In 1983, in an open letter to the journal Nature, Karl Popper and David Miller set forth a particularly strong critical argument which sought to demonstrate the impossibility of inductive probability. Since its publication the argument has faced many criticisms and we argue in this article that they do not reach their objectives. We will first reconstruct the demonstration made by Popper and Miller in their initial article and then try to evaluate the main arguments against it. Although it is (...) possible to conceptualize logically the idea of induction, it is shown that it is not possible on traditional Bayesian grounds. (shrink)

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. (shrink)