โ Scribed by James Cussens
No coin nor oath required. For personal study only.
Elementary results concerning the connections between deductive relations and probabilistic support are given. These are used to show that Popper-Miller's result is a special case of a more general result, and that their result is not "very unexpected" as claimed. According to Popper-Miller, a purely inductively supports b only if they are "deductively independent" -but this means that ~a F-b. Hence, it is argued that viewing induction as occurring only in the absence of deductive relations, as Popper-Miller sometimes do, is untenable. Finally, it is shown that Popper-Miller's claim that deductive relations determine probabilistic support is untrue. In general, probabilistic support can vary greatly with fixed deductive relations as determined by the relevant Lindenbaum algebra.
๐ SIMILAR VOLUMES
INDUCTION AND DEDUCTION IN STATISTICAL ANALYSIS 9 it will be found useful to distinguish three types of propositions, each of which presents its own kind of probability problem; namely (1) the singular proposition...(2) the class-fractional proposition 9 (3) the universal proposition. W. E. Johnson,
We introduce a deductive probabilistic and fuzzy object-oriented model where a class property (i.e., an attribute or a method) can contain fuzzy set values, and uncertain class membership and property applicability are measured by lower and upper bounds on probability. Each uncertainly applicable pr