New PDF release: Aspects of Inductive Logic

By Jaakko Hintikka

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Without this restriction the stimulus-sampling model is a slight generalization of the Bayesian one. H may be remarked that the stimulus-sampling model, with c estimated from experimental data, does not appear to fit data very well (for some results in this connection, see Suppes and Atkinson [1960], Ch. 10). Of course, many Bayesians would almost be pleased that the stimulus-sampling model did not fit well for they could say "I would hardly expect the simple Bayesian model you have defined to provide any sort of decent fit to human CONCEPT FORMATION AND BAYESIAN DECISIONS 41 prediction data".

Corresponding to the space just constructed a space of this sort is easily described for the strings oflength two, but I shall not go into details, because the present stage of our analysis of these problems, reinforced by some preliminary experimental evidence, indicates that this latter method is not the most desirable theoretical approach. The space [ did describe above for the strings of length two is deceptively simple. The extension of this same kind of description to strings of lengths greater than two soon becomes rather awkward if sufficient dimensions are required to locate with precision any grammar (or concept) in the set of all grammars.

The point of this section is to examine empirical situations, or simplified experimental situations roughly corresponding to the empirical situations in which it does not seem possible to avoid these combinatorial problems. It is a fundamental thesis of this paper that it is in dealing with situations in which new concepts must be formed that the standard formulations of the Bayesian approach are most inadequate. To give the discussion some definiteness and concreteness, I shall primarily restrict myself to description of a class of experiments in which the problem facing the subject is to learn the grammar of a set of strings.

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Aspects of Inductive Logic by Jaakko Hintikka

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