Inductive Inconsistencies and The Problems of Probabilistic Predictions
It is rather generally believed that the application of statistical propositions for the indirect assessment of unobserved properties of certain individual objects or for the purpose of prediction of future events may create certain logical and practical problems discussed among others by Hempel in his paper on ‘Inductive Inconsistencies’.1 The nature of this problem can be illustrated by an example taken from Hempel’s paper. Suppose that we meet a certain Mr. Petersen, and we would like to know whether or not he is a Roman Catholic. For some peculiar reason we decide not to use the method of direct (i.e. observational) assessment of Mr. Petersen’s religion (e.g. by asking him about his religion, or looking into his documents) but prefer to approach the problem indirectly, by inferring the answer from other information. Such information will be of two kinds: propositions which describe some characteristics of Mr. Petersen other than his religion, and propositions describing in general terms the relations between these characteristics we observe as properties of Mr. Petersen and the property of being a Roman Catholic.
KeywordsRelative Frequency Probabilistic Relation Weak Sense Frequency Limit Natural Sequence
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