Skip to main content

Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 9))

  • 899 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Carnap, R. (1910–1914). Frege’s Lectures on Logic: Carnap’s Jena Notes, in Reck and Awodey [59].

    Google Scholar 

  2. Carnap, R. (1950). Logical Foundations of Probability, Chicago: University of Chicago Press, 2nd ed., 1962.

    Google Scholar 

  3. Carnap, R. (1952). The Continuum of Inductive Methods, Chicago: University of Chicago Press.

    Google Scholar 

  4. Cassirer, E. (1907/22). Das Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit, Vol. II, reprint of 3rd ed., Darmstadt:Wissenschaftliche Buchgesellschaft, 1991.

    Google Scholar 

  5. Clark, P. and Hale, B. (eds.) (1994). Reading Putnam, London: Blackwell.

    Google Scholar 

  6. Cottingham, J. (ed.) (1994). Reason, Will and Sensation: Studies in Cartesian Metaphysics, Oxford: Oxford University Press.

    Google Scholar 

  7. Dalla Chiara, M.L., et al. (eds.) (1997). Logic and Scientific Methods, Dordrecht: Kluwer.

    Google Scholar 

  8. Earman, J. (1992). Bayes or Bust? Cambridge (Mass.): MIT Press.

    Google Scholar 

  9. Fichant, M. (1991). G.W. Leibniz, De l·Horizon de la doctrine humaine (1693). Paris: Vrin.

    Google Scholar 

  10. Garber D.(2001), Descartes Embodied. Cambridge: Cambridge University Press.

    Google Scholar 

  11. 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].

    Google Scholar 

  12. Gaukroger, S. (1994). “The Sources of Descartes’ Procedure of Deductive Demonstration in Metaphysics and Natural Philosophy”, in Cottingham [6], 47–60.

    Google Scholar 

  13. Goethe, N.B. (2007). “How Did Bertrand Russell Make Leibniz into a ‘Fellow Spirit’?”, in Phemister and Brown [53], 195–205.

    Google Scholar 

  14. Gold, E.M. (1965). “Limiting Recursion”, Journal of Symbolic Logic 30, 28–48.

    Article  Google Scholar 

  15. Gold, E.M. (1967). “Language Identification in the Limit”, Information and Control 10, 447–474.

    Article  Google Scholar 

  16. Goodman, N. (1954). Fact, Fiction, and Forecast, 1st ed., University of London: Athlone Press; Cambridge (Mass.): Harvard University Press, 4th ed., 1983.

    Google Scholar 

  17. Grayling, A.C., Pyle, A. and Goulder, N. (2006). Continuum Encyclopedia of British Philosophy 3, 2106–2109.

    Google Scholar 

  18. Grosholz, E. and Breger, H. (eds.) (2000). The Growth of Mathematical Knowledge, Dordrecht: Kluwer.

    Google Scholar 

  19. Hitchcock, C. (ed.) (2004). Contemporary Debates in the Philosophy of Science, Oxford: Blackwell.

    Google Scholar 

  20. Hume, D. (1739). A Treatise of Human Nature, Vol. 1, Selby-Bigge, L.A. (ed.), (reprinted from the original edition), Oxford: Clarendon Press, 1958.

    Google Scholar 

  21. 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.

    Google Scholar 

  22. 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.

    Google Scholar 

  23. James, W. (1948). “The Will to Believe”, in Thayer [65].

    Google Scholar 

  24. Kant, I. (A, 1781/B, 1787). Kritik der reinen Vernunft, Göttingen: Akademie Ausgabe, AA: IV (1781)/AA: III(1787).

    Google Scholar 

  25. 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.

    Google Scholar 

  26. Kelly, K. (1987). “The Logic of Discovery”, Philosophy of Science 54, 435–452.

    Article  Google Scholar 

  27. Kelly, K. (1991). “Reichenbach, Induction, and Discovery”, Erkenntnis 35, 123–149.

    Google Scholar 

  28. Kelly, K. (1993). “Learning Theory and Descriptive Set Theory”, Logic and Computation 3, 27–45.

    Article  Google Scholar 

  29. Kelly, K. (1996). The Logic of Reliable Inquiry, Oxford: Oxford University Press.

    Google Scholar 

  30. Kelly, K. (1998). “Iterated Belief Revision, Reliability, and Inductive Amnesia”, Erkenntnis 50, 11–58.

    Google Scholar 

  31. Kelly, K. (2000). “The Logic of Success”, The British Journal for the Philosophy of Science, Special Millennium Issue 51, 639–666.

    Google Scholar 

  32. Kelly, K. (2004). “Uncomputability: The Problem of Induction Internalized”, Theoretical Computer Science 317, 227–249.

    Article  Google Scholar 

  33. Kelly, K. and Glymour, C. (1992). “Inductive Inference from Theory Laden Data”, Journal of Philosophical Logic 21, 391–444.

    Article  Google Scholar 

  34. Kelly, K. and Glymour, C. (2004). “Why Probability Does Not Capture the Logic of Scientific Justification”, in Hitchcock [19], 94–114.

    Google Scholar 

  35. Kelly, K. and Schulte, O. (1997). “Church’s Thesis and Hume’s Problem”, in Dalla Chiara, et al. [7], 159–177.

    Google Scholar 

  36. Kelly, K., Juhl, C. and Glymour, C. (1994). “Reliability, Realism, and Relativism”, in Clark [5], 98–161.

    Google Scholar 

  37. Kelly, K., Schulte, O. and Juhl, C. (1997). “Learning Theory and the Philosophy of Science”, Philosophy of Science 64, 245–267.

    Article  Google Scholar 

  38. Kuhn, T.S. (1970). The Structure of Scientific Revolutions, Chicago: University of Chicago Press.

    Google Scholar 

  39. Larvor, B. (2006). “Philosophy of Mathematics”, in Grayling et al. [17].

    Google Scholar 

  40. Laudan, L. (1980). “Why Was the Logic of Discovery Abandoned?”, in Nickles [48], 173–183.

    Google Scholar 

  41. Leibniz, G.W. (1693). De l’Horizon de la Doctrine Humaine, in Fichant [9].

    Google Scholar 

  42. Lipton, P. (1991). Inference to the Best Explanation, Cambridge: Routledge (expanded 2nd ed., 2004).

    Google Scholar 

  43. 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].

    Google Scholar 

  44. Maat, J. (2006). “The Status of Logic in the Seventeenth Century”, in Löwe et al. [43], 157–167.

    Google Scholar 

  45. Mancosu, P. (1996). Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century, Oxford: Oxford University Press.

    Google Scholar 

  46. Mancosu, P. (2000). “On Mathematical Explanation”, in Grosholz and Breger [18], 103–119.

    Google Scholar 

  47. Martin, E. and Osherson, D. (1998). Elements of Scientific Inquiry, Cambridge (Mass.): MIT Press.

    Google Scholar 

  48. Nickles, T. (ed.) (1980). Scientific Discovery, Logic, and Rationality, Dordrectht: Reidel.

    Google Scholar 

  49. 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.

    Google Scholar 

  50. Peirce, C.S. (1878). “How to Make Our Ideas Clear”, Popular Science Monthly 12 (January); reprinted in Peirce [52], 32–60.

    Google Scholar 

  51. Peirce, C.S. (1878). “Deduction, Induction and Hypothesis”, Popular Science Monthly 13 (August); reprinted in Peirce [52], 131–153.

    Google Scholar 

  52. Peirce, C.S. (1998). Chance, Love, and Logic, Philosophical Essays, Lincoln: University of Nebraska Press.

    Google Scholar 

  53. Phemister, P. and Brown, S. (eds.) (2007). Leibniz and the English-Speaking World, The New Synthese Historical Library, vol. 62, Dordrecht: Springer.

    Google Scholar 

  54. Popper, K. (1958). The Logic of Scientific Discovery, New York: Harper.

    Google Scholar 

  55. Putnam, H. (1963). “‘Degree of Confirmation’ and Inductive Logic”, in Schilpp [63], 761–784; reprinted in Putnam [58], 270–292.

    Google Scholar 

  56. 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.

    Google Scholar 

  57. Putnam, H. (1965). “Trial and Error Predicates and the Solution to a Problem of Mostowski”, Journal of Symbolic Logic 30, I, 49–57.

    Google Scholar 

  58. Putnam, H. (1975). Mathematics, Matter, and Method, Cambridge: Cambridge University Press.

    Google Scholar 

  59. 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.

    Google Scholar 

  60. Reichenbach, H. (1938). Experience and Prediction: An Analysis of the Foundations and the Structure of Knowledge, Chicago: University of Chicago Press.

    Google Scholar 

  61. Rescher, N. (2004). “Leibniz’s Quantitative Epistemology”, Studia Leibnitiana, Band XXXVI/2, 210–231.

    Google Scholar 

  62. Salmon, W.C. (1966). The Foundations of Scientific Inference, Pittsburgh: University of Pittsburgh Press.

    Google Scholar 

  63. Schilpp, P.A. (ed.) (1963). The Philosophy of Rudolf Carnap, La Salle (Ill.): Open Court.

    Google Scholar 

  64. Schulte, O. (2000). “Review of Martin and Osherson’s ‘Elements of Scientific Inquiry’”, The British Journal for the Philosophy of Science 51, 347–352.

    Article  Google Scholar 

  65. Thayer, H.S. (ed.) (1982). Pragmatism, Indianapolis: Hackett.

    Google Scholar 

  66. Timmermans, B. (1999). “The Originality of Descartes’s Conception of Analysis as Discovery”, Journal of the History of Ideas 60, 433–447.

    Google Scholar 

  67. Worrall, J. (2000). “Lakatos and After”, Centre for Philosophy of Natural and Social Science, Discussion Paper Series, London: London School of Economics.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer

About this chapter

Cite this chapter

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

Download citation

Publish with us

Policies and ethics