Many different modes of definition have been proposed over time, but none of them allows for circular definitions, since, according to the prevalent view, the term defined would then be lacking a precise signification. I argue that although circular definitions may at times fail uniquely to pick out a concept or an object, sense still can be made of them by using a rule of revision in the style adopted by Anil Gupta and Nuel Belnap in the theory (...) of truth. (shrink)

Aristotle said that induction (epagōgē) is a proceeding from particulars to a universal, and the definition has been conventional ever since. But there is an ambiguity here. Induction in the Scholastic and the (so-called) Humean tradition has presumed that Aristotle meant going from particular statements to universal statements. But the alternate view, namely that Aristotle meant going from particular things to universal ideas, prevailed all through antiquity and then again from the time of Francis Bacon until the mid-nineteenth century. Recent (...) scholarship is so steeped in the first-mentioned tradition that we have virtually forgotten the other. In this essay McCaskey seeks to recover that alternate tradition, a tradition whose leading theoreticians were William Whewell, Francis Bacon, Socrates, and in fact Aristotle himself. The examination is both historical and philosophical. The first part of the essay fills out the history. The latter part examines the most mature of the philosophies in the Socratic tradition, specifically Bacon’s and Whewell’s. After tracing out this tradition, McCaskey shows how this alternate view of induction is indeed employed in science, as exemplified by several instances taken from actual scientific practice. In this manner, McCaskey proposes to us that the Humean problem of induction is merely an artifact of a bad conception of induction and that a return to the Socratic conception might be warranted. (shrink)

The argument from inductive risk has been embraced by many as a successful account of the role of values in science that challenges the value-free ideal. We argue that it is not obvious that the argument from inductive risk actually undermines the value-free ideal. This is because the inductive risk argument endorses an assumption held by proponents of the value-free ideal: that contextual values never play an appropriate role in determining evidence. We show that challenging the value-free (...) ideal ultimately requires rejecting this assumption. (shrink)

A common style of argument in the literature on free will and moral responsibility is the Manipulation Argument. These tend to begin with a case of an agent in a deterministic universe who is manipulated, say, via brain surgery, into performing some action. Intuitively, this agent is not responsible for that action. Yet, since there is no relevant difference, with respect to whether an agent is responsible, between the manipulated agent and a typical agent in a deterministic universe, responsibility is (...) not compatible with the truth of determinism. In response, some theorists have argued that there is a relevant difference, and have developed two sorts of accounts of that difference: bypassing views, and manipulator-focused views. Manipulator-focused views suggest that the difference concerns the presence of a manipulator, whereas bypassing views suggest that the relevant difference concerns the fact that the action issues from attitudes that the manipulated agent acquired in a way that bypassed her capacities for control over her mental life. One sort of case used to decide between these sorts of accounts is a case of machine induction, which is just like a manipulation case, yet the change in the agent is the result of some natural force. Against the received view, Xiaofei Liu argues that such cases pose problems for bypassing views, and favor manipulator-focused views instead. This paper addresses Liu’s arguments, as well as a variety of cases, concluding that cases of machine induction do not provide motivation for a bypassing theorist to adopt a manipulator-focused view. (shrink)

Le § 9 de la Krisis expose les étapes : idéalisation géométrique, mathématisation indirecte des qualités, induction savante, opérations aveugles du calcul. Une enquête historique confirme-t-elle le récit de Husserl ?

The idea of a probabilistic logic of inductive inference based on some form of the principle of indifference has always retained a powerful appeal. However, up to now all modifications of the principle failed. In this paper, a new formulation of such a principle is provided that avoids generating paradoxes and inconsistencies. Because of these results, the thesis that probabilities cannot be logical quantities, determined in an objective way through some form of the principle of indifference, is no longer (...) supportable. Later, the paper investigates some implications of the new principle of indifference. To conclude, a re-examination of the foundations of the so-called objective Bayesian inference is called for. (shrink)

Shame has been found to promote both approach and withdrawal behaviours. Shame theories have not been able to explain how shame can promote such contrasting behaviours. In the present article, the authors provide an explanation for this. Shame was hypothesised to activate approach behaviours to restore the threatened self, and in situations when this is not possible or too risky, to activate withdrawal behaviours to protect the self from further damage. Five studies with different shame inductions and different dependent measures (...) confirmed our predictions. We therefore showed that different behavioural responses to shame can be understood in terms of restore and protect motives. Implications for theory and behavioural research on shame are discussed. (shrink)

We develop a logical system that captures two different interpretations of what extensive games model, and we apply this to a long-standing debate in game theory between those who defend the claim that common knowledge of rationality leads to backward induction or subgame perfect (Nash) equilibria and those who reject this claim. We show that a defense of the claim à la Aumann (1995) rests on a conception of extensive game playing as a one-shot event in combination with a principle (...) of rationality that is incompatible with it, while a rejection of the claim à la Reny (1988) assumes a temporally extended, many-moment interpretation of extensive games in combination with implausible belief revision policies. In addition, the logical system provides an original inductive and implicit axiomatization of rationality in extensive games based on relations of dominance rather than the usual direct axiomatization of rationality as maximization of expected utility. (shrink)

Hume follows Newton in replacing the mechanical philosophy’s demonstrative ideal of science by the Principia’s ideal of inductive proof ; in this respect, Hume differs sharply from Locke. Hume is also guided by Newton’s own criticisms of the mechanical philosophers’ hypotheses. The first stage of Hume’s skeptical argument concerning causation targets central tenets of the mechanical philosophers’ conception of causation, all of which rely on the a priori postulation of a hidden configuration of primary qualities. The skeptical argument concerning (...) the causal inductive inference then raises doubts about what Hume himself regards as our very best inductive method. Hume’s own “Rules” further substantiate his reliance on Newton. Finally, Locke’s distinction between “Knowledge” and “Probability” does not leave room for Hume’s Newtonian notion of inductive proof. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.3 (2001) 351-383 [Access article in PDF] Hume's Pyrrhonian Skepticism and the Belief in Causal Laws Graciela De Pierris Hume endorses in no uncertain terms the normative use of causal reasoning. The most striking example of this commitment is Hume's argument in the Enquiry against the possibility of miracles. The argument sanctions, in particular, the use of scientific reflection on uniform experience issuing (...) in causal laws of nature (E 114): "A miracle is a violation of the laws of nature; and as a firm and unalterable experience has established these laws, the proof against a miracle, from the very nature of the fact, is as entire as any argument from experience can possibly be imagined." 1 These words should give us pause; for how can Hume so confidently say, after his skeptical conclusions concerning our causal beliefs, that "a firm and unalterable experience has established" the laws of nature, and that we can therefore produce "proofs" against miracles? The Treatise gives rise to the same puzzle. In this text, too, Hume confidently prescribes methodical reflection based on causal reasoning. For example, in Book One, Part Three, Section Fifteen, Hume offers eight "Rules by which to judge of causes and effects." These rules are more than descriptions of our natural causal inferences. They are meant to guide us in making better causal inferences; in Hume's words they "ought to regulate" our probable reasoning since (T 149): "by them we learn to distinguish the accidental circumstances from the efficacious causes." 2Moreover, Hume consistently takes Newtonian science as a model for the proper employment of causal inferences in inquiries into matters of fact and, [End Page 351] in particular, as a model to be followed in his own science of human nature. 3 This paradigm of what the science of nature ought to be is understood by Hume as an inductive, experimental inquiry. 4 In the Enquiry, for example, Hume uses the label "sciences" for "politics, natural philosophy, physic, chemistry, &c." and in the preceding discussion argues that these sciences are not a priori but are based on causal reasoning (E 164-165). Thus, there are for Hume inquiries into matters of fact and existence that amount to more than blindly following natural propensities and habit. The sciences and many of our causal inferences in common life involve more than mere belief as a sentiment. They involve, in addition, careful reflection that results in improved causal inferences and thus provides normative standards. Yet, in thus upholding the normative use of causal reasoning in science and in everyday life, Hume appears to contradict his own radical skeptical conclusions concerning our knowledge of causation and induction. I here propose a novel way to resolve this puzzle.To acknowledge the existence of a puzzle, however, amounts to accepting the now controversial view that Hume provides, and takes at face value, a radical skeptical argument concerning our knowledge of causation and induction. 5 Moreover, the attempt to resolve this puzzle involves rejecting the suggestion [End Page 352] that Hume, without awareness or concern, happily holds flatly inconsistent views. 6 It also goes against the more sophisticated suggestion that Hume lightly alternates among different psychological moods, or perhaps different perspectives, which might eventually issue in results that contradict each other but are sufficiently localized so as to prevent serious conflict. Such a view might lead us to conceive Hume's texts as an unstructured and arbitrary patchwork of reflections, driven by different psychological moods or by the embellishments of a radiant literary style. This kind of reading is unacceptable as an interpretative tool, however, as H. J. Paton has acutely noted in his criticism of the patchwork interpretation of Kant's Critique of Pure Reason. 7 For such a reading would place no constraints at all on the task of establishing which parts of Hume's text belong to which moods or perspectives. The suggestion that Hume offers an unstructured patchwork of reflections masks the novel and systematic distinction Hume draws between his radical philosophical... (shrink)

In Fact, Fiction and Forecast, Nelson Goodman claims that the problem of justifying induction is not something over and above the problem of describing valid induction. Such claim, besides suggesting his commitment to the collapse of the distinction between the context of description and the context of justification, seems to open the possibility that the new riddle of induction could be addressed empirically. Discoveries about psychological preferences for projecting certain classes of objects could function as a criterion for determining which (...) predicates are after all projectible. In this paper, I argue that Goodman's claim must be construed within his project for constructional definitions, which is methodologically oriented by reflective equilibrium. The description of inductive practice is committed to the articulation of the extension of the class selected by the predicate ‘valid induction’. The mutual adjustment between theoretical considerations and inductive practice involved in the proposal of a definition of ‘valid induction’ must preserve that practice as much as possible, there is no way to get rid of entrenchment. Empirical discoveries about the psychological mechanism that underlies projections may help that adjustment but they cannot substitute the role played by the entrenchment of predicates. (shrink)

TAPP is a total applicative theory, conservative over intuitionistic arithmetic. In this paper, we first show that the same holds for TAPP+ the choice principle EAC; then we extend TAPP with choice sequences and study the principle EBIa0 . The resulting theories are used to characterise the arithmetical fragment of EL +EBIa0. As a digression, we use TAPP to show that P. Martin-Löf's basic extensional theory ML0 is conservative over intuitionistic arithmetic.

El artículo se concentra en el cruce conceptual y político de dos escrituras, las de Frantz Fanon y Gilles Deleuze y Félix Guattari, en el momento en que trabajan una crítica a la representación como categoría filosófica y política. Aprovechamos las inducciones que están en él para trazar nuestra propia intervención en dicha crítica. Hemos puesto en contacto estas dos escrituras porque apostamos a comprenderlas dentro de un movimiento crítico de la modernidad, pero también de la colonialidad. Esta última categoría, (...) con frecuencia escamoteada, permite conectar textos, conceptos y escrituras para entender la dimensión organizacional de los cuerpos en la diferencia colonial y en la racialización. Los textos de Fanon son anteriores, cronológicamente hablando, a los de Deleuze y Guattari. No obstante, los tres autores participan del proceso crítico que se inició a mediados de siglo XX, en particular a partir del movimiento histórico de la descolonización. Si bien cada una de estas escrituras apunta inicialmente a audiencias distintas, ambas ofrecen intervenciones asimilables entre sí para una heurística en nuestro presente de la relación modernidad/colonialidad. Abstract This article focuses on the conceptual and political crossroads of two contemporary writings, Frantz Fanon´s and Gilles Deleuze and Felix Guattari´s, and it read them in the precise moment they develop a critique of representation as a philosophical and political category. We take inductions that are in it to draw our own involvement in such criticism. Both writings are committed not only to produce a critical movement of modernity but also of coloniality, especially Fanon. The latter category, often retracted, is crucial to connect texts and concepts to understand the organizational dimension of bodies in the colonial difference and racialization. Fanon´s texts predate, chronologically speaking, to Deleuze and Guattari work. However, both are part of the critical process that began in the mid-twentieth century, particularly from the historical movement of decolonization. While each of these writings is initially aimed at different audiences, both offer comparable interventions which make sense for a heuristic, in our present, of modern/colonial relationships. (shrink)

This article investigates the pervasive influence of the pharmaceutical industry in Pakistan and primarily the attitudes of the medical community toward such interactions. We used an inductive approach informed by grounded theory principles to analyze interviews and focus groups with consultants, residents, medical students, and a pharmaceutical industry representative in Karachi and Lahore, and participant-observation data from two biomedical conferences. Data were then analyzed through a deontological and teleological ethical theoretical framework. Findings highlight the reasons leading to the continuation (...) of norms including weak regulations, physicians’ expectations of receiving favors, and limited exposure to bioethics education. Recommendations for practice, policy, and research are discussed. (shrink)

The question of the dimensionality of space has informed the development of physics since the beginning of the twentieth century in the quest for a unified picture of quantum processes and gravitation. Scientists have worked within various approaches to explain why the universe appears to have a certain number of spatial dimensions. The question of why space has three dimensions has a genuinely philosophical nature that can be shaped as a problem of justifying a contingent necessity of the world. In (...) contrast to explanations of three-dimensionality based on anthropic arguments, we support the search for a theory that provides a justification for the dimensionality of space based on a combination of deductive and inductive reasoning applied to science. In doing so, we argue that Kant correctly approached the question in “Thoughts on the true estimation of living forces” by connecting space dimensionality and the inverse square law. In expounding the strategy of Kant’s argument, we describe the main features of a general Kantian explanation of the dimensionality of space and discuss them with respect to current accounts of explanation in the philosophy of science, such as inference to the best explanation and the deductive-nomological model. (shrink)

Heterocyst spacing in blue -green bacteria is widely assumed to be due to a diffusible inhibitor. The inhibitor, a nitrogen-rich compound, probably glutamine, is produced via the N2-fixing enzymes of the heterocyst and in turn serves to suppress the induction of these enzymes and of the differentiation of vegetative cells to heterocysts. This simple morphogenetic mechanism operating in growing cellular filaments ofAnabaena species is investigated on the basis of a continuous and a discrete cellular model, as well as by cell-by-cell (...) simulation of the inhibitor transport. The resulting distances between heterocysts and kinetics of their production are compared with observations, and the values of physical parameters are estimated from the models. (shrink)

The problem of induction is formulated as a set of three questions, namely: ‘What is the nature of the attitude of acceptance that we adopt in relation to certain theories?’ ‘What are the rules according to which we select those theories which we accept?’ and, ‘What is the justification for the adoption of those rules?’. An original answer is proposed for each question in turn, with the help of the new concepts of sub-theory, established sub-theory, aberrant, arbitrary and degenerate theories. (...) The answer to the third question follows the lines of Reichenbach's pragmatic strategy. (shrink)

As part of a wider program that studies the legislative creation process regarding work conditions in the Argentine Republic, the purpose of this research is to examine the different ways in which the written press represents, on one hand, the formulation and approval process of the Labor Risk Law reform, which concluded on 25 October 2012 with the passing of Law 26,773, and, on the other hand, the scope, content, and sense of said regulation. The perspective of the research is (...) interdisciplinary, its methodology is qualitative, and the process guiding the textual analysis is inductive and hermeneutic. The corpus is made up of the news related to the studied legislative process. The news analysis was carried out according to the proposal of a Sociological and Linguistic Discourse Analysis. Thus, the argumentative strategies and the linguistic resources deployed were associated with the interpretive models of reality underlying those texts, and moreover, the similarities and differences among the various news articles were examined as regards the representation of working conditions; workers and employers and their respective rights and obligations; the legitimacy, need, and legality of the regulation passed; the scope of the protection granted to workers; and the effect of this regulation on workers’ constitutional rights and guarantees. (shrink)

Calibration inductive logics are based on accepting estimates of relative frequencies, which are used to generate imprecise probabilities. In turn, these imprecise probabilities are intended to guide beliefs and decisions — a process called “calibration”. Two prominent examples are Henry E. Kyburg's system of Evidential Probability and Jon Williamson's version of Objective Bayesianism. There are many unexplored questions about these logics. How well do they perform in the short-run? Under what circumstances do they do better or worse? What is (...) their performance relative to traditional Bayesianism? -/- In this article, we develop an agent-based model of a classic binomial decision problem, including players based on variations of Evidential Probability and Objective Bayesianism. We compare the performances of these players, including against a benchmark player who uses standard Bayesian inductive logic. We find that the calibrated players can match the performance of the Bayesian player, but only with particular acceptance thresholds and decision rules. Among other points, our discussion raises some challenges for characterising “cautious” reasoning using imprecise probabilities. Thus, we demonstrate a new way of systematically comparing imprecise probability systems, and we conclude that calibration inductive logics are surprisingly promising for making decisions. (shrink)

Dans ses recherches empiriques, philosophiques et métaphysiques la conscience humaine ne sort pas de sa propre sphère. C'est toujours la conscience qui parle. Par sa connaissance l'homme ne peut dépasser la conscience directe. Par sa pensée il tend à dépasser médiatement la conscience. Cette constatation nous est dictée par le fait scientifiquement fondé que tant la conscience humaine que son contenu sont tirés, c.a.d. révélés, des profondeurs cachées où ils sont recélés. C'est ce qui rend évident que l'homme possède un (...) merveilleux "sens sondeur", lui permettant de reconnaître les hauteurs et les profondeurs de notre conscience et aspirant à la transcendance. Le domaine de l'expérience se borne nécessairement aux phénomènes, et tandis que celui de la philosophie s'étend au fondement de ces phénomènes et à leurs rapports réciproques, la métaphysique, la science des principes, se propose de pénétrer l'origine et le sens profond de toute chose, du néant à l'ultime perfection. Après Kant qui a voulu en finir avec la métaphysique dogmatique unilatéralement déductive, la méthode inductive a pris définitivement le dessus. Cette méthode ne s'arroge pas le droit de juger d'une façon apodictique en ce qui touche aux problèmes de l'existence, qui ont donné naissance aux dispositions de la conscience humaine. Elle s'efforce, au contraire, de faire en cette matière une large part à l'inconnu en démontrant que les résultats sont heuristiques, hypothétiques et problématiques. Ainsi la théorie de la connaissance, la philosophie et la théologie s'accordent à dire que les données microcosmiques dans la sphère de la conscience humaine peuvent être les représentants des entités macrocosmiques. Si la conscience humaine poursuit ses recherches philosophiques et métaphysiques, c'est qu'elle doit sa genèse à une relation universelle dont elle est la représentation. (shrink)

Lesson observation is frequently used in teacher induction programmes to support newly-qualified teachers in their reflection and classroom enquiry. This article uses an elaboration of Peirce’s abduction to illustrate how the post-observation conversation supports a teacher’s reflection on her teaching, and in particular, her teaching of language to young children. It shows that abduction involves an expert-like intuition, where the interaction and co-enquiry with the advisor was crucial. The analytical framework used is based on six modes of abductive reasoning or (...) inference that deal with potential or possibility, three modes of induction dealing with actuality, and one mode of deduction focusing on rules and regulations. In a context of lifelong learning, with emphasis on teacher learning across the professional lifespan, the article shows how newly-qualified teachers can be supported in using abductive reasoning and engage in worthwhile classroom enquiry. The article contributes to edusemiotics, a recently developed direction in educational theory that explores the philosophical specifics of semiotics in educational contexts. (shrink)

Einstein's mass-energy equivalence law, argues de Broglie, by fixing the zero of the potential energy of a system,ipso facto selects a gauge in electromagnetism. We examine how this works in electrostatics and in magnetostatics and bring in, as a “trump card,” the familiar, but highly peculiar, system consisting of a toroidal magnet m and a current coil c, where none of the mutual energy W resides in the vacuum. We propose the principle of a crucial test for measuring the fractions (...) of W residing in m and in c; if the latter is nonzero, the (fieldless) vector potential has physicality. Also, using induction for transferring energy from the magnet to a superconducting current, we prove that W is equipartitioned between m and c. (shrink)

Avant tout l'auteur marque la place qu'occupe le christianisme dans l'évolution de la pensée philosophique et relève en même temps l'universalité de la révélation chrétienne relativement aux principes de la connaissance. L'idée de Dieu et la notion de la totalité sont considérées dans leurs rapports intimes et l'auteur fait ressortir comment le pluralisme conduit nécessairement au monisme pour aboutir au trinitarisme. Il envisage ensuite la doctrine chrétienne de la création et de la rédemption dans son acceptation la plus rationnelle en (...) accentuant surtout l'idée de la motilité divine. La transcendance, l'immanence et la glorification de l'ingérence divine dans la toute-contingence sont les trois aspects qui contiennent toutes les considérations possibles. Il met en évidence l'état de l'homme-dieu et du dieu-homme en rapport avec les principes de la régénération et de l'évolution ainsi qu'avec les indications de Nietzsche. Il montre la valeur des notions de Sujet et de Substance et indique comment les principes philosophiques du christianisme sont pas seulement par la méthode déductive, mais encore comment ils sont affirmés et sanctionnés par la méthode inductive en relation avec les principes de l'activité et de l'idéalité. (shrink)

The problem of rational prediction, launched by Wesley Salmon, is without doubt the Achilles heel of the critical method defended by Popper. In this paper, I assess the response given both by Popper and by the popperian Alan Musgrave to this problem. Both responses are inadequate and thus the conclusion of Salmon is reinforced: without appeal to induction, there is no way to make of the practical prediction a rational action. Furthermore, the critical method needs to be vindicated if one (...) pretends that its application is suitable for the preference of a hypothesis. I argue that the nature of this vindication is such that it may be applied also to induction. Thus, to be a popperian is a good reason also to be an inductivist. (shrink)

ABSTRACTAt present, the consequences and functions of experiences of shame are not yet well understood. Whereas psychology literature typically portrays shame as being bad for social relations, motivating social avoidance and withdrawal, there are recent indications that shame can be reinterpreted as having clear social tendencies in the form of motivating approach and social affiliation. Yet, until now, no research has ever put these alternative interpretations of shame-motivated behaviours directly to the test. The present paper presents such a test by (...) studying the extent to which shame motivates a preference for social withdrawal versus a preference for social approach. Two studies using different shame inductions both showed people experiencing shame to prefer to be together with others over being alone. In addition, the preference for a social situation was found to be unique for shame; it was not found for the closely related emotion of gui... (shrink)

This article gives a conceptual review of the e-value, ev(H|X) – the epistemic value of hypothesis H given observations X. This statistical significance measure was developed in order to allow logically coherent and consistent tests of hypotheses, including sharp or precise hypotheses, via the Full Bayesian Significance Test (FBST). Arguments of analysis allow a full characterization of this statistical test by its logical or compositional properties, showing a mutual complementarity between results of mathematical statistics and the logical desiderata lying at (...) the foundations of this theory. (shrink)

The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...) and (3) the specific forms of representation and notation shared and selected by the practitioners. Moreover, it is claimed that a broadening of the notion of ‘permissible action’ as introduced by Larvor (2012) with respect to mathematical arguments, allows for a consideration of all these three elements simultaneously. Second, a case from topology – the proof of Alexander’s theorem – is presented to illustrate a concrete analysis of a mathematical practice and to exemplify the proposed method. It is discussed that the attention to the three elements of the practice identified above brings to the emergence of philosophically relevant features in the practice of topology: the need for a revision in the definition of criteria of validity, the interest in tracking the operations that are performed on the notation, and the constant and fruitful back-and-forth from one representation to another in dealing with mathematical content. Finally, some suggestions for further research are given in the conclusions. (shrink)

Graciela De Pierris presents a novel interpretation of the relationship between skepticism and naturalism in Hume's epistemology, and a new appraisal of Hume's place within early modern thought. Contrary to dominant readings, she argues that Hume does offer skeptical arguments concerning causation and induction in Book I, Part III of the Treatise, and presents a detailed reading of the skeptical argument she finds there and how this argument initiates a train of skeptical reasoning that begins in Part III and culminates (...) in Part IV. She goes on to demonstrate that Hume was committed to the Newtonian inductive method while rejecting the place of the supernatural in our understanding of nature. (shrink)

How should we make decisions when we do not know the relevant physical probabilities? In these ambiguous situations, we cannot use our knowledge to determine expected utilities or payoffs. The traditional Bayesian answer is that we should create a probability distribution using some mix of subjective intuition and objective constraints. Imprecise Bayesians argue that this approach is inadequate for modelling ambiguity. Instead, they represent doxastic states using credal sets. Generally, insofar as we are more uncertain about the physical probability of (...) an event, there is more divergence in the credal set. Hence, their approach can represent these ambiguities via the extent of the divergence. Imprecise Bayesianism has mostly been advocated for its epistemological features. In this article, we examine its properties for decision-making. We develop a model for comparing standard and Imprecise Bayesianism by testing their performances in a classic decision problem. We find that the representational tools of Imprecise Bayesianism also cause it to underperform in our tests. This issue has been overlooked, because previous research on Imprecise Bayesianism has not utilised agent-based modelling to provide information about its performance in the short-run. Overall, we reveal the Ambiguity Dilemma for Imprecise Bayesianism: To what extent should one value representational power or decision-making performance? (shrink)

The debates between Bayesian, frequentist, and other methodologies of statistics have tended to focus on conceptual justifications, sociological arguments, or mathematical proofs of their long run properties. Both Bayesian statistics and frequentist (“classical”) statistics have strong cases on these grounds. In this article, we instead approach the debates in the “Statistics Wars” from a largely unexplored angle: simulations of different methodologies’ performance in the short to medium run. We conducted a large number of simulations using a straightforward decision problem based (...) around tossing a coin with unknown bias and then placing bets. In this simulation, we programmed four players, inspired by Bayesian statistics, frequentist statistics, Jon Williamson’s version of Objective Bayesianism, and a player who simply extrapolates from observed frequencies to general frequencies. The last player functions as a benchmark: a statistical methodology should at least outperform a crude form of induction. We focused on the performance of these methodologies in guiding the players towards good decisions. Unlike an earlier simulation study of this type, we found no systematic difference in performance between the Bayesian and frequentist players, provided the Bayesian used a flat prior and the frequentist used a low confidence level. Unlike that study, we were able to use Big Data methods to mitigate problems of random error in the simulation results. The Williamsonian player, who is a novel element of our study, also had no systematic differences in their performance, provided that they use a low confidence level. These players performed similarly even in the very short run, when players were making different decisions. Our study indicates that all three methodologies should be taken seriously by philosophers and practitioners of statistics. However, the frequentist and Williamsonian performed poorly when their confidence levels were high, and the Bayesian was surprisingly harmed by biased priors, providing some unexpected lessons for these methodologies when facing this type of decision problem. (shrink)