Abstract
In this chapter some basic features and applications of the theory of inductive probabilities (TIP) are described.
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Notes
All non-quantified variables - such as n, e„ and e„ - contained in the formulae and requirements of adequacy stated herein should be interpreted as universally quantified.
The axiom of convergence was suggested to Carnap in 1953 by Hilary Putnam, who proposed for it the name “Reichenbach axiom” (cf. Carnap, 1980, p. 120).
It can also be proved that (Exc) is logically equivalent to the conjunction of two requirements given in terms of special values (see Kuipers, 1978, pp. 40–41).
Later this view was defended by Carnap (1950, pp. 208 and 571–575).
Apart from some slight terminological modification, this classification is borrowed from Carnap (1950, pp. 205–208).
The inference from a sample to the population is usually referred to as the inverse inference (cf. Carnap, 1950, pp. 207–208).
On the whole, Carnap devotes little attention to statistical inferences. He only provides some formulae to calculate the probability of point hypotheses such as “q 1 = 0.3“ for a finite population (Carnap, 1950, p. 570 and 1952, pp. 30–32). As far as I know during the fifties one of the few attempts to investigate the possible statistical implications of Carnap’s TIP was made by Tintner (1949) who referred to the manuscript of The Logical Foundations of Probability (Carnap, 1950).
For a more detailed description of (multivariate) Bernoulli processes see Feller (1968, Ch. 6) and La Valle (1970, Ch. 11).
The notions of “multivariate Bernoulli process/multinomial context” used herein correspond approximately to the notions of “repeatable experiment/multinomial context” as defined by Kuipers (1978, pp. 114–115).
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© 1993 Springer Science+Business Media Dordrecht
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Festa, R. (1993). The Theory of Inductive Probabilities: Basic Features and Applications. In: Optimum Inductive Methods. Synthese Library, vol 232. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8131-8_2
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DOI: https://doi.org/10.1007/978-94-015-8131-8_2
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