Karl Popper et David Miller ont soutenu l'idée selon laquelle le soutien probabiliste positif = p − p > 0) que e apporte á h, lorsque de h on déduit e, ne justifie en rien l'espoir de pouvoir construire une logique inductive fondée sur le calcul des probabilityés.

Popper and Miller (1983) have presented an argument purporting to establish the impossibility of inductive probability. Here I discuss critically their characterization of a deductive part of nondeductive support, a point that has not figured centrally in previous responses.

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)

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)

Support functions $s(h,e)=p(h\backslash e)-p(h)$ are widely used in discussion of explanation, causality and, recently, in connection with the possibility or otherwise of probabilistic induction. With this latter application in view, a rather complete analysis of the variety of support functions, their interrelationships and their "non-deductive" and "inductive" components is presented. With the restriction to two propositions, three variable probabilities are enough to discuss such problems. The analysis is illustrated by graphs, a Venn diagram and by using the Laplace Rule of (...) Succession as an illustrative example. It is concluded that within this framework one cannot prove or disprove the possibility of probabilistic induction. (shrink)

Dunn and Hellman's objection to Popper and Miller's alleged disproof of inductive probability is considered and rejected. Dunn and Hellman base their objection on a decomposition of the incremental support P(h/e)-P(h) of h by e dual to that of Popper and Miller, and argue, dually to Popper and Miller, to a conclusion contrary to the latters' that all support is deductive in character. I contend that Dunn and Hellman's dualizing argument fails because the elements of their decomposition are not supports (...) of parts of h. I conclude by reinforcing a different line of criticism of Popper and Miller due to Redhead. (shrink)