The Methods of Knowledge

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Rethinking Knowledge

Part of the book series: European Studies in Philosophy of Science ((ESPS,volume 4))

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Abstract

This chapter examines the methods to acquire knowledge. The methods considered are the analytic method, the analytic-synthetic method, the material axiomatic method, and the formal axiomatic method. The chapter also examines the original formulation of these methods, and the relations between them. Since deductive and non-deductive rules play a crucial role in the methods in question, the chapter discusses which of these rules are ampliative, in the sense that the conclusion is not contained in the premisses.

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References

  • Bacon, Francis. 1961–1986. Works. Stuttgart Bad Cannstatt: Frommann Holzboog.

    Google Scholar 

  • Boole, George. 1958. An investigation of the laws of thought on which are founded the mathematical theories of logic and probabilities. Mineola: Dover.

    Google Scholar 

  • Cambiano, Giuseppe. 1967. Il metodo ipotetico e le origini della sistemazione euclidea della geometria. Rivista di Filosofia 58: 115–149.

    Google Scholar 

  • Cantor, Georg. 1996. Foundations of a general theory of manifolds: A mathematico-philosophical investigation into the theory of the infinite. In From Kant to Hilbert: A source book in the foundations of mathematics, ed. William Ewald, vol. 2, 881–920. Oxford: Oxford University Press.

    Google Scholar 

  • Cellucci, Carlo. 1998. Le ragioni della logica. Rome: Laterza.

    Google Scholar 

  • ———. 2013a. Rethinking logic: Logic in relation to mathematics, evolution, and method. Dordrecht: Springer.

    Book  Google Scholar 

  • Dedekind, Richard. 1967. Letter to Keferstein, 27 February 1890. In From Frege to Gödel: A source book in mathematical logic, 1879–1931, ed. Jean van Heijenoort, 99–103. Cambridge: Harvard University Press.

    Google Scholar 

  • ———. 1996a. Was sind und was sollen die Zahlen? In From Kant to Hilbert: A source book in the foundations of mathematics, ed. William Ewald, vol. 2, 790–833. Oxford: Oxford University Press.

    Google Scholar 

  • ———. 1996b. Letter to Heinrich Weber, 24 January 1888. In From Kant to Hilbert: A source book in the foundations of mathematics, ed. William Ewald, vol. 2, 834–835. Oxford: Oxford University Press.

    Google Scholar 

  • De Morgan, Augustus. 1835. Review of George Peacock, A treatise on algebra. Quarterly Journal of Education 9: 91–110, 293–311.

    Google Scholar 

  • Descartes, René. 1996. Oeuvres. Paris: Vrin.

    Google Scholar 

  • Doxiadis, Apostolos, and Michalis Sialaros. 2013. Sing, Muse, of the hypotenuse: Influences of poetry and rhetoric on the formation of Greek mathematics. In Writing science: Medical and mathematical authorship in ancient Greece, ed. Markus Asper, 367–409. Berlin: De Gruyter.

    Google Scholar 

  • Doyle, Arthur Conan. 2003. Sherlock Holmes: The complete novels and stories. Volume I. New York: Bantham.

    Google Scholar 

  • Dummett, Michael. 1991. The logical basis of metaphysics. Cambridge: Harvard University Press.

    Google Scholar 

  • Frankfurt, Harry. 1958. Peirce’s notion of abduction. The Journal of Philosophy 55: 593–597.

    Article  Google Scholar 

  • Frege, Gottlob. 1960. The foundations of arithmetic: A logico-mathematical enquiry into the concept of number. New York: Harper.

    Google Scholar 

  • Gödel, Kurt. 1986–2002. Collected works. Oxford: Oxford University Press.

    Google Scholar 

  • Hilbert, David. 1902–1903. Ãœber den Satz von der Gleichheit der Basiswinkel im gleichschenkligen Dreieck. Proceedings of the London Mathematical Society 35: 50–68.

    Article  Google Scholar 

  • ———. 1980a. Letter to Frege, 29 December 1899. In Gottlob Frege, Philosophical and mathematical correspondence, ed. Gottlob Frege, 38–41. Oxford: Blackwell.

    Google Scholar 

  • ———. 1996a. On the concept of number. In From Kant to Hilbert: A source book in the foundations of mathematics, II, ed. William Ewald, 1092–1095. Oxford: Oxford University Press.

    Google Scholar 

  • ———. 1996c. The new grounding of mathematics: First report. In From Brouwer to Hilbert, II, ed. William Ewald, 1117–1134. Oxford: Oxford University Press.

    Google Scholar 

  • ———. 1996f. Logic and the knowledge of nature. In From Kant to Hilbert: A source book in the foundations of mathematics, II, ed. William Ewald, 1157–1165. Oxford: Oxford University Press.

    Google Scholar 

  • ———. 2000. Mathematical problems. Appendix to Jeremy Gray, The Hilbert challenge, 240–282. Oxford: Oxford University Press.

    Google Scholar 

  • ———. 2013. Beweis des Tertium non datur. In David Hilbert, Lectures on the foundations of arithmetic and logic 1917–1933, ed. William Ewald, and Wilfried Sieg, 985–990. Berlin: Springer.

    Google Scholar 

  • Hintikka, Jaakko, and Unto Remes. 1976. Ancient geometrical analysis and modern logic. In Essays in memory of Imre Lakatos, ed. Robert Cohen, Paul Feyerabend, and Max Wartofsky, 253–276. Dordrecht: Springer.

    Chapter  Google Scholar 

  • Hippocrates. 2005. On ancient medicine. Leiden: Brill.

    Google Scholar 

  • Hoffmann, Michael. 1999. Problems with Peirce’s concept of abduction. Foundations of Science 4: 271–305.

    Article  Google Scholar 

  • Husserl, Edmund. 1970. The crisis of European sciences and transcendental phenomenology. Evanston: Northwestern University Press.

    Google Scholar 

  • Kant, Immanuel. 1998. Critique of pure reason. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • ———. 2002. Theoretical philosophy after 1781. Cambridge: Cambridge University Press.

    Google Scholar 

  • Lakatos, Imre. 1978. Philosophical papers. Cambridge: Cambridge University Press.

    Google Scholar 

  • Lewis, David. 1996. Elusive knowledge. Australasian Journal of Philosophy 74: 549–567.

    Article  Google Scholar 

  • Lobachevsky, Nikolai. 1898–1899. Zwei geometrische Abhandlungen. Leipzig: Teubner.

    Google Scholar 

  • Menn, Stephen. 2002. Plato and the method of analysis. Phronesis 47: 193–223.

    Article  Google Scholar 

  • Mill, John Stuart. 1963–1986. Collected works. Toronto: University of Toronto Press.

    Google Scholar 

  • Patokorpi, Erkki. 2007. Logic of Sherlock Holmes in technology enhanced learning. Educational Technology & Society 10 (1): 171–185.

    Google Scholar 

  • Peirce, Charles Sanders. 1931–1958. Collected papers. Cambridge: Harvard University Press.

    Google Scholar 

  • Poincaré, Henri. 2013. The foundations of science: Science and hypothesis – The value of science – Science and method. Cambridge: Cambridge University Press.

    Google Scholar 

  • Pólya, George. 1971. How to solve it: A new aspect of mathematical method. Princeton: Princeton University Press.

    Google Scholar 

  • Proclus. 1992. In primum Euclidis Elementorum librum commentarii. Hildesheim: Olms.

    Google Scholar 

  • Ribet, Kenneth A. 1990. From the Taniyama-Shimura conjecture to Fermat’s last theorem. Annales de la Faculté Mathematiques et des Sciences de Toulouse 11: 116–139.

    Article  Google Scholar 

  • Suppes, Patrick. 1993. Models and methods in the philosophy of science: Selected essays. Dordrecht: Springer.

    Book  Google Scholar 

  • Wittgenstein, Ludwig. 2002. Tractatus Logico-Philosophicus. London: Routledge.

    Google Scholar 

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Cellucci, C. (2017). The Methods of Knowledge. In: Rethinking Knowledge. European Studies in Philosophy of Science, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-53237-0_12

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