Abstract
In this chapter the so-called de Finetti’s representation theorem (DFRT) is used to elucidate some conceptual relationships between TIP and the analysis of multinomial inferences in BS.
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Notes
De Finetti (1937, pp. 124–129) proved his representation theorem for the case where k = 2. Subsequently, DFRT has been generalized to k > 2 (cf. Good, 1965, pp. 21–23).
Cf. Hintikka (1971, pp. 329–336).
Cf. Gaifman (1971, § 3) and Fine (1973, p. 194). See also Jeffrey’s Editor’s Note to Carnap (1980, § 20, p. 120 ).
De Finetti conceived his representation theorem as a tool to get rid of unknown objective probabilities and, accordingly, considered probability distributions on unknown objective probabilities as “mere mathematical fictions” (Hintikka, 1971, p. 333).
It may also be assumed that, in certain cases, X believes that the ‘multivariate Bernoulli model’ provides a convenient approximation to (idealization of) the real ‘structure’ of the multicategorical process Ex in examination.
For the ‘convergence towards the truth’ of predictive probabilities see Hintikka (1971, pp. 336–339). See also Niiniluoto (1980, pp. 433–434 and p. 454, note 34).
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© 1993 Springer Science+Business Media Dordrecht
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Festa, R. (1993). Exchangeable Inductive Methods, Bayesian Statistics, and Convergence Towards the Truth. In: Optimum Inductive Methods. Synthese Library, vol 232. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8131-8_5
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DOI: https://doi.org/10.1007/978-94-015-8131-8_5
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