Advertisement

Theory Choice, Theory Change, and Inductive Truth-Conduciveness

  • Konstantin GeninEmail author
  • Kevin T. Kelly
Article
  • 89 Downloads

Abstract

(I) Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. (II) Diachronic norms of theory change, as studied in belief revision, restrict how one should change one’s current beliefs in light of new information. (III) Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning (III), we explicate inductive truth conduciveness in terms of optimally direct convergence to the truth, where optimal directness is explicated in terms of reversals and cycles of opinion prior to convergence. Concerning (I), we explicate Ockham’s razor and related principles of choice in terms of the information topology of the empirical problem context and show that the principles are necessary for reversal or cycle optimal convergence to the truth. Concerning (II), we weaken the standard principles of agm belief revision theory in intuitive ways that are also necessary (and in some cases, sufficient) for reversal or cycle optimal convergence. Then we show that some of our weakened principles of change entail corresponding principles of choice, completing the triangle of relations between (I), (II), and (III).

Keywords

Theory choice Simplicity Ockham’s razor Learning Belief revision Reliability Formal epistemology 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

In Spring 2000, John Case suggested to the second author to consider the consequences of U-shaped learning for Ockham’s razor. We are indebted to Thomas Icard for suggesting connections between our topological conception of simplicity and related work in the semantics of provability logic, which proved to be very fruitful. We are indebted to Hanti Lin for the Maxwell example. We are indebted to Alexandru Baltag, Nina Gierasimczuk, and Sonja Smets, for comments and discussions, for informing us of related work by Debrecht and Yamamoto [8], and for sharing their related results with us, particularly Proposition 10.2.

References

  1. 1.
    Baker, A., Simplicity, in E. N. Zalta, (ed.), The Stanford Encyclopedia of Philosophy, fall 2013 edn., 2013.Google Scholar
  2. 2.
    Baltag, A., N. Gierasimczuk, and S. Smets, On the solvability of inductive problems: a study in epistemic topology (forthcoming), in Proceedings of the fifteenth conference on Theoretical Aspects of Rationality and Knowledge, 2015.Google Scholar
  3. 3.
    Baltag, A., N. Gierasimczuk, and S. Smets, Truth-tracking by belief revision (to appear), Studia Logica, 2018.Google Scholar
  4. 4.
    Carlucci, L., and J. Case, On the necessity of U-Shaped learning, Topics in Cognitive Science 5(1):56–88, 2013.CrossRefGoogle Scholar
  5. 5.
    Carlucci, L., J. Case, S. Jain, and F. Stephan, Non U-shaped vacillatory and team learning, in Algorithmic Learning Theory, Springer, Berlin, 2005, pp. 241–255.Google Scholar
  6. 6.
    Carnap, R., On inductive logic, Philosophy of Science 12(2):72, 1945.CrossRefGoogle Scholar
  7. 7.
    Case, J., and C. Smith, Comparison of identification criteria for machine inductive inference, Theoretical Computer Science 25(2):193–220, 1983.CrossRefGoogle Scholar
  8. 8.
    de Brecht, M., and A. Yamamoto, Interpreting learners as realizers for \({\Sigma }_2^0\) -measurable functions, (Manuscript), 2009.Google Scholar
  9. 9.
    Douglas, H., Inductive risk and values in science, Philosophy of Science 67(4):559–579, 2000.Google Scholar
  10. 10.
    Gärdenfors, P., Knowledge in Flux, MIT Press, Cambridge, 1988.Google Scholar
  11. 11.
    Glymour, C., Theory and Evidence, Princeton University Press, Princeton, 1980.Google Scholar
  12. 12.
    Gold, E. M., Language identification in the limit, Information and Control 10(5):447–474, 1967.CrossRefGoogle Scholar
  13. 13.
    Hempel, C., Valuation and objectivity in science, 1983. Reprinted in J. Fetzer, (ed.), The philosophy of Carl G. Hempel, 2001.Google Scholar
  14. 14.
    Jain, S., D. N. Osherson, J. S. Royer, and A. Sharma, Systems that Learn: An Introduction to Learning Theory, MIT Press, Cambridge, 1999.Google Scholar
  15. 15.
    Kelly, K. T., The Logic of Reliable Inquiry, Oxford University Press, Oxford, 1996.Google Scholar
  16. 16.
    Kelly, K. T., Justification as truth-finding efficiency: How Ockham’s razor works, Minds and Machines 14(4):485–505, 2004.CrossRefGoogle Scholar
  17. 17.
    Kelly, K. T., A topological theory of learning and simplicity, Manuscript, 2005.Google Scholar
  18. 18.
    Kelly, K. T., How simplicity helps you find the truth without pointing at it, in Induction, Algorithmic Learning Theory, and Philosophy, Springer, Berlin, 2007, pp. 111–143.Google Scholar
  19. 19.
    Kelly, K. T., A new solution to the puzzle of simplicity, Philosophy of Science 74(5):561–573, 2007.CrossRefGoogle Scholar
  20. 20.
    Kelly, K. T., Ockham’s razor, empirical complexity, and truth-finding efficiency, Theoretical Computer Science 383(2):270–289, 2007.CrossRefGoogle Scholar
  21. 21.
    Kelly, K. T., Simplicity, truth, and the unending game of science, in T. Raesch, J. van Benthem, S. Bold, B. Loewe, (eds.), Infinite Games: Foundations of the Formal Sciences V, College Press, New York, 2007.Google Scholar
  22. 22.
    Kelly, K. T., Ockham’s Razor, Truth, and Information, Elsevier, Dordrecht, 2008.Google Scholar
  23. 23.
    Kelly, K. T., Simplicity, truth and probability, in P. S. Bandyopadhyay, and M. Forster, (eds.), Handbook of the Philosophy of Science. Volume 7: Philosophy of Statistics, North Holland, Amsterdam, 2011.Google Scholar
  24. 24.
    Kelly, K. T., K. Genin, and H. Lin, Simplicity, truth, and topology, Manuscript, 2014.Google Scholar
  25. 25.
    Kelly, K. T., and C. Glymour, Why probability does not capture the logic of scientific justification, in C. Hitchcock, (ed.), Debates in the Philosophy of Science, Blackwell, New York, 2004, pp. 94–114.Google Scholar
  26. 26.
    Laudan, L., Science and Values, vol. 87, Cambridge Univ Press, Cambridge, 1984.Google Scholar
  27. 27.
    Lin, Hanti, and Kevin T Kelly, Propositional reasoning that tracks probabilistic reasoning, Journal of Philosophical Logic 41(6):957–981, 2012.CrossRefGoogle Scholar
  28. 28.
    Luo, W., and O. Schulte, Mind change efficient learning, Information and Computation 204(6):989–1011, 2006.CrossRefGoogle Scholar
  29. 29.
    Martin, E., and D. N. Osherson, Elements of Scientific Inquiry, MIT Press, Cambridge, 1998.Google Scholar
  30. 30.
    Morrison, M., Unifying Scientific Theories: Physical Concepts and Mathematical Structures, Cambridge University Press, Cambridge, 2007.Google Scholar
  31. 31.
    Osherson, D. N., M. Stob, and S. Weinstein, Systems that Learn: An Introduction to Learning Theory for Cognitive and Computer Scientists, The MIT Press, Cambridge, 1986.Google Scholar
  32. 32.
    Popper, K. R., The Logic of Scientific Discovery, Hutchinson, London, 1959.Google Scholar
  33. 33.
    Putnam, H., Trial and error predicates and the solution to a problem of Mostowski, Journal of Symbolic Logic 30:49–57, 1965.Google Scholar
  34. 34.
    Rott, H., Two dogmas of belief revision, The Journal of Philosophy 97(9):503–522, 2000.Google Scholar
  35. 35.
    Schurz, G., Abductive belief revision in science, in Belief Revision Meets Philosophy of Science, Springer, Berlin, 2011, pp. 77–104.Google Scholar
  36. 36.
    Sharma, A., F. Stephan, and Y. Ventsov, Generalized notions of mind change complexity, in Proceedings of the Tenth Annual Conference on Computational Learning Theory, ACM, 1997, pp. 96–108.Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of PhilosophyCarnegie Mellon UniversityPittsburghUSA

Personalised recommendations