Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T00:06:38.289Z Has data issue: false hasContentIssue false
  • English
  • Français

A Theory of Conclusions

Published online by Cambridge University Press:  01 April 2022

Raymond Dacey
Raymond Dacey*
Affiliation:
University of Oklahoma
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents a theory of conclusions based upon the suggestions of Tukey [21]. The logic offered here is based upon two rules of detachment that occur naturally in probabilistic inference, a traditional rule of acceptance, and a rule of rejection. The rules of detachment provide flexibility: the theory of conclusions can account for both statistical and deductive arguments. The rule of acceptance governs the acceptance of new conclusions, is a variant of the rule of high probability, and is a limiting case of a decision-theoretic rule of acceptance. The rule of rejection governs the removal of previously accepted conclusions on the basis of new evidence. The resulting theory of conclusions is not a decision-theoretic logic but does, through the aforementioned limiting property, provide a line of demarcation between decision and conclusion (i.e., nondecision) logics of acceptance. The theory of conclusions therefore complements decision-theoretic inference.

The theory of conclusions presented here satisfies Tukey's desiderata, specifically:

  1. (1) conclusions are statements which are accepted on the basis of unusually strong evidence;

  2. (2) conclusions are to remain accepted unless and until unusually strong evidence to the contrary arises;

  3. (3) conclusions are subject to future rejection, when and if the evidence against them becomes strong enough.

Finally, the preferred theory of conclusions has a strong conservative bias, reflecting Tukey's aims.

Type
Research Article
Information
Philosophy of Science , Volume 45 , Issue 4 , December 1978 , pp. 563 - 574
Copyright
Copyright © Philosophy of Science Association 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

I would like to thank C. Glymour, K. Lehrer, J. Pitt, S. Spielman, P. Suppes, and an anonymous referee for their criticisms and suggestions.

References

[1] Bezdek, X. and Hannon, B. “Energy, Manpower, and the Highway Trust Fund.” Science 4152 (1974): 669–675.CrossRefGoogle Scholar
[2] Birnbaum, Allen. “The Neyman-Pearson Theory as Decision Theory, and as Inference Theory; with a Criticism of The Lindley-Savage Argument for Bayesian Theory.” Synthese 36 (1977): 19–49.CrossRefGoogle Scholar
[3] Dacey, R. “The Effects of Theory and Data in Economic Prediction.” Kyklos 28 (1975): 407–411.CrossRefGoogle Scholar
[4] Freund, J. “On the Confirmation of Scientific Theories.” Philosophy of Science 17 (1950): 87–94.CrossRefGoogle Scholar
[5] Hesse, Mary. The Structure of Scientific Inference. Berkeley: University of California Press, 1974.CrossRefGoogle Scholar
[6] Hilpinen, R. Rules of Acceptance and Inductive Logic. (Fasc. 22 in Acta Philosophica Fennica). Amsterdam: North-Holland Publishing Company, 1968.Google Scholar
[7] Hintikka, J. “Towards a Theory of Inductive Generalization.” Proceedings of the 1964 International Congress for Logic, Methodology, and Philosophy of Science. Y. Bar-Hillel, Editor. Amsterdam: North-Holland Publishing Company, 1965, pp. 274–288.Google Scholar
[8] Hintikka, J. “On a Combined System of Inductive Logic.” Studia Logico-Mathematica et Philosophica in Honorem Rolf Nevanlinna (Fasc. 18 in Acta Philosophica Fennica). Amsterdam: North-Holland Publishing Company, 1965, pp. 21–30.Google Scholar
[9] Hintikka, J. “A Two-Dimensional Continuum of Inductive Methods.” In Aspects of Inductive Logic, Edited by Hintikka, and Suppes, . Amsterdam: North-Holland Publishing Company, 1966, pp. 113–132.CrossRefGoogle Scholar
[10] Jeffrey, Richard C. The Logic of Decision. New York: McGraw-Hill Book Company, 1965.Google Scholar
[11] Lehrer, K. “Induction and Conceptual Change.” Synthese 23 (1971): 206–225.CrossRefGoogle Scholar
[12] Lehrer, K. “Induction, Rational Acceptance, and Minimally Inconsistent Sets.” In G. Maxwell and R. M. Anderson (eds.), Induction, Probability, and Confirmation (Minnesota Studies in the Philosophy of Science, Vol. VI). Minneapolis: University of Minnesota Press, 1975, pp. 295–323.Google Scholar
[13] Levi, I. Gambling With Truth. Cambridge: MIT Press, 1973.Google Scholar
[14] Lewis, David. “Probabilities of Conditionals and Conditional Probabilities.” The Philosophical Review 85 (1976): 297–315.CrossRefGoogle Scholar
[15] Marschak, J. “Information, Decision, and the Scientist.” In C. Cherry (ed.), Pragmatic Aspects of Human Communication. Dordrecht: D. Reidel Publishing Company, 1976, pp. 145–178.Google Scholar
[16] Niiniluoto, I. and Tuomela, R. Theoretical Concepts and Hypothetico-Inductive Inference. Dordrecht: D. Reidel Publishing Company, 1973.CrossRefGoogle Scholar
[17] Savage, L. J. The Foundations of Statistics. New York: J. Wiley and Sons, Inc., 1954.Google Scholar
[18] Schaefer, D. and Weiss, T. “The Use of Simulation Techniques in Historical Analysis: Railroads versus Canals.” The Journal of Economic History 31 (1971): 854–884.CrossRefGoogle Scholar
[19] Shafer, Glenn. A Mathematical Theory of Evidence. Princeton: Princeton University Press, 1976.CrossRefGoogle Scholar
[20] Suppes, P. “Probabilistic Inference and the Concept of Total Evidence.” In Aspects of Inductive Logic, Edited by Hintikka, and Suppes, . Amsterdam: North-Holland Publishing Company, 1966. pp. 49–65.CrossRefGoogle Scholar
[21] Tukey, J. “Conclusions vs. Decisions.” Technometrics 2 (1960): 423–433.CrossRefGoogle Scholar
[22] von Neumann, J. and Morgenstern, O. The Theory of Games and Economic Behavior. Princeton: Princeton University Press, 1944.Google Scholar
[23] Weibull, W. “A Statistical Distribution Function of Wide Applicability.” The Journal of Applied Mechanics (1951): 293–297.CrossRefGoogle Scholar