Probability, Dynamics and Causality pp 89-112 | Cite as

# Analogy and Exchangeability in Predictive Inferences

## Abstract

An important problem in inductive probability theory is the design of exchangeable analogical methods, i.e., of exchangeable inductive methods that take into account certain considerations of analogy by similarity for predictive inferences. Here a precise reformulation of the problem of predictive analogy is given and a new family of exchangeable analogical methods is introduced.

Firstly, it is proved that the exchangeable analogical method introduced by Skyrms (1993) does not satisfy the best known general principles of predictive analogy. Secondly, Skyrms’s approach — consisting of the usage of particular hyper-Carnapian methods, i.e., mixtures of Carnapian inductive methods — is adopted in the design of a new family of exchangeable analogical methods. Lastly, it is proved that such methods satisfy an interesting general principle of predictive analogy.

## Keywords

Prior Probability Inductive Method Inductive Logic Analogy Property Prior Vector## Preview

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## References

- Carnap, R.: 1950,
*The Logical Foundations of Probability*, The University of Chicago Press, Chicago (2nd ed. 1962).Google Scholar - Carnap, R.: 1952,
*The Continuum of Inductive Methods*, University of Chicago Press, Chicago.MATHGoogle Scholar - Carnap, R.: 1980, ‘A Basic System of Inductive Logic, Part 2’, in R. Jeffrey (ed.),
*Studies in Inductive Logic and Probability*, Vol. II, University of California Press, Berkeley, pp. 7–155.Google Scholar - Carnap, R. and Stegmüller, W.: 1959,
*Induktive Logik und Wahrscheinlichkeit*, Springer-Verlag, Wien.MATHCrossRefGoogle Scholar - Festa, R.: 1987, ‘Theory of Similarity, Similarity of Theories, and Verisimilitude’, in T. Kuipers (ed.),
*What is Closer-to-the-truth?*, Rodopi, Amsterdam, pp. 145–176.Google Scholar - Festa, R.: 1993,
*Optimum Inductive Methods. A Study in Inductive Probabilities, Bayesian Statistics, and Verisimilitude*, Kluwer, Dordrecht.Google Scholar - Helman, D. H. (ed.): 1988,
*Analogical Reasoning*, Kluwer, Dordrecht.MATHGoogle Scholar - Kuipers, T.: 1978,
*Studies in Inductive Probability and Rational Expectation*, Reidel, Dordrecht.MATHCrossRefGoogle Scholar - Kuipers, T.: 1984a, ‘Two Types of Inductive Analogy by Similarity’,
*Erkenntnis***21**,63–87.MathSciNetCrossRefGoogle Scholar - Kuipers, T.: 1984a, ‘Inductive Analogy in Carnapian Spirit’, in: P. Asquith and P. Kitcher (eds.),
*PSA 1984*, Vol. I, Philosophy of Science Association, East Lansing, pp. 157–167.Google Scholar - Kuipers, T.: 1988, ‘Inductive Analogy by Similarity and Proximity’, in Helman (1988), pp. 299–313.Google Scholar
- Lindgren, B.: 1976,
*Statistical Theory*, Third Edition, Macmillan Publishing Co., New York.MATHGoogle Scholar - Niiniluoto, I.: 1988, ‘Analogy by Similarity in Scientific Reasoning’, in Helman (1988), pp. 271–298.Google Scholar
- Skyrms, B.: 1993, ‘Analogy by Similarity in Hyper-Carnapian Inductive Logic’, in J. Earman (ed.),
*Philosophical Problems of the Internal and External Worlds. Essays in the Philosophy of Adolf Grünbaum*, University of Pittsburgh Press, Pittsburgh, pp. 273–282.Google Scholar - Spohn, W.: 1983, ‘Analogy and Inductive Logic: a Note on Niiniluoto’,
*Erkenntnis***16**, 35–52.MathSciNetGoogle Scholar