The arrow of time is a familiar phenomenon we all know from our experience: we remember the past but not the future and control the future but not the past. However, it takes an effort to keep records of the past, and to affect the future. For example, it would take an immense effort to unmix coffee and milk, although we easily mix them. Such time directed phenomena are sub- sumed under the Second Law of Thermodynamics. This law characterizes our (...) experience of the arrow of time in terms of an increase of a theoretical magnitude called entropy. Statistical mechan- ics tries to explain the Second Law as an effect of the behavior of the microscopic particles that make up the universe. Since our senses are too coarse to see this microstructure, statistical mechanics describes our experience in terms of probability, or in terms of the partial information we have about the particles. In this paper we explain the workings of statistical mechanics; how it accounts for probability as an objective feature of the world based on the underlying dynamics; how it accounts for our memories of the past; how the statistical mechanical probability under- writes the Second Law; and how, at the same time, it leads to a violation of the Second Law by the so-called Maxwell’s Demon. (shrink)

This Element has two main aims. The first one is an historically informed review of the philosophy of probability. It describes recent historiography, lays out the distinction between subjective and objective notions, and concludes by applying the historical lessons to the main interpretations of probability. The second aim focuses entirely on objective probability, and advances a number of novel theses regarding its role in scientific practice. A distinction is drawn between traditional attempts to interpret chance, and a novel methodological (...) study of its application. A radical form of pluralism is then introduced, advocating a tripartite distinction between propensities, probabilities and frequencies. Finally, a distinction is drawn between two different applications of chance in statistical modelling which, it is argued, vindicates the overall methodological approach. The ensuing conception of objective probability in practice is the 'complex nexus of chance'. (shrink)

The Philosophy of Quantitative Methods undertakes a philosophical examination of a number of important quantitative research methods within the behavioral sciences in order to overcome the non-critical approaches typically provided by textbooks. These research methods are exploratory data analysis, statistical significance testing, Bayesian confirmation theory and statistics, meta-analysis, and exploratory factor analysis. Further readings are provided to extend the reader's overall understanding of these methods.

The arrow of time is a familiar phenomenon we all know from our experience: we remember the past but not the future and control the future but not the past. However, it takes an effort to keep records of the past, and to affect the future. For example, it would take an immense effort to unmix coffee and milk, although we easily mix them. Such time directed phenomena are subsumed under the Second Law of Thermodynamics. This law characterizes our experience (...) of the arrow of time in terms of an increase of a theoretical magnitude called entropy. Statistical mechanics tries to explain the Second Law as an effect of the behavior of the microscopic particles that make up the universe. Since our senses are too coarse to see this microstructure, statistical mechanics describes our experience in terms of probability, or in terms of the partial information we have about the particles. In this paper we explain the workings of statistical mechanics; how it accounts for probability as an objective feature of the world based on the underlying dynamics; how it accounts for our memories of the past; how the statistical mechanical probability underwrites the Second Law; and how, at the same time, it leads to a violation of the Second Law by the so‐called Maxwell’s Demon. (shrink)

I document some of the main evidence showing that E. S. Pearson rejected the key features of the behavioral-decision philosophy that became associated with the Neyman-Pearson Theory of statistics (NPT). I argue that NPT principles arose not out of behavioral aims, where the concern is solely with behaving correctly sufficiently often in some long run, but out of the epistemological aim of learning about causes of experimental results (e.g., distinguishing genuine from spurious effects). The view Pearson did hold (...) gives a deeper understanding of NPT tests than their typical formulation as accept-reject routines, against which criticisms of NPT are really directed. The Pearsonian view that emerges suggests how NPT tests may avoid these criticisms while still retaining what is central to these methods: the control of error probabilities. (shrink)

This article focuses on the role of statistical concepts in both experiment and theory in various scientific disciplines, especially physics, including astronomy, and psychology. In Sect. 1 the concept of uncertainty in astronomy is analyzed from Ptolemy to Laplace and Gauss. In Sect. 2 theoretical uses of probability and statistics in science are surveyed. Attention is focused on the historically important example of radioactive decay. In Sect. 3 the use of statistics in biology and the social sciences is (...) examined, with detailed consideration of various Chi-square statistical tests. Such tests are essential for proper evaluation of many different kinds of scientific hypotheses. (shrink)

Statistical mechanics is a strange theory. Its aims are debated, its methods are contested, its main claims have never been fully proven, and their very truth is challenged, yet at the same time, it enjoys huge empirical success and gives us the feeling that we understand important phenomena. What is this weird theory, exactly? Statistical mechanics is the name of the ongoing attempt to apply mechanics, together with some auxiliary hypotheses, to explain and predict certain phenomena, above all those described (...) by thermodynamics. This paper shows what parts of this objective can be achieved with mechanics by itself. It thus clarifies what roles remain for the auxiliary assumptions that are needed to achieve the rest of the desiderata. Those auxiliary hypotheses are described in another paper in this journal, Foundations of statistical mechanics: The auxiliary hypotheses. (shrink)

The quality of doctoral-level chemistry (N=145), computer science (N=58), geoscience (N=91), mathematics (N=115), physics (N=123), and statistics/biostatistics (N=64) programs at United States universities was assessed, using 16 measures. These measures focused on variables related to: program size; characteristics of graduates; reputational factors (scholarly quality of faculty, effectiveness of programs in educating research scholars/scientists, improvement in program quality during the last 5 years); university library size; research support; and publication records. Chapter I discusses prior attempts to assess quality in graduate (...) education, development of the study plans, and the selection of disciplines and programs to be evaluated. Chapter II discusses the methodology used, focusing on each of the assessment measures. Chapters III to VIII present, respectively, findings from the analyses of the chemistry, computer science, geoscience, mathematics, physics, and statistics/biostatistics programs. Chapter IX includes a summary of results, correlations among measures, several additional analyses, and suggestions for future studies. Among the findings reported are those indicating that mathematics programs had, on the average, the largest number of faculty (N=33) in December 1980 followed closely by physics (N=28) and chemistry (N=23), and that 80 percent of computer science students had job commitments by graduation. (Survey instruments and supporting documentation are included in appendices.) (JN). (shrink)

Statistical mechanics is the name of the ongoing attempt to explain and predict certain phenomena, above all those described by thermodynamics on the basis of the fundamental theories of physics, in particular mechanics, together with certain auxiliary assumptions. In another paper in this journal, Foundations of statistical mechanics: Mechanics by itself, I have shown that some of the thermodynamic regularities, including the probabilistic ones, can be described in terms of mechanics by itself. But in order to prove those regularities, in (...) particular the time asymmetric ones, it is necessary to add to mechanics assumptions of three kinds, all of which are under debate in contemporary literature. One kind of assumptions concerns measure and probability, and here, a major debate is around the notion of “typicality.” A second assumption concerns initial conditions, and here, the debate is about the nature and status of the so-called past hypothesis. The third kind of assumptions concerns the dynamics, and here, the possibility and significance of “Maxwell's Demon” is the main topic of discussions. This article describes these assumptions and examines the justification for introducing them, emphasizing the contemporary debates around them. (shrink)

Clark Glymour, Richard Scheines, Peter Spirtes and Kevin Kelly. Discovering Causal Structure: Artifical Intelligence, Philosophy of Science and Statistical Modeling.

The Fifth International Congress of Logic, Methodology and Philosophy of Science was held at the University of Western Ontario, London, Canada, 27 August to 2 September 1975. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science, and was sponsored by the National Research Council of Canada and the University of Western Ontario. As those associated closely with the work of the Division (...) over the years know well, the work undertaken by its members varies greatly and spans a number of fields not always obviously related. In addition, the volume of work done by first rate scholars and scientists in the various fields of the Division has risen enormously. For these and related reasons it seemed to the editors chosen by the Divisional officers that the usual format of publishing the proceedings of the Congress be abandoned in favour of a somewhat more flexible, and hopefully acceptable, method of pre sentation. Accordingly, the work of the invited participants to the Congress has been divided into four volumes appearing in the University of Western Ontario Series in Philosophy of Science. The volumes are entitled, Logic, Foundations of Mathematics and Computability Theory, Foun dational Problems in the Special Sciences, Basic Problems in Methodol ogy and Linguistics, and Historical and Philosophical Dimensions of Logic, Methodology and Philosophy of Science. (shrink)

In this paper, I examine William Whewell’s (1794–1866) ‘Discoverer’s Induction’, and argue that it 21 supplies a strikingly accurate characterization of the logic behind many statistical methods, exploratory 22 data analysis (EDA) in particular. Such methods are additionally well-suited as a point of evaluation of 23 Whewell’s philosophy since the central techniques of EDA were not invented until after Whewell’s death, 24 and so couldn’t have influenced his views. The fact that the quantitative details of some very general 25 (...) methods designed to suggest hypotheses would so closely resemble Whewell’s views of how theories 26 are formed is, I suggest, a strongly positive comment on these views. (shrink)

The recent discovery of a Higgs boson prompted increased attention of statisticians and philosophers of science to the statistical methodology of High Energy Physics. Amidst long-standing debates within the field, HEP has adopted a mixed statistical methodology drawing upon both frequentist and Bayesian methods, but with standard frequentist techniques such as significance testing and confidence interval estimation playing a primary role. Physicists within HEP typically deny that their methodological decisions are guided by philosophical convictions, but are instead based on “pragmatic” (...) considerations, thus distancing themselves from what they perhaps perceive as an ongoing pitched ideological battle between frequentists and Bayesians. Here I argue that there is a philosophical orientation to HEP that is neither exclusively frequentist nor Bayesian, but that lies squarely in the tradition of philosophical pragmatism. I further argue that understanding the statistical methodology of HEP through the perspective of pragmatism clarifies the role of and rationale for significance testing in the search for new phenomena such as the Higgs boson. (shrink)

The main argument of this paper is that an evaluation of the overall explanatory power of a theory is less problematic and more relevant as an assessment of the state of knowledge than evaluation of statistical explanations of single occurrences in terms of likelihoods that are assigned to explananda.

There are two motivations commonly ascribed to historical actors for taking up statistics: to reduce complicated data to a mean value (e.g., Quetelet), and to take account of diversity (e.g., Galton). Different motivations will, it is assumed, lead to different methodological decisions in the practice of the statistical sciences. Karl Pearson and W. F. R. Weldon are generally seen as following directly in Galton’s footsteps. I argue for two related theses in light of this standard interpretation, based on a (...) reading of several sources in which Weldon, independently of Pearson, reflects on his own motivations. First, while Pearson does approach statistics from this "Galtonian" perspective, he is, consistent with his positivist philosophy of science, utilizing statistics to simplify the highly variable data of biology. Weldon, on the other hand, is brought to statistics by a rich empiricism and a desire to preserve the diversity of biological data. Secondly, we have here a counterexample to the claim that divergence in motivation will lead to a corresponding separation in methodology. Pearson and Weldon, despite embracing biometry for different reasons, settled on precisely the same set of statistical tools for the investigation of evolution. (shrink)

This paper is a discussion of David Albert's approach to the foundations of classical statistical menchanics. I point out a respect in which his account makes a stronger claim about the statistical mechanical probabilities than is usually made, and I suggest what might be motivation for this. I outline a less radical approach, which I attribute to Boltzmann, and I give some reasons for thinking that this approach is all we need, and also the most we are likely to get. (...) The issue between the two accounts turns out to be one about the explanatory role probabilities play in statistical mechanics. (shrink)

Indeed, this is the first serious book-length study of the subject by a philosopher of science.

In this talk I present the main results from Anta (2021), namely, that the theoretical division between Boltzmannian and Gibbsian statistical mechanics should be understood as a separation in the epistemic capabilities of this physical discipline. In particular, while from the Boltzmannian framework one can generate powerful explanations of thermal processes by appealing to their microdynamics, from the Gibbsian framework one can predict observable values in a computationally effective way. Finally, I argue that this statistical mechanical schism contradicts the Hempelian (...) (1958) thesis that the predictive power of a scientific theory is directly proportional to its explanatory potential, and vice versa. (shrink)

This chapter contains sections titled: Introduction Claims of Culture: Three Views Coercion Reciprocity Conclusion Acknowledgments References.

How should we reason in science? Jan Sprenger and Stephan Hartmann offer a refreshing take on classical topics in philosophy of science, using a single key concept to explain and to elucidate manifold aspects of scientific reasoning. They present good arguments and good inferences as being characterized by their effect on our rational degrees of belief. Refuting the view that there is no place for subjective attitudes in 'objective science', Sprenger and Hartmann explain the value of convincing evidence in (...) terms of a cycle of variations on the theme of representing rational degrees of belief by means of subjective probabilities (and changing them by Bayesian conditionalization). In doing so, they integrate Bayesian inference—the leading theory of rationality in social science—with the practice of 21st century science. Bayesian Philosophy of Science thereby shows how modeling such attitudes improves our understanding of causes, explanations, confirming evidence, and scientific models in general. It combines a scientifically minded and mathematically sophisticated approach with conceptual analysis and attention to methodological problems of modern science, especially in statistical inference, and is therefore a valuable resource for philosophers and scientific practitioners. (shrink)

Contents Preface General Introduction 1 | Science and Pseudoscience Introduction Karl Popper, Science: Conjectures and Refutations Thomas S. Kuhn, Logic of Discovery or Psychology of Research? Imre Lakatos, Science and Pseudoscience Paul R. Thagard, Why Astrology Is a Pseudoscience Michael Ruse, Creation-Science Is Not Science Larry Laudan, Commentary: Science at the Bar---Causes for Concern Commentary 2 | Rationality, Objectivity, and Values in Science Introduction Thomas S. Kuhn, The Nature and Necessity of Scientific Revolutions Thomas S. Kuhn, Objectivity, Value Judgment, and (...) Theory Choice Ernan McMullin, Rationality and Paradigm Change in Science Larry Laudan, Kuhn’s Critique of Methodology Helen E. Longino, Values and Objectivity Kathleen Okruhlik, Gender and the Biological Sciences Commentary 3 | The Duhem-Quine Thesis and Underdetermination Introduction Pierre Duhem, Physical Theory and Experiment W. V. Quine, Two Dogmas of Empiricism Donald Gillies, The Duhem Thesis and the Quine Thesis Larry Laudan, Demystifying Underdetermination *Colin Howson and Peter Urbach, The Duhem Problem Commentary 4 | Induction, Prediction, and Evidence Introduction Peter Lipton, Induction Karl Popper, The Problem of Induction Wesley C. Salmon, Rational Prediction Carl G. Hempel, Criteria of Confirmation and Acceptability Peter Achinstein, Explanation v. Prediction: Which Carries More Weight? *Nelson Goodman, The New Riddle of Induction Commentary 5 | Confirmation and Relevance: Bayesian Approaches Introduction Wesley C. Salmon, Rationality and Objectivity in Science *Deborah G. Mayo, A Critique of Salmon’s Bayesian Way *Alan Chalmers, The Bayesian Approach Paul Horwich, Therapeutic Bayesianism Commentary 6 | Models of Explanation Introduction Rudolf Carnap, The Value of Laws: Explanation and Prediction Carl G. Hempel, Two Basic Types of Scientific Explanation Carl G. Hempel, The Thesis of Structural Identity Carl G. Hempel, Inductive-Statistical Explanation Peter Railton, A Deductive-Nomological Model of Probabilistic Explanation *Philip Kitcher, Explanatory Unification *James Woodward, The Manipulability Conception of Causal Explanation Commentary 7 | Laws of Nature Introduction A. J. Ayer, What Is a Law of Nature? Fred I. Dretske, Laws of Nature D. H. Mellor, Necessities and Universals in Natural Laws Nancy Cartwright, Do the Laws of Physics State the Facts? Commentary 8 | Intertheoretic Reduction Introduction Ernest Nagel, Issues in the Logic of Reductive Explanations Paul K. Feyerabend, How to Be a Good Empiricist *Jerry A. Fodor, Special Sciences Philip Kitcher, 1953 and All That: A Tale of Two Sciences Commentary 9 | Empiricism and Scientific Realism Introduction Grover Maxwell, The Ontological Status of Theoretical Entities Bas C. van Fraassen, Arguments Concerning Scientific Realism Alan Musgrave, Realism versus Constructive Empiricism Larry Laudan, A Confutation of Convergent Realism *Juha T. Saatsi, On the Pessimistic Induction and Two Fallacies Ian Hacking, Experimentation and Scientific Realism David B. Resnik, Hacking’s Experimental Realism *Martin Carrier, What Is Right with the Miracle Argument Arthur Fine, The Natural Ontological Attitude Alan Musgrave, NOA’s Ark---Fine for Realism Commentary Glossary Bibliography Name Index Subject Index. (shrink)

Statistical mechanics is often taken to be the paradigm of a successful inter-theoretic reduction, which explains the high-level phenomena (primarily those described by thermodynamics) by using the fundamental theories of physics together with some auxiliary hypotheses. In my view, the scope of statistical mechanics is wider since it is the type-identity physicalist account of all the special sciences. But in this chapter, I focus on the more traditional and less controversial domain of this theory, namely, that of explaining the thermodynamic (...) phenomena.What are the fundamental theories that are taken to explain the thermodynamic phenomena? The lively research into the foundations of classical statistical mechanics suggests that using classical mechanics to explain the thermodynamic phenomena is fruitful. Strictly speaking, in contemporary physics, classical mechanics is considered to be false. Since classical mechanics preserves certain explanatory and predictive aspects of the true fundamental theories, it can be successfully applied in certain cases. In other circumstances, classical mechanics has to be replaced by quantum mechanics. In this chapter I ask the following two questions: I) How does quantum statistical mechanics differ from classical statistical mechanics? How are the well-known differences between the two fundamental theories reflected in the statistical mechanical account of high-level phenomena? II) How does quantum statistical mechanics differ from quantum mechanics simpliciter? To make our main points I need to only consider non-relativistic quantum mechanics. Most of the ideas described and addressed in this chapter hold irrespective of the choice of a (so-called) interpretation of quantum mechanics, and so I will mention interpretations only when the differences between them are important to the matter discussed. (shrink)

In a pair of articles and in his recent book, Miklos Redei has taken enormous strides toward characterizing the conditions under which relativistic quantum field theory is a safe setting for the deployment of causal talk. Here, we challenge the adequacy of the accounts of causal dependence and screening off on which rests the relevance of Redei's theorems to the question of causal good behavior in the theory.

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)

Whenever a litigant needs to prove that a certain result was caused in a specific way, what could be more compelling than citing the infinitesimal probability of that result emanating from an alternative natural cause? Contrary to this intuitive position, in the present article, I argue that the contention that a result was due to a certain cause should remain unaffected by statistical evidence of the extremely low probability of an alternative cause. The only scenario in which the low probability (...) of a natural cause would be relevant to the case at hand is if it were contrasted with another piece of statistical evidence: the frequency of the criminal activity among people who are similar to the accused. However, by connecting the use of probabilistic generalisations in legal fact-finding to the issue of free will, I hold that, in Criminal Law, contrasting frequencies in this manner is objectionable—as a matter of principle—regardless of how reliable the statistical analysis is. Consequently, if the low probability of a natural cause is probative only if contrasted with another piece of statistical evidence that is objectionable, then neither piece of evidence should be admitted in criminal trials. (shrink)

Hacking’s Law of Likelihood says—paraphrasing—that data support hypothesis H1 over hypothesis H2 whenever the likelihood ratio for H1 over H2 exceeds 1. But Hacking later noted a seemingly fatal flaw in the LR itself: it cannot be interpreted as the degree of “evidential significance” across applications. I agree with Hacking about the problem, but I do not believe the condition is incurable. I argue here that the LR can be properly calibrated with respect to the underlying evidence, and I sketch (...) the rudiments of a methodology for so doing. (shrink)

This short article is based on my special lecture entitled "Aristotle and the Philosophy of Education" at Tamagawa University Research Institute in Tokyo on September 19, 2015, through a recording of the spoken language transcribed in written form with some corrections. The lecture delivered on that day consists of two parts: referring to historical research and a statistical survey, the first half focuses on uncovering the fact that the philosophy of education has been slighted both in Japanese and (...) Western academia and that this fact is valid for both Aristotle's and contemporary studies on the philosophy of education; the second half endeavors to describe two possible research projects - namely, a classical-philosophical and interpretative study of Aristotle's philosophy of education and a contemporary-philosophical and Aristotelian study of the philosophy education. Some of these topics have been published but others have not. This short article concerns the first half of the lecture and measures the gap between philosophy and the philosophy of education in Japan through a statistical survey of the largest competitive research funding database in Japan: KAKEN. (shrink)

Philosophers of physics are very familiar with foundational problems in quantum mechanics and in the theory of relativity. In both fields, the puzzles, if not solved, are at least reasonably well formulated and possess well-characterized solution strategies. Sklar’s book Physics and Chance focuses on a pair of theories, thermodynamics and statistical mechanics, for which puzzles and foundational paradoxes abound, but where there is very little agreement upon the means with which they may best be approached. As he notes in the (...) introduction. (shrink)

This volume addresses relations between macroscopic and microscopic description; essential roles of visualization and representation in chemical understanding; historical questions involving chemical concepts; the impacts of chemical ideas on wider cultural concerns; and relationships between contemporary chemistry and other sciences. The authors demonstrate, assert, or tacitly assume that chemical explanation is functionally autonomous. This volume should he of interest not only to professional chemists and philosophers, but also to workers in medicine, psychology, and other fields in which relationships between explanations (...) based on diverse levels of description and investigation are important. (Listed on Google books). (shrink)