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A.P. Dempster 269tion is simply unexplained variation whose associated probabilities are quiteproperly interpretable as personal numerical assessments of specific targeteduncertainties. Such models inevitably run a gamut from objective to subjective,and from broadly accepted to proposed and adopted by a single analystwho becomes the “person” in a personalist narrative. Good statistical practiceaims at the left ends of both scales, while actual practice necessarily makescompromises. As Jack Good used to say, “inference is possible.”The concept of personalist interpretation of specific probabilities is usuallywell understood by statisticians, but is mostly kept hidden as possibly unscientific.Nevertheless, all approaches to statistical inference imply the exercise ofmature judgment in the construction and use of formal models that integratedescriptions of empirical phenomena with prescriptions for reasoning underuncertainty. By limiting attention to long run averages, “frequentist” interpretationsare designed to remove any real or imagined taint from personalprobabilities, but paradoxically do not remove the presence of nonprobabilisticreasoning about deterministic long runs. The latter reasoning is just as personalistas the former. Why the fear of reasoning with personal probabilities,but not a similar fear of ordinary propositional logic? This makes no sense tome, if the goal is to remove any role for a “person” performing logical analysisin establishing valid scientific findings.I believe that, as partners in scientific inquiry, applied statisticians shouldseek credible models directly aimed at uncertainties through precisely formulateddirect and transparent reasoning with personal probabilities. I arguethat DS logic is at present the best available system for doing this.24.3 Personal probabilities of “don’t know”DS “gives up something big,” as John Tukey once described it to me, or asInowprefertodescribeit,bymodifyingtherootconceptsofpersonalprobabilities“for” and “against” that sum to one, by appending a third personalprobability of “don’t know.” The extra term adds substantially to the flexibilityof modeling, and to the expressiveness of inputs and outputs of DSprobabilistic reasoning.The targets of DS inference are binary outcomes, or equivalent assertionsthat the true state of some identified small world is either in one subset of thefull set of possible true states, or in the complementary subset. Under whatI shall refer to as the “ordinary” calculus of probability (OCP), the user isrequired to supply a pair of non-negative probabilities summing to one thatcharacterize “your” uncertainty about which subset contains the true state.DS requires instead that “you” adopt an “extended” calculus of probability(ECP) wherein the traditional pair of probabilities that the true state lies ordoes not lie in the subset associated with a targeted outcome is supplemented