In clinical and agricultural trials, there is the danger that an experimental outcome appears to arise from the causal process or treatment one is interested in when, in reality, it was produced by some extraneous variation in the experimental conditions. The remedy prescribed by classical statisticians involves the procedure of randomization, whose effectiveness and appropriateness is criticized. An alternative, Bayesian analysis of experimental design, is shown, on the other hand, to provide a coherent and intuitively satisfactory solution to the problem.

The paper attempts to elucidate and evaluate William Whewell's notion of a "consilience of inductions." In section I Whewellian consilience is defined and shown to differ considerably from what latter-day writers talk about when they use the term. In section II a primary analysis of consilience is shown to yield two types of consilient processes, one in which one of the lower-level laws undergoes a conceptual change (the case aptly discussed in Butts [1977]), and one in which the explanatory theory (...) undergoes conceptual "stretching." In section III both consilient cases are compared to the non-consilient case in reference to L. J. Cohen's method of relevant variables. In section IV we examine the test procedures of the theory in all three cases, and it is shown that in the event of genuine consilience (consilience of the second type) a theory acquires extraordinarily high support. In the final section something is said of the short-comings of standard Bayesian confirmation theories that are highlighted by Whewellian consilience. (shrink)

The object of this paper is to show why recent research in the psychology of deductive and probabilistic reasoning does not have.

L. Jonathan Cohen has written a number of important books and articles in which he argues that mathematical probability provides a poor model of much of what paradigmatically passes for sound reasoning, whether this be in the sciences, in common discourse, or in the law. In his book, The Probable and the Provable, Cohen elaborates six paradoxes faced by advocates of mathematical probability (PM) when treating issues of evidence as they would arise in a court of law. He argues that (...) his system of inductive probability (PI) satisfactorily handles the issues that proved paradoxical for mathematical probability, and consequently PI deserves to be thought of as an important standard of rational thinking. I argue that a careful look at each of the alleged paradoxes shows that there is no conflict between mathematical probability and the law, except when for reasons of policy we opt for values in addition to accuracy maximization. Recognizing the role of such policies provides no basis for questioning the adequacy of PM. The significance of this critical treatment of Cohen's work is that those interested in revising the laws of evidence to allow for more explicitly mathematical approaches ought to feel that such revisions will not violate the spirit of forensic rationality. (shrink)