Deduction, induction and probabilistic support

Abstract

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 ⊢ 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.