In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations of mathematical problems. As a paradigmatic example, we apply a Peircean semiotic framework to answer the question of how students learned the concept of "distribution" in a statistics course by "diagrammatic reasoning" and by developing "hypostatic abstractions," that is (...) by forming new mathematical objects which can be used as means for communication and further reasoning. Peirce's semiotic terminology is used as an alternative for notions such as modeling, symbolizing, and reification. We will show that it is a precise instrument of analysis with regard to the complexity of learning and of communication in mathematics classroom. (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)

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)

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)

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)

In order to perform certain actions – such as incarcerating a person or revoking parental rights – the state must establish certain facts to a particular standard of proof. These standards – such as preponderance of evidence and beyond reasonable doubt – are often interpreted as likelihoods or epistemic confidences. Many theorists construe them numerically; beyond reasonable doubt, for example, is often construed as 90 to 95% confidence in the guilt of the defendant. -/- A family of influential cases suggests (...) standards of proof should not be interpreted numerically. These ‘proof paradoxes’ illustrate that purely statistical evidence can warrant high credence in a disputed fact without satisfying the relevant legal standard. In this essay I evaluate three influential attempts to explain why merely statistical evidence cannot satisfy legal standards. (shrink)

I argue that generic generalizations expressed in language (i.e. ‘generics’) are apt for clinical reasoning. I introduce generics and describe two problems in the use and interpretation of generics: Generics may license inaccurate judgements about the frequency of events or properties within a group (i.e. a problem with the ‘truth-aptness’ of generics) and may facilitate problematic beliefs about social kinds (e.g. prejudice or essentializing). I provide an account of clinical reasoning and describe some features of what I call (...) ‘good’ clinical reasoning. I offer examples of generics in clinical contexts and examine how the two problems with generics (i.e. of truth-aptness and social generics) can harm patients and impair clinical reasoning. However, I ultimately argue that generics are important for good clinical reasoning because they track ‘conspicuous’ features of disease processes (e.g. severe possible outcomes). Further, I argue that prejudicial generics are often irrational to believe. Social generics that are rational to believe need not lead to problematic implicatures about social kinds and can instead facilitate meaningfully articulating societal injustices. I then argue that statistical statements, which are tempting alternatives to generics in clinical reasoning, are no better than generics for good clinical reasoning. (shrink)

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

There is widespread recognition at universities that a proper understanding of science is needed for all undergraduates. Good jobs are increasingly found in fields related to Science, Technology, Engineering, and Medicine, and science now enters almost all aspects of our daily lives. For these reasons, scientific literacy and an understanding of scientific methodology are a foundational part of any undergraduate education. Recipes for Science provides an accessible introduction to the main concepts and methods of scientific reasoning. With the help (...) of an array of contemporary and historical examples, definitions, visual aids, and exercises for active learning, the textbook helps to increase students’ scientific literacy. The first part of the book covers the definitive features of science: naturalism, experimentation, modeling, and the merits and shortcomings of both activities. The second part covers the main forms of inference in science: deductive, inductive, abductive, probabilistic, statistical, and causal. The book concludes with a discussion of explanation, theorizing and theory-change, and the relationship between science and society. The textbook is designed to be adaptable to a wide variety of different kinds of courses. In any of these different uses, the book helps students better navigate our scientific, 21st-century world, and it lays the foundation for more advanced undergraduate coursework in a wide variety of liberal arts and science courses. Selling Points Helps students develop scientific literacy—an essential aspect of _any_ undergraduate education in the 21 st century, including a broad understanding of scientific reasoning, methods, and concepts Written for all beginning college students: preparing science majors for more focused work in particular science; introducing the humanities’ investigations of science; and helping non-science majors become more sophisticated consumers of scientific information Provides an abundance of both contemporary and historical examples Covers reasoning strategies and norms applicable in all fields of physical, life, and social sciences, _as well as_ strategies and norms distinctive of specific sciences Includes visual aids to clarify and illustrate ideas Provides text boxes with related topics and helpful definitions of key terms, and includes a final Glossary with all key terms Includes Exercises for Active Learning at the end of each chapter, which will ensure full student engagement and mastery of the information include earlier in the chapter Provides annotated ‘For Further Reading’ sections at the end of each chapter, guiding students to the best primary and secondary sources available Offers a Companion Website, with: For Students: direct links to many of the primary sources discussed in the text, student self-check assessments, a bank of exam questions, and ideas for extended out-of-class projects For Instructors: a password-protected Teacher’s Manual, which provides student exam questions with answers, extensive lecture notes, classroom-ready Power Point presentations, and sample syllabi Extensive Curricular Development materials, helping any instructor who needs to create a Scientific Reasoning Course, ex nihilo. (shrink)

The purpose of this paper is twofold: -/- 1) to highlight the widely ignored but fundamental problem of ‘superpopulations’ for the use of inferential statistics in development studies. We do not to dwell on this problem however as it has been sufficiently discussed in older papers by statisticians that social scientists have nevertheless long chosen to ignore; the interested reader can turn to those for greater detail. -/- 2) to show that descriptive statistics both avoid the problem of superpopulations and (...) can be a powerful tool when used correctly. A few examples are provided. -/- The paper ends with considerations of some reasons we think are behind the adherence to methods that are known to be inapplicable to many of the types of questions asked in development studies yet still widely practiced. (shrink)

I discuss two arguments against the view that reasons are propositions. I consider responses to each argument, including recent responses due to Mark Schroeder, and suggest further responses of my own. In each case, the discussion proceeds by comparing reasons to answers and goals.

This paper takes a closer look at ordinary thought and talk about motivating reasons, in an effort to better understand how it works. This is an important first step in understanding whether—and if so, how—such thought and talk should inform or constrain our substantive theorizing. One of the upshots is that ordinary judgments about motivating reasons are at best a partial and defeasible guide to what really matters, and that so-called factualists, propositionalists, and statists are all partly right, as well (...) as partly wrong, when it comes to the question of what motivating reasons “are”. (shrink)

In a world filled with information overload and complex problems, the ability to think logically is a superpower. "A Little More Logical" is your guide to mastering this essential skill. This engaging and accessible open educational resource is perfect for students, teachers, and lifelong learners who want to improve their critical thinking abilities and make better decisions in all aspects of life. -/- Through a series of fun and interactive chapters, "A Little More Logical" covers a wide range of topics, (...) from the basics of constructing sound arguments to the application of logic in fields like ethics, science, and computing. You'll learn how to spot and avoid common fallacies, analyze real-world arguments, and use logical reasoning to solve problems and make informed choices. -/- But this book isn't just about abstract concepts – it's about the human story behind logic. You'll discover the fascinating lives and ideas of diverse thinkers, from ancient philosophers to modern-day pioneers, who have shaped the development of logical reasoning throughout history. With thought-provoking examples, engaging exercises, and plenty of humor along the way, "A Little More Logical" makes the study of logic both rigorous and entertaining. -/- Whether you're a student looking to ace your philosophy class, a teacher searching for high-quality educational resources, or a curious reader who wants to sharpen your mind, "A Little More Logical" is the perfect companion on your journey to becoming a more effective thinker. Unlock the power of logical thinking today with this one-of-a-kind open educational resource! (shrink)

This paper discusses the issue of the identity and individuality (or lack thereof) of quantum mechanical particles. It first reconstructs, on the basis of the extant literature, a general argument in favour of the conclusion that such particles are not individual objects. Then, it critically assesses each one of the argument’s premises. The upshot is that, in fact, there is no compelling reason for believing that quantum particles are not individual objects.

Many tasks in statistical and causal inference can be construed as problems of entailment in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for causal probabilistic languages than for pure probabilistic (or “associational”) languages. Despite several senses in which causal reasoning is indeed more complex—both expressively and inferentially—we show that causal entailment (or satisfiability) problems can be systematically and robustly reduced to purely probabilistic problems. Thus there is no jump in (...) computational complexity. Along the way we answer several open problems concerning the complexity of well-known probability logics, in particular demonstrating the ${\exists \mathbb {R}}$ -completeness of a polynomial probability calculus, as well as a seemingly much simpler system, the logic of comparative conditional probability. (shrink)

The article focuses on prosecutor's fallacy and interrogator's fallacy, the two kinds of reasoning in inferring a suspect's guilt. The prosecutor's fallacy is a combination of two conditional probabilities that lead to unfortunate commission of error in the process due to the inclination of the prosecutor in the establishment of strong evidence that will indict the defendant. It provides a comprehensive discussion of Gerd Gigerenzer's discourse on a criminal case in Germany explaining the perils of prosecutor's fallacy in his (...) application of probability to practical problems. It also discusses the interrogator's fallacy which was introduced by Robert A. J. Matthews as the error on the assumption that confessional evidence can never reduce the probability of guilt. (shrink)

A classic debate concerns whether reasonableness should be understood statistically (e.g., reasonableness is what is common) or prescriptively (e.g., reasonableness is what is good). This Article elaborates and defends a third possibility. Reasonableness is a partly statistical and partly prescriptive “hybrid,” reflecting both statistical and prescriptive considerations. Experiments reveal that people apply reasonableness as a hybrid concept, and the Article argues that a hybrid account offers the best general theory of reasonableness. -/- First, the Article investigates how ordinary (...) people judge what is reasonable. Reasonableness sits at the core of countless legal standards, yet little work has investigated how ordinary people (i.e., potential jurors) actually make reasonableness judgments. Experiments reveal that judgments of reasonableness are systematically intermediate between judgments of the relevant average and ideal across numerous legal domains. For example, participants’ mean judgment of the legally reasonable number of weeks’ delay before a criminal trial (ten weeks) falls between the judged average (seventeen weeks) and ideal (seven weeks). So too for the reasonable num- ber of days to accept a contract offer, the reasonable rate of attorneys’ fees, the reasonable loan interest rate, and the reasonable annual number of loud events on a football field in a residential neighborhood. Judgment of reasonableness is better predicted by both statistical and prescriptive factors than by either factor alone. -/- This Article uses this experimental discovery to develop a normative view of reasonableness. It elaborates an account of reasonableness as a hybrid standard, arguing that this view offers the best general theory of reasonableness, one that applies correctly across multiple legal domains. Moreover, this hybrid feature is the historical essence of legal reasonableness: the original use of the “reasonable person” and the “man on the Clapham omnibus” aimed to reflect both statistical and prescriptive considerations. Empirically, reasonableness is a hybrid judgment. And normatively, reasonableness should be applied as a hybrid standard. (shrink)

Most social policies cannot be defended without making inductive inferences. For example, consider certain arguments for racial profiling and affirmative action, respectively. They begin with statistics about crime or socioeconomic indicators. Next, there is an inductive step in which the statistic is projected from the past to the future. Finally, there is a normative step in which a policy is proposed as a response in the service of some goal—for example, to reduce crime or to correct socioeconomic imbalances. In comparison (...) to the normative step, the inductive step of a policy defense may seem trivial. We argue that this is not so. Satisfying the demands of the inductive step is difficult, and doing so has important but underappreciated implications for the normative step. In this paper, we provide an account of induction in social contexts and explore its implications for policy. Our account helps to explain which normative principles we ought to accept, and as a result it can explain why it is acceptable to make inferences involving race in some contexts (e.g., in defense of affirmative action) but not in others (e.g., in defense of racial profiling). (shrink)

Ranking theory is a formal epistemology that has been developed in over 600 pages in Spohn's recent book The Laws of Belief, which aims to provide a normative account of the dynamics of beliefs that presents an alternative to current probabilistic approaches. It has long been received in the AI community, but it has not yet found application in experimental psychology. The purpose of this paper is to derive clear, quantitative predictions by exploiting a parallel between ranking theory and a (...) statistical model called logistic regression. This approach is illustrated by the development of a model for the conditional inference task using Spohn's ranking theoretic approach to conditionals. (shrink)

Over almost a half-century, evidence law scholars and philosophers have contended with what have come to be called the “Proof Paradoxes.” In brief, the following sort of paradox arises: Factfinders in criminal and civil trials are charged with reaching a verdict if the evidence presented meets a particular standard of proof—beyond a reasonable doubt, in criminal cases, and preponderance of the evidence, in civil trials. It seems that purely statistical evidence can suffice for just such a level of certainty (...) in a variety of cases where our intuition is that it would nonetheless be wrong to convict the defendant, or find in favor of the plaintiff, on merely statistical evidence. So, we either have to convict with statistical evidence, in spite of an intuition that this is unsettling, or else explain what (dispositive) deficiency statistical evidence has. -/- Most scholars have tried to justify the resistance to relying on merely statistical evidence: by relying on epistemic deficiencies in this kind of evidence; by relying on court practice; and also by reference to the psychological literature. In fact, I argue, the epistemic deficiencies philosophers and legal scholars allege are suspect. And, I argue, while scholars often discuss unfairness to civil defendants, they ignore a long history of relying on statistical evidence in a variety of civil matters, including employment discrimination, toxic torts, and market share liability cases. Were the dominant arguments in the literature to prevail, it would extremely difficult for plaintiffs to recover in a variety of cases. -/- The various considerations I advance lead to the conclusion that when it comes to naked statistical evidence, philosophers and legal scholars who argue for its insufficiency have been caught with their pants down. (shrink)

Many philosophers have argued that statistical evidence regarding group characteristics (particularly stereotypical ones) can create normative conflicts between the requirements of epistemic rationality and our moral obligations to each other. In a recent article, Johnson-King and Babic argue that such conflicts can usually be avoided: what ordinary morality requires, they argue, epistemic rationality permits. In this article, we show that as data get large, Johnson-King and Babic’s approach becomes less plausible. More constructively, we build on their project and develop (...) a generalized model of reasoning about stereotypes under which one can indeed avoid normative conflicts, even in a big data world, when data contain some noise. In doing so, we also articulate a general approach to rational belief updating for noisy data. (shrink)

In his recent book, John Norton has created a theory of inference to the best explanation, within the context of his "material theory of induction". I apply it to the problem of scientific explanations that are false: if we want the theories in our explanations to be true, then why do historians and scientists often say that false theories explained phenomena? I also defend Norton's theory against some possible objections.

This paper defines the form of prior knowledge that is required for sound inferences by analogy and single-instance generalizations, in both logical and probabilistic reasoning. In the logical case, the first order determination rule defined in Davies (1985) is shown to solve both the justification and non-redundancy problems for analogical inference. The statistical analogue of determination that is put forward is termed 'uniformity'. Based on the semantics of determination and uniformity, a third notion of "relevance" is defined, both (...) logically and probabilistically. The statistical relevance of one function in determining another is put forward as a way of defining the value of information: The statistical relevance of a function F to a function G is the absolute value of the change in one's information about the value of G afforded by specifying the value of F. This theory provides normative justifications for conclusions projected by analogy from one case to another, and for generalization from an instance to a rule. The soundness of such conclusions, in either the logical or the probabilistic case, can be identified with the extent to which the corresponding criteria (determination and uniformity) actually hold for the features being related. (shrink)

Logical and philosophical literature provides different classifications of reasoning. In the Polish literature on the subject, for instance, there are three popular ones accepted by representatives of the Lvov-Warsaw School: Jan Łukasiewicz, Tadeusz Czeżowski and Kazimierz Ajdukiewicz (Ajdukiewicz in Logika pragmatyczna [Pragmatic Logic]. PWN, Warsaw (1965, 2nd ed. 1974). Translated as: Pragmatic Logic. Reidel & PWN, Dordrecht, 1975). The author of this paper, having modified those classifications, distinguished the following types of reasoning: (1) deductive and (2) non-deductive, and (...) additionally two types of them in each of the two, depending on the manner of combining their premises with the conclusion through the relation of classical logical entailment. Consequently, the four types of reasoning: unilateral deductive (incl. its sub-types: deductive inference and proof), bilateral deductive (incl. complete induction), and reductive (incl. the sub-types: explanation and verification), logically nonvaluable (incl. inference by analogy, statistic inference), correspond to four operators of derivability. They are defined formally on the ground of Tarski’s axiomatic theory of deductive systems, by means of the consequence operation _Cn_ (Tarski in Monatshefte Math Phys 37:361–404, 1930a, C R Soc Sci Lett Vars 23:22–29, 1930b). Also, certain metalogical properties of these operators are given, as well as their relations with Tarski’s consequence operations \(Cn^+\) ( \(Cn^+ = Cn\) ) and dual consequences \(Cn^{-1}\) (Słupecki in Zeszyty Naukowe Uniwersytetu Wrocławskiego Seria B Nr 3:33–40, 1959, Słupecki et al. in Stud Log 29:76–123, 1971, Wybraniec-Skardowska, in: Wybraniec-Skardowska, Bryll (eds) Z badań nad teorią zdań odrzuconych [Studies in the Theory of Rejected Propositions], Series B, Studia i Monografie, Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Opole, 1969), and \(Cn^-\) (Wójcicki in Bull Sect Log 2(2):54–57, 1973)). (shrink)

In this paper I propose a novel defence of political cosmopolitanism grounded in a familiar principle: universal moral equality. Critics of cosmopolitanism generally agree to universal moral equality, but disagree about what moral equality means politically. According to my argument, if we accept that all people are morally equal, then we ought to accept their equal moral standing. We should therefore prefer socio-political arrangements that reflect the equal moral standing of all people over those that reflect differentiated moral standing. A (...) reasonable cosmopolitanism need not preclude partialist attachment to co-nationals, or undermine the significance of self-determination, so long as political arrangements do not produce differentiated moral standing. As the political application of an uncontroversial moral principle, I defend reasonable cosmopolitanism against nationalism and statism. Neither of these, I argue, are suitable foundations for global justice in migration because they each conceive of justice as a local concern for insiders. (shrink)

In the human sciences, experimental research is used to establish causal relationships. However, the extrapolation of these results to the target population can be problematic. To facilitate extrapolation, we propose to use the statistical technique Latent Class Regression Analysis in combination with the analogical reasoning theory for extrapolation. This statistical technique can identify latent classes that differ in the effect of X on Y. In order to extrapolate by means of analogical reasoning, one can characterize the (...) latent classes by a combination of features, and then compare these features to features of the target. (shrink)

In this paper, I reconstruct the development and the complex character of Zilsel’s conception of scientific laws. This concept functions as a fil rouge for understanding Zilsel’s philosophy throughout different times (here, the focus is on his Viennese writings and how they pave the way to the more renown American ones) and across his many fields of work (from physics to politics). A good decade before Heisenberg’s uncertainty principle was going to mark the outbreak of indeterminism in quantum physics, Edgar (...) Zilsel started to develop a complex logical-philosophical theory in which statistical and causal laws were given an indeterministic foundation (Zilsel 1916). However, in developing his thoughts on the emergence of regularities from disorder, Zilsel arrives at a profound ambiguity with respect to the ontological or the epistemic nature of laws and order in the world: Whether this order is to be conceived of as an empirical finding or as the product of reason – this would have to remain unclear. This tension between rationalism and empiricism, as well as a tension between a realist and an anti-realist conception of lawfulness, can be identified in both Zilsel’s Viennese and American writings: a tension which touches the core of the “application problem” that would keep haunting Zilsel until his premature death. (shrink)

The article examines the so-called slippery slope argument (SSA) against the legalization of active voluntary euthanasia (AVE). According to the SSA, by legalizing AVE, the least morally controversial type of euthanasia, we will take the first step onto a slippery slope and inevitably end up in the moral abyss of widespread abuse and violations of the rights of the weakest and most vulnerable patients. In the first part of the paper, empirical evidence to the contrary is presented and analyzed: None (...) of the forecast regrettable trends can be elicited from the body of existing statistical data. Accordingly, we have no good reason to believe either that we already are, or are sooner or later going to be, sliding into a moral abyss. A related question is then considered: Would it not be wiser and safer to stick to the status quo and preserve the existing legal ban on AVE even if the risk of its abuse is uncertain and may well turn out to be relatively low? It is argued that such an appeal to precautionary reasoning fails to justify an outright legal ban on AVE for at least two reasons: (i) it grossly underestimates the hidden moral costs of current legal arrangements (competent terminal patients suffer both disrespect for their autonomous will and deprivation of the good of a timely death) and (ii) the ban is both too inefficient and disproportionate to qualify as a reasonable measure of precaution. (shrink)

This chapter expounds Hacking’s project of styles of reasoning more systematically than Hacking himself has done, while the following chapters examine its philosophical implications. I shall show that, in addition to the statistical and the laboratory style described in Chap. 3, there exist other four styles of reasoning that share a set of common characterizing features: the algorithmic, the postulational, the historico-genetic and the taxonomic style of reasoning. All the differences notwithstanding, striking parallels can be drawn (...) between these different styles of reasoning: they emerged suddenly at certain points in time, crystallized around communities that shared certain standards of evidence and represent basic and inescapable forms of reasoning. Finally, I shall argue that there are other ways of thinking that differ from styles of reasoning in the sense of Hacking. What I consider a relevant difference is that only styles of reasoning have strong techniques of self-authentication, techniques that are intrinsic to their forms of reasoning. (shrink)

The violation of Bell inequalities seems to establish an important fact about the world: that it is non-local. However, this result relies on the assumption of the statistical independence of the measurement settings with respect to potential past events that might have determined them. Superdeterminism refers to the view that a local, and determinist, account of Bell inequalities violations is possible, by rejecting this assumption of statistical independence. We examine and clarify various problems with superdeterminism, looking in particular (...) at its consequences on the nature of scientific laws and scientific reasoning. We argue that the view requires a neo-Humean account of at least some laws, and creates a significant problem for the use of statistical independence in other parts of physics and science more generally. (shrink)

There is something puzzling about statistical evidence. One place this manifests is in the law, where courts are reluctant to base affirmative verdicts on evidence that is purely statistical, in spite of the fact that it is perfectly capable of meeting the standards of proof enshrined in legal doctrine. After surveying some proposed explanations for this, I shall outline a new approach – one that makes use of a notion of normalcy that is distinct from the idea of (...) statistical frequency. The puzzle is not, however, merely a legal one. Our unwillingness to base beliefs on statistical evidence is by no means limited to the courtroom, and is at odds with almost every general principle that epistemologists have proposed as to how we ought to manage our beliefs. (shrink)

We review the definition of the Full Bayesian Significance Test (FBST), and summarize its main statistical and epistemological characteristics. We review also the Abstract Belief Calculus (ABC) of Darwiche and Ginsberg, and use it to analyze the FBST’s value of evidence. This analysis helps us understand the FBST properties and interpretation. The definition of value of evidence against a sharp hypothesis, in the FBST setup, was motivated by applications of Bayesian statistical reasoning to legal matters where the (...) sharp hypotheses were defendants statements, to be judged according to the Onus Probandi juridical principle. (shrink)

We offer two arguments against the halving repose to Sleeping Beauty. First, we show that halving violates the Epistemological Sure-Thing Principle, which we argue is a necessary constraint on any reasonable probability assignment. The constraint is that if hypothetically on C you assign to A the same probability you assign to A hypothetical on not-C, you must assign that probability to A simpliciter. Epistemically, it's a sure thing for you that A has this probability. Second, we show that halving violates (...) solid statistical reasoning (or draws absurdly irrelevant distinctions). (shrink)

Ian Hacking (born in 1936, Vancouver, British Columbia) is most well-known for his work in the philosophy of the natural and social sciences, but his contributions to philosophy are broad, spanning many areas and traditions. In his detailed case studies of the development of probabilistic and statistical reasoning, Hacking pioneered the naturalistic approach in the philosophy of science. Hacking’s research on social constructionism, transient mental illnesses, and the looping effect of the human kinds make use of historical materials (...) to shed light on how developments in the social, medical, and behavioural sciences have shaped our contemporary conceptions of identity and agency. Hacking’s other contributions to philosophy include his work on the philosophy of mathematics (Hacking, 2014), philosophy of statistics, philosophy of logic, inductive logic (Hacking, 1965, 1979, 2001) and natural kinds (Hacking, 1991, 2007a). (shrink)

Darwin famously held that his use of the term "chance" in evolutionary theory merely "serves to acknowledge plainly our ignorance of the causes of each particular variation". Is this a tenable view today? Or should we revise our thinking about chance in evolution in light of the more advanced, quantitative models of Neo-Darwinian theory, which make substantial use of statistical reasoning and the concept of probability? Is determinism still a viable metaphysical doctrine about biological reality after the quantum (...) revolution in physics, or dowe have to abandon it in favor of an objective indeterminism? In light of such reflections, what is the relevant interpretation of probability in evolutionary theory? Do biologists use the concept of probability because they are finite cognitive agents or because the evolutionary process is fundamentally probabilistic? In this paper, I will show that we do not yet fully understand the nature of chance in evolution. (shrink)

The multi premise closure principle states that the logical conjunction of known facts yields again a known fact. For absolute knowledge this principle holds. We show that for fallible knowledge, assuming knowing requires a minimum level of statistical certainty (whatever else it requires), and that there is a sufficient number of known facts above a given level of uncertainty, it does not hold, for simple statistical reasons. We present a modified version, the dependent conjunctive closure principle, that does (...) hold. (shrink)

One of the reasons why most of us feel puzzled about the problem of abortion is that we want, and do not want, to allow to the unborn child the rights that belong to adults and children. When we think of a baby about to be born it seems absurd to think that the next few minutes or even hours could make so radical a difference to its status; yet as we go back in the life of the fetus we (...) are more and more reluctant to say that this is a human being and must be treated as such. No doubt this is the deepest source of our dilemma, but it is not the only one. For we are also confused about the general question of what we may and may not do where the interests of human beings conflict. We have strong intuitions about certain cases; saying, for instance, that it is all right to raise the level of education in our country, though statistics allow us to predict that a rise in the suicide rate will follow, while it is not all right to kill the feeble-minded to aid cancer research. It is not easy, however, to see the principles involved, and one way of throwing light on the abortion issue will be by setting up parallels involving adults or children once born. So we will be able to isolate the “equal rights” issue and should be able to make some advance... (shrink)

Why can testimony alone be enough for findings of liability? Why statistical evidence alone can’t? These questions underpin the “Proof Paradox” (Redmayne 2008, Enoch et al. 2012). Many epistemologists have attempted to explain this paradox from a purely epistemic perspective. I call it the “Epistemic Project”. In this paper, I take a step back from this recent trend. Stemming from considerations about the nature and role of standards of proof, I define three requirements that any successful account in line (...) with the Epistemic Project should meet. I then consider three recent epistemic accounts on which the standard is met when the evidence rules out modal risk (Pritchard 2018), normic risk (Ebert et al. 2020), or relevant alternatives (Gardiner 2019 2020). I argue that none of these accounts meets all the requirements. Finally, I offer reasons to be pessimistic about the prospects of having a successful epistemic explanation of the paradox. I suggest the discussion on the proof paradox would benefit from undergoing a ‘value-turn’. (shrink)

The movement called Experimental Philosophy (‘x-Phi’) has now passed its tenth anniversary. Its central insight is compelling: When an argument hinges on accepting certain ‘facts’ about human perception, knowledge, or judging, the evoking of relevant intuitions by thought experiments is intended to make those facts seem obvious. But these intuitions may not be shared universally. Experimentalists propose testing claims that traditionally were intuition-based using real experiments, with real samples. Demanding that empirical claims be empirically supported is certainly reasonable; though experiments (...) are not necessarily the only means available. When experiments are conducted, adequately interpreting their results requires understanding the study’s design (and possibly flaws) that produced them. Experiment-based reports should document the design clearly. If Plato, writing his Meno, replaced accounts of Socrates demonstrating geometry to a slave-boy, with a survey of 100 real boys—some grasping his demonstrations, others not—what conclusions could be reached? Before answering, the reader needs details on key design questions, including (among others): (a) What population are these samples intended to represent? (E.g., ‘all slave boys’?; ‘math-ignorant people’?; ‘everyone’?) (b) What statistical tests were conducted, on what assumptions? (c) How was ‘significance’ of results determined? (d) Was the test instrument’s validity established? For readers wishing to explore x-Phi’s potentials, as contributors or as interpreters of their findings, this paper offers some cautionary considerations. Throughout their literature, examples can be found casting doubt on some experimentalists’ findings, due to design-related issues. Increased awareness of methodological questions would tighten the x-phi literature, going forward . (shrink)

In this article, I argue that the use of scientific models that attribute intentional content to complex systems bears a striking similarity to the way in which statistical descriptions are used. To demonstrate this, I compare and contrast an intentional model with a statistical model, and argue that key similarities between the two give us compelling reasons to consider both as a type of phenomenological model. I then demonstrate how intentional descriptions play an important role in scientific methodology (...) as a type of phenomenal model, and argue that this makes them as essential as any other model of this type. (shrink)

Philosophical reflection on racial profiling tends to take one of two forms. The first sees it as an example of ‘statistical discrimination,’ (SD), raising the question of when, if ever, probabilistic generalisations about group behaviour or characteristics can be used to judge particular individuals.(Applbaum 2014; Harcourt 2004; Hellman, 2014; Risse and Zeckhauser 2004; Risse 2007; Lippert-Rasmussen 2006; Lippert-Rasmussen 2007; Lippert-Rasmussen 2014) . This approach treats racial profiling as one example amongst many others of a general problem in egalitarian political (...) philosophy, occasioned by the fact that treating people as equals does not always require, or permit, us to treat them the same. The second form is concerned with how racial profiling illuminates the nature, justification, and reproduction of hierarchies of power and privilege based on skin colour and morphology. This form of reflection on racial profiling is therefore less about the justification for judging people based on the characteristics of the group to which they (appear to) belong, and more concerned with the specific ways in which the association of racialized minorities – and, in particular, black people – with crime, contributes to, and reflects, racial inequality, and oppression.(Kennedy 1998; Zack, 2015; Lever, 2005; Lever 2007). Both approaches to profiling have much to recommend them and, taken together, they form an essential component of the political philosophy of race. The statistical approach has the merits of linking racial profiling, as practice, to a body of other practices that generate and justify inequalities based on factors other than race, but it typically offers little by way of insight into the role of racial profiling itself in sustaining racial inequality and injustice. The racial construction approach, for obvious reasons, is rather better at the latter task, but its insights tend to come at the price of a broader understanding of the ways in which inequality is reproduced and justified, or of the ethical dilemmas raised by our competing claims to security. As we will see, insights from both approaches can be synthesized to clarify what, if anything, is wrong with racial profiling and what broader conclusions for equality and security follow from the study of profiling. (shrink)

Introduction: Clinical practice guidelines (CPGs) are an important source of justification for clinical decisions in modern evidence-based practice. Yet, we have given little attention to how they argue their evidence. In particular, how do CPGs argue for treatment with long-term medications that are increasingly prescribed to older patients? Approach and rationale: I selected six disease-specific guidelines recommending treatment with five of the medication classes most commonly prescribed for seniors in Ontario, Canada. I considered the stated aims of these CPGs and (...) the techniques employed towards those aims. Finally, I reconstructed and logically analysed the arguments supporting recommendations for pharmacotherapy. Analysis: The primary function of CPGs is rhetorical, or persuasive, and their means of persuasion include both a display of their credibility and their argumentation. Arguments supporting pharmacotherapy recommendations for the target population follow a common inductive pattern: statistical generalization from randomized controlled trial (RCT) and meta-analysis evidence. Two of the CPGs also argue their treatment recommendations for older patients in this style, while three fail to justify pharmacotherapy specifically for the older population. Discussion: The arguments analysed lack the auxiliary assumptions that would warrant making a generalization about the clinical effectiveness of medications for the older population. Guidelines reason using simple induction, while ignoring important inferential gaps. Future guidelines should aspire to be well-reasoned rather than simply evidence-based; argue from a plurality of evidence; be wary of hasty inductions; appropriately limit the scope of their recommendations; and avoid making law-like, prescriptive generalizations. (shrink)

Women continue to be in charge of most childrearing; men continue to be responsible for most breadwinning. There is no consensus on whether this state of affairs, and the informal norms that encourage it, are matters of justice to be tackled by state action. Feminists have criticized political liberalism for its alleged inability to embrace a full feminist agenda, inability explained by political liberals’ commitment to the ideal of state neutrality. The debate continues on whether neutral states can accommodate two (...) feminist demands: to enact policies aimed at dismantling the feminization of caregiving, especially childrearing, and to compensate women for some of the disadvantages they incur by being primary care-givers. I contribute to this debate with three arguments in support of policies meant to de-gender care-giving and compensate care-givers. The first appeals to equality of opportunity to positions of advantage and justifies policies that prevent or mitigate statistical discrimination and implicit biases. The second draws attention to a possible causal relationship between the specialization of women in early childcare and misogyny; since the latter is incompatible with political liberal justice, it yields the conclusion that political liberals ought to further investigate the causal hypothesis with the aim of establishing or refuting it. The third argument concludes that legitimate childrearing prohibits adults from socializing children or, at least girls, into gender norms; it justifies duties of justice on the side of parents, educators, and economic agents, and state policies meant to offset foreseeable breaches of some of these duties. (shrink)

In this paper, we examine the extent to which the concept of emergence can be applied to questions about the nature and moral justification of territorial borders. Although the term is used with many different senses in philosophy, the concept of “weak emergence”—advocated by, for example, Sawyer (2002, 2005) and Bedau (1997)—is especially applicable, since it forces a distinction between prediction and explanation that connects with several issues in the dis-cussion of territory. In particular, we argue, weak emergentism about borders (...) allows us to distinguish between (a) using a theory of territory to say where a border should be drawn, and (b) looking at an existing border and saying whether or not it is justified (Miller, 2012; Nine, 2012; Stilz, 2011). Many authors conflate these two factors, or identify them by claiming that having one without the other is in some sense incoherent. But on our account—given the concept of emergence—one might unproblematically be able to have (b) without (a); at the very least, the distinction between these two issues is much more significant than has often been recognised, and more importantly gives us some reason to prefer “statist” as opposed to “cultural” theories of territorial borders. We conclude with some further reflections on related matters concerning, firstly, the apparent causal powers of borders, and secondly, the different ways in which borders are physically implemented (e.g., land vs. water). (shrink)

Increasing empirical research on productivity supports the use of statistical or ‘rational’ discrimination in hiring. The practice is legal for features of job applicants not covered by human rights discrimination laws, such as being a smoker, residing in a particular neighbourhood or being a particular height. The practice appears largely morally innocuous under existing philosophical accounts of wrongful discrimination. This paper argues that lawful statistical discrimination treats job applicants in a way that may be considered degrading, and is (...) likely to constrain people’s freedoms in relation to employment, thus giving us reason for moral concern. (shrink)

This essay is an accessible introduction to the proof paradox in legal epistemology. -/- In 1902 the Supreme Judicial Court of Maine filed an influential legal verdict. The judge claimed that in order to find a defendant culpable, the plaintiff “must adduce evidence other than a majority of chances”. The judge thereby claimed that bare statistical evidence does not suffice for legal proof. -/- In this essay I first motivate the claim that bare statistical evidence does not suffice (...) for legal proof. I then introduce and motivate a knowledge-centred explanation of this fact. The knowledge-centred explanation rests on two premises. The first is that legal proof requires knowledge of culpability. The second is that one cannot attain knowledge that p from bare statistical evidence that p. To motivate the second premise, I suggest that beliefs based on bare statistical evidence fail to be safe—they could easily be wrong—and bare statistical evidence cannot eliminate relevant alternatives. -/- I then cast doubt on the first premise; I argue that legal proof does not require knowledge. I thereby dispute the knowledge-centred explanation of the inadequacy of bare statistical evidence for legal proof. Instead of appealing to the nature of knowledge, I suggest we should seek a more direct explanation by appealing to those more foundational epistemic properties, such as safety or eliminating relevant alternatives. (shrink)

Is there some general reason to expect organisms that have beliefs to have false beliefs? And after you observe that an organism occasionally occupies a given neural state that you think encodes a perceptual belief, how do you evaluate hypotheses about the semantic content that that state has, where some of those hypotheses attribute beliefs that are sometimes false while others attribute beliefs that are always true? To address the first of these questions, we discuss evolution by natural selection and (...) show how organisms that are risk-prone in the beliefs they form can be fitter than organisms that are risk-free. To address the second question, we discuss a problem that is widely recognized in statistics – the problem of over-fitting – and one influential device for addressing that problem, the Akaike Information Criterion (AIC). We then use AIC to solve epistemological versions of the disjunction and distality problems, which are two key problems concerning what it is for a belief state to have one semantic content rather than another. (shrink)

The study aims to determine the socio-demographic and debt profile of the public-school teachers in the Schools Division of Aklan, Philippines, their reasons on acquiring debt and perceived ways to avoid debts. This study utilized descriptive correlational research design utilizing a researcher-made instrument on socio-demographic profile, pattern of expenditures, debt profile covering the type of debts, total cost of debts, reasons for having debts and perceived ways to manage debts. The data gathered were tabulated and analyzed using the IBM (...) class='Hi'>Statistical Package for Social Sciences (SPSS) version 26. The take-home pay of the teachers was only more than half of their gross income. Most of the spouses of the married teachers were employed but many of them have relatively lower income. Their monthly family income was higher than the reported average family income for 2022 and their expenditures are also relatively higher than the average family expenditures in provinces for 2022. Almost one-half of the income of the teachers was used to pay their debts – both thru automatic payroll deduction and thru personal transactions. The bigger the household size, the higher the expenditure because there were more needs and there were many people consuming commodities. The higher the family income, the bigger the expenditure since lifestyle often adjusts with income. Young; married teachers; those occupying higher position and longer tenure have higher cumulative debts. Increase in family expenditure could cause increase in the number of debts as linked to the Theory of Reasoned Action and Theory of Planned Behavior. High regard for education, health, and safety triggered teachers to have debts, which can only be avoided thru better money and lifestyle management and having additional source of income. (shrink)

The extended mind thesis claims that a subject’s mind sometimes encompasses the environmental props the subject interacts with while solving cognitive tasks. Recently, the debate over the extended mind has been focused on Markov Blankets: the statistical boundaries separating biological systems from the environment. Here, I argue such a focus is mistaken, because Markov Blankets neither adjudicate, nor help us adjudicate, whether the extended mind thesis is true. To do so, I briefly introduce Markov Blankets and the free energy (...) principle in Section 2. I then turn from exposition to criticism. In Section 3, I argue that using Markov Blankets to determine whether the mind extends will provide us with an answer based on circular reasoning. In Section 4, I consider whether Markov Blankets help us track the boundaries of the mind, answering in the negative. This is because resorting to Markov Blankets to track the boundaries of the mind yields extensionally inadequate conclusions which violate the parity principle. In Section 5, I further argue that Markov Blankets led us to sidestep the debate over the extended mind, as they make internalism about the mind vacuously true. A brief concluding paragraph follows. (shrink)

Michael Huemer argues, on statistical grounds, that ``existence is evidence for immortality". On reasoning derived from the anthropic principle, however, mere existence cannot be evidence against any non-indexical, ``eternal'' hypothesis that predicts observers. This note attempts to advertise the much-flouted anthropic principle's virtues and workings in a new way, namely by calling attention to the fact that it is the primary intension of one's indexically-described evidence that best characterizes one's epistemic position.