Abstract
Three decades ago Laudan posed the challenge: Why should the logic of discovery be revived? This paper tries to answer this question arguing that the logic of discovery should be revived, on the one hand, because, by Gödel’s second incompleteness theorem, mathematical logic fails to be the logic of justification, and only reviving the logic of discovery logic may continue to have an important role. On the other hand, scientists use heuristic tools in their work, and it may be useful to study such tools systematically in order to improve current heuristic tools or to develop new ones. As a step towards reviving the logic of discovery, the paper follows Aristotle in asserting that logic must be a tool for the method of science, and outlines an approach to the logic of discovery based on the analytic method and on ampliative inference rules.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Planck, M.: Scientific Autobiography and Other Papers. Williams & Norgate, London (1950)
Einstein, A.: Ideas and Opinions. Crown Publishers, New York (1954)
Einstein, A.: Induction and deduction in physics. In: Einstein, A. (ed.) Collected Papers, vol. 7, pp. 108–109. Princeton University Press, Princeton (2002)
Reichenbach, H.: The Rise of Scientific Philosophy. University of California Press, Berkeley (1951)
Reichenbach, H.: The Theory of Probability: An Inquiry into the Logical and Mathematical Foundations of the Calculus of Probability. University of California Press, Berkeley (1949)
Novalis (von Hardenberg, Friedrich): Notes for a romantic encyclopedia. Das Allgemeine Brouillon. In: Wood DW (ed.) State University of New York Press, Albany (2007)
Cellucci, C.: Romanticism in mathematics. Newslett. HPM Group 64, 17–19 (2007)
Lakatos, I.: Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press, Cambridge (1976)
Cellucci, C.: Top-down and bottom-up philosophy of mathematics. Found. Sci. 18, 93–106 (2013)
Lakatos, I.: Philosophical papers. In: Worrall, J., Currie, G. (eds.) Cambridge University Press, Cambridge (1978)
Bacon, F.: Works. ed. In: Spedding, J., Ellis, R.L., Heath, D.D. (eds.) Frommann Holzboog, Stuttgart Bad Cannstatt (1961–1986)
Descartes, R.: Œuvres. In: Adam, C., Tannery, P (eds.). Vrin, Paris (1996)
Blanché, R.: La logique et son histoire, d’Aristote à Russell. Armand Colin, Paris (1970)
Frege, G.: The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number. Blackwell, Oxford (1959)
Frege, G.: Posthumous writings. In: Hermes, H., Kambartel, F., Kaulbach, F. (eds.). Blackwell, Oxford (1979)
Frege, G.: Collected papers on mathematics, logic, and philosophy. McGuinness, B. (ed.). Blackwell, Oxford
Cellucci, C.: Rethinking Logic. Logic in Relation to Mathematics, Evolution, and Method. Springer, Berlin (2013)
Hilbert, D.: Grundlagen der Geometrie. In: Hallett, M., Majer, U. (eds.) David Hilbert’s Lectures on the Foundations of Geometry (1891–1902), pp. 540–606. Oxford University Press, Oxford (2004)
Hilbert, D.: On the concept of number. In: Ewald, W.B. (ed.) From Kant to Hilbert: A Source Book in the Foundations of Mathematics, II edn, pp. 1092–1095. Oxford University Press, Oxford (1996)
Hilbert, D.: Letter to Frege 29.12.1899. In: Gabriel, G., Hermes, H., Kambartel, F. (eds.) Gottlob Frege: Philosophical and Mathematical Correspondence, pp. 38–41. Blackwell, Oxford (1980)
Hilbert, D.: Axiomatic thought. In: Ewald, W.B. (ed.) From Kant to Hilbert: a source book in the foundations of mathematics, II edn, pp. 1107–1115. Oxford University Press, Oxford (1996)
Poincaré, H.: Science and Method. Nelson, London (1914)
Tarski, A.: Introduction to logic and to the methodology of deductive sciences. Tarski, J. (ed.). Oxford University Press, Oxford (1994)
Aliseda, A.: Abductive Reasoning: Logical Investigations into Discovery and Explanations. Springer, Berlin (2006)
Laudan, L.: Why Was the logic of discovery abandoned? In: Nickles, T. (ed.) Scientific Discovery, Logic, and Rationality, pp. 173–183. Reidel, Dordrecht (1980)
Machado, A.: Border of a dream: selected poems. In: Barnstone, W. (ed.). Copper Canyon Press, Port Townsend (2004)
Boger, G.: Aristotle’s underlying logic. In: Gabbay, D.M., Woods, J. (eds.) Handbook of the History of Logic: Greek, Indian and Arabic logic, vol. 1, pp. 101–246. Elsevier, Amsterdam (2004)
Galileo, G.: Opere. In: Favaro, A. (ed.). Barbera, Florence (1968)
Newton, I.: Opticks, or a Treatise of the Reflections, Refractions, Inflections & Colours of Light. Dover, Mineola (1952)
Cohen, I.B.: Introduction to Newton’s ‘Principia’. Cambridge University Press, Cambridge (1971)
Ribet, K.A.: From the Taniyama-Shimura conjecture to fermat’s last theorem. Annales de la Faculté des Sciences de Toulouse—Mathématiques 11, 116–139 (1990)
Morris, R.C., Nagel, E.: An Introduction to Logic and Scientific Method. Routledge, London (1964)
Peirce, C.S.: Collected papers. In: Hartshorne, C., Weiss, P., Burks, A.W. (eds.). Cambridge University Press, Cambridge (1931–1958)
Frankfurt, H.G.: Peirce’s notion of abduction. J. Philos. 55, 593–597 (1958)
Peirce, C.S.: Reasoning and the logic of things. In: Ketner KL (ed.). Harvard University Press, Cambridge (1992)
Popper, K.: The Logic of Scientific Discovery. Routledge, London (2005)
Popper, K.: Realism and the aim of science. In: Bartley WW (ed.), III. Routledge, London (2000)
Popper, K.: Conjectures and Refutations: The Growth of Scientific Knowledge. Routledge, London (1974)
Davis, P.J.: Mathematics and Common Sense: A Case of Creative Tension. A K Peters, Natick (2006)
Kant, I.: Prolegomena to Any Future Metaphysics. Cambridge University Press, Cambridge (2004)
Russell, B.: An Outline of Philosophy. Routledge, London (1995)
Pólya, G.: Mathematics and Plausible Reasoning. Princeton University Press, Princeton (1954)
Hempel, C.G.: Philosophy of Natural Science. Prentice Hall, Upper Saddle River (1966)
Girard, J.Y.: Le champ du signe ou la faillite du réductionnisme. In: Nagel, E., Newman, J.R., Gödel, K., Girard, J.Y. (eds.) Le théorème de Gödel, pp. 147–171. Éditions du Seuil, Paris (1989)
Gillies, D.: Artificial Intelligence and Scientific Method. Oxford University Press, Oxford (1996)
Acknowledgments
I am very grateful to Atocha Aliseda and Thomas Nickles for comments on an earlier draft of the manuscript.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Cellucci, C. (2015). Why Should the Logic of Discovery Be Revived? A Reappraisal. In: Ippoliti, E. (eds) Heuristic Reasoning. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-319-09159-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-09159-4_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09158-7
Online ISBN: 978-3-319-09159-4
eBook Packages: EngineeringEngineering (R0)