W. Stegmüller sees the decisive difficulty of the Laplacean interpretation of Carnaps probability in the lack of the required equiprobable possibilities. It is argued that the required equiprobabilities in physics are given by statistical mechanics and can easily be transferred from physics to general statistical problems.

Kaum eine Äußerung Einsteins ist so bekannt wie sein Wort, dass Gott nicht würfelt. In ähnlicher Weise, wie Einstein dies unerläutert gelassen hat, ist seine gesamte Position zur Quantenmechanik, auf die es sich bezieht, von Uneindeutigkeiten nicht frei geblieben. Für seine Würfelmetapher ergibt sich ein Spielraum von gegensätzlichen Sichtweisen. Sie lässt sich zum einen mit jüngeren Forschungsresultaten verbinden und weist zum anderen auf rückschrittliche Elemente in Einsteins Denken hin. Ich wende mich zuerst diesen Elementen zu und betrachte dann eine dazu (...) entgegengerichtete Interpretationsvariante, die an den neueren Resultaten anknüpft. (shrink)

A compatible statistical interpretation of a wave packet is proposed. De Broglian probabilities which unite wave and particle features of quantons are evaluated for free wave packets and Jor a superposition of wave packets. The obtained expressions provide a very plausible and physically appealing explanation of coherence in apparently incoherent beams and of the characteristic modulation of the momentum distribution, found recently in neutron interferometry combined with spectral filtering. Certain conclusions about dualism and objectivity in quantum domain are (...) also derived. (shrink)

The statistical interpretation introduced by Born in mid-1926 is not the interpretation now associated with his name. Born's own understanding of that interpretation is revealed by looking at some of its roots in Born's earlier work with Franck on collisions, his collaboration with Jordan on that topic, his contributions to matrix mechanics, his attempt in collaboration with Wiener at an operator formulation of quantum mechanics, and at the exposition of the interpretation in Born's first papers (...) on a wave mechanical treatment of collisions. (shrink)

The ontological models framework distinguishes ψ-ontic from ψ-epistemic wave- functions. It is, in general, quite straightforward to categorize the wave-function of a certain quantum theory. Nevertheless, there has been a debate about the ontological status of the wave-function in the statistical interpretation of quantum mechanics: is it ψ-epistemic and incomplete or ψ-ontic and complete? I will argue that the wave- function in this interpretation is best regarded as ψ-ontic and incomplete.

In his paper titled ‘Against “measurement” ’ [Physics World 3(8), 33–40 [1990]], Bell criticised arguments that use the concept of measurement to justify the statistical interpretation of quantum theory. Among these was the text of Gottfried [Quantum Mechanics (Benjamin, New York, [1966])]. Gottfried has replied to this criticism, claiming to show that, for systems with both continuous and discrete degrees of freedom, the statistical interpretation for the discrete variables is implied by requiring that the continuous variables (...) are described classically. In the present paper, Gottfried’s argument is criticised. It is suggested that he takes over aspects of classical physics which are in conflict with the classical limit of the Schrödinger equation. He incorrectly assumes that, in the output from a Stern-Gerlach apparatus, the wave-function of any ion is restricted to one or another of the beams. (shrink)

It is argued that the so-called minimal statistical interpretation of quantum mechanics does not completely resolve the measurement problem in that this view is unable to show that quantjum mechanics can dispense with classical physics when it comes to a treatment of the measuring interaction. It is suggested that the view that quantum mechanics applies to individual systems should not be too hastily abandoned, in that this view gives perhaps the best hope of leading to a version of (...) quantum mechanics which does provide a complete solution to the measurement problem. (shrink)

Starting with the Born interpretation of quantum mechanics, we show that the quantum theory of measurement, supplemented by the strong law of large numbers, leads to a measurement statistics interpretation of quantum mechanics. A probabilistic characterization of the spectrum of a physical quantity is given, and an analysis of the notions of possible values and possible measurement results is carried out.

Population-level theories of evolution—the stock and trade of population genetics—are statistical theories par excellence. But what accounts for the statistical character of population-level phenomena? One view is that the population-level statistics are a product of, are generated by, probabilities that attach to the individuals in the population. On this conception, population-level phenomena are explained by individual-level probabilities and their population-level combinations. Another view, which arguably goes back to Fisher but has been defended recently, is that the population-level statistics (...) are sui generis, that they somehow emerge from the underlying deterministic behavior of the individuals composing the population. Walsh et al. label this the statistical interpretation. We are not willing to give them that term, since everyone will admit that the population-level theories of evolution are statistical, so we will call this the emergentist statistical interpretation. Our goals are to show that: This interpretation is based on gross factual errors concerning the practice of evolutionary biology, concerning both what is done and what can be done; its adoption would entail giving up on most of the explanatory and predictive projects of evolutionary biology; and finally a rival interpretation, which we will label the propensity statistical interpretation succeeds exactly where the emergentist interpretation fails. (shrink)

Population-level theories of evolution—the stock and trade of population genetics—are statistical theories par excellence. But what accounts for the statistical character of population-level phenomena? One view is that the population-level statistics are a product of, are generated by, probabilities that attach to the individuals in the population. On this conception, population-level phenomena are explained by individual-level probabilities and their population-level combinations. Another view, which arguably goes back to Fisher but has been defended recently, is that the population-level statistics (...) are sui generis, that they somehow emerge from the underlying deterministic behavior of the individuals composing the population. Walsh et al. label this the statistical interpretation. We are not willing to give them that term, since everyone will admit that the population-level theories of evolution are statistical, so we will call this the emergentist statistical interpretation. Our goals are to show that: This interpretation is based on gross factual errors concerning the practice of evolutionary biology, concerning both what is done and what can be done; its adoption would entail giving up on most of the explanatory and predictive projects of evolutionary biology; and finally a rival interpretation, which we will label the propensity statistical interpretation succeeds exactly where the emergentist interpretation fails. (shrink)

The Born’s rule to interpret the square of wave function as the probability to get a specific value in measurement has been accepted as a postulate in foundations of quantum mechanics. Although there have been so many attempts at deriving this rule theoretically using different approaches such as frequency operator approach, many-world theory, Bayesian probability and envariance, literature shows that arguments in each of these methods are circular. In view of absence of a convincing theoretical proof, recently some researchers have (...) carried out experiments to validate the rule up-to maximum possible accuracy using multi-order interference (Sinha et al, Science, 329, 418 [2010]). But, a convincing analytical proof of Born’s rule will make us understand the basic process responsible for exact square dependency of probability on wave function. In this paper, by generalizing the method of calculating probability in common experience into quantum mechanics, we prove the Born’s rule for statistical interpretation of wave function. (shrink)

What is natural selection? I address this question by exploring the relation between two debates: Is natural selection a mechanism? Is natural selection a causal or a statistical theory? I argue that the first can be assessed only relative to a model and that, following the second, there are two fundamentally different and independent kinds of models, Modern-Synthesis and Darwinian models. MS-models, I argue, are not mechanistic even if they are causal. D-models, in contrast, are mechanistic. A causal-mechanistic (...) class='Hi'>interpretation of D-models is thus compatible with a statistical interpretation of MS-models. Natural selection, I conclude, lacks a single, unifying nature. (shrink)

The paper is thematically divided into two parts. In the first part, we will address the arguments raised against the anti-intellectualist thesis that ability is a necessary condition for knowledge-how, present Katherine Hawley’s proposed generic solution based on counterfactual success in order to overcome these arguments, followed by an analysis of Bengson & Moffett’s counterargument to Hawley’s counterfactual success thesis [CST]. We will conclude that Bengson & Moffett’s counterargument misses its target, so that, as far as we are concerned, Katherine (...) Hawley’s proposal, namely CST, is safe. In the second part of the paper, we will provide a statistical interpretation of one of Hawley’s more specific proposals, counterfactual success with occasional failure [CSTF], and assess a couple of philosophically challenging consequences that follow from such an interpretation. (shrink)

In this article I examine how psychologists, amateurs and actors in the police and in juridical fields positioned themselves in the 1920s and 1930s on the scientific nature of graphology. Graphology, the study of the character from handwriting, was linked with the hope of providing reliable methods for the investigation of psychological states and dispositions. The essay argues that on an epistemic level two different models have been represented to support the scientific nature of graphology: for one thing resorting to (...) the special individual skill, the “genius” of a graphologist; or rather depersonalized techniques predominantly based on statistics. Amateur graphologists used both of these forms.On a methodological level, I argue that in order to historicize the human sciences in general, and psychology in particular, it is useful to examine the translation processes that turn everyday interpretative practices into scientific legitimate investigative procedures. In order to investigate precisely this translation process, it is useful to look at what Thomas Gieryn calls “boundary work” at the border between scientific and non-scientific interpretation practices, for which graphology is used here as an example. It is particularly illuminating to examine how representatives of the official sciences distinguish themselves from presumed “charlatans”, which is why the article focuses on court cases and the demarcation strategies used by the police against fraudulent amateur graphologists.ZusammenfassungIn dem Aufsatz wird untersucht, in welcher Weise sich Psycholog*innen, Amateur*innen und Akteur*innen der Polizei und des Rechtswesens in den 1920er und 1930er Jahren zur Wissenschaftlichkeit der Graphologie positioniert haben. Mit der Graphologie, der Lehre von der Deutung der Handschrift als Ausdruck des Charakters, war die Hoffnung verbunden worden, zuverlässige Methoden zur Untersuchung psychischer Zustände und Dispositionen zur Verfügung zu haben. In dem Aufsatz wird argumentiert, dass auf epistemischer Ebene zwei verschiedene Modelle vertreten worden sind, um die Wissenschaftlichkeit der Graphologie zu untermauern: zum einen der Rekurs auf eine spezielle persönliche Eignung, das „Genie“, des Graphologen, zum anderen entpersonalisierte, zumeist statistisch gestützte Techniken. Die Amateurgraphologen haben sich auf beide Formen bezogen.Auf methodologischer Ebene argumentiere ich, dass es zur Historisierung der Wissenschaften von der Psyche im Allgemeinen und der Psychologie im Besonderen nützlich sein kann, den Übersetzungsprozess zu untersuchen, der aus alltäglichen Deutungspraktiken wissenschaftlich legitim erscheinende Untersuchungsverfahren macht. Um genau diesen Übersetzungsprozesses zu untersuchen wird das „boundary work“ an der Grenze von wissenschaftlichen und nicht-wissenschaftlichen Deutungspraktiken am Beispiel der Graphologie betrachtet. Dabei erweist sich als besonders aufschlussreich zu untersuchen, wie sich Vertreter*innen offizieller Wissenschaften von den mutmaßlichen „Scharlatanen“ abgrenzten. Der zentrale Quellentypus, auf dem der Artikel beruht, sind deshalb Gerichtsprozesse gegen Amateurgraphologen, denen Betrug vorgeworfen wurde, in denen explizit gemacht werden musste, was die Wissenschaftlichkeit von Graphologie ausmachte. (shrink)

I attempt to develop further the statistical interpretation of quantum mechanics proposed by Einstein and developed by Popper, Ballentine, etc. Two ideas are proposed in the present paper. One is to interpret momentum as a property of an ensemble of similarly prepared systems which is not satisfied by any one member of the ensemble of systems. Momentum is regarded as a statistical parameter like temperature in statistical mechanics. The other is the holistic assumption that a probability (...) distribution is determined as a whole as most likely to be realized. This is the same as the chief assumption in statistical mechanics, and maximum likelihood in classical statistics. These ideas enable us to understand statistically (1) the formalism of quantum mechanics, (2) Heisenberg's uncertainty relations, and (3) the origin of quantum equations. They also explain violation of Bell's inequality and the interference of probabilities. (shrink)

A statistical mechanical treatment is given of thermal contact between two systems. Reciprocal temperature emerges from this as the relative change in the number of microscopic states a macroscopic system at equilibrium ranges over, at constant volume and chemical composition, with change in internal energy. The significance of this is discussed in detail with reference to a monatomic gas and an Einstein solid.

The conspicuous similarities between interpretive strategies in classical statistical mechanics and in quantum mechanics may be grounded on their employment of common implementations of probability. The objective probabilities which represent the underlying stochasticity of these theories can be naturally associated with three of their common formal features: initial conditions, dynamics, and observables. Various well-known interpretations of the two theories line up with particular choices among these three ways of implementing probability. This perspective has significant application to debates on primitive (...) ontology and to the quantum measurement problem. (shrink)

In this paper I propose an interpretation of classical statistical mechanics that centers on taking seriously the idea that probability measures represent complete states of statistical mechanical systems. I show how this leads naturally to the idea that the stochasticity of statistical mechanics is associated directly with the observables of the theory rather than with the microstates (as traditional accounts would have it). The usual assumption that microstates are representationally significant in the theory is therefore dispensable, (...) a consequence which suggests interesting possibilities for developing non-equilibrium statistical mechanics and investigating inter-theoretic answers to the foundational questions of statistical mechanics. (shrink)

It is widely held that falsification of statistical hypotheses is impossible. This view is supported by an analysis of the most important theories of statistical testing: these theories are not compatible with falsificationism. On the other hand, falsificationism yields a basically viable solution to the problems of explanation, prediction and theory testing in a deterministic context. The present paper shows how to introduce the falsificationist solution into the realm of statistics. This is done mainly by applying the concept (...) of empirical content to statistical hypotheses. It is shown that empirical content is a substitute for ‘power’ as defined by Neyman and Pearson. Since the empirical content of a hypothesis is independent of alternative hypotheses, the proposed theory of statistical testing allows for tests of isolated hypotheses. (shrink)

Scientific findings nowadays often rely on statistical analyses, are expressed in terms of probabilities, and are frequently developed based on model calculations. These circumstances contribute to a disconnect between scientific predictions and people's everyday risk assessments. Situations such as the COVID-19 pandemic, climate issues, or the downsides of global trade are particularly affected by this phenomenon. In these areas especially, the growth of knowledge implies new and far-reaching ethical (preventive) obligations for humanity. This chapter argues that a successful relationship (...) between scientific knowledge and people's everyday decision-making behavior in these domains can only emerge if several demanding prerequisites are met: understanding statistical findings and probabilities must be generally improved; the ethical implications resulting from this understanding must be recognized as moral progress; and the challenging delineations of new ethical obligations and political necessities that arise in risk contexts require careful and patient consideration, rather than being used as an excuse to maintain the status quo. -/- ----- Wissenschaftliche Erkenntnisse basieren heutzutage oft auf statistischen Auswertungen, werden in Wahrscheinlichkeit angegeben und sind nicht selten auf Grundlage von Modellrechnungen entwickelt. Diese Umstände tragen zu einer Abkoppelung der wissenschaftlichen Prognosen von den lebens- weltlichen Risikoeinschätzungen der Menschen bei. Situationen wie die COVID-19-Pandemie, die Klimaproblematik oder auch die Nachteile des globalen Handels sind von diesem Phänomen in besonderem Maße betroffen. Gerade auf diesen Gebieten impliziert der Wissenszuwachs neue und weitreichende ethische (Verhinderungs-)Pflichten für die Menschen. In diesem Kapitel wird argumentiert, dass ein gelingendes Verhältnis zwischen wissenschaftlicher Erkenntnis und dem alltäglichen Entscheidungsverhalten der Menschen in diesen Bereichen nur dann entstehen kann, wenn mehrere anspruchsvolle Voraussetzungen erfüllt sind: Das Verständnis von statistischen Erkenntnissen und Wahrscheinlichkeiten muss generell verbessert werden; das Verständnis der hierdurch resultierenden ethischen Implikationen muss als moralischer Fortschritt verstanden werden; und die schwierigen Grenzziehungen für die neuen ethischen Pflichten sowie politischen Notwendigkeiten, die im Rahmen von Risikokontexten notwendig werden, bedürfen einer differenzierten und geduldigen Bearbeitung, anstatt als Ausflucht in ein Weiter-so genutzt zu werden. -/- . (shrink)

Philosophical accounts of quantum theory commonly suppose that the observables of a quantum system form a Type-I factor von Neumann algebra. Such algebras always have atoms, which are minimal projection operators in the case of quantum mechanics. However, relativistic quantum field theory and the thermodynamic limit of quantum statistical mechanics make extensive use of von Neumann algebras of more general types. This chapter addresses the question whether interpretations of quantum probability devised in the usual manner continue to apply in (...) the more general setting. Features of non-type I factor von Neumann algebras are cataloged. It is shown that these novel features do not cause the familiar formalism of quantum probability to falter, since Gleason's Theorem and the Lüders Rule can be generalized. However, the features render the problem of the interpretation of quantum probability more intricate. (shrink)

To complete our ontological interpretation of quantum theory we have to conclude a treatment of quantum statistical mechanics. The basic concepts in the ontological approach are the particle and the wave function. The density matrix cannot play a fundamental role here. Therefore quantum statistical mechanics will require a further statistical distribution over wave functions in addition to the distribution of particles that have a specified wave function. Ultimately the wave function of the universe will he required, (...) but we show that if the universe in not in thermodynamic equilibrium then it can he treated in terms of weakly interacting large scale constituents that are very nearly independent of each other. In this way we obtain the same results as those of the usual approach within the framework of the ontological interpretation. (shrink)

Although philosophers have considered some of the implications of the nature of quantum statistics of many-particle systems for the interpretation problem, e.g., Reichenbach, they have not produced a complete analysis of the relationship between aspects of quantum statistics and complications and/or possible solutions of the interpretation problem. While the present work by no means provides a complete account, it does explore some heretofore uncharted regions. One of the latter is an analysis of a situation that I call 'The (...) Paradox of Identical Particles ,' which arises in Bose-Einstein statistics. PIP refers to the fact that Elementary Quantum Mechanics seems to be committed to the thesis that systems of particles of the same species, "identical" particles, exhibit behavior differing from that of systems of particles of different species, simply in virtue of the fact that the former contain entities of the same species while the latter do not. Taken at face value this is tantamount to the Empedoclean "axiom" that like attracts like, while like and unlike repel, a somewhat embarassingly naive proposition for modern physicists to embrace, and one which, furthermore, poses a host of perplexing problems, e.g., how do the particles "know" whether they are of the same species or not? A result proven in the present work is that any "pluralistic" interpretation of quantum theory is unable to provide a satisfactory way of ridding quantum physicists of this appeal to what I call "species sensitivity." Arguing that Quantum Field Theory is most naturally and plausibly interpreted as a "monistic" theory--which means, inter alia, that for a system of n identical particles to exist is not for n distinct objects of any kind to exist, but rather for one unified underlying entity, a quantum field, to be in a certain kind of state or condition--I show that from this point of view PIP can be dissolved. On the basis of this and other considerations, I argue that the interpretation problem is more amenable to solution if we take the QFT point of view as the fundamental expression of quantum theory. (shrink)

The statistical aspects of quantum explanation are intrinsic to quantum physics; individual quantum events are created in the interactions associated with observation and are not describable by predictive theory. The superposition principle shows the essential difference between quantum and non-quantum physics, and the principle is exemplified in the classic single-photon two-slit interference experiment. Recently Mandel and Pfleegor have done an experiment somewhat similar to the optical single-photon experiment but with two independently operated lasers; interference is obtained even with beam (...) intensity so small that only one photon is in the apparatus at a time. The result can be understood in terms of the superposition of states; or, in terms of the Uncertainty Principle, which is found to forbid the determination of which of the two lasers is the source of a given photon (if conditions for interference are to obtain). The Mandel-Pfleegor experiment gives a physical argument against the continuous localization of a photon that is assumed in the hidden variable theories and therefore gives further support for the generally accepted view that an observed entity (observed state) is created in the observation event. This aspect of quantum physics implies a subjectivism on the level of individual quantum-level occurrences, since there is in quantum theory no basis for asserting the existence of the event independently of observation of it. Extension of this subjectivism to large scale, non-quantum phenomena falls within the principles of quantum theory; counter considerations that argue against such an extension are noted. (shrink)

It has been claimed that if statistical power and p-values are both used to measure the strength of our evidence for the null-hypothesis when the results of our tests are not significant, then they can also be used to derive inconsistent epistemic judgements as we compare two different experiments. Those problematic derivations are known as power approach paradoxes. The consensus is that we can avoid them if we abandon the idea that statistical power can measure the strength of (...) our evidence. In this paper however, I put forward a different solution. I argue that every power approach paradox rests on an equivocation on "strong evidence". The main idea is that we need to make a careful distinction between the evidence provided by the quality of the test and the evidence provided by the outcome of the test. Both provide different types of evidence and their respective strength are to be evaluated differently. (shrink)

The traditional use of ergodic theory in the foundations of equilibrium statistical mechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time averages (albeit for a special class of systems, and up to a measure zero set of exceptions). Secondly, one argues that actual measurements of thermodynamic quantities yield time averaged quantities, since measurements take a long time. The combination of (...) these two points is held to be an explanation why calculating microcanonical phase averages is a successful algorithm for predicting the values of thermodynamic observables. It is also well-known that this account is problematic.

This survey intends to show that ergodic theory nevertheless may have important roles to play, and it explores three other uses of ergodic theory. Particular attention is paid, firstly, to the relevance of specific interpretations of probability, and secondly, to the way in which the concern with systems in thermal equilibrium is translated into probabilistic language. With respect to the latter point, it is argued that equilibrium should not be represented as a stationary probability distribution as is standardly done; instead, a weaker definition is presented. (shrink)

The attempt to derive (rather than assume) the statistical postulate of quantum theory from the many-universes interpretation of Everett and De Witt is analyzed The many-universes interpretation is found to be neither necessary nor sufficient for the task.

Die hier zusammengefassten statistischen Daten waren ursprünglich als Teil meiner Habilitationsschrift "〈Deutscher Empirismus〉. Studien zur Philosophie im deutschsprachigen Raum 1830-1930" (erscheint 2016 oder 2017 bei Springer) gedacht. In der Endfassung des Manuskripts wurden diese Daten jedoch nicht mehr im Detail aufgenommen, weil sich herausgestellt hat, dass eine plausible Interpretation dieses Materials den Rahmen meiner Arbeit bei weitem sprengen und umfangreiche zusätzliche Recherchen erfordern würde. Dieses Dokument versteht sich als Skizze zu einer in Zukunft noch zu schreibenden Arbeit zur Universitätsstatistik (...) und als Ergänzung zu dem oben genannten Buch. (shrink)

The purpose of this paper is, while discussing in detail Helmut Rüßmann's theory of judicial factfinding, to demonstrate how probability theory can be used in dealing with a situation where the court has not obtained full evidence, but probability assumptions are possible with regard to circumstantial evidence. After giving a brief overview of provisions of German law which include the concept of probability, elementary features of probability calculus and statistical inference are outlined. The focus of the discussion of Rüßmann's (...) theory is on evaluating testimony and on combining the impact of several pieces of evidence which bear on the same event or proposition; the relevant concepts of Ekelöf, Schreiber, Rüßmann and Dempster are analyzed and then compared with a new proposal. The paper concludes that alternative approaches to probability need not be invoked;,classical' probability calculus seems to best cope with the questions courts are confronted with in situations such as discussed in the paper. (shrink)

In The Point of View for my Work as an Author, Kierkegaard declares that the works discussed therein move from the aesthetic to the religious, that the Postscript represents the turning point in this movement, etc. In this brief and preliminary study we use a ?change?point? version of the chi?square test on the frequencies of selected sets of ?aesthetic? and ?religious? words to determine the degree of statistical evidence for these and other related claims. Briefly, these tests show that (...) there is strong statistical evidence for all but one of these various claims and that there are therefore good statistical grounds for taking Kierkegaard's ?aesthetic/religious? interpretation seriously. (shrink)

Statistical tests of the primality of some numbers look similar to statistical tests of many nonmathematical, clearly empirical propositions. Yet interpretations of probability prima facie appear to preclude the possibility of statistical tests of mathematical propositions. For example, it is hard to understand how the statement that n is prime could have a frequentist probability other than 0 or 1. On the other hand, subjectivist approaches appear to be saddled with ‘coherence’ constraints on rational probabilities that require (...) rational agents to assign extremal probabilities to logical and mathematical propositions. In the light of these problems, many philosophers have come to think that there must be some way to generalize a Bayesian statistical account. In this article I propose that a classical frequentist approach should be reconsidered. I conclude that we can give a conditional justification of statistical testing of at least some mathematical hypotheses: if statistical tests provide us with reasons to believe or bet on empirical hypotheses in the standard situations, then they also provide us with reasons to believe or bet on mathematical hypotheses in the structurally similar mathematical cases. (shrink)

In following paper an attempt will be made to analyse the statistical relationships between variables as the functions of causal relations existing between them. Our basic assumption here is that statistical relationships between traits, events, or characteristics of objects, may be logically derived from the pattern of their mutual causal connections, if this pattern is described by appropriate concepts and with sufficient precision. The first part of the paper presents basic concepts, which according to author's view may serve (...) for the description of different patterns of causal relations in such a way, that statistical relationships corresponding to each pattern may be derived. It gives also examples of such a derivation for some less complicated cases. The second part of the paper is an attempt of application of proposed method to the understanding and critical consideration of some standard techniques of statistical analysis, especially those mostly used in social sciences. (shrink)

In their influential paper “Ceteris Paribus, There is No Problem of Provisos”, Earman and Roberts (Synthese 118:439–478, 1999) propose to interpret the non-strict generalizations of the special sciences as statistical generalizations about correlations. I call this view the “statistical account”. Earman and Roberts claim that statistical generalizations are not qualified by “non-lazy” ceteris paribus conditions. The statistical account is an attractive view, since it looks exactly like what everybody wants: it is a simple and intelligible theory (...) of special science laws without the need for mysterious ceteris paribus conditions. I present two challenges to the statistical account. According to the first challenge, the statistical account does not get rid of so-called “non-lazy” ceteris paribus conditions. This result undermines one of the alleged and central advantages of the statistical account. The second challenge is that the statistical account, qua general theory of special science laws, is weakened by the fact that idealized law statements resist a purely statistical interpretation. (shrink)

Tooze provides an interpretation of the dramatic period of statistical innovation between 1900 and the end of World War II. At the turn of the century, virtually none of the economic statistics that we take for granted today were available. By 1944, the entire repertoire of modern economic statistics was being put to work in wartime economic management. As this book reveals, the Weimar Republic and the Third Reich were in the forefront of statistical innovation in the (...) interwar decades. New ways of measuring the economy were inspired both by contemporary developments in macroeconomic theory and the needs of government. The Weimar Republic invested heavily in macroeconomic research. Under the Nazi regime, these statistical tools were to provide the basis for a radical experiment in economic planning. Based on the German example, this book presents the case for a more wide-ranging reconsideration of the history of modern economic knowledge. (shrink)

We analyze the quantum mechanical measuring process from the standpoint of information theory. Statistical inference is used in order to define the most likely state of the measured system that is compatible with the readings of the measuring instrument and the a priori information about the correlations between the system and the instrument. This approach has the advantage that no reference to the time evolution of the combined system need be made. It must, however, be emphasized that the result (...) is to be interpreted as the statistically inferred state of the original system rather than the state of the system after measurement. The phenomenon of “reduction of states” appears in this light as a consequence of incomplete information rather than the physical interaction between measured system and measuring instrument. (shrink)

A subarea of the debate over the nature of evolutionary theory addresses what the nature of the explanations yielded by evolutionary theory are. The statisticalist line is that the general principles of evolutionary theory are not only amenable to a mathematical interpretation but that they need not invoke causes to furnish explanations. Causalists object that construction of these general principles involves crucial causal assumptions. A recent view claims that some biological explanations are statistically autonomous explanations (SAEs) whereby phenomena are (...) accounted for statistically and which prescind from micro-causal details. I raise three major problems for this account and then advance a view which unifies SAEs as mathematical explanations: the MSAE view. The MSAE view not only resolves the issues bedeviling the original SAE account but serves to importantly broaden the class of non-causal explanations in population biology. (shrink)

Over the past fifteen years there has been a considerable amount of debate concerning what theoretical population dynamic models tell us about the nature of natural selection and drift. On the causal interpretation, these models describe the causes of population change. On the statistical interpretation, the models of population dynamics models specify statistical parameters that explain, predict, and quantify changes in population structure, without identifying the causes of those changes. Selection and drift are part of a (...) statistical description of population change; they are not discrete, apportionable causes. Our objective here is to provide a definitive statement of the statistical position, so as to allay some confusions in the current literature. We outline four commitments that are central to statisticalism. They are: 1. Natural Selection is a higher order effect; 2. Trait fitness is primitive; 3. Modern Synthesis (MS)-models are substrate neutral; 4. MS-selection and drift are model-relative. (shrink)

This paper attempts to analyze the concept of quantum statistical determinism. This is done after we have clarified the epistemic difference between causality and determinism and discussed the content of classical forms of determinism—mechanical and dynamical. Quantum statistical determinism transcends the classical forms, for it expresses the multiple potentialities of quantum systems. The whole argument is consistent with a statistical interpretation of quantum mechanics.

This paper deals with meta-statistical questions concerning frequentist statistics. In Sections 2 to 4 I analyse the dispute between Fisher and Neyman on the so called logic of statistical inference, a polemic that has been concomitant of the development of mathematical statistics. My conclusion is that, whenever mathematical statistics makes it possible to draw inferences, it only uses deductive reasoning. Therefore I reject Fisher's inductive approach to the statistical estimation theory and adhere to Neyman's deductive one. On (...) the other hand, I assert that Neyman-Pearson's testing theory, as well as Fisher's tests of significance, properly belong to decision theory, not to logic, neither deductive nor inductive. I then also disagree with Costantini's view of Fisher's testing model as a theory of hypothetico-deductive inferences.In Section 5 I disapprove Hacking1's evidentialists criticisms of the Neyman-Pearson's theory of statistics (NPT), as well as Hacking2's interpretation of NPT as a theory of probable inference. In both cases Hacking misses the point. I conclude, by claiming that Mayo's conception of the Neyman-Pearson's testing theory, as a model of learning from experience, does not purport any advantages over Neyman's behavioristic model. (shrink)

Statistical evidence is crucial throughout disparate impact’s three-stage analysis: during (1) the plaintiff’s prima facie demonstration of a policy’s disparate impact; (2) the defendant’s job-related business necessity defense of the discriminatory policy; and (3) the plaintiff’s demonstration of an alternative policy without the same discriminatory impact. The circuit courts are split on a vital question about the “practical significance” of statistics at Stage 1: Are “small” impacts legally insignificant? For example, is an employment policy that causes a one percent (...) disparate impact an appropriate policy for redress through disparate impact litigation? This circuit split calls for a comprehensive analysis of practical significance testing across disparate impact’s stages. Importantly, courts and commentators use “practical significance” ambiguously between two aspects of practical significance: the magnitude of an effect and confidence in statistical evidence. For example, at Stage 1 courts might ask whether statistical evidence supports a disparate impact (a confidence inquiry) and whether such an impact is large enough to be legally relevant (a magnitude inquiry). Disparate impact’s texts, purposes, and controlling interpretations are consistent with confidence inquires at all three stages, but not magnitude inquiries. Specifically, magnitude inquiries are inappropriate at Stages 1 and 3—there is no discriminatory impact or reduction too small or subtle for the purposes of the disparate impact analysis. Magnitude inquiries are appropriate at Stage 2, when an employer defends a discriminatory policy on the basis of its job-related business necessity. (shrink)