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Convergence to the Truth and Nothing but the Truth

Published online by Cambridge University Press:  01 April 2022

Kevin T. Kelly  and
Clark Glymour
Kevin T. Kelly
Affiliation:
Department of Philosophy, Carnegie-Mellon University
Clark Glymour
Affiliation:
University of Pittsburgh
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Abstract

One construal of convergent realism is that for each clear question, scientific inquiry eventually answers it. In this paper we adapt the techniques of formal learning theory to determine in a precise manner the circumstances under which this ideal is achievable. In particular, we define two criteria of convergence to the truth on the basis of evidence. The first, which we call EA convergence, demands that the theorist converge to the complete truth “all at once”. The second, which we call AE convergence, demands only that for every sentence in the theorist's language, there is a time at which the theorist settles the status of the sentence. The relative difficulties of these criteria are compared for effective and ineffective agents. We then examine in detail how the enrichment of an agent's hypothesis language makes the task of converging to the truth more difficult. In particular, we parametrize first-order languages by predicate and function symbol arity, presence or absence of identity, and quantifier prefix complexity. For nearly each choice of values of these parameters, we determine the senses in which effective and ineffective agents can converge to the complete truth on an arbitrary structure for the language. Finally, we sketch directions in which our learning theoretic setting can be generalized or made more realistic.

Type
Research Article
Information
Philosophy of Science , Volume 56 , Issue 2 , June 1989 , pp. 185 - 220
Copyright
Copyright © 1989 by the Philosophy of Science Association

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Footnotes

†

We thank Dan Osherson for helpful comments on a draft of this paper.

References

REFERENCES

Angluin, D. and Smith, C. H. (1982), A Survey of Inductive Inference Methods. Technical Report 250, Yale University.Google Scholar
Biermann, A. W. and Feldman, J. A. (1972), “A Survey of Results in Grammatical Inference”, in S. Watanabe (ed.), Frontiers of Pattern Recognition. New York: Academic Press, pp. 32–43.Google Scholar
Carbonell, J. and Gil, Y. (1987), “Learning by Experimentation”, in M. B. Morgan (ed.), Proceedings of the Fourth International Workshop on Machine Learning. Los Altos, CA: Morgan Kaufmann, pp. 256–266.CrossRefGoogle Scholar
Dreben, B. and Goldfarb, W. (1979), The Decision Problem: Solvable Classes of Quantificational Formulas. Reading, Mass.: Addison-Wesley.Google Scholar
Gold, E. M. (1965), “Limiting Recursion”, Journal of Symbolic Logic 30: 28–48.CrossRefGoogle Scholar
Gold, E. M. (1967), “Language Identification in the Limit”, Information and Control 10: 447–474.CrossRefGoogle Scholar
Hilbert, D. and Bernays, P. (1968), Grundlagen der Mathematik. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Kearns, M.; Li, M.; Pitt, L.; and Valiant, L. (1987), “Recent Results on Boolean Concept Learning”, in M. B. Morgan (ed.), Proceedings of the Fourth International Workshop on Machine Learning. Los Altos, CA: Morgan Kaufmann, pp. 337–352.CrossRefGoogle Scholar
Osherson, D.; Stob, M.; and Weinstein, S. (1986), Systems that Learn. Cambridge, Mass.: MIT Press.Google Scholar
Osherson, D., and Weinstein, S. (1986), “Identification in the Limit of First Order Structures”, Journal of Philosophical Logic 15: 44–81.CrossRefGoogle Scholar
Osherson, D., and Weinstein, S. (1989), “Identifiable Collections of Countable Structures”, Philosophy of Science 56: 94–105.CrossRefGoogle Scholar
Peirce, C. S. (1965), The Collected Papers of Charles Sanders Peirce, vol. 5. Hartshorne, C. and Weiss, P., (eds.). Cambridge, Mass.: Belknap Press.Google Scholar
Popper, K. R. (1963), Conjectures and Refutations. New York: Harper and Row.Google Scholar
Rogers, H. (1987), Theory of Recursive Functions and Effective Computability. Cambridge, Mass.: MIT Press.Google Scholar
Schank, R.; Collins, G.; and Hunter, L. (1986), “Transcending Inductive Category Formation in Learning”, Brain and Behavioral Sciences 9: 639–686.CrossRefGoogle Scholar