Abstract
In the analytic method, knowledge is obtained by use of deductive and non-deductive rules. Since such rules are not plausibility preserving, they may give rise to errors. On this basis, contrary to a tradition according to which error is heterogeneous to knowledge, this chapter maintains that error is homogeneous to knowledge and inherent to it. Indeed, error is even homogeneous and inherent to logical and mathematical knowledge. The chapter also maintains that, though error may be a serious problem for logic, mathematics and science, it may also be fruitful. For, an analysis of the causes of error may provide useful indications for forming new hypotheses, and may also help to formulate new concepts.
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References
Capozzi, Mirella. 2013. Kant e la logica I. Naples: Bibliopolis.
Davis, Philip. 1972. Fidelity in mathematical discourse: Is one and one really two? The American Mathematical Monthly 79 : 252–263.
Gödel, Kurt. 1986–2002. Collected works. Oxford: Oxford University Press.
Hersh, Reuben. 1979. Some proposals for reviving the philosophy of mathematics. Advances in Mathematics 31 : 31–50.
Hilbert, David. 1967b. The foundations of mathematics. In From Frege to Gödel: A source book in mathematical logic, 1879–1931, ed. Jean van Heijenoort, 464–479. Cambridge: Harvard University Press.
———. 1996e. The grounding of elementary number theory. In From Kant to Hilbert: A source book in the foundations of mathematics, II, ed. William Ewald, 1149–1157. Oxford: Oxford University Press.
Hume, David. 1978. A treatise of human nature. Oxford: Oxford University Press.
Kant, Immanuel. 1992. Lectures on logic. Cambridge: Cambridge University Press.
———. 1998. Critique of pure reason. Cambridge: Cambridge University Press.
Lam, Clement. 1990. How reliable is a computer-based proof? The Mathematical Intelligencer 12 (1): 8–12.
Lecat, Maurice. 1935. Erreurs de mathématiciens des origines à nos jours. Bruxelles: Castaigne.
Mach, Ernst. 1976. Knowledge and error: Sketches on the psychology of enquiry. Dordrecht: Springer.
Popper, Karl Raimund. 1972. Objective knowledge. Oxford: Oxford University Press.
———. 1974. Conjectures and refutations: The growth of scientific knowledge. London: Routledge.
———. 2002. Unended quest: An intellectual autobiography. London: Routledge.
Proclus. 1992. In primum Euclidis Elementorum librum commentarii. Hildesheim: Olms.
Rota, Gian-Carlo. 1997. Indiscrete thoughts. Boston: Birkhäuser.
Singh, Simon. 1998. Fermat’s last theorem. New York: Anchor Books.
Thom, René. 1998. ‘Modern’ mathematics: An educational and philosophical error? In New directions in the philosophy of mathematics, ed. Thomas Tymoczko, 67–78. Princeton: Princeton University Press.
Wang, Hao. 1996. A logical journey: From Gödel to philosophy. Cambridge: The MIT Press.
Wiedijk, Freek. 2008. Formal proof – Getting started. Notices of the American Mathematical Society 55 : 1408–1414.
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Cellucci, C. (2017). Knowledge and Error. In: Rethinking Knowledge. European Studies in Philosophy of Science, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-53237-0_16
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DOI: https://doi.org/10.1007/978-3-319-53237-0_16
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