I argue against the claim, advanced by David Albert and Barry Loewer, that all non-fundamental laws can be derived from those required to underwrite the second law of thermodynamics.

Through his S–R model of statistical relevance, Wesley Salmon offers a solution to the scientific explanation of objectively improbable events.

An examination of topics involved in statistical reasoning with imprecise probabilities. The book discusses assessment and elicitation, extensions, envelopes and decisions, the importance of imprecision, conditional previsions and coherent statistical models.

The law views with suspicion statistical evidence, even evidence that is probabilistically on a par with direct, individual evidence that the law is in no way suspicious of. But it has proved remarkably hard to either justify this suspicion, or to debunk it. In this paper, we connect the discussion of statistical evidence to broader epistemological discussions of similar phenomena. We highlight Sensitivity – the requirement that a belief be counterfactually sensitive to the truth in a specific way – as (...) a way of epistemically explaining the legal suspicion towards statistical evidence. Still, we do not think of this as a satisfactory vindication of the reluctance to rely on statistical evidence. Knowledge – and Sensitivity, and indeed epistemology in general – are of little, if any, legal value. Instead, we tell an incentive-based story vindicating the suspicion towards statistical evidence. We conclude by showing that the epistemological story and the incentive-based story are closely and interestingly related, and by offering initial thoughts about the role of statistical evidence in morality. (shrink)

The application of statistical methods and models both in the natural and social sciences is nowadays a trivial fact which nobody would deny. Bold analogies even suggest the application of the same statistical models to fields as different as statistical mechanics and economics, among them the case of the young and controversial discipline of Econophysics . Less trivial, however, is the answer to the philosophical question, which has been raised ever since the possibility of “commuting” statistical thinking and models between (...) natural and social sciences emerged: whether such a methodological kinship would imply some kind of more profound unity of the natural and the social domain. Starting with Adolphe Quetelet (1796-1874) and ending with the Vienna Circle (from the late 1920s until the 1940s), this paper offers a brief historical and philosophical reconstruction of some important stages in the development of statistics as “commuting” between the natural and the social sciences. This reconstruction is meant to highlight (with respect to the authors under consideration): (1) the existence of a significant correlation between the readiness to “transfer” statistical thinking from natural to social sciences and vice versa, on the one hand, and the standpoints on the issue of the unity/disunity of science, on the other; (2) the historical roots and the fortunes of the analogy between statistical models of society and statistical models of gases. (shrink)

Statistical evidence—say, that 95% of your co-workers badmouth each other—can never render resenting your colleague appropriate, in the way that other evidence (say, the testimony of a reliable friend) can. The problem of statistical resentment is to explain why. We put the problem of statistical resentment in several wider contexts: The context of the problem of statistical evidence in legal theory; the epistemological context—with problems like the lottery paradox for knowledge, epistemic impurism and doxastic wrongdoing; and the context of a (...) wider set of examples of responses and attitudes that seem not to be appropriately groundable in statistical evidence. Regrettably, we do not come up with a fully general, fully adequate, fully unified account of all the phenomena discussed. But we give reasons to believe that no such account is forthcoming, and we sketch a somewhat messier account that may be the best that can be had here. (shrink)

Recently, the practice of deciding legal cases on purely statistical evidence has been widely criticised. Many feel uncomfortable with finding someone guilty on the basis of bare probabilities, even though the chance of error might be stupendously small. This is an important issue: with the rise of DNA profiling, courts are increasingly faced with purely statistical evidence. A prominent line of argument—endorsed by Blome-Tillmann 2017; Smith 2018; and Littlejohn 2018—rejects the use of such evidence by appealing to epistemic norms that (...) apply to individual inquirers. My aim in this paper is to rehabilitate purely statistical evidence by arguing that, given the broader aims of legal systems, there are scenarios in which relying on such evidence is appropriate. Along the way I explain why popular arguments appealing to individual epistemic norms to reject legal reliance on bare statistics are unconvincing, by showing that courts and individuals face different epistemic predicaments (in short, individuals can hedge when confronted with statistical evidence, whilst legal tribunals cannot). I also correct some misconceptions about legal practice that have found their way into the recent literature. (shrink)

A popular informal argument suggests that statistics about the preponderance of criminal involvement among particular demographic groups partially justify others in making defensive mistakes against members of the group. One could worry that evidence-relative accounts of moral rights vindicate this argument. After constructing the strongest form of this objection, I offer several replies: most demographic statistics face an unmet challenge from reference class problems, even those that meet it fail to ground non-negligible conditional probabilities, even if they did, (...) they introduce new costs likely to cancel out any justificatory contribution of the statistic, but even if they didn’t, demographic facts are the wrong sort to make a moral difference to agents’ negative rights. I conclude that the popular argument should be rejected, and evidence-relative theories do not have the worrisome implication. (shrink)

Predictive algorithms are playing an increasingly prominent role in society, being used to predict recidivism, loan repayment, job performance, and so on. With this increasing influence has come an increasing concern with the ways in which they might be unfair or biased against individuals in virtue of their race, gender, or, more generally, their group membership. Many purported criteria of algorithmic fairness concern statistical relationships between the algorithm’s predictions and the actual outcomes, for instance requiring that the rate of false (...) positives be equal across the relevant groups. We might seek to ensure that algorithms satisfy all of these purported fairness criteria. But a series of impossibility results shows that this is impossible, unless base rates are equal across the relevant groups. What are we to make of these pessimistic results? I argue that none of the purported criteria, except for a calibration criterion, are necessary conditions for fairness, on the grounds that they can all be simultaneously violated by a manifestly fair and uniquely optimal predictive algorithm, even when base rates are equal. I conclude with some general reflections on algorithmic fairness. (shrink)

In typical statistical learning studies, researchers define sequences in terms of the probability of the next item in the sequence given the current item (or items), and they show that high probability sequences are treated as more familiar than low probability sequences. Existing accounts of these phenomena all assume that participants represent statistical regularities more or less as they are defined by the experimenters—as sequential probabilities of symbols in a string. Here we offer an alternative, or possibly supplementary, hypothesis. Specifically, (...) rather than identifying or labeling individual stimuli discretely in order to predict the next item in a sequence, we need only assume that the participant is able to represent the stimuli as evincing particular similarity relations to one another, with sequences represented as trajectories through this similarity space. We present experiments in which this hypothesis makes sharply different predictions from hypotheses based on the assumption that sequences are learned over discrete, labeled stimuli. We also present a series of simulation models that encode stimuli as positions in a continuous two‐dimensional space, and predict the next location from the current location. Although no model captures all of the data presented here, the results of three critical experiments are more consistent with the view that participants represent trajectories through similarity space rather than sequences of discrete labels under particular conditions. (shrink)

In this review article, Christiansen provides a historical perspective on the two research traditions, implicit learning and statistical learning, thus nicely setting the scene for this special issue of Topics in Cognitive Science. In this “tale of two literatures”, he first traces the history of both literatures before sketching a framework that provides a basis for understanding implicit learning and statistical learning as a unified phenomenon.

The book explores several open questions in the philosophy of statistical mechanics. Each chapter is written by a leading expert in the field. Here is a list of some questions that are addressed in the book: 1) Boltzmann showed how the phenomenological gas laws of thermodynamics can be derived from statistical mechanics. Since classical mechanics is a deterministic theory there are no probabilities in it. Since statistical mechanics is based on classical mechanics, all the probabilities statistical mechanics talks about cannot (...) be fundamental. However, if probabilities are epistemic, how can they play a role, as they seem to do, in laws, explanation, and prediction? 2) Many physicists use the notion of typicality instead of the one of probability when discussing statistical mechanics. What is the connection between the two notions? 3) How can one extend Boltzmann’s analysis to the quantum domain, where some theories are indeterministic? 4) Boltzmann’s explanation fundamentally involves cosmology: for the explanation to go through the Big Bang needs to have had extremely low entropy. Does the fact that the Big Bang was a low entropy state imply that it was, in some sense, “highly improbable” and requires an explanation? 5) What exactly is the connection between statistical and classical mechanics? Is the one of theory reduction or there is no such thing? 6) Statistical mechanics has two main formulation: one due to Botzmann and the other due to Gibbs. What is the connection between the two formulations . (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and (...) made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Martin Smith has recently proposed, in this journal, a novel and intriguing approach to puzzles and paradoxes in evidence law arising from the evidential standard of the Preponderance of the Evidence. According to Smith, the relation of normic support provides us with an elegant solution to those puzzles. In this paper I develop a counterexample to Smith’s approach and argue that normic support can neither account for our reluctance to base affirmative verdicts on bare statistical evidence nor resolve the pertinent (...) paradoxes. Normic support is, as a consequence, not a successful epistemic anti-luck condition. (shrink)

The fundamental problem on which Ilya Prigogine and the Brussels–Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of time (...) was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels–Austin Group, is to consider the observed direction of time to be a basic physical phenomenon due to the dynamics of physical systems. This essay focuses mainly on recent developments in the Brussels–Austin Group after the mid-1980s. The fundamental concerns are the same as in their earlier approaches (subdynamics, similarity transformations), but the contemporary approach utilizes rigged Hilbert space (whereas the older approaches used Hilbert space). While the emphasis on nonequilibrium statistical mechanics remains the same, their more recent approach addresses the physical features of large Poincare systems, nonlinear dynamics and the mathematical tools necessary to analyze them. (shrink)

A naturalistic scheme of primitive conceptual representations is proposed using the statistical measure of mutual information. It is argued that a concept represents, not the class of objects that caused its tokening, but the class of objects that is most likely to have caused it (had it been tokened), as specified by the statistical measure of mutual information. This solves the problem of misrepresentation which plagues causal accounts, by taking the representation relation to be determined via ordinal relationships between conditional (...) probabilities. The scheme can deal with statistical biases and does not rely on arbitrary criteria. Implications for the theory of meaning and semantic content are addressed. (shrink)

The computations involved in statistical learning have long been debated. Here, we build on work suggesting that a basic memory process, chunking, may account for the processing of statistical regularities into larger units. Drawing on methods from the memory literature, we developed a novel paradigm to test statistical learning by leveraging a robust phenomenon observed in serial recall tasks: that short‐term memory is fundamentally shaped by long‐term distributional learning. In the statistically induced chunking recall (SICR) task, participants are exposed to (...) an artificial language, using a standard statistical learning exposure phase. Afterward, they recall strings of syllables that either follow the statistics of the artificial language or comprise the same syllables presented in a random order. We hypothesized that if individuals had chunked the artificial language into word‐like units, then the statistically structured items would be more accurately recalled relative to the random controls. Our results demonstrate that SICR effectively captures learning in both the auditory and visual modalities, with participants displaying significantly improved recall of the statistically structured items, and even recall specific trigram chunks from the input. SICR also exhibits greater test–retest reliability in the auditory modality and sensitivity to individual differences in both modalities than the standard two‐alternative forced‐choice task. These results thereby provide key empirical support to the chunking account of statistical learning and contribute a valuable new tool to the literature. (shrink)

There is little empirical evidence showing a direct link between a capacity for statistical learning (SL) and proficiency with natural language. Moreover, discussion of the role of SL in language acquisition has seldom focused on literacy development. Our study addressed these issues by investigating the relationship between SL and reading ability in typically developing children and healthy adults. We tested SL using visually presented stimuli within a triplet learning paradigm and examined reading ability by administering the Wide Range Achievement Test (...) (WRAT-4; Wilkinson & Robertson, 2006). A total of 38 typically developing children (mean age of 9;5 years, range 6;4–12;5) and 37 healthy adults (mean age of 21 years, range 18–34) were assessed. In children, SL was significantly related to reading ability. Importantly, this relationship was independent of grade and also age. The adult data, too, revealed that SL was significantly related to reading ability. A regression analysis of the combined child and adult data revealed that SL accounted for a unique amount of variance in reading ability, after age and attention had been taken into consideration. For the first time, this study provides empirical evidence that a capacity for more effective SL is related to higher reading ability in the general population. (shrink)

One finds, in Maxwell's writings on thermodynamics and statistical physics, a conception of the nature of these subjects that differs in interesting ways from the way that they are usually conceived. In particular, though—in agreement with the currently accepted view—Maxwell maintains that the second law of thermodynamics, as originally conceived, cannot be strictly true, the replacement he proposes is different from the version accepted by most physicists today. The modification of the second law accepted by most physicists is a probabilistic (...) one: although statistical fluctuations will result in occasional spontaneous differences in temperature or pressure, there is no way to predictably and reliably harness these to produce large violations of the original version of the second law. Maxwell advocates a version of the second law that is strictly weaker; the validity of even this probabilistic version is of limited scope, limited to situations in which we are dealing with large numbers of molecules en masse and have no ability to manipulate individual molecules. Connected with this is his concept of the thermodynamic concepts of heat, work, and entropy; on the Maxwellian view, these are concepts that must be relativized to the means we have available for gathering information about and manipulating physical systems. The Maxwellian view is one that deserves serious consideration in discussions of the foundation of statistical mechanics. It has relevance for the project of recovering thermodynamics from statistical mechanics because, in such a project, it matters which version of the second law we are trying to recover. (shrink)

It is one thing to hold that merely statistical evidence is _sometimes_ insufficient for rational belief, as in typical lottery and profiling cases. It is another thing to hold that merely statistical evidence is _always_ insufficient for rational belief. Indeed, there are cases where statistical evidence plainly does justify belief. This project develops a dispositional account of the normativity of statistical evidence, where the dispositions that ground justifying statistical evidence are connected to the goals (= proper function) of objects. There (...) are strong intuitive motivations for doing this. For we can turn almost any case of _non-justifying_ merely statistical evidence into a case of _justifying_ merely statistical evidence by adding information about the dispositions and goals of the objects involved. The resulting view not only helps us understand when and why merely statistical evidence is normatively significant, but it also helps us understand how statistical evidence relates to more standard forms of evidence (perceptual, testimonial). The emerging view also has surprising applications, as it imposes limitations on the epistemic value of fine-tuning arguments for theism as well as undermines a standard class of case-based arguments for moral encroachment. (shrink)

The twentieth century witnessed a dramatic increase in the use of statistics by biologists, including systematists. The modern synthesis and new systematics stimulated this development, particularly after World War II. The rise of "the statistical frame of mind " resulted in a rethinking of the relationship between biological and mathematical points of view, the roles of objectivity and subjectivity in systematic research, the implications of new computing technologies, and the place of systematics among the biological disciplines.

Really statistical explanation is a hitherto neglected form of noncausal scientific explanation. Explanations in population biology that appeal to drift are RS explanations. An RS explanation supplies a kind of understanding that a causal explanation of the same result cannot supply. Roughly speaking, an RS explanation shows the result to be mere statistical fallout.

I consider the error-statistical account as both a theory of evidence and as a theory of inference. I seek to show how inferences regarding the truth of hypotheses can be upheld by avoiding a certain kind of alternative hypothesis problem. In addition to the testing of assumptions behind the experimental model, I discuss the role of judgments of implausibility. A benefit of my analysis is that it reveals a continuity in the application of error-statistical assessment to low-level empirical hypotheses and (...) highly general theoretical principles. This last point is illustrated with a brief sketch of the issues involved in the parametric framework analysis of tests of physical theories such as General Relativity and of fundamental physical principles such as the Einstein Equivalence Principle. (shrink)

Causation is a macroscopic phenomenon. The temporal asymmetry displayed by causation must somehow emerge along with other asymmetric macroscopic phenomena like entropy increase and the arrow of radiation. I shall approach this issue by considering ‘causal inference’ techniques that allow causal relations to be inferred from sets of observed correlations. I shall show that these techniques are best explained by a reduction of causation to structures of equations with probabilistically independent exogenous terms. This exogenous probabilistic independence imposes a recursive order (...) on these equations and a consequent distinction between dependent and independent variables that lines up with the temporal asymmetry of causation. (shrink)

Humans are capable of extracting recurring patterns from their environment via statistical learning (SL), an ability thought to play an important role in language learning and learning more generally. While much work has examined statistical learning in infants and adults, less work has looked at the developmental trajectory of SL during childhood to see whether it is fully developed in infancy or improves with age, like many other cognitive abilities. A recent study showed modality‐based differences in the effect of age (...) during childhood: While visual SL improved with age, auditory SL did not. This finding was taken as evidence for modality‐based differences in SL. However, since that study used auditory linguistic stimuli (syllables), the differential effect of age may have been driven by stimulus type (linguistic vs. non‐linguistic) rather than modality. Here, we ask whether age will affect performance similarly in the two modalities when non‐linguistic auditory stimuli are used (familiar sounds instead of syllables). We conduct a large‐scale study of children's performance on visual and non‐linguistic auditory SL during childhood (ages 5–12 years). The results show a similar effect of age in both modalities: Unlike previous findings, both visual and non‐linguistic auditory SL improved with age. These findings highlight the stimuli‐sensitive nature of SL and suggest that modality‐based differences may be stimuli‐dependent, and that age‐invariance may be limited to linguistic stimuli. (shrink)

A major problem for interpersonal aggregation is how to compare utility across individuals; a major problem for decision-making under normative uncertainty is the formally analogous problem of how to compare choice-worthiness across theories. We introduce and study a class of methods, which we call statistical normalization methods, for making interpersonal comparisons of utility and intertheoretic comparisons of choice-worthiness. We argue against the statistical normalization methods that have been proposed in the literature. We argue, instead, in favor of normalization of variance: (...) we claim that this is the account that most plausibly gives all individuals or theories ‘equal say’. To this end, we provide two proofs that variance normalization has desirable properties that all other normalization methods lack, though we also show how different assumptions could lead one to axiomatize alternative statistical normalization methods. (shrink)

Several decades ago, Christopher Boorse formulated an influential statistical theory of normative biological functions but it has often been claimed that his theory suffers from insuperable problems such as an inability to handle cases of epidemic and universal diseases. This paper develops a new statistical theory of normative functions that is capable of dealing with the notorious problem of epidemic and universal diseases. The theory is also more detailed than its predecessors and offers other important advantages over them. It is (...) argued here that statistical theories of biological functions should not be so quickly dismissed. (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)

With his new riddle of induction, Goodman raised a problem for enumerative induction which many have taken to show that only some ‘natural’ properties can be used for making inductive inferences. Arguably, however, (i) enumerative induction is not a method that scientists use for making inductive inferences in the first place. Moreover, it seems at first sight that (ii) Goodman’s problem does not affect the method that scientists actually use for making such inferences—namely, classical statistics. Taken together, this would (...) indicate that (iii) ‘naturalness’ is not such a relevant concept for the problem of induction, after all. I have no objections against (i) and (iii). But, contrary to (ii), I argue that classical statistics does face a version of Goodman’s problem, which I call the statistical riddle of induction. Given that his problem merely is an instance of the more general problem of underdetermination, this is hardly surprising. Perhaps more importantly, I also show how my riddle can be used for exposing a common fallacy in probabilistic reasoning, without relying on Bayesian assumptions. (shrink)

Recently, Jennifer Saul (“Racial Figleaves, the Shifting Boundaries of the Permissible, and the Rise of Donald Trump”, 2017; “Racist and Sexist Figleaves”, 2021) has explored the use of what she calls “figleaves” in the discourse on race and gender. Following Saul, a figleaf is an utterance that, for some portion of the audience, blocks the conclusion that some other utterance, R, or the person who uttered R is racist or sexist. Such racial and gender figleaves are pernicious, says Saul, because, (...) among other things, they can shift the boundaries of what is deemed acceptable to think or say. This paper expands on Saul’s picture in a threefold way: It is first argued that appeals to statistics can function as figleaves. It is then argued that—as far as figleaves go—there is reason to believe that statistics-as-figleaves are especially pernicious. Finally, the paper explores some strategies for counterspeech. (shrink)

As a contribution to current debates on the ‘social life of methods’, in this article we present an ethnomethodological study of the role of understanding within statistical practice. After reviewing the empirical turn in the methods literature and the challenges to the qualitative-quantitative divide it has given rise to, we argue such case studies are relevant because they enable us to see different ways in which ‘methods’, here quantitative methods, come to have a social life – by embodying and exhibiting (...) understanding they ‘make the social structures of everyday activities observable’ ( Garfinkel, 1967 : 75), thereby putting society on display. Exhibited understandings rest on distinctive lines of practical social and cultural inquiry – ethnographic ‘forays’ into the worlds of the producers and users of statistics – which are central to good statistical work but are not themselves quantitative. In highlighting these non-statistical forms of social and cultural inquiry at work in statistical practice, our case study is an addition to understandings of statistics and usefully points to ways in which studies of the social life of methods might be further developed from here. (shrink)

This study investigated visual statistical learning (VSL) in 24 deaf signers and 24 hearing non‐signers. Previous research with hearing individuals suggests that SL mechanisms support literacy. Our first goal was to assess whether VSL was associated with reading ability in deaf individuals, and whether this relation was sustained by a link between VSL and sign language skill. Our second goal was to test the Auditory Scaffolding Hypothesis, which makes the prediction that deaf people should be impaired in sequential processing tasks. (...) For the VSL task, we adopted a modified version of the triplet learning paradigm, with stimuli presented sequentially across space and time. Results revealed that measures of sign language skill (sentence comprehension/repetition) did not correlate with VSL scores, possibly due to the sequential nature of our VSL task. Reading comprehension scores (PIAT‐R) were a significant predictor of VSL accuracy in hearing but not deaf people. This finding might be due to the sequential nature of the VSL task and to a less salient role of the sequential orthography‐to‐phonology mapping in deaf readers compared to hearing readers. The two groups did not differ in VSL scores. However, when reading ability was taken into account, VSL scores were higher for the deaf group than the hearing group. Overall, this evidence is inconsistent with the Auditory Scaffolding Hypothesis, suggesting that humans can develop efficient sequencing abilities even in the absence of sound. (shrink)

It was proposed that the data from Monte Carlo statistical investigations be subjected to analysis of variance methods rather than the conventional techniques of tabling, graphing, and inspecting the data. Two examples in which analysis of variance methods were applied to published Monte Carlo studies were presented. It was suggested that balanced factorial designs should be used whenever possible in Monte Carlo studies so that analysis of variance methods would be directly applicable. Finally, three advantages of analysis of variance methods (...) over conventional techniques were described and analysis of variance methods were contrasted with a possible alternative analytical method, multiple regression analysis. (shrink)

Philosophical debates over statistical evidence have long been framed and dominated by L. Jonathan Cohen's Paradox of the Gatecrasher and a related hypothetical example commonly called Prison Yard. These examples, however, raise an issue not discussed in the large and growing literature on statistical evidence – the question of what statistical evidence is supposed to be evidence of. In actual practice, the legal system does not start with a defendant and then attempt to determine if that defendant has committed some (...) unspecified or under-specified act, as these examples appear to suppose. Rather, both criminal and civil litigation start with a sufficiently specified act and then attempt to determine if the defendant has committed it. And when we start with a more fully specified act, the statistics look very different, and these prominent examples no longer present the paradox they are claimed to support. Examining the issue of specification, however, does more than simply undercut the prominent examples in a long and extensive literature. The examination also raises normative issues challenging the legal system's traditional reluctance to base liability on the conjunction of probabilities. (shrink)

A modal analysis of luck, due to Duncan Pritchard, has become quite popular in recent years. There are many reasons to like Pritchard’s analysis, but at least two compelling problems have been identified. So I propose an alternative analysis of luck based on the laws of statistical mechanics. The statistical analysis avoids the two problems facing Pritchard’s analysis, and it has many other attractive features.

This paper is a preliminary exploration of the connections between the statistical style of reasoning and the research practices of statistical mechanics in the early period of the long quantum revolution. It suggests that before 1925 the instantiations of the statistical style in physics went through two phases. The first phase consisted of the formulation of the Maxwell‐Boltzmann statistics on the basis of the population‐gas analogy. The second phase was characterized by the generalization of the Maxwell‐Boltzmann statistics through (...) analogies between ideal gas molecules and other microphysical entities, analogies that shaped and were shaped by the rise of quantum theory. Einstein's invention of the Bose‐Einstein statistics started a third phase and created the conditions of possibility for a new classification of microphysical entities according to their different statistics. (shrink)

Many philosophers have pointed out that statistical evidence, or at least some forms of it, lack desirable epistemic or non-epistemic properties, and that this should make us wary of litigations in which the case against the defendant rests in whole or in part on statistical evidence. Others have responded that such broad reservations about statistical evidence are overly restrictive since appellate courts have expressed nuanced views about statistical evidence. In an effort to clarify and reconcile, I put forward an interpretive (...) analysis of why statistical evidence should raise concerns in some cases but not others. I argue that when there is a mismatch between the specificity of the evidence and the expected specificity of the accusation, statistical evidence—as any other kind of evidence—should be considered insufficient to sustain a conviction. I rely on different stylized court cases to illustrate the explanatory power of this analysis. (shrink)

There are two theoretical approaches in statistical mechanics, one associated with Boltzmann and the other with Gibbs. The theoretical apparatus of the two approaches offer distinct descriptions of the same physical system with no obvious way to translate the concepts of one formalism into those of the other. This raises the question of the status of one approach vis-à-vis the other. We answer this question by arguing that the Boltzmannian approach is a fundamental theory while Gibbsian statistical mechanics is an (...) effective theory, and we describe circumstances under which Gibbsian calculations coincide with the Boltzmannian results. We then point out that regarding GSM as an effective theory has important repercussions for a number of projects, in particular attempts to turn GSM into a nonequilibrium theory. (shrink)

In empirical modeling, an important desiderata for deeming theoretical entities and processes as real is that they can be reproducible in a statistical sense. Current day crises regarding replicability in science intertwines with the question of how statistical methods link data to statistical and substantive theories and models. Different answers to this question have important methodological consequences for inference, which are intertwined with a contrast between the ontological commitments of the two types of models. The key to untangling them is (...) the realization that behind every substantive model there is a statistical model that pertains exclusively to the probabilistic assumptions imposed on the data. It is not that the methodology determines whether to be a realist about entities and processes in a substantive field. It is rather that the substantive and statistical models refer to different entities and processes, and therefore call for different criteria of adequacy. (shrink)

Courts and jurors sometimes refuse to assign liability to defendants on the basis of statistics alone, despite their apparent reliability. I argue that this refusal is best understood as a recognition of defendants’ right to security. Understood as a robust good in Philip Pettit’s sense, security requires that someone risking harm to others’ protected interests adopt a disposition of concern that controls against wrongfully harming them. Since trials risk harm, the state must adopt such a disposition. Statistics leave (...) open the possibility of innocence and so wrongful harm in a way that the state cannot ignore; if it does use such statistics, it makes defendants wrongfully insecure. This explanation of the problem of bare statistical evidence is especially apt because security grounds the right to a fair trial and judicial procedural rights more generally. (shrink)

Children acquiring languages with noun classes have ample statistical information available that characterizes the distribution of nouns into these classes, but their use of this information to classify novel nouns differs from the predictions made by an optimal Bayesian classifier. We use rational analysis to investigate the hypothesis that children are classifying nouns optimally with respect to a distribution that does not match the surface distribution of statistical features in their input. We propose three ways in which children's apparent statistical (...) insensitivity might arise, and find that all three provide ways to account for the difference between children's behavior and the optimal classifier. A fourth model combines two of these proposals and finds that children's insensitivity is best modeled as a bias to ignore certain features during classification, rather than an inability to encode those features during learning. These results provide insight into children's developing knowledge of noun classes and highlight the complex ways in which statistical information from the input interacts with children's learning processes. (shrink)

I give a brief account of the way in which thermodynamics and statistical mechanics actually work as contemporary scientific theories, and in particular of what statistical mechanics contributes to thermodynamics over and above any supposed underpinning of the latter's general principles. In doing so, I attempt to illustrate that statistical mechanics should not be thought of wholly or even primarily as itself a foundational project for thermodynamics, and that conceiving of it this way potentially distorts the foundational study of statistical (...) mechanics itself. (shrink)

Shapiro and Sober claim that Walsh, Ariew, Lewens, and Matthen give a mistaken, a priori defense of natural selection and drift as epiphenomenal. Contrary to Shapiro and Sober’s claims, we first argue that WALM’s explanatory doctrine does not require a defense of epiphenomenalism. We then defend WALM’s explanatory doctrine by arguing that the explanations provided by the modern genetical theory of natural selection are ‘autonomous-statistical explanations’ analogous to Galton’s explanation of reversion to mediocrity and an explanation of the diffusion ofgases. (...) We then argue that whereas Sober’s theory of forces is an adequate description of Darwin’s theory, WALM’s explanatory doctrine is required to understand how themodern genetical theory of natural selection explains large-scale statistical regularities. 1 Introduction2 Shapiro and Sober’s ‘Epiphenomenalism Do’s and Don’ts’3 WALM’s Explanatory Doctrine4 Galton’s Autonomous-Statistical Explanation5 A Second Example: The Statistical Explanation of the Diffusion of Gases6 Distinguishing Two Theories of Evolution by Natural Selection7 A Possible Objection: Are Statistical Laws Sufficient for Explanation?8 Conclusion. (shrink)

In "Counterfactual Dependence and Time's Arrow", David Lewis defends an analysis of counterfactuals intended to yield the asymmetry of counterfactual dependence: that later affairs depend counterfactually on earlier ones, and not the other way around. I argue that careful attention to the dynamical properties of thermodynamically irreversible processes shows that in many ordinary cases, Lewis's analysis fails to yield this asymmetry. Furthermore, the analysis fails in an instructive way: it teaches us something about the connection between the asymmetry of overdetermination (...) and the asymmetry of entropy. (shrink)

Over the last twenty-five years, climate scientists working on the attribution of climate change to humans have developed increasingly sophisticated statistical models in a process that can be understood as a kind of calibration: the gradual changes to the statistical models employed in attribution studies served as iterative revisions to a measurement(-like) procedure motivated primarily by the aim of neutralizing particularly troublesome sources of error or uncertainty. This practice is in keeping with recent work on the evaluation of models more (...) generally that views models as tools for particular tasks: what drives the process is the desire for models that provide more reliable grounds for inference rather than accuracy to the underlying mechanisms of data-generation. (shrink)

This chapter will review selected aspects of the terrain of discussions about probabilities in statistical mechanics (with no pretensions to exhaustiveness, though the major issues will be touched upon), and will argue for a number of claims. None of the claims to be defended is entirely original, but all deserve emphasis. The first, and least controversial, is that probabilistic notions are needed to make sense of statistical mechanics. The reason for this is the same reason that convinced Maxwell, Gibbs, and (...) Boltzmann that probabilities would be needed, namely, that the second law of thermodynamics, which in its original formulation says that certain processes are impossible, must, on the kinetic theory, be replaced by a weaker formulation according to which what the original version deems impossible is merely improbable. Second is that we ought not take the standard measures invoked in equilibrium statistical mechanics as giving, in any sense, the correct probabilities about microstates of the system. We can settle for a much weaker claim: that the probabilities for outcomes of experiments yielded by the standard distributions are effectively the same as those yielded by any distribution that we should take as a representing probabilities over microstates. Lastly, (and most controversially): in asking about the status of probabilities in statistical mechanics, the familiar dichotomy between epistemic probabilities (credences, or degrees of belief) and ontic (physical) probabilities is insufficient; the concept of probability that is best suited to the needs of statistical mechanics is one that combines epistemic and physical considerations. (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)

In this article, Arnon explores the link between implicit learning, statistical learning and language development. She focuses on two central themes, namely the issue of age invariance and the question of variation in learning outcomes. Arnon suggests that the two literatures are studying a fundamentally similar phenomenon and argues in favor of a closer alignment. However, she also raises important methodological concerns.

In the last years, the surprising bosonic behavior that a many-fermion system may acquire has raised interest because of theoretical and practical reasons. This trans-statistical behavior is usually considered to be the result of approximation modeling methods generally employed by physicists when faced with complexity. In this paper, we take a tensor product structure and an ontology of properties approach and provide two versions of a toy model in order to argue that trans-statistical behavior allows for a realistic interpretation.