Suppose one hundred prisoners are in a yard under the supervision of a guard, and at some point, ninety-nine of them collectively kill the guard. If, after the fact, a prisoner is picked at random and tried, the probability of his guilt is 99%. But despite the high probability, the statistical chances, by themselves, seem insufficient to justify a conviction. The question is why. Two arguments are offered. The first, decision-theoretic argument shows that a conviction solely based on the statistics (...) in the prisoner scenario is unacceptable so long as the goal of expected utility maximization is combined with fairness constraints. The second, risk-based argument shows that a conviction solely based on the statistics in the prisoner scenario lets the risk of mistaken conviction surge potentially too high. The same, by contrast, cannot be said of convictions solely based on DNA evidence or eyewitness testimony. A noteworthy feature of the two arguments in the paper is that they are not confined to criminal trials and can in fact be extended to civil trials. (shrink)

This paper seeks to defend the following conclusions: The program advanced by Carnap and other necessarians for probability logic has little to recommend it except for one important point. Credal probability judgments ought to be adapted to changes in evidence or states of full belief in a principled manner in conformity with the inquirer’s confirmational commitments—except when the inquirer has good reason to modify his or her confirmational commitment. Probability logic ought to spell out the constraints on rationally coherent confirmational (...) commitments. In the case where credal judgments are numerically determinate confirmational commitments correspond to Carnap’s credibility functions mathematically represented by so—called confirmation functions. Serious investigation of the conditions under which confirmational commitments should be changed ought to be a prime target for critical reflection. The necessarians were mistaken in thinking that confirmational commitments are immune to legitimate modification altogether. But their personalist or subjectivist critics went too far in suggesting that we might dispense with confirmational commitments. There is room for serious reflection on conditions under which changes in confirmational commitments may be brought under critical control. Undertaking such reflection need not become embroiled in the anti inductivism that has characterized the work of Popper, Carnap and Jeffrey and narrowed the focus of students of logical and methodological issues pertaining to inquiry. (shrink)

A unifying framework of probabilistic reasoning Content Type Journal Article Category Book Review Pages 1-4 DOI 10.1007/s11016-011-9573-x Authors Jan Sprenger, Tilburg Center for Logic and Philosophy of Science, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

An inductive logic is a system of inference that describes the relation between propositions on data, and propositions that extend beyond the data, such as predictions over future data, and general conclusions on all possible data. Statistics, on the other hand, is a mathematical discipline that describes procedures for deriving results about a population from sample data. These results include predictions on future samples, decisions on rejecting or accepting a hypothesis about the population, the determination of probability assignments over such (...) hypotheses, the selection of a statistical model for studying the population, and so on. Both inductive logic and statistics are calculi for getting from the given data to propositions or results that transcend the data. (shrink)

The orthodox view in statistics has it that frequentism and Bayesianism are diametrically opposed—two totally incompatible takes on the problem of statistical inference. This paper argues to the contrary that the two approaches are complementary and need to mesh if probabilistic reasoning is to be carried out correctly.