How Simplicity Helps You Find the Truth without Pointing at it
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.
Unable to display preview. Download preview PDF.
- Garey, M. and Johnson, D. (1979). Computers and Intractability, New York: Freeman.Google Scholar
- Glymour, C. (1980). Theory and Evidence, Princeton: Princeton University Press.Google Scholar
- Goodman, N. (1983). Fact, Fiction, and Forecast, 4th ed., Cambridge (Mass.): Harvard University Press.Google Scholar
- Hitchcock, C. (ed.) (2004). Contemporary Debates in the Philosophy of Science, Oxford: Blackwell.Google Scholar
- 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
- 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
- Kelly, K. and Glymour, C. (2004). “Why Probability Does Not Capture the Logic of Scientific Justification”, in Hitchcock, C. , 94–114.Google Scholar
- Kuhn, T.S. (1970). The Structure of Scientific Revolutions, Chicago: University of Chicago Press.Google Scholar
- Mitchell, T. (1997). Machine Learning, New York: McGraw-Hill.Google Scholar
- Popper, K. (1968). The Logic of Scientific Discovery, New York: Harper and Row.Google Scholar
- Sklar, L. (1977). Space, Time, and Spacetime, Berkeley: University of California Press.Google Scholar
- Van Fraassen, B. (1981). The Scientific Image, Oxford: Clarendon Press.Google Scholar