The question of whether conscious experience is restricted by cognitive access and exhausted by report, or whether it overflows it—comprising more information than can be reported—is hotly debated. Recently, we provided evidence in favor of Overflow, showing that observers discriminated the color‐diversity (CD) of letters in an array, while their working‐memory and attention were dedicated to encoding and reporting a set of cued letters. An alternative interpretation is that CD‐discriminations do not entail conscious experience of the underlying colors. Here we (...) argue, based on conceptual considerations and consistency with neuroscience and phenomenology, in favor of the Overflow interpretation. (shrink)

The usefulness of the statistic known as the p-value, as a means of quantify-ing the strength of evidence for the presence of an effect from empirical data has long been questioned in the statistical community. In recent years there has been a notable increase in the awareness of both fundamental and practical limitations of the statistic within the target research fields, and especially biomedicine. In this article I analyse the recently published article which, in summary, argues that with a (...) better understand-ing and thus more appropriate use of the statistic, many of the aforementioned limitations can be addressed. In particular, I demonstrate that the (often implicit) premises of this counterargument are questionable, in some cases arguably inconsistent, and that therefore the counterargument provides little if any justification for the continued use of the p-value. Additionally, my analysis should help researchers seeking to interpret their empirical data by illustrating the nuanced nature and the multiplicity of statistical, methodological, and epistemological issues which must be considered in this process. (shrink)

The received wisdom in statistical mechanics is that isolated systems, when left to themselves, approach equilibrium. But under what circumstances does an equilibrium state exist and an approach to equilibrium take place? In this paper we address these questions from the vantage point of the long-run fraction of time definition of Boltzmannian equilibrium that we developed in two recent papers. After a short summary of Boltzmannian statistical mechanics and our definition of equilibrium, we state an existence theorem which provides (...) general criteria for the existence of an equilibrium state. We first illustrate how the theorem works with a toy example, which allows us to illustrate the various elements of the theorem in a simple setting. After a look at the ergodic programme, we discuss equilibria in a number of different gas systems: the ideal gas, the dilute gas, the Kac gas, the stadium gas, the mushroom gas and the multi-mushroom gas. In the conclusion we briefly summarise the main points and highlight open questions. (shrink)

The purpose of this paper is to provide a detailed technical protocol analysis of chess masters' evaluative expertise, paying particular attention to the analysis of the structure of their memory process in evaluating foreseen possibilities in games of dynamic equilibrium. The paper has two purposes. First, to publish a results chapter from my DPhil thesis (in revised journal article form) attending to the measurement of foresight in chess masters' evaluation process, testing alternative theories of cognitive expertise in the domain of (...) chess; and second to provide a subset of the technical graphical analysis that corresponds to that measurement to preserve this protocol analysis for access in the academic domain for future studies of expert memory and foresight (e.g., Ericsson & Simon, 1993). The step-by-step protocol analysis consists of: (i) an introduction to foresight cognition as hypothesis testing, (ii) a theoretical review in the domain of chess masters' expertise according to the theoretical frameworks in that field purporting hypotheses relevant to chess masters' evaluative skill processes, and (iii) summary tables and non-parametric statistical analysis corroborating chunking theory frameworks of expert cognition (e.g., DeGroot, 1965; Newell & Simon, 1972; Gobet, 1998; Gobet et al., 2004), and refuting the alternative search-evaluation models (e.g., Holding & Reynolds, 1982). Moreover, the journal article espouses the preservation of the traditional protocol analysis method core to the field of expert cognition (DeGroot, 1969; Kotov, 1971). The full protocol analysis can be found in monograph form here on my SSRN profile in ‘The role of falsification in hypothesis testing’. It takes the form of a specialist population study (e.g., detailed case study work; Luria, 1987). Thus the outline consists of a short introduction, a theoretical methodological review discussing protocol analysis methods for specialist population studies in cognition (with particular attention to the preservation of protocol analysis methods for chess studies in cognition and expert memory/ with a fresh angle on the foresight process), and the full set of protocol analyses with corresponding problem behaviour graphs. A subset of the main results has been published elsewhere (e.g., Cowley & Byrne, 2004; Cowley 2006), receiving scientific and scientific journalistic acclaim (e.g., Nature Online News 2004). (shrink)

The terms “collaborative economy” or “sharing economy” have been commonly used in recent years to refer to a proliferation of initiatives, business models and forms of work. To observe this significant phenomenon is necessary to take into consideration a new perspective on social, economic, environmental, and political processes that can be created from a number of assets and skills, in innovative ways and at an unprecedented scale. Using of digital technologies for collaboration, communication, coordination, and value creation purposes is included (...) under the same umbrella of the collaborative economy. Market-focused digital innovation is able to disrupt existing business models and support economic activity. The situation in the area of the collaborative economy in Slovakia seems to be different from that of the Western European countries. Data from the area of sharing economy are not registered with the Statistical Office of the Slovak Republic, and there is no analysis examining its impact. We introduce a short summary of case studies examining the collaborative economy platforms in Slovakia and some issues of taxation of the collaborative economy. (shrink)

Many who think that naked statistical evidence alone is inadequate for a trial verdict think that use of probability is the problem, and something other than probability – knowledge, full belief, causal relations – is the solution. I argue that the issue of whether naked statistical evidence is weak can be formulated within the probabilistic idiom, as the question whether likelihoods or only posterior probabilities should be taken into account in our judgment of a case. This question also identifies a (...) major difference between the Process Reliabilist and Probabilistic Tracking views of knowledge and other concepts. Though both are externalist, and probabilistic, epistemic theories, Tracking does and Process Reliabilism does not put conditions on likelihoods. So Tracking implies that a naked statistic is not adequate evidence about an individual, and does not yield knowledge, whereas the Reliabilist thinks it gives justified belief and knowledge. Not only does the Tracking view imply that naked statistical evidence is insufficient for a verdict, but it gives us resources to explain why, in terms of risk and the special conditions of a trial. (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)

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)

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)

Elements of Mind (EM) has two themes, one major and one minor. The major theme is intentionality, the mind’s direction upon its objects; the other is the mind–body problem. I treat these themes separately: chapters 1, and 3–5 are concerned with intentionality, while chapter 2 is about the mind–body problem. In this summary I will first describe my view of the mind–body problem, and then describe the book’s main theme. Like many philosophers, I see the mind–body problem as containing (...) two sub–problems: the problem of mental causation and the problem of consciousness. I see these problems forming the two horns of a dilemma. Just as the problem of mental causation pushes us towards physicalism, so the problem of consciousness pushes us away from it. Each problem reveals the inadequacy of the solution to the other. Essentially the problem of mental causation is the conflict between (i) the apparent fact that mental states and events have effects in the physical world and (ii) a general principle about the causal nature of the physical world, which is sometimes called the ‘causal closure’ or the ‘causal completeness’ of the physical world. This principle says that all physical effects have physical causes which are enough to bring them about. The problem then is simple: how can a mental cause have a physical effect if that effect also has a physical cause which is enough to bring it about? Barring massive overdetermination of our actions by independent causes, it seems that the best answer is to identify the mental and the physical causes. And this is traditionally how physicalists have argued for their identity theory of mind and body. However, many physicalists reject the identity theory, and therefore they have to solve the mental causation problem in some other way. At present, there is no consensus among physicalists on which of the currently proposed solutions is correct. In chapter 2 of EM I propose an alternative, which I call ‘emergentism’. Inspired by the rejection of the identity theory, Emergentism is the idea that mental properties are genu.. (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)

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)

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)

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)

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.

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)

The origins of testing scientific models with statistical techniques go back to 18th century mathematics. However, the modern theory of statistical testing was primarily developed through the work of Sir R.A. Fisher, Jerzy Neyman, and Egon Pearson in the inter-war period. Some of Fisher's papers on testing were published in economics journals (Fisher, 1923, 1935) and exerted a notable influence on the discipline. The development of econometrics and the rise of quantitative economic models in the mid-20th century made statistical significance (...) testing a commonplace, albeit controversial tool within economics. -/- In the debate about significance testing, methodological controversies intertwine with epistemological issues and sociological developments. Our aim in this chapter is to expound these connections and to show how the use of, and the debate about, significance testing in economics differs from other social sciences, such as psychology. (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)

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)

The replication crisis has prompted many to call for statistical reform within the psychological sciences. Here we examine issues within Frequentist statistics that may have led to the replication crisis, and we examine the alternative—Bayesian statistics—that many have suggested as a replacement. The Frequentist approach and the Bayesian approach offer radically different perspectives on evidence and inference with the Frequentist approach prioritising error control and the Bayesian approach offering a formal method for quantifying the relative strength of evidence (...) for hypotheses. We suggest that rather than mere statistical reform, what is needed is a better understanding of the different modes of statistical inference and a better understanding of how statistical inference relates to scientific inference. (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 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)

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)

At its strongest, Hume's problem of induction denies the existence of any well justified assumptionless inductive inference rule. At the weakest, it challenges our ability to articulate and apply good inductive inference rules. This paper examines an analysis that is closer to the latter camp. It reviews one answer to this problem drawn from the VC theorem in statistical learning theory and argues for its inadequacy. In particular, I show that it cannot be computed, in general, whether we are in (...) a situation where the VC theorem can be applied for the purpose we want it to. (shrink)

In this summary I introduce the interpretive framework for Hegel's Conscience and then provide an overview of the book’s six chapters.

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)

The Unity of Perception: Content, Consciousness and Evidence By SchellenbergSusannaOxford University Press, 2018. 272 pp.

In this paper, we prove that Neutrosophic Statistics is more general than Interval Statistics, since it may deal with all types of indeterminacies (with respect to the data, inferential procedures, probability distributions, graphical representations, etc.), it allows the reduction of indeterminacy, and it uses the neutrosophic probability that is more general than imprecise and classical probabilities and has more detailed corresponding probability density functions. While Interval Statistics only deals with indeterminacy that can be represented by intervals. And (...) we respond to the arguments by Woodall et al. [1]. We show that not all indeterminacies (uncertainties) may be represented by intervals. Also, in some cases, we should better use hesitant sets (that have less indeterminacy) instead of intervals. We redirect the authors to the Plithogenic Probability and Plithogenic Statistics which are the most general forms of MultiVariate Probability and Multivariate Statistics respectively (including, of course, the Imprecise Probability and Interval Statistics as subclasses). (shrink)

A question, long discussed by legal scholars, has recently provoked a considerable amount of philosophical attention: ‘Is it ever appropriate to base a legal verdict on statistical evidence alone?’ Many philosophers who have considered this question reject legal reliance on bare statistics, even when the odds of error are extremely low. This paper develops a puzzle for the dominant theories concerning why we should eschew bare statistics. Namely, there seem to be compelling scenarios in which there are multiple (...) sources of incriminating statistical evidence. As we conjoin together different types of statistical evidence, it becomes increasingly incredible to suppose that a positive verdict would be impermissible. I suggest that none of the dominant views in the literature can easily accommodate such cases, and close by offering a diagnosis of my own. (shrink)

In statistics, there are two main paradigms: classical and Bayesian statistics. The purpose of this article is to investigate the extent to which classicists and Bayesians can agree. My conclusion is that, in certain situations, they cannot. The upshot is that, if we assume that the classicist is not allowed to have a higher degree of belief in a null hypothesis after he has rejected it than before, then he has to either have trivial or incoherent credences to (...) begin with or fail to update his credences by conditionalization. (shrink)

Summary measures of health, such as the quality-adjusted life year and disability-adjusted life year, have long been known to incorporate a number of value choices. In this paper, though, I show that the value choices in the construction of such measures extend far beyond what is generally recognized. In showing this, I hope both to improve the understanding of those measures by epidemiologists, health economists and policy-makers, and also to contribute to the general debate about the extent to which (...) such measures should be adjusted to reflect ethical values. (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)

The paper takes a closer look at the role of knowledge and evidence in legal theory. In particular, the paper examines a puzzle arising from the evidential standard Preponderance of the Evidence and its application in civil procedure. Legal scholars have argued since at least the 1940s that the rule of the Preponderance of the Evidence gives rise to a puzzle concerning the role of statistical evidence in judicial proceedings, sometimes referred to as the Problem of Bare Statistical Evidence. While (...) this puzzle has led to the development of a multitude of accounts and approaches in the legal literature, I argue here that the problem can be resolved fairly straightforwardly within a knowledge-first framework. (shrink)

Math prospective teachers must be able to think creatively and solve problems. The study looked into preservice teachers’ creative thinking and problem-solving abilities in statistics. The investigation was guided by a correlational design in a public university in the Philippines. Stratified random sampling was used to select the 103 study participants from two teacher education programs. Through google forms, data were collected using Torrance et al. (2008)’s tests of creative thinking and researcher-made statistics problem test. The findings revealed (...) that preservice teachers have commendable creative thinking, particularly fluency, flexibility, and elaboration skills. Still, they lack problem-solving skills in statistics, specifically with central tendency, dispersion, and position measures. The correlational analysis revealed no link between creative thinking and problem-solving. Still, creative thinking and problem-solving courses are recommended to help preservice teachers develop their fundamental skills as mathematics educators. (shrink)

This paper puts forward the hypothesis that the distinctive features of quantum statistics are exclusively determined by the nature of the properties it describes. In particular, all statistically relevant properties of identical quantum particles in many-particle systems are conjectured to be irreducible, ‘inherent’ properties only belonging to the whole system. This allows one to explain quantum statistics without endorsing the ‘Received View’ that particles are non-individuals, or postulating that quantum systems obey peculiar probability distributions, or assuming that there (...) are primitive restrictions on the range of states accessible to such systems. With this, the need for an unambiguously metaphysical explanation of certain physical facts is acknowledged and satisfied. (shrink)

The Generality Problem is widely recognized to be a serious problem for reliabilist theories of justification. James R. Beebe's Statistical Solution is one of only a handful of attempted solutions that has garnered serious attention in the literature. In their recent response to Beebe, Julien Dutant and Erik J. Olsson successfully refute Beebe's Statistical Solution. This paper presents a New Statistical Solution that countenances Dutant and Olsson's objections, dodges the serious problems that trouble rival solutions, and retains the theoretical virtues (...) that made Beebe's solution so attractive in the first place. There indeed exists a principled, rigorous, conceptually sparse, and plausible solution to the Generality Problem: it is the New Statistical Solution. (shrink)

Recent attempts to resolve the Paradox of the Gatecrasher rest on a now familiar distinction between individual and bare statistical evidence. This paper investigates two such approaches, the causal approach to individual evidence and a recently influential (and award-winning) modal account that explicates individual evidence in terms of Nozick's notion of sensitivity. This paper offers counterexamples to both approaches, explicates a problem concerning necessary truths for the sensitivity account, and argues that either view is implausibly committed to the impossibility of (...) no-fault wrongful convictions. The paper finally concludes that the distinction between individual and bare statistical evidence cannot be maintained in terms of causation or sensitivity. We have to look elsewhere for a solution of the Paradox of the Gatecrasher. (shrink)

The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability.

According to the Rational Threshold View, a rational agent believes p if and only if her credence in p is equal to or greater than a certain threshold. One of the most serious challenges for this view is the problem of statistical evidence: statistical evidence is often not sufficient to make an outright belief rational, no matter how probable the target proposition is given such evidence. This indicates that rational belief is not as sensitive to statistical evidence as rational credence. (...) The aim of this paper is twofold. First, we argue that, in addition to playing a decisive role in rationalizing outright belief, non-statistical evidence also plays a preponderant role in rationalizing credence. More precisely, when both types of evidence are present in a context, non-statistical evidence should receive a heavier weight than statistical evidence in determining rational credence. Second, based on this result, we argue that a modified version of the Rational Threshold View can avoid the problem of statistical evidence. We conclude by suggesting a possible explanation of the varying sensitivity to different types of evidence for belief and credence based on the respective aims of these attitudes. (shrink)

This paper, “Cultural Statistics, the Media and the Planning and Development of Calabar, Nigeria” stresses the need for the use of Cultural Statistics and effective media communication in the planning and development of Calabar, the Cross River State Capital. This position is anchored on the fact that in virtually every sphere of life, there can be no development without planning, and there can be no proper planning without accurate data or information. Cultural Statistics, and effective use of (...) the media thus become imperative in the planning and development of Calabar, especially as the Cross River State capital, is fast becoming an internationally recognized cultural city due largely to its annual Calabar Festival and Carnival. The paper among other things argues that cultural statistics and the use of the media will reposition the city of Calabar, not only in terms of development, but also in marketing and branding, taking into consideration the new economy and globalization which involve technology, creativity, human capital and capacity for innovation. The paper concludes that although some effort has been made by the Cross River State government in gathering and publishing some cultural information in brochures and other periodicals, there will be need for deliberate and conscientious effort to be made by the relevant government authorities to collect, collate, analyze and interpret cultural data in Calabar and project same in the media with a view to enhancing the planning and development of the Cross River State capital so as to truly make it a tourism and cultural haven in Nigeria and in the continent of Africa. (shrink)

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor (−1)2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under (...) control. This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required. (shrink)

Racial discrimination uses race as grounds to discriminate in the treatment owed to others; sexual discrimination uses people’s sexual features as grounds for determining how they should be treated compared to others. Analogously, statistical discrimination treats statistical inferences about the groups to which individuals belong as grounds for discriminating amongst them in thought, word and deed. Examples of statistical discrimination include the employer who won’t hire women of childbearing age, because they are likely to take maternity leave at some point (...) in their careers; or insurers who wish to charge more to young drivers than to more experienced ones, because they are more likely to have accidents than the latter – or to favour women over men in the cost of premiums for similar reasons. Finally, a famous – infamous – example of statistical discrimination is racial profiling for police purposes, where statistical evidence of differential propensities to crime are used to justify preventive police measures, such as ‘stop and search’, which mainly target young black men, and other racialized minorities. The philosophical appeal of the concept of statistical discrimination is fairly easy to see: it draws our attention to the way that probabilistic claims figure, or might figure, in the distribution of social costs and benefits such as jobs, security, insurance. It therefore gives us a way to test our moral intuitions across different cases, enables us to see how far our moral judgements can be generalised, and whether they have been affected by particularly emotive examples, or by the particular features of a real or hypothetical case. But does that mean that statistical discrimination is unproblematic? This article takes issue with some arguments of Kasper Lippert Rasmussen on the topic. (shrink)

This pair of articles provides a critical commentary on contemporary approaches to statistical mechanical probabilities. These articles focus on the two ways of understanding these probabilities that have received the most attention in the recent literature: the epistemic indifference approach, and the Lewis-style regularity approach. These articles describe these approaches, highlight the main points of contention, and make some attempts to advance the discussion. The first of these articles provides a brief sketch of statistical mechanics, and discusses the indifference approach (...) to statistical mechanical probabilities. (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)

A brief idea on statistics and epistemology.

A hitherto neglected form of explanation is explored, especially its role in population genetics. “Statistically abstractive explanation” (SA explanation) mandates the suppression of factors probabilistically relevant to an explanandum when these factors are extraneous to the theoretical project being pursued. When these factors are suppressed, the explanandum is rendered uncertain. But this uncertainty traces to the theoretically constrained character of SA explanation, not to any real indeterminacy. Random genetic drift is an artifact of such uncertainty, and it is therefore wrong (...) to reify it as a cause of evolution or as a process in its own right. *Received July 2009. †To contact the author, please write to: Department of Philosophy, University of Toronto, 170 St. George St., Toronto, ON M5R 2M8, Canada; e‐mail: [email protected]. (shrink)