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 reviewer welcomes Von Mises' book as a most valuable contribution to the nowadays so badly needed clarifying of philosophical terminology. The author confesses himself to positivism, but his work bears a far more psychological and significal stamp than those of most present positivists.

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)

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)

ArgumentThe article describes a special type of scientific and philosophical “non-conformism” as exemplified in the versatile work of Richard von Mises. While the historical impact of von Mises' practical and organizational work in applied mathematics is beyond doubt, it is shown that von Mises' insistence on cognitive connectibility of various scientific domains was not, in the end, successful although it stimulated the theoretical discussion considerably. Von Mises developed a principally critical attitude towards what he considered (...) “one-sided” in several streams of modernity and tended to be “anti-modern” even in those of his activities which belonged to “modernism.” Reasons can be found in his biographical experiences, in particular in his unorthodox academic education and repeated emigrations. Thus biographical research has considerable potential for historical explanation. The paper delves into the existing premises and sources for a scientific biography of Richard von Mises which is yet to be written, and publishes in the appendix a revealing biographical sketch authored by von Mises' widow, the applied mathematician Hilda Geiringer. (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)

This paper continues an earlier investigation into the philosophical tradition of Vienna Indeterminism until the formation of the Vienna Circle in 1929. It focuses in particular on how Philipp Frank and Richard von Mises were able to contemplate genuine indeterminism in physics before the advent of quantum mechanics. On this account, all apparently deterministic laws could well be the macroscopic limit of indeterministic basic laws valid for the single mirco-events. Philosophically Vienna Indeterminism was launched by Mach's redefinition of (...) causality in terms of functional dependencies. This severed the rigid bond between causality and empirical realism characteristic of the Kantian conception and made possible to adjust the ontology according to the needs of a single theory. The debates between Max Planck and Franz Serafin Exner teach that the indeterminism issue was also a struggle about Boltzmann's philosophical legacy between Vienna and Berlin. Quite in line with Mach's firm empiricism, Vienna Indeterminists rejected any final decision between determinism and indeterminism on the metaphysical level. Once the frequency interpretation had won favor, the empiricist stance, moreover, permitted them to consider mass phenomena as generic observational facts coordinated to statistical collectives and to treat them on a par with moving point particles. The only condition imposed on this ontology was the uniqueness of this coordination, a condition that could be viewed as a late heir of Mach's principle of unique determination which had complemented his relational ontology. (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)

Von Mises defined a "physical" probability as a strict limit of the relative frequency of occurrence of an event in repeated trials. As a result of a number of criticisms of von Mises's approach, the more favored approach became the "propensity" interpretation. It is argued here that this interpretation is not compelling and that the only problem in von Mises's approach is the assumption that the relative frequency converges in a strict sense. This problem is then remedied (...) by deducing the axioms of probability theory from the assumption that the relative frequency converges only in the sense of the weak law of large numbers. (shrink)

Like Hayek, Mises moved beyond economics in his later years to address questions regarding the foundation of all social science. But unlike Hayeks attempts, Misess writings on these matters have received less attention than they deserve. Theory and Histor, writes Rothbard in his introduction, "remains by far the most neglected masterwork of Mises. Here Mises defends his all-important idea of methodological dualism: one approach to the hard sciences and another for the social sciences. He defends the epistemological (...) status of economic proposition. He has his most extended analysis of those who want to claim that there is more than one logical structure by which we think about reality. He grapples with the problem of determinism and free will. And presents philosophy of history and historical research. Overall, this is a tremendously lucid defense of the fundamental Misesian approach to social philosophy. "It is Misess great methodological work, explaining the basis of his approach to economics, and providing scintillating critiques of such fallacious alternatives as historicism, scientism, and Marxian dialectical materialism. Austrian economics will never enjoy a genuine renaissance until economists read and absorb the vital lessons of this unfortunately neglected work." Theory and History should be required for any student of 20th century ideas. (shrink)

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 ...

ArgumentThe paper is based on a hitherto unexplored document (audiotape of an interview accompanied by a German transcript) from 1953, located in the Freud Papers at the Library of Congress. It contributes to a better understanding of the impact of Freud and of Psychoanalysis on personalities from the exact sciences, here represented by the noted applied mathematicians Richard von Mises and Hilda Geiringer from Vienna. The detailed discussion of the interview sheds some new light on the different roles (...) of Kraus and Freud in the Vienna culture, on the Vienna Jugendkulturbewegung (youth culture movement) during WWI in which Geiringer was involved, on Freud’s and Siegfried Bernfeld’s standing around 1930 among German philosophers and psychologists, and on Wilhelm Fließ’ theory of periodicity, which von Mises—based on his attitude as an applied mathematician—defended against superficial accusations. Finally, new biographical material is provided for von Mises and the remotely related Freud family, and for Geiringer’s and von Mises’ early lives. The interview, which was taken during the Cold War, also allows conclusions as to how politics influenced the memories and views of the participants. Part of the aim of the paper is historical documentation of unknown material (letters by Karl Kraus and Wolfgang Köhler, one book review by Wilhelm Ostwald, a file on Richard Pfennig), including some correction of erroneous information in the literature. (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 ...

What does it mean for ethics to say, as Wittgenstein did, that philosophy “leaves everything as it is”? -/- Though clearly absorbed with ethical questions throughout his life and work, Wittgenstein's remarks about the subject do not easily lend themselves to summation or theorizing. Although many moral philosophers cite the influence or inspiration of Wittgenstein, there is little agreement about precisely what it means to do ethics in the light of Wittgenstein. -/- Ethics after Wittgenstein brings together an international cohort (...) of leading scholars in the field to address this problem. The chapters advance a conception of philosophical ethics characterized by an attention to detail, meaning and importance which itself makes ethical demands on its practitioners. Working in conversation with literature and film, engaging deeply with anthropology and critical theory, and addressing contemporary problems from racialized sexual violence against women to the Islamic State, these contributors reclaim Wittgenstein's legacy as an indispensable resource for contemporary ethics. (shrink)

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 ...

The book deals with the changing nature and with the history of the concept of scientific determinism from the classical mechanics until the time immediately preceding quantum mechanics: such a historical-philosophical reconstruction is aimed at (1) signalizing and overcoming the deficiencies of the received opinion on the topic and (2) understanding better a concept which has influenced science from the beginning. -/- Before dealing with historical matters I develop in the first Chapter a kind of new, three-dimensional “measurement system” for (...) analyzing any concept of scientific determinism: many different concepts have been developed in the course of history, and we need a classification system which, on the one hand, is inclusive and broad enough to deal with different concepts; on the other hand, which makes possible to differentiate with some precision between them. My “measurement system” has three dimension or parameter: the “strength” (of the determining link between different states of the physical system), the “depth” (depending on how strong the ontological commitment of the particular concept of scientific determinism is), and the breadth (referring to the domain or the object, to which a deterministic evolution is ascribed). -/- In the second chapter I discuss briefly some main shortcomings of the received opinion about scientific determinism. Then I try to identify the “core” of scientific determinism at its origins while at the same time embedding it in the broader historical-cultural context especially of the Renaissance. On the one hand I show how the core of scientific determinism was mathematical, and this distinguished it from other related concepts, as mechanism, the principle of sufficient reason, and the aristotelic conception of science. On the other hand, precisely the support which these related concepts provided to scientific determinism, together with its mathematical nature, endowed it with an incredible resistance against empirical classification. -/- In the following three chapters I analyze the historic-philosophical development of scientific determinism along the three parameter of my measurement system. -/- In the third Chapter I reconstruct the weakening of scientific determinism with respect to its depth: the starting point is the question about the extent in which the deterministic mathematical descriptions do refer. In the development of mechanics into analytical mechanics the more and more formal character of its mathematical descriptions became evident and it became less obvious that these formal, deterministic structures also have an immediate material truth. Parallel developments within epistemology, starting with Kantian philosophy (which I deal with quite in detail), let the deterministic structures (principle, laws, equations, causal relations) appear less absolute and real and more as a product of reason, as conventions, or as models. A brief consideration of the interpretation of mechanics and its principles by Jacobi, Hertz, Mach and Poincaré shows the implications of these developments. -/- The fourth chapter reconstructs the weakening of scientific determinism with respect to the strength of the determining link: here my work deepens the track which has been opened by Ian Hacking, who interpreted the so-called “probabilistic revolution” in the 19th Century as the main reason for the erosion of determinism. The increasing pervasiveness of statistical methods in the social and natural sciences in the course of the 19th Century gave rise to a conception of scientific laws which could dispense with strict determinism. A new, empirical interpretation of probability (Frequentism) and the statistical explanation of thermodynamic phenomena in physics even suggested chance phenomena to be a necessary condition for the emergence of natural laws. -/- The last part of my work (Ch. 5, 6 and 7) considers the period (2nd half of the 19th century until ca. 1920) in which the concept of scientific determinism became explicit and was discussed as a world-picture or a world-view – that is, in its maximal breadth. I argue that there were two main reasons for the emergence of an explicit and ideological opposition “determinism vs. indeterminism” at that time: the first was the successful application of the deterministic paradigm to sociology, history, physiology and psychology in the course of the 19th Century, which provided scientific determinism with ethical implications (in particular with respect to the problem of free will, which scientific determinism seemed to deny). The second, related reason is that in the 19th Century natural scientists became public men, science was increasingly popularized and scientific issues were increasingly related to life-issues, to worldview-questions, and even to politics. In Chapter 6 I reconstruct the debates on the issue “determinism vs. indeterminism” in such a public, ideological and sometimes even political context. Among the discussants were Fechner, Du Bois-Reymond, Helmholtz, Bernard, Ostwald, Haeckel, Boussinesq, Maxwell, Boutroux, Poincaré, Renouvier, James und Peirce. Also in Vienna the debate on the issue of determinism was fervid and took ideological and political connotations: Michael Stöltzner and Deborah Coen have pointed to a particular tradition of “Vienna Indeterminism” (Stöltzner), or Viennese liberal probabilism (Coen), which was characterized by a strongly empirical conception of science and by the full acceptance and appreciation of statistical thinking in science. In the last Chapter of my work I focus on the early philosophy of Edgar Zilsel, a philosopher who stood near to the Vienna Circle and who has been much neglected in the literature by now, and I suggest considering it as part of the “Vienna Indeterminism”. First, I show how he gave an indeterministic foundation both to statistical and causal knowledge as well as to irreversibility in physics. Second, I inquire into his philosophy of probability and show how it developed in parallel to the ones of Hans Reichenbach and Richard von Mises. Finally, Zilsel happens to be a further, relevant case-study for pointing to the ideological and political side of the issue of determinism. -/- At the end of this reconstruction it should have become clear how no physical theory, no empirical evidence and no experimental confirmation can support or contradict scientific determinism in its non-trivial formulations. The validity of any such formulation depends strongly not only (from the systematical point of view) from the definition of other concepts (like time, physical state, causality etc.), but also from the particular conception of science which more or less implicitly constitutes its background, and which is subjected to historical change. -/- (ISBN: 9783495491034). (shrink)