How Simplicity Helps You Find the Truth without Pointing at it

  • Kevin T. Kelly
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 9)

Abstract

It seems that a fixed bias toward simplicity should help one find the truth, since scientific theorizing is guided by such a bias. But it also seems that a fixed bias toward simplicity cannot indicate or point at the truth, since an indicator has to be sensitive to what it indicates. I argue that both views are correct. It is demonstrated, for a broad range of cases, that the Ockham strategy of favoring the simplest hypothesis, together with the strategy of never dropping the simplest hypothesis until it is no longer simplest, uniquely minimizes reversals of opinion and the times at which the reversals occur prior to convergence to the truth. Thus, simplicity guides one down the straightest path to the truth, even though that path may involve twists and turns along the way. The proof does not appeal to prior probabilities biased toward simplicity. Instead, it is based upon minimization of worst-case cost bounds over complexity classes of possibilities.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Chart, D. (2000). “Discussion: Schulte and Goodman’s Riddle”, The British Journal for the Philosophy of Science 51, 147–149.CrossRefGoogle Scholar
  2. [2]
    Forster, M. and Sober, E. (1994). “How to Tell When Simpler, More Unified, or Less ad Hoc Theories Will Provide More Accurate Predictions”, The British Journal for the Philosophy of Science 45, 1–35.CrossRefGoogle Scholar
  3. [3]
    Freivalds, R. and Smith, C. (1993). “On the Role of Procrastination in Machine Learning”, Information and Computation 107, 237–271.CrossRefGoogle Scholar
  4. [4]
    Garey, M. and Johnson, D. (1979). Computers and Intractability, New York: Freeman.Google Scholar
  5. [5]
    Glymour, C. (1980). Theory and Evidence, Princeton: Princeton University Press.Google Scholar
  6. [6]
    Goodman, N. (1983). Fact, Fiction, and Forecast, 4th ed., Cambridge (Mass.): Harvard University Press.Google Scholar
  7. [7]
    Harman, G. (1965). “The Inference to the Best Explanation”, Philosophical Review 74, 88–95.CrossRefGoogle Scholar
  8. [8]
    Hitchcock, C. (ed.) (2004). Contemporary Debates in the Philosophy of Science, Oxford: Blackwell.Google Scholar
  9. [9]
    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
  10. [10]
    Kelly, K. (2002). “Efficient Convergence Implies Ockham’s Razor”, in Proceedings of the 2002 International Workshop on Computational Models of Scientific Reasoning and Applications(CMSRA 2002), Las Vegas, USA, June 24–27.Google Scholar
  11. [11]
    Kelly, K. (2004). “Uncomputability: The Problem of Induction Internalized”, Theoretical Computer Science 317, 227–249.CrossRefGoogle Scholar
  12. [12]
    Kelly, K. and Glymour, C. (2004). “Why Probability Does Not Capture the Logic of Scientific Justification”, in Hitchcock, C. [8], 94–114.Google Scholar
  13. [13]
    Kuhn, T.S. (1970). The Structure of Scientific Revolutions, Chicago: University of Chicago Press.Google Scholar
  14. [14]
    Laudan, L. (1981). “A Confutation of Convergent Realism”, Philosophy of Science 48, 19–48.CrossRefGoogle Scholar
  15. [15]
    Mitchell, T. (1997). Machine Learning, New York: McGraw-Hill.Google Scholar
  16. [16]
    Popper, K. (1968). The Logic of Scientific Discovery, New York: Harper and Row.Google Scholar
  17. [17]
    Schulte, O. (1999). “Means-Ends Epistemology”, The British Journal for the Philosophy of Science 50, 1–31.CrossRefGoogle Scholar
  18. [18]
    Schulte, O. (2000a). “Inferring Conservation Principles in Particle Physics: A Case Study in the Problem of Induction”, The British Journal for the Philosophy of Science 51, 771–806.CrossRefGoogle Scholar
  19. [19]
    Schulte, O. (2000b). “What to Believe and What to Take Seriously: A Reply to David Chart Concerning the Riddle of Induction”, The British Journal for the Philosophy of Science 51, 151–153.CrossRefGoogle Scholar
  20. [20]
    Sklar, L. (1977). Space, Time, and Spacetime, Berkeley: University of California Press.Google Scholar
  21. [21]
    Van Fraassen, B. (1981). The Scientific Image, Oxford: Clarendon Press.Google Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Kevin T. Kelly
    • 1
  1. 1.Department of PhilosophyCarnegie Mellon UniversityPittsburgU.S.A.

Personalised recommendations