Journal | Synthese |
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Date | Published - 1 Jul 1996 |
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Issue number | 1 |
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Volume | 108 |
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Number of pages | 10 |
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Pages (from-to) | 1-10 |
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Original language | English |
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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 $neg a vdash b$. 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.