Abstract
Inductive inference has always been a major concern in philosophy. This paper considers two different ways of thinking about induction: the classical way and the new, learning-theoretic way. After a brief introduction, I discuss the classical style of thinking about induction, which conceives of inductive inference as an extension of deductive argumentation. Then, I focus on the new, alternative learning-theoretic approach which sees induction as a type of computational process that converges to the truth. I conclude the paper by considering some of the important philosophical consequences of this fundamental shift in the metaphor through which philosophers conceive of inductive reasoning.
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References
Carnap, R. (1910–1914). Frege’s Lectures on Logic: Carnap’s Jena Notes, in Reck and Awodey [59].
Carnap, R. (1950). Logical Foundations of Probability, Chicago: University of Chicago Press, 2nd ed., 1962.
Carnap, R. (1952). The Continuum of Inductive Methods, Chicago: University of Chicago Press.
Cassirer, E. (1907/22). Das Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit, Vol. II, reprint of 3rd ed., Darmstadt:Wissenschaftliche Buchgesellschaft, 1991.
Clark, P. and Hale, B. (eds.) (1994). Reading Putnam, London: Blackwell.
Cottingham, J. (ed.) (1994). Reason, Will and Sensation: Studies in Cartesian Metaphysics, Oxford: Oxford University Press.
Dalla Chiara, M.L., et al. (eds.) (1997). Logic and Scientific Methods, Dordrecht: Kluwer.
Earman, J. (1992). Bayes or Bust? Cambridge (Mass.): MIT Press.
Fichant, M. (1991). G.W. Leibniz, De l·Horizon de la doctrine humaine (1693). Paris: Vrin.
Garber D.(2001), Descartes Embodied. Cambridge: Cambridge University Press.
Garber, D. and Cohen L. (1982). “A Point of Order. Análisis, Síntesis, and Descar-tes’ Principles”, Archiv für Geschichte der Philosophie 64, 136–147; reprinted in [10].
Gaukroger, S. (1994). “The Sources of Descartes’ Procedure of Deductive Demonstration in Metaphysics and Natural Philosophy”, in Cottingham [6], 47–60.
Goethe, N.B. (2007). “How Did Bertrand Russell Make Leibniz into a ‘Fellow Spirit’?”, in Phemister and Brown [53], 195–205.
Gold, E.M. (1965). “Limiting Recursion”, Journal of Symbolic Logic 30, 28–48.
Gold, E.M. (1967). “Language Identification in the Limit”, Information and Control 10, 447–474.
Goodman, N. (1954). Fact, Fiction, and Forecast, 1st ed., University of London: Athlone Press; Cambridge (Mass.): Harvard University Press, 4th ed., 1983.
Grayling, A.C., Pyle, A. and Goulder, N. (2006). Continuum Encyclopedia of British Philosophy 3, 2106–2109.
Grosholz, E. and Breger, H. (eds.) (2000). The Growth of Mathematical Knowledge, Dordrecht: Kluwer.
Hitchcock, C. (ed.) (2004). Contemporary Debates in the Philosophy of Science, Oxford: Blackwell.
Hume, D. (1739). A Treatise of Human Nature, Vol. 1, Selby-Bigge, L.A. (ed.), (reprinted from the original edition), Oxford: Clarendon Press, 1958.
Hume, D. (1748). Enquiries Concerning Human Understanding and Concerning the Principles of Morals, Selby-Bigge, L.A. (ed.), (2nd ed. of 1902, reprinted from 1777 ed.), Oxford: Clarendon Press, 1957.
Jain, S., Osherson, D., Royer, J.S. and Sharma, A. (1999). Systems That Learn: An Introduction to Learning Theory, 2nd ed., Cambridge (Mass.): MIT Press.
James, W. (1948). “The Will to Believe”, in Thayer [65].
Kant, I. (A, 1781/B, 1787). Kritik der reinen Vernunft, Göttingen: Akademie Ausgabe, AA: IV (1781)/AA: III(1787).
Kant, I. (1800). Logik (Jäsche), AA: IX, English translation in: Introduction to Logic and his Essay on the Mistaken Subtlety of the Four Figures, Abbott, T.K. (ed. & trans.), London, 1885.
Kelly, K. (1987). “The Logic of Discovery”, Philosophy of Science 54, 435–452.
Kelly, K. (1991). “Reichenbach, Induction, and Discovery”, Erkenntnis 35, 123–149.
Kelly, K. (1993). “Learning Theory and Descriptive Set Theory”, Logic and Computation 3, 27–45.
Kelly, K. (1996). The Logic of Reliable Inquiry, Oxford: Oxford University Press.
Kelly, K. (1998). “Iterated Belief Revision, Reliability, and Inductive Amnesia”, Erkenntnis 50, 11–58.
Kelly, K. (2000). “The Logic of Success”, The British Journal for the Philosophy of Science, Special Millennium Issue 51, 639–666.
Kelly, K. (2004). “Uncomputability: The Problem of Induction Internalized”, Theoretical Computer Science 317, 227–249.
Kelly, K. and Glymour, C. (1992). “Inductive Inference from Theory Laden Data”, Journal of Philosophical Logic 21, 391–444.
Kelly, K. and Glymour, C. (2004). “Why Probability Does Not Capture the Logic of Scientific Justification”, in Hitchcock [19], 94–114.
Kelly, K. and Schulte, O. (1997). “Church’s Thesis and Hume’s Problem”, in Dalla Chiara, et al. [7], 159–177.
Kelly, K., Juhl, C. and Glymour, C. (1994). “Reliability, Realism, and Relativism”, in Clark [5], 98–161.
Kelly, K., Schulte, O. and Juhl, C. (1997). “Learning Theory and the Philosophy of Science”, Philosophy of Science 64, 245–267.
Kuhn, T.S. (1970). The Structure of Scientific Revolutions, Chicago: University of Chicago Press.
Larvor, B. (2006). “Philosophy of Mathematics”, in Grayling et al. [17].
Laudan, L. (1980). “Why Was the Logic of Discovery Abandoned?”, in Nickles [48], 173–183.
Leibniz, G.W. (1693). De l’Horizon de la Doctrine Humaine, in Fichant [9].
Lipton, P. (1991). Inference to the Best Explanation, Cambridge: Routledge (expanded 2nd ed., 2004).
Löwe, B., Peckhaus, V. and Räsch, T. (eds.) (2006). Foundations of the Formal Sciences IV, The History of the Concept of the Formal Sciences, College Publications, London 2006 [Studies in Logic 3].
Maat, J. (2006). “The Status of Logic in the Seventeenth Century”, in Löwe et al. [43], 157–167.
Mancosu, P. (1996). Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century, Oxford: Oxford University Press.
Mancosu, P. (2000). “On Mathematical Explanation”, in Grosholz and Breger [18], 103–119.
Martin, E. and Osherson, D. (1998). Elements of Scientific Inquiry, Cambridge (Mass.): MIT Press.
Nickles, T. (ed.) (1980). Scientific Discovery, Logic, and Rationality, Dordrectht: Reidel.
Osherson, D., Stob, M. and Weinstein, S. (1986). Systems That Learn: An Introduction to Learning Theory for Cognitive and Computer Scientists, Cambridge (Mass.): MIT Press.
Peirce, C.S. (1878). “How to Make Our Ideas Clear”, Popular Science Monthly 12 (January); reprinted in Peirce [52], 32–60.
Peirce, C.S. (1878). “Deduction, Induction and Hypothesis”, Popular Science Monthly 13 (August); reprinted in Peirce [52], 131–153.
Peirce, C.S. (1998). Chance, Love, and Logic, Philosophical Essays, Lincoln: University of Nebraska Press.
Phemister, P. and Brown, S. (eds.) (2007). Leibniz and the English-Speaking World, The New Synthese Historical Library, vol. 62, Dordrecht: Springer.
Popper, K. (1958). The Logic of Scientific Discovery, New York: Harper.
Putnam, H. (1963). “‘Degree of Confirmation’ and Inductive Logic”, in Schilpp [63], 761–784; reprinted in Putnam [58], 270–292.
Putnam, H. (1963). “Probability and Confirmation”, in The Voice of America Forum Lectures, Philosophy of Science Series 10, Washington, D.C.; reprinted in Putnam [58], 293–304.
Putnam, H. (1965). “Trial and Error Predicates and the Solution to a Problem of Mostowski”, Journal of Symbolic Logic 30, I, 49–57.
Putnam, H. (1975). Mathematics, Matter, and Method, Cambridge: Cambridge University Press.
Reck, E. and Awodey, S. (eds.) (2004). Frege’s Lectures on Logic: Carnap’s Jena Notes 1910–1914, translated and edited, with an introductory essay by the editors, Chicago-La Salle, (Ill.): Open Court.
Reichenbach, H. (1938). Experience and Prediction: An Analysis of the Foundations and the Structure of Knowledge, Chicago: University of Chicago Press.
Rescher, N. (2004). “Leibniz’s Quantitative Epistemology”, Studia Leibnitiana, Band XXXVI/2, 210–231.
Salmon, W.C. (1966). The Foundations of Scientific Inference, Pittsburgh: University of Pittsburgh Press.
Schilpp, P.A. (ed.) (1963). The Philosophy of Rudolf Carnap, La Salle (Ill.): Open Court.
Schulte, O. (2000). “Review of Martin and Osherson’s ‘Elements of Scientific Inquiry’”, The British Journal for the Philosophy of Science 51, 347–352.
Thayer, H.S. (ed.) (1982). Pragmatism, Indianapolis: Hackett.
Timmermans, B. (1999). “The Originality of Descartes’s Conception of Analysis as Discovery”, Journal of the History of Ideas 60, 433–447.
Worrall, J. (2000). “Lakatos and After”, Centre for Philosophy of Natural and Social Science, Discussion Paper Series, London: London School of Economics.
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Goethe, N.B. (2007). Two Ways of Thinking about Induction. In: Friend, M., Goethe, N.B., Harizanov, V.S. (eds) Induction, Algorithmic Learning Theory, and Philosophy. Logic, Epistemology, and the Unity of Science, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6127-1_10
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DOI: https://doi.org/10.1007/978-1-4020-6127-1_10
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