Abstract
Every probability must have the definite content of a judgment as its object: a propositional content which is either true or false. The pursuit of a method to transpose or compare probabilities by way of logical argument is largely futile. Probability is not transposed by simple inference: the same probability must be attributed to two premises, only if neither may be established in absence of the other. However, the probability derived from two ranges which are very small and nearly adjacent may be represented in numeric terms by Bayes’s rule. Suppose there are two ranges which stand in definite ratio; then say there are gaps in the ranges, so that parts of the ranges remain. The ratio of the residual part-ranges may be shown to follow Bayes’s rule. Yet Bayes’s rule is applied frequently in inappropriate situations, where probabilities are combined more or less arbitrarily. That can lead to meaningless or incorrect statements of probability.
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Notes
- 1.
The result just derived – that there is no transposition of probability to be made – needs a certain qualification. In the whole exposition just set out, we proceeded on the assumption that a definite probability could be attributed to either of the two premises separately. Clearly this is not the case if for example, one of the premises cannot be advanced as either probable or improbable at all, independently of the other. So all our conjectures about future events are exclusively constrained by what we can say about present or past behavior in the world. Such is the nature of things that there cannot be a probability with which this or that future event can be expected, independently of the probability of those present varieties of behavior with which we are forced to think those future events must be connected. Admittedly in such a case a transposition of probability is made, if one really wants to call it that.
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Niall, K.K. (2023). Varieties of Numeric Probability. In: Johannes von Kries: Principles of the Probability Calculus. Studies in History and Philosophy of Science, vol 59. Springer, Cham. https://doi.org/10.1007/978-3-031-36506-5_5
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DOI: https://doi.org/10.1007/978-3-031-36506-5_5
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