This comprehensive study of probability considers the approaches of Pascal, Laplace, Poisson, and others. It also discusses Laws of Large Numbers, the theory of errors, and other relevant topics.

The most interesting and completely overlooked aspect of Ludwig von Mises’s theory of probability is the total absence of any explicit definition for probability in his theory. This paper examines Mises’s theory of probability in light of the fact that his theory possesses no definition for probability. It is argued, first, that Mises’s theory differs in important respects from his brother’s famous theory of probability. A defense of the subjective definition for (...) class='Hi'>probability is then provided, which is subsequently used to critique Ludwig von Mises’s theory. It is argued that only the subjective definition for probability comports with Mises’s other philosophical positions. Since Mises did not provide an explicit definition for probability, it is suggested that he ought to have adopted a subjective definition. (shrink)

The correspondence between Richard von Mises and George Pólya of 1919/20 contains reflections on two well-known articles by von Mises on the foundations of probability in the Mathematische Zeitschrift of 1919, and one paper from the Physikalische Zeitschrift of 1918. The topics touched on in the correspondence are: the proof of the central limit theorem of probability theory, von Mises' notion of randomness, and a statistical criterion for integer-valuedness of physical data. The investigation will hint (...) at both the fruitfulness and the limits of several of von Mises' notions such as ``collective'', ``distribution'' and ``complex adjuncts'' (characteristic functions) for further developments in probability theory and in ``directional statistics''. By pointing to the selectiveness of Pólya's criticism, the historical analysis shows the differing expectations of the two men with respect to the further development of the theory of probability and its applications. The paper thus gives a glimpse of the provisional state of the theory around 1920, before others such as P. Lévy (1886–1971) and A. N. Kolmogorov (1903–1987) stepped in and created a new paradigm for probability theory. (shrink)

In the following we will investigate whether von Mises’ frequency interpretation of probability can be modified to make it philosophically acceptable. We will reject certain elements of von Mises’ theory, but retain others. In the interpretation we propose we do not use von Mises’ often criticized ‘infinite collectives’ but we retain two essential claims of his interpretation, stating that probability can only be defined for events that can be repeated in similar conditions, and that exhibit (...) frequency stabilization. The central idea of the present article is that the mentioned ‘conditions’ should be well-defined and ‘partitioned’. More precisely, we will divide probabilistic systems into object, initializing, and probing subsystem, and show that such partitioning allows to solve problems. Moreover we will argue that a key idea of the Copenhagen interpretation of quantum mechanics (the determinant role of the observing system) can be seen as deriving from an analytic definition of probability as frequency. Thus a secondary aim of the article is to illustrate the virtues of analytic definition of concepts, consisting of making explicit what is implicit. (shrink)

What follows shall provide an introduction to a predominantly philosophical and polemical, but historically revealing, paper on the foundations of the theory of probability. The leading Russian probabilist Aleksandr Yakovlevich Khinchin wrote the paper in the late 1930s, commenting on a slightly older, but still competing approach to probability theory by Richard von Mises. Together with the even more influential Andrey Nikolayevich Kolmogorov, who was nine years his junior, Khinchin had revolutionized probability theory around 1930 by (...) introducing the modern measure-theoretic approach, which is still standard today and which allowed for a sufficiently general treatment of important new notions such as “stochastic processes.” This development had its first culmination in Kolmogorov's booklet, Grundbegriffe der Wahrscheinlichkeitsrechnung, written in German in 1933, which has exerted an enormous influence world wide. (shrink)

RésuméNous analysons un épisode important dans ľévolution de la théorie des probabilityés: la phase?on;axioraatisation. La premiere approche de ce type fut proposeée par Mises en 1919. Elle šappuie sur le concept de collectif. La probabilityé y est définie comme la valeur‐limite de la fréquence relative. La seconde approche, élaborée en 1933 par Kolmogorov, šinscrit dans la lignée des travaux de Borel?on;inspiration purement analytique. Cette dernière axiomatique fut unanimement choisie tant par les théoriciens que par les empiristes. Après avoir présente (...) les divers arguments invoqués lors de la confrontation des deux théories, nous en proposons une interprétation épistémologique.SummaryWe analyse an important episode of the evolution of the theory of probability: the axiomatic phase. The first approach was proposed by Mises in 1919. It is based on the concept of “collective”. The probability is defined as the limit‐value of the relative frequency. The second one, elaborated by Kolmogorov in 1933, follows the work of Borel which is inspired by purely analytical considerations. This last axiomatisation was unanimously chosen by the theoreticians and empiricists. After having presented the different arguments raised when both theories were confronted, we suggest an epistemological interpretation.ZusammenfassungWir untersuchen eine wichtige Episode in der Entwicklung der Wahrscheinlichkeitsrechnung: die Phase ihrer Axiomatisierung. Der erste Versuch einer solchen wurde 1919 von Mises vorgelegt. Er stützt sich auf den Begriff eines Kollektivs ab. Die Wahrscheinlichkeit wird dabei als Grenzwert der relativen Häufigkeit definiert. Der zweite 1933 von Kolomogorov ausgearbeitete Versuch liegt in der rein analytischen Richtung, die von den Arbeiten Borels inspiriert wurde. Dieses Axiomatisierungsverfahren wurde einhellig sowohl von den Theoretikern als auch von den Empiristen vorgezogen. Nachdem wir die verschiedenen Argumente angeführt haben, die während der Konfrontation der beiden Theorien ins Feld geführt wurden, geben wir eine erkenntnis‐theoretische Deutung von diesen. (shrink)

The first formal definition of randomness, seen as a property of sequences of events or experimental outcomes, dates back to Richard von Mises' work in the foundations of probability and statistics. The randomness notion introduced by von Mises is nowadays widely regarded as being too weak. This is, to a large extent, due to the work of Jean Ville, which is often described as having dealt the death blow to von Mises' approach, and which was integral (...) to the development of algorithmic randomness—the now-standard theory of randomness for elements of a probability space. The main goal of this article is to trace the history and provide an in-depth appraisal of two lesser-known, yet historically and methodologically notable proposals for how to modify von Mises' definition so as to avoid Ville's objection. The first proposal is due to Abraham Wald, while the second one is due to Claus-Peter Schnorr. We show that, once made precise in a natural way using computability theory, Wald's proposal constitutes a much more radical departure from von Mises' framework than intended. Schnorr's proposal, on the other hand, does provide a partial vindication of von Mises' approach: it demonstrates that it is possible to obtain a satisfactory randomness notion—indeed, a canonical algorithmic randomness notion—by characterizing randomness in terms of the invariance of limiting relative frequencies. More generally, we argue that Schnorr's proposal, together with a number of little-known related results, reveals that there is more continuity than typically acknowledged between von Mises' approach and algorithmic randomness. Even though von Mises' exclusive focus on limiting relative frequencies did not survive the passage to the theory of algorithmic randomness, another crucial aspect of his conception of randomness did endure; namely, the idea that randomness amounts to a certain type of stability or invariance under an appropriate class of transformations. (shrink)

This is the only book to chart the history and development of modern probability theory. It shows how in the first thirty years of this century probability theory became a mathematical science. The author also traces the development of probabilistic concepts and theories in statistical and quantum physics. There are chapters dealing with chance phenomena, as well as the main mathematical theories of today, together with their foundational and philosophical problems. Among the theorists whose work is treated at (...) some length are Kolmogorov, von Mises and de Finetti. The principal audience for the book comprises philosophers and historians of science, mathematicians concerned with probability and statistics, and physicists. The book will also interest anyone fascinated by twentieth-century scientific developments because the birth of modern probability is closely tied to the change from a determinist to an indeterminist world-view. (shrink)

This paper is divided into a surveying and argumentative part and a slightly longer documentary part, which is meant to verify or at least make more plausible claims made in the first part. The first part deals in broad outline with the relationship of Frank and von Mises to the Vienna Circle of Logical Empiricism on the one hand and to the physicists and mathematicians in the German-speaking world on the other. The varying special positions, partly the non-conformity of (...) the two Austrian scientists are emphasized, in particular, their adherence to Ernst Mach’s epistemology and their shared interest in probability theory and applied mathematics. The impact of emigration and the after-effects in the U.S. are discussed. This leads to new insights into the fine structure of the Vienna Circle and the latter’s relationship to German academia within ‘Weimar Culture’. P. Forman’s interpretation (1971) of von Mises’ position is critically discussed. The second, documentary part, uses recently discovered correspondence between Frank and von Mises, and, to a lesser extent, von Mises’ personal diary. It aims at further substantiating some of the introductory theses and will at the same time provide material for a thorough biographical appreciation of the two scholars and friends. (shrink)

INTRODUCTION TO THE THIRD EDITION: FROM VALUE THEORY TO PRAXEOLOGY Ludwig von Mises (1881–1973) is arguably the most important economist of the twentieth ...

Preface LUDWIG von Mises published many books and articles in his long and productive life, each of them making important contributions to the theory and ...

This reissue of D. A. Gillies highly influential work, first published in 1973, is a philosophical theory of probability which seeks to develop von Mises’ views on the subject. In agreement with von Mises, the author regards probability theory as a mathematical science like mechanics or electrodynamics, and probability as an objective, measurable concept like force, mass or charge. On the other hand, Dr Gillies rejects von Mises’ definition of probability in terms of (...) limiting frequency and claims that probability should be taken as a primitive or undefined term in accordance with modern axiomatic approaches. This of course raises the problem of how the abstract calculus of probability should be connected with the ‘actual world of experiments’. It is suggested that this link should be established, not by a definition of probability, but by an application of Popper’s concept of falsifiability. In addition to formulating his own interesting theory, Dr Gillies gives a detailed criticism of the generally accepted Neyman Pearson theory of testing, as well as of alternative philosophical approaches to probability theory. The reissue will be of interest both to philosophers with no previous knowledge of probability theory and to mathematicians interested in the foundations of probability theory and statistics. (shrink)

This memorandum was written at the request of Henry Hazlitt to provide Mises’s comments on and concerns about F.A. Hayek’s initial proposals for what became the Mont Pèlerin Society. Mises stresses that those who favor liberty and freedom and oppose totalitarianism must also oppose interventionism. The memo argues that those who fought and lost against the rising tide of totalitarianism at the turn of the 20th Century lost their battles because they settled for middle-of-the-road policies that conceded considerable (...) ground to the socialists. The weak point in Professor Hayek’s plan is that it relies upon the cooperation of many men who are today’s middle-of-the-roaders. As interventionists, they may not be the hoped-for intellectual pioneers to inspire people to build a freer world. (shrink)

_Philosophy of Probability: Contemporary Readings_ is the first anthology to collect essential readings in this important area of philosophy. Featuring the work of leading philosophers in the field such as Carnap, Hájek, Jeffrey, Joyce, Lewis, Loewer, Popper, Ramsey, van Fraassen, von Mises, and many others, the book looks in depth at the following key topics: subjective probability and credence probability updating: conditionalization and reflection Bayesian confirmation theory classical, logical, and evidential probability frequentism physical probability: (...) propensities and objective chances. The book features a useful primer on the mathematics of probability, and each section includes an introduction by the editor, as well as a guide to further reading. A broad-ranging and highly accessible exploration of the subject, _Philosophy of Probability_ is ideal for any student of formal epistemology, philosophy of science, metaphysics, or philosophy of mathematics. (shrink)