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Inductive systematization: Definition and a critical survey

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Abstract

In 1958, to refute the argument known as ‘the theoretician's dilemma’, Hempel suggested that theoretical terms might be logically indispensable for inductive systematization of observational statements. This thesis, in some form or another, has later been supported by Scheffler, Lehrer, and Tuomela, and opposed by Bohnert, Hooker, Stegmüller, and Cornman. In this paper, a critical survey of this discussion is given. Several different putative definitions of the crucial notion ‘inductive systematization achieved by a theory’ are discussed by reference to the properties of inductive inference. The consequences of the following differences between deductive and inductive inference are emphasized: the lack of simple transitivity properties (even in a modified sense) of inductive inference, and the failure of the inductive analogue of the converse of The Deduction Theorem. The main conclusions are: (i) Hempel's original thesis may very well be right but his argument for it is unsatisfactory, (ii) theoretical terms can be logically indispensable for a non-Hempelian kind of inductive systematization, relative to both Craigian and Ramseyan elimination, (iii) Lehrer's attempt to prove the indispensability of theoretical terms for inductive-probabilistic systematization is, as a modification of Hempelian kind of inductive-deterministic systematization, unsatisfactory, and (iv) there does not seem to be much hope of escaping the conclusion (ii), if it is true, by extending the Craigian replacement programme along the lines suggested by Cornman.

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Bibliography

  • Batens, D., ‘Some Objections to Keith Lehrer's Rule IR’, The British Journal for the Philosophy of Science 22 (1971), 357–62.

    Google Scholar 

  • Bohnert, H., The Interpretation of a Theory, Ph.D. Dissertation, University of Pennsylvania, 1961.

  • Bohnert, H., ‘Communication by Ramsey-Sentence Clause’, Philosophy of Science 34 (1967), 341–7.

    Google Scholar 

  • Bohnert, H., ‘In Defense of Ramsey's Elimination Method’, Journal of Philosophy 65, (1968), 275–81.

    Google Scholar 

  • Brody, B. A., ‘Confirmation and Explanation’, Journal of Philosophy 65, (1968), 282–99.

    Google Scholar 

  • Carnap, R., Logical Foundations of Probability, The University of Chicago Press, Chicago, 1950.

    Google Scholar 

  • Carnap, R., ‘The Aim of Inductive Logic’, in Logic, Methodology, and Philosophy of Science (ed. by E. Nagel, P. Suppes, and A. Tarski), Stanford University Press, Stanford, 1962.

    Google Scholar 

  • Carnap, R., Philosophical Foundations of Physics (ed. by M. Gardner), New York 1966.

  • Coffa, J., ‘Deductive Predictions’, Philosophy of Science 35 (1968), 279–83.

    Google Scholar 

  • Cornman, J. W., ‘Craig's Theorem, Ramsey-Sentences, and Scientific Instrumentalism’, this issue, p. 82–128, 1973.

  • Craig, W., ‘On Axiomatizability Within a System’, The Journal of Symbolic Logic 18 (1953), 30–2.

    Google Scholar 

  • Craig, W., ‘Replacement of Auxiliary Expressions’, Philosophical Review 65 (1956), 38–55.

    Google Scholar 

  • Craig, W., ‘Replacement of Auxiliary Expressions’, Philosophical Review 65 (1956), 38–55.

    Google Scholar 

  • Craig, W., ‘Bases for First-Order Theories and Subtheories’, The Journal of Symbolic Logic 25 (1960), 97–142.

    Google Scholar 

  • Good, I. J., ‘Weight of Evidence, Corroboration, Explanatory Power, Information and the Utility of Experiments’, Journal of Royal Statistical Society B 22 (1959), 319–31.

    Google Scholar 

  • Greeno, J. G., ‘Evaluation of Statistical Hypotheses Using Information Transmitted’, Philosophy of Science 37 (1970), 279–94.

    Google Scholar 

  • Greeno, J. G., ‘Theoretical Entities in Statistical Explanation’, in PSA 1970, Boston Studies in the Philosophy of Science, Vol. VIII. (ed. by R. C. Buck and R. S. Cohen), D. Reidel Publishing Company, Dordrecht, 1971, p. 3.

    Google Scholar 

  • Hacking, I., Logic of Statistical Inference, Cambridge University Press, Cambridge 1965.

    Google Scholar 

  • Hempel, C. G., ‘Studies in the Logic of Confirmation’, Mind 54 (1945), 1–26, 97–121. Reprinted in C. G. Hempel, Aspects of Scientific Explanation and Other Essays in the Philosophy of Science, The Free Press, New York, 1965.

    Google Scholar 

  • Hempel, C. G., ‘Studies in the Logic of Explanation’, Philosophy of Science 15 (1948) 135–75. Reprinted in Aspect of Scientific Explanation.

    Google Scholar 

  • Hempel, C. G., ‘Theoretician's Dilemma: A Study in the Logic of Theory Construction’, in Minnesota Studies in the Philosophy of Science, Vol. II (ed. by H. Feigl, M. Scriven, and G. Maxwell), University of Minnesota Press, Minneapolis 1958. Reprinted in Aspects in Scientific Explanation. References are to this book.

    Google Scholar 

  • Hempel, C. G., ‘Inductive Inconsistencies’, Synthese 12 (1960), 439–69. Reprinted in Aspects of Scientific Explanation.

    Google Scholar 

  • Hempel, C. G., ‘Deductive-Nomological vs. Statistical Explanation’, in Minnesota Studies in the Philosophy of Science, Vol. III (ed. by H. Feigl, and G. Maxwell), University of Minnesota Press, Minneapolis, 1962.

    Google Scholar 

  • Hempel, C. G., ‘Implications of Carnap's Work for the Philosophy of Science’, The Philosophy of Rudolf Carnap (The Library of Living Philosophers Vol. XI) (ed. by P. A. Schilpp), Open Court, La Salle, Illinois 1963.

    Google Scholar 

  • Hempel, C. G., ‘Aspects of Scientific Explanation’, in Aspects of Scientific Explanation, 1965.

  • Hempel, C. G., ‘Maximal Specificity and Lawlikeness in Probabilistic Explanation’, Philosophy of Science 35 (1968), 116–33.

    Google Scholar 

  • Hempel, C. G., ‘On the “Standard Conception” of Scientific Theories’, in Analyses of Theories and Methods of Physics and Psychology (Minnesota Studies in the Philosophy of Science, Vol. IV) (ed. by M. Radner and S. Winokur), University of Minnesota Press, Minneapolis, 1970.

    Google Scholar 

  • Hesse, M. B., ‘Consilience of Inductions’, in The Problem of Inductive Logic (ed. by I. Lakatos), North-Holland, Amsterdam, 1968.

    Google Scholar 

  • Hesse, M. B., ‘Theories and Transitivity of Confirmation’, Philosophy of Science 37 (1970a), 50–63.

    Google Scholar 

  • Hesse, M. B., ‘An Inductive Logic of Theories’, in Analyses of Theories and Methods of Physics and Psychology (Minnesota Studies in the Philosophy of Science, Vol. IV) (ed. by M. Radner and S. Winokur), University of Minnesota Press, Minneapolis, 1970b.

    Google Scholar 

  • Hilpinen, R., Rules of Acceptance and Inductive Logic, Acta Philosophica Fennica, Fasc. XXII, North-Holland, Amsterdam, 1968.

    Google Scholar 

  • Hilpinen, R., ‘On the Information Provided by Observations’, in Information and Inference (ed. by J. Hintikka and P. Suppes), D. Reidel Publishing Company, Dordrecht, 1970, p. 97.

    Google Scholar 

  • Hintikka, K. J., ‘Distributive Normal Forms and Deductive Interpolation’, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 10 (1964), 185–91.

    Google Scholar 

  • Hintikka, K. J., ‘Distributive Normal Forms in First-Order Logic’, in Formal Systems and Recursive Functions (ed. by J. Crossley and M. Dummett), Amsterdam 1965.

  • Hintikka, K. J., ‘The Varieties of Information and Scientific Explanation’, in Logic, Methodology and Philosophy of Science III, Proceedings of the 1967 International Congress (ed. by B. van Rootselaar and J. F. Staal), North-Holland, Amsterdam, 1968.

    Google Scholar 

  • Hintikka, K. J., ‘On the Different Ingredients of an Empirical Theory’, forthcoming in Logic, Methodology, and Philosophy of Science IV, Proceedings of the 1971 International Congress (ed. by P. Suppes et al.), North-Holland, Amsterdam, 1973.

    Google Scholar 

  • Hintikka, K. J. and Hilpinen, R., ‘Knowledge, Acceptance, and Inductive Logic’, in Aspects of Inductive Logic (ed. by J. Hintikka and P. Suppes), North-Holland, Amsterdam, 1966.

    Google Scholar 

  • Hintikka, K. J. and Niiniluoto, I., ‘On Theoretical Terms and Their Ramsey-Elimination: An Essay in the Logic of Science’, forthcoming, 1973.

  • Hintikka, K. J. and Tuomela, R., ‘Towards a General Theory of Auxiliary Concepts and Definability in First-Order Theories’, in Information and Inference (ed. by J. Hintikka and P. Suppes), D. Reidel Publishing Company, Dordrecht, 1970, p. 298.

    Google Scholar 

  • Hooker, C. A., ‘Craigian Transcriptionism’, American Philosophical Quarterly 5 (1968), 152–63.

    Google Scholar 

  • Jeffrey, R. C., ‘Valuation and Acceptance of Scientific Hypotheses’, Philosophy of Science 23 (1956), 237–46.

    Google Scholar 

  • Jeffrey, R. C., ‘Statistical Explanation vs. Statistical Inference’, in Essays in Honor of Carl G. Hempel, D. Reidel Publishing Company, Dordrecht, 1969, p. 104.

    Google Scholar 

  • Jeffrey, R. C., ‘Remarks on Explanatory Power’, in PSA 1970, Boston Studies in the Philosophy of Science, Vol. VIII (ed. by R. C. Buck and R. S. Cohen), D. Reidel Publishing Company, Dordrecht, 1971, p. 40.

    Google Scholar 

  • Kyburg, H. E. Jr., ‘Probability, Rationality, and a Rule of Detachment’, in Proceedings of the 1964 Intenational Congress for Logic, Methodology, and Philosophy of Science (ed. by Y. Bar-Hillel), North-Holland, Amsterdam, 1965.

    Google Scholar 

  • Kyburg, H. E. Jr., Probability and Inductive Logic, The Macmillan Company, Collier-Macmillan Limited, London, 1970a.

    Google Scholar 

  • Kyburg, H. E. Jr., ‘Conjunctivitis’, in Swain (1970), 1970b.

    Google Scholar 

  • Lehrer, K., ‘Theoretical Terms and Inductive Inference’, American Philosophical Quarterly, Monograph Series, Studies in the Philosophy of Science, Monograph No. 3, 1969, 30–41.

  • Lehrer, K., ‘Justification, Explanation, and Induction’, in Swain (1970), 1970a.

    Google Scholar 

  • Lehrer, K., ‘Induction, Reason, and Consistency’, The British Journal for the Philosophy of Science 21 (1970b), 103–14.

    Google Scholar 

  • Lehrer, K., ‘Induction and Conceptual Change’, Synthese 23 (1971), 206–25.

    Google Scholar 

  • Levi, I., Gambling with Truth: An Essay on Induction and the Aims of Science, Routledge & Kegan Paul Ltd., London, 1967.

    Google Scholar 

  • Lewis, D., ‘How to Define Theoretical Terms’, The Journal of Philosophy 67 (1970), 427–46.

    Google Scholar 

  • Mackie, J. L., ‘The Relevance Criterion of Confirmation’, The British Journal for the Philosophy of Science 20 (1969), 27–40.

    Google Scholar 

  • Maxwell, G., ‘Structural Realism and the Meaning of Theoretical Terms’, in Analysis of Theories and Methods of Physics and Psychology (Minnesota Studies in the Philosophy of Science, Vol. IV) (ed. by M. Radner and S. Winokur), University of Minnesota Press, Minneapolis 1970.

    Google Scholar 

  • Niiniluoto, I., ‘Can We Accept Lehrer's Inductive Rule?’, Ajatus 33, Yearbook of the Philosophical Society of Finland, (1971), 254-65.

  • Niiniluoto, I., ‘Empirically Trivial Theories and Inductive Systematization’, forthcoming in Logic, Language, and Probability, A Selection of Papers Contributed to Sections 4, 6, and 11 of the IVth International Congress in Logic, Methodology, and Philosophy of Science, (ed. by Radu J. Bogdan and I. Niiniluoto), D. Reidel Publishing Company, Dordrecht, 1973.

    Google Scholar 

  • Niiniluoto, I. and Tuomela, R., Theoretical Concepts and Hypothetico-Inductive Inference, forthcoming, 1973.

  • Pietarinen, J., ‘Quantitative Tools for Evaluating Scientific Systematizations’, in Information and Inference (ed. by J. Hintikka and P. Suppes), D. Reidel Publishing Company, Dordrecht, 1970, p. 123.

    Google Scholar 

  • Pietarinen, J. and Tuomela, R., ‘On Measures of the Explanatory Power of Scientific Theories’, Akten des 14. Internationalen Kongresses für Philosophie, Wien 2.–9. September 1968, Vol. 3, Universität Wien, Verlag Herder, Wien, 1968.

    Google Scholar 

  • Popper, K., The Logic of Scientific Discovery, Hutchinson and Company, London, 1959.

    Google Scholar 

  • Popper, K., ‘The Propensity Interpretation of Probability’, The British Journal for the Philosophy of Science 10 (1959–60), 25–42.

    Google Scholar 

  • Putnam, H., ‘Craig's Theorem’, The Journal of Philosophy 62 (1965), 152–60.

    Google Scholar 

  • Ramsey, F. P., ‘Theories’, in F. P. Ramsey, The Foundations of Mathematics and Other Logical Essays, Littlefield, Adams & Co., Paterson, New Jersey 1931.

    Google Scholar 

  • Rescher, N., ‘Theory of Evidence’, Philosophy of Science 25 (1958) 83–94.

    Google Scholar 

  • Rosenkrantz, R. D., ‘On Explanation’, Synthese 20 (1969) 335–70.

    Google Scholar 

  • Rosenkrantz, R. D., ‘Experimentation as Communication with Nature’, in Information and Inference (ed. by J. Hintikka and P. Suppes), D. Reidel Publishing Company, Dordrecht, 1970, p. 58.

    Google Scholar 

  • Salmon, W. C., ‘Consistency, Transitivity, and Inductive Support’, Ratio 7 (1965), 164–69.

    Google Scholar 

  • Salmon, W. C., ‘Statistical Explanation’, in The Nature and Function of Scientific Theories (ed. by R. G. Colodny), University of Pittsburgh Press, Pittsburgh 1970.

    Google Scholar 

  • Salmon, W. C., ‘Explanation and Relevance: Comments on James G. Greeno's “Theoretical Entities in Statistical Explanation”’, in PSA 1970, Boston Studies in The Philosophy of Science, Vol. VIII (ed. by R. C. Buck and R. S. Cohen), D. Reidel Publishing Company, Dordrecht, 1971, p. 27.

    Google Scholar 

  • Savage, L. J., The Foundations of Statistics, John Wiley and Sons Inc., New York, 1954.

    Google Scholar 

  • Scheffler, I., The Anatomy of Inquiry: Philosophical Studies in the Theory of Science, Alfred A. Knopf, New York, 1963.

    Google Scholar 

  • Scheffler, I., ‘Reflections on the Ramsey Method’, The Journal of Philosophy 65 (1968), 269–74.

    Google Scholar 

  • Schick, F., ‘Three Logics of Belief’, in Swain (1970)

    Google Scholar 

  • Skyrms, B., ‘Nomological Necessity and the Paradoxes of Confirmation’, Philosophy of Science 33 (1966), 230–49.

    Google Scholar 

  • Smokler, H., ‘Conflicting Conception of Confirmation’, Journal of Philosophy 65 (1968), 300–12.

    Google Scholar 

  • Sneed, J., The Logical Structure of Mathematical Physics, D. Reidel Publishing Company, Dordrecht, 1971.

    Google Scholar 

  • Stegmüller, W., Wissenschaftliche Erklärung und Begründung, Probleme und Resultate der Wissenschaftstheorie und Analytischen Philosophie, Band I, Springer-Verlag, Berlin, Heidelberg & New York, 1969.

    Google Scholar 

  • Stegmüller, W., Theorie und Erfahrung, Probleme und Resultate der Wissenschaftstheorie und Analytischen Philosophie, Band II, Springer-Verlag, Berlin, Heidelberg & New York, 1970.

    Google Scholar 

  • Swain, M. (ed.), Induction, Acceptance, and Rational Belief, D. Reidel Publishing Company, Dordrecht, 1970.

    Google Scholar 

  • Tuomela, R., Auxiliary Concepts Within First-Order Scientific Theories, Dept. of Philosophy, Stanford University, Stanford, 1969.

    Google Scholar 

  • Tuomela, R., The Role of Theoretical Concepts in Neobehavioristic Theories, Reports from the Institute of Philosophy, University of Helsinki, No. 1, 1971.

  • Tuomela, R., Theoretical Concepts, Springer-Verlag, Wien, forthcoming 1973.

    Google Scholar 

  • von Wright, G. H., ‘A Note on Confirmation Theory and on the Concept of Evidence’, Scientia, Vol. CV, No. DCCI–DCCII (1970), 1–12.

    Google Scholar 

  • von Wright, G. H., Explanation and Understanding. Cornell University Press, Cornell, 1971.

    Google Scholar 

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Authors and Affiliations

  1. National Research Council for Humanities, Academy of Finland, Finland

    Ilkka Niiniluoto

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  1. Ilkka Niiniluoto
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The work for this paper was initiated in a research group supported by The Emil Aaltonen Foundation (Emil Aaltosen Säätiö). I am greatly indebted to Professor Raimo Tuomela for many discussions concerning the subject-matter of this paper and earlier drafts of it.

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Niiniluoto, I. Inductive systematization: Definition and a critical survey. Synthese 25, 25–81 (1972). https://doi.org/10.1007/BF00484998

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