This paper has the aim of making Johannes von Kries’s masterpiece, Die Principien der Wahrscheinlichkeitsrechnung of 1886, a little more accessible to the modern reader in three modest ways: first, it discusses the historical background to the book ; next, it summarizes the basic elements of von Kries’s approach ; and finally, it examines the so-called “principle of cogent reason” with which von Kries’s name is often identified in the English literature.

The prospects of a causal interpretation of probability are examined. Various accounts both from the history of scientific method and from recent developments in the tradition of the method of arbitrary functions, in particular by Strevens, Rosenthal, and Abrams, are briefly introduced and assessed. I then present a specific account of causal probability with the following features: First, the link between causal probability and a particular account of induction and causation is established, namely eliminative induction and the related difference-making account (...) of causation in the tradition of Bacon, Herschel, and Mill. Second, it is shown how a causal approach is useful beyond applications of the method of arbitrary functions and is able to deal with various shades of both ontic and epistemic probabilities. Furthermore, I clarify the notion of causal symmetry as a central element of an objective version of the principle of indifference and relate probabilistic independence to causal irrelevance. (shrink)

This paper addresses the question of how we should regard the probability distributions introduced into statistical mechanics. It will be argued that it is problematic to take them either as purely subjective credences, or as objective chances. I will propose a third alternative: they are "almost objective" probabilities, or "epistemic chances". The definition of such probabilities involves an interweaving of epistemic and physical considerations, and so cannot be classified as either purely subjective or purely objective. This conception, it will be (...) argued, resolves some of the puzzles associated with statistical mechanical probabilities; it explains how probabilistic posits introduced on the basis of incomplete knowledge can yield testable predictions, and it also bypasses the problem of disastrous retrodictions, that is, the fact the standard equilibrium measures yield high probability of the system being in equilibrium in the recent past, even when we know otherwise. As the problem does not arise on the conception of probabilities considered here, there is no need to invoke a Past Hypothesis as a special posit to avoid it. (shrink)

The principle of maximum entropy is a general method to assign values to probability distributions on the basis of partial information. This principle, introduced by Jaynes in 1957, forms an extension of the classical principle of insufficient reason. It has been further generalized, both in mathematical formulation and in intended scope, into the principle of maximum relative entropy or of minimum information. It has been claimed that these principles are singled out as unique methods of statistical inference that agree with (...) certain compelling consistency requirements. This paper reviews these consistency arguments and the surrounding controversy. It is shown that the uniqueness proofs are flawed, or rest on unreasonably strong assumptions. A more general class of inference rules, maximizing the so-called Re[acute ]nyi entropies, is exhibited which also fulfill the reasonable part of the consistency assumptions. (shrink)

The view that chances are relative frequencies of occurrence within actual, finite reference classes has long been written off. I argue that it ought to be reconsidered. Focusing on non-deterministic chance, I defend a version of finite frequentism in which reference classmates are required to have qualitatively identical pasts. While my analysis can evade or resist several standard objections, it has a counterintuitive consequence: non-trivial chances entail the existence of past light cones that are perfect intrinsic duplicates. In mitigation, I (...) argue that our scientific knowledge is consistent with the hypothesis that there are many such duplicates in the actual world. Moreover, my analysis has some striking advantages: it is simple, it is metaphysically undemanding, and it makes possible a satisfying explanation of the chance–credence connection. 1 Introduction2 Target3 Sketch and Skirmish4 Articulation5 Standard Worries5.1 Frequency tolerance5.2 Leibniz’s dictum5.3 Single case chance5.4 Missing values5.5 Explanation5.6 Counterfactual chances6 Chance and Credence6.1 An indefeasible indifference intuition6.2 Articulating the credence principle6.3 Appraising the credence principle7 Confirmation8 Laws9 Summing Up. (shrink)

The history of the mathematical probability includes two phases: 1) From Pascal and Fermat to Laplace, the theory gained in application fields; 2) In the first half of the 20th Century, two competing axiomatic systems were respectively proposed by von Mises in 1919 and Kolmogorov in 1933. This paper places this historical sketch in the context of the philosophical complexity of the probability concept and explains the resounding success of Kolmogorov’s theory through its ability to avoid direct interpretation. Indeed, unlike (...) experimental sciences, and despite its numerous applications, probability theory cannot be tested per se. Rather it relates to practical matters by means of transition hypotheses or bridging principles that match the structure of practical problems with abstract theory. In this respect probability theory has a very special status among scientific disciplines. (shrink)

„De incerti aestimatione” („O szacowaniu rzeczy niepewnych”) G.W. Leibniza z 1678-ego roku stanowi próbę wyprowadzenia ogólnej metody dla rozwiązania problemu punktów, czyli podziału puli w dowolnej rundzie gry. Część wyjaśniająca zawiera szereg definicji i pomysłów pojawiających się w pismach Leibniza w poprzednich latach. Wśród nich znajduje się definicja pojęcia prawdopodobieństwa (probabilitas) kojarzonego wówczas z niezakończonym jeszcze sporem o probabilizm moralno-teologiczny. Jest to w tym wypadku skojarzenie uzasadnione faktem, że w korespondencji i późniejszych pismach Leibniz proponuje rozważać prawdopodobieństwo w znaczeniu matematycznym (...) w przeciwieństwie do znaczenia używanego w teologii moralnej. „De incerti aestimatione” jest drugą pracą Leibniza, w której poświęca on uwagę grom, zagadnieniu ich sprawiedliwości i oczekiwanej wartości, którą nazywa nadzieją. W artykule omówiono prawne, moralne i metafizyczne konteksty pojęć probabilitas, jus (prawa) i ratio, jak również ograniczenia moralnego zastosowania pojęcia prawdopodobieństwa. Przedstawiono także rozwiązanie problemu punktów przez Leibniza, które, choć błędne, stanowi niezależną od Pascala propozycję zastosowania do tego problemu metody rekurencyjnej. (shrink)

In this paper, a concept of chance is introduced that is compatible with deterministic physical laws, yet does justice to our use of chance-talk in connection with typical games of chance. We take our cue from what Poincaré called "the method of arbitrary functions," and elaborate upon a suggestion made by Savage in connection with this. Comparison is made between this notion of chance, and David Lewis' conception.

Some of the problem areas in which British philosophers of science have recently been engaged are described and some of the major contributions noted. Two sets of problems are given special attention: one concerned with the analysis of probability statements and one concerned with the appraisal of scientific theories. Three traditions in the approach to this second set of problems are distinguished. These might be called the Carnapian, the Popperian and the Wittgensteinian traditions.

The physiologist and neo-Kantian philosopher Johannes von Kries (1853-1928) wrote one of the most philosophically important works on the foundation of probability after P.S. Laplace and before the First World War, his Principien der Wohrscheinlich-keitsrechnung (1886, repr. 1927). In this book, von Kries developed a highly original interpretation of probability, which maintains it to be both logical and objectively physical. After presenting his approach I shall pursue the influence it had on Ludwig Wittgenstein and Friedrich Waismann. It seems that von (...) Kries's approach had more potential than recognized in his time and that putting Waismann's and Wittgenstein's early work in a von Kries perspective is able to shed light on the notion of an elementary proposition. (shrink)

This paper addresses the question of how we should regard the probability distributions introduced into statistical mechanics. It will be argued that it is problematic to take them either as purely ontic, or purely epistemic. I will propose a third alternative: they are almost objective probabilities, or epistemic chances. The definition of such probabilities involves an interweaving of epistemic and physical considerations, and thus they cannot be classified as either purely epistemic or purely ontic. This conception, it will be argued, (...) resolves some of the puzzles associated with statistical mechanical probabilities: it explains how probabilistic posits introduced on the basis of incomplete knowledge can yield testable predictions, and it also bypasses the problem of disastrous retrodictions, that is, the fact the standard equilibrium measures yield high probability of the system being in equilibrium in the recent past, even when we know otherwise. As the problem does not arise on the conception of probabilities considered here, there is no need to invoke a Past Hypothesis as a special posit to avoid it. (shrink)