Abstract
In this chapter the relationships between the contextual view of prior probabilities and some recent methodological programmes of research are considered; moreover some possible developments of the contextual view are suggested.
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This reflects a limitation common to most studies on scientific enterprise. With reference to this, Laudan (1983, p. 2) points out that “students of the development of science, whether sociologists or philosophers, have alternatively been preoccupied with explaining consensus in science or with highlighting disagreement and divergence. Those contrasting focuses would be harmless if all they represented were differences of emphasis or interest.… What creates tension is that neither approach has shown itself to have the explanatory resources for dealing with both.”
Niiniluoto (1987, p. 473) points out that “measures of verisimilitude always have a pragmatic dimension, by being dependent on our cognitive interests”. More generally, he remarks that “science is a fallible and progressive enterprise which is run by historically developing scientific communities. Our tools for analyzing science should be flexible enough to take into account this richness of scientific practice.” Other interesting remarks on the context-dependence of verisimilitude measures are made by Niiniluoto (ibid., Chapter 13.4).
For instance, one might look for a contextual justification of certain mixtures of Dirichlet distributions which have been suggested as appropriate priors for some kinds of multinomial contexts: see Good (1965, 1983), Dalai and Hall (1983), and Skyrms (1993?). In particular, Skyrms (1993?) shows that certain Dirichlet mixtures can be used to build exchangeable inductive methods capable of dealing with the so-called analogy by similarity (cf. Chapter 6.1). Moreover, one might look for a contextual justification of certain exchangeable inductive methods which attribute a positive probability to generalizations: see Hintikka (1966), Hintikka and Niiniluoto (1976), Kuipers (1978, Chapter 6) and Jamison (1970, pp. 50–53). In particular, Jamison (ibid.) specifies the prior distribution (on a parameter vector q) equivalent to Hintikka’s inductive methods.
Several Bayesian statistical analyses of Markov processes have been proposed, e.g., Martin (1967). The problems concerning the inductive inferences relative to Markov processes and other `non-Bernoulli’ multicategorical processes have also been considered within the conceptual framework of TIP: see Achinstein (1963), Carnap (1963), Diaconis and Freedman (1980), Kuipers (1988), Skyrms (1991).
More generally, quantitative processes include all those experimental processes where the result of a trial is the value of a given quantity.
For instance, a CC-solution to EPO might be based on an external estimate of the entropy of the multivariate Bernoulli process under consideration (cf. Chapter 9, note 13).
Note that various measures of quantitative variability have been defined in statistics and in some empirical sciences (see, for instance, formula (10.1)).
Moreover, an interesting problem concerns the analysis of LPO in those cases where the inductive conclusion of a Bayesian inference is equated with the posterior distribution on the parameter (vector). Of course a necessary presupposition for such analysis is the definition of an appropriate measure of the distance between any possible posterior distribution and any possible value of the parameter (vector).
In Chapter 8.6 the equivalence between the CC-solution and the V-solution to EPO was proved and explained. The existence of similar relationships between alternative V-solutions to EPO and alternative CC-solutions remains an open question.
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© 1993 Springer Science+Business Media Dordrecht
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Festa, R. (1993). Concluding Remarks. In: Optimum Inductive Methods. Synthese Library, vol 232. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8131-8_11
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DOI: https://doi.org/10.1007/978-94-015-8131-8_11
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