- 34.
Franklin (1859, II, 295).
- 35.
Maxwell (1965, I, 377–378).
- 36.
Mill (1963–1986, VII, 557).
- 37.
Ibid.
- 38.
Ibid., VII, 557–558.
- 39.
Ibid.,VII, 558.
- 40.
Kant (1992, 232).
- 41.
Ibid.
- 42.
Hume (2007, 26).
- 43.
Ibid.
- 44.
Ibid.
- 45.
Mill (1963–1986, VII, 556).
- 46.
Ibid., VII, 557.
- 47.
Ibid.
References
Archimedes. 1880–81. Opera Omnia, ed. Johnan Ludvig Heiberg. Leipzig: Teubner.
Bacon, Francis. 1961–1986. Works, ed. James Spedding, Robert Leslie Ellis, and Douglas Denon Heath. Stuttgart Bad Cannstatt: Frommann Holzboog.
Carnap, Rudolf. 1962. Logical foundations of probability. Chicago: The University of Chicago Press.
Carnap, Rudolf. 1966. Philosophical foundations of physics. An introduction to the philosophy of science. New York: Basic Books.
Franklin, Benjamin. 1859. Memoirs. New York: Derby and Jackson.
Fuss, Paul Heinrich (ed.). 1843. Correspondance mathématique et physique de quelques célebres géomètres du XVIIIème siècle. Saint Pétersbourg: Académie Impériale des Sciences.
Herschel, William. 2008. Letter to Sir Joseph Bank. In James Sime, William Herschel and his work, 73–74. Charleston: BiblioBazaar.
Hume, David. 2007. An enquiry concerning human understanding, ed. Lewis Amherst Selby-Bigge and Peter Harold Nidditch. Oxford: Oxford University Press.
Kant, Immanuel. 1992. Lectures on logic, ed. J. Michael Young. Cambridge: Cambridge University Press.
Leibniz, Gottfried Wilhelm. 1971. Mathematische Schriften, ed. Carl Immanuel Gerhardt. Hildesheim: Georg Olms.
Maxwell, James Clerk. 1965. Scientific papers, ed. William Davidson Niven. Mineola: Dover.
Mill, John Stuart. 1963–1986. Collected works, ed. John M. Robson. Toronto: University of Toronto Press.
Pólya, George. 1954. Mathematics and plausible reasoning. Princeton: Princeton University Press.
Popper, Karl Raimund. 1972. Objective knowledge. An evolutionary approach. Oxford: Oxford University Press.
Popper, Karl Raimund. 2002. The logic of scientific discovery. London: Routledge.
Rutherford, Ernest. 1911. The scattering of α and β particles by matter and the structure of the atom. Philosophical Magazine 21: 669–688.
Salmon, Wesley Charles. 1965b. Rejoinder to Barker and Kyburg. American Philosophical Quarterly 2: 277–280.
Swetz, Frank J., and T.I. Kao. 1977. Was Pythagoras Chinese? An examination of right triangle theory in ancient China. University Park: The Pennsylvania State University Press.
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Cellucci, C. (2013). Induction and Analogy. 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_20
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