Jonah N. Schupbach and Jan Sprenger and Vincenzo Crupi and Katya Tentori have recently proposed measures of explanatory power and have shown that they are characterized by certain arguably desirable conditions or axioms. I further examine the properties of these two measures, and a third measure considered by I. J. Good and Timothy McGrew . This third measure also has an axiomatic representation. I consider a simple coin-tossing example in which only the Crupi–Tentori measure does not perform well. The (...) Schupbach–Sprenger and Good–McGrew measures are based on different notions of explanatory power, but both are tenable. 1 Introduction2 Measures of Explanatory Power3 The Schupbach–Sprenger Measure4 The Crupi–Tentori Measure5 The Good–McGrew Measure6 Affirmative versus Comprehensive Explanatory Power7 Coin-Flipping Examples8 Decomposition9 Conclusion. (shrink)

Jonah N. Schupbach and Jan Sprenger have proposed conditions of adequacy for measures of explanatory power. They derive and defend a measure of explanatory power satisfying their conditions of adequacy. This article furthers the development of their measure. The requirement that the measure be multidimensional analytic is avoided. Several proofs are simplified, and gaps in proofs are filled.

This article introduces and defends a probabilistic measure of the explanatory power that a particular explanans has over its explanandum. To this end, we propose several intuitive, formal conditions of adequacy for an account of explanatory power. Then, we show that these conditions are uniquely satisfied by one particular probabilistic function. We proceed to strengthen the case for this measure of explanatory power by proving several theorems, all of which show that this measure neatly corresponds to our explanatory intuitions. Finally, (...) we briefly describe some promising future projects inspired by our account. (shrink)

Despite decades of focused philosophical investigation, Inference to the Best Explanation still lacks a precise articulation and compelling defense. The primary reason for this is that it is not at all clear what it means for a hypothesis to be the best available explanation of the evidence. This paper first seeks to rectify this problem by developing a formal explication of the explanatory virtue of power. A resulting account of IBE is then evaluated as a form of uncertain inference. Overall, (...) this paper offers a precise account and novel defense of one important version of IBE. (shrink)

Two recently popular metaphilosophical movements, formal philosophy and experimental philosophy, promote what seem to be conflicting methodologies. Nonetheless, I argue that the two can be mutually supportive. I propose an experimentally-informed variation on explication, a powerful formal philosophical tool introduced by Carnap. The resulting method, which I call “experimental explication,” provides the formalist with a means of responding to explication's gravest criticism. Moreover, this method introduces a philosophically salient, positive role for survey-style experiments while steering clear of several objections that (...) critics of “positive experimental philosophy” raise. Thus, it provides the experimentalist with a more defensible example of how empirical work can have positive philosophical import. For these reasons, experimental explication should appeal to experimental philosophers and formal philosophers alike. (shrink)

Competition between scientific hypotheses is not always a matter of mutual exclusivity. Consistent hypotheses can compete to varying degrees either directly or indirectly via a body of evidence. We motivate and defend a particular account of hypothesis competition by showing how it captures these features. Computer simulations of Bayesian inference are used to highlight the limitations of adopting mutual exclusivity as a simplifying assumption to model scientific reasoning, particularly due to the exclusion of hypotheses that may be true. We end (...) with a case study demonstrating the subtleties involved in hypothesis competition in scientific practice. (shrink)

In this paper, I argue that van Fraassen's "bad lot objection" against Inference to the Best Explanation [IBE] severely misses its mark. First, I show that the objection holds no special relevance to IBE; if the bad lot objection poses a serious problem for IBE, then it poses a serious problem for any inference form whatever. Second, I argue that, thankfully, it does not pose a serious threat to any inference form. Rather, the objection misguidedly blames a form of inference (...) for not achieving what it never set out to achieve in the first place. (shrink)

This paper responds to Terry Horgan’s recent critique of Bayesian formal epistemology. I argue that each of Horgan’s criticisms misses its mark when Bayesianism is viewed as putting forward an inductive logic of confidences. Along the way, I explore the nature, scope, and limits of a defensible brand of Bayesianism.

I show that the two most devastating objections to Shogenji's formal account of coherence necessarily involve information sets of cardinality . Given this, I surmise that the problem with Shogenji's measure has more to do with his means of generalizing the measure than with the measure itself. I defend this claim by offering an alternative generalization of Shogenji's measure. This alternative retains the intuitive merits of the original measure while avoiding both of the relevant problems that befall it. In the (...) light of all of this, I suggest that there is new hope for Shogenji's analysis: Shogenji's early and influential attempt at measuring coherence, when generalized in a subset-sensitive way, is able to clear its most troubling objections. (shrink)

When scientists seek further confirmation of their results, they often attempt to duplicate the results using diverse means. To the extent that they are successful in doing so, their results are said to be robust. This paper investigates the logic of such "robustness analysis" [RA]. The most important and challenging question an account of RA can answer is what sense of evidential diversity is involved in RAs. I argue that prevailing formal explications of such diversity are unsatisfactory. I propose a (...) unified, explanatory account of diversity in RAs. The resulting account is, I argue, truer to actual cases of RA in science; moreover, this account affords us a helpful, new foothold on the logic undergirding RAs. (shrink)

The success of Bovens and Hartmann’s recent “impossibility result” against Bayesian Coherentism relies upon the adoption of a specific set of ceteris paribus conditions. In this paper, I argue that these conditions are not clearly appropriate; certain proposed coherence measures motivate different such conditions and also call for the rejection of at least one of Bovens and Hartmann’s conditions. I show that there exist sets of intuitively plausible ceteris paribus conditions that allow one to sidestep the impossibility result. This shifts (...) the debate from the merits of the impossibility result itself to the underlying choice of ceteris paribus conditions. (shrink)

This book explores the Bayesian approach to the logic and epistemology of scientific reasoning. Section 1 introduces the probability calculus as an appealing generalization of classical logic for uncertain reasoning. Section 2 explores some of the vast terrain of Bayesian epistemology. Three epistemological postulates suggested by Thomas Bayes in his seminal work guide the exploration. This section discusses modern developments and defenses of these postulates as well as some important criticisms and complications that lie in wait for the Bayesian epistemologist. (...) Section 3 applies the formal tools and principles of the first two sections to a handful of topics in the epistemology of scientific reasoning: confirmation, explanatory reasoning, evidential diversity and robustness analysis, hypothesis competition, and Ockham's Razor. (shrink)

In three recent papers, Wayne Myrvold and Timothy McGrew have developed Bayesian accounts of the virtue of unification. In his account, McGrew demonstrates that, ceteris paribus, a hypothesis that unifies its evidence will have a higher posterior probability than a hypothesis that does not. Myrvold, on the other hand, offers a specific measure of unification that can be applied to individual hypotheses. He argues that one must account for this measure in order to calculate correctly the degree of confirmation that (...) a hypothesis receives from its evidence. Using the probability calculus, I prove that the two accounts of unification require the same underlying inequality; thus, McGrew and Myrvold have accounted for unification in fundamentally identical probabilistic terms. I then evaluate five putative counterexamples to this account and show that these examples, far from disqualifying it, serve to clarify our notion of unification by disentangling it from a host of other concepts. (shrink)

Human reasoning often involves explanation. In everyday affairs, people reason to hypotheses based on the explanatory power these hypotheses afford; I might, for example, surmise that my toddler has been playing in my office because I judge that this hypothesis delivers a good explanation of the disarranged state of the books on my shelves. But such explanatory reasoning also has relevance far beyond the commonplace. Indeed, explanatory reasoning plays an important role in such varied fields as the sciences, philosophy, theology, (...) medicine, forensics, and law. -/- This dissertation provides an extended study into the logic of explanatory reasoning via two general questions. First, I approach the question of what exactly we have in mind when we make judgments pertaining to the explanatory power that a hypothesis has over some evidence. This question is important to this study because these are the sorts of judgments that we constantly rely on when we use explanations to reason about the world. Ultimately, I introduce and defend an explication of the concept of explanatory power in the form of a probabilistic measure. This formal explication allows us to articulate precisely some of the various ways in which we might reason explanatorily. -/- The second question this dissertation examines is whether explanatory reasoning constitutes an epistemically respectable means of gaining knowledge. I defend the following ideas: The probability theory can be used to describe the logic of explanatory reasoning, the normative standard to which such reasoning attains. Explanatory judgments, on the other hand, constitute heuristics that allow us to approximate reasoning in accordance with this logical standard while staying within our human bounds. The most well known model of explanatory reasoning, Inference to the Best Explanation, describes a cogent, nondeductive inference form. And reasoning by Inference to the Best Explanation approximates reasoning directly via the probability theory in the real world. Finally, I respond to some possible objections to my work, and then to some more general, classic criticisms of Inference to the Best Explanation. In the end, this dissertation puts forward a clearer articulation and novel defense of explanatory reasoning. (shrink)

Recently, in attempting to account for explanatory reasoning in probabilistic terms, Bayesians have proposed several measures of the degree to which a hypothesis explains a given set of facts. These candidate measures of "explanatory power" are shown to have interesting normative interpretations and consequences. What has not yet been investigated, however, is whether any of these measures are also descriptive of people’s actual explanatory judgments. Here, I present my own experimental work investigating this question. I argue that one measure in (...) particular is an accurate descriptor of explanatory judgments. Then, I discuss some interesting implications of this result for both the epistemology and the psychology of explanatory reasoning. (shrink)

Standard articulations of Inference to the Best Explanation (IBE) imply the uniqueness claim that exactly one explanation should be inferred in response to an explanandum. This claim has been challenged as being both too strong (sometimes agnosticism between candidate explanatory hypotheses seems the rational conclusion) and too weak (in cases where multiple hypotheses might sensibly be conjointly inferred). I propose a novel interpretation of IBE that retains the uniqueness claim while also allowing for agnostic and conjunctive conclusions. I then argue (...) that a particular probabilistic explication of explanatory goodness helpfully guides us in navigating such options when using IBE. (shrink)

In robustness analysis, hypotheses are supported to the extent that a result proves robust, and a result is robust to the extent that we detect it in diverse ways. But what precise sense of diversity is at work here? In this paper, I show that the formal explications of evidential diversity most often appealed to in work on robustness – which all draw in one way or another on probabilistic independence – fail to shed light on the notion of diversity (...) relevant to robustness analysis. I close by briefly outlining a promising alternative approach inspired by Horwich’s (1982) eliminative account of evidential diversity. (shrink)

Crupi et al. (2008) offer a confirmation-theoretic, Bayesian account of the conjunction fallacy—an error in reasoning that occurs when subjects judge that Pr( h 1 & h 2 | e ) > Pr( h 1 | e ). They introduce three formal conditions that are satisfied by classical conjunction fallacy cases, and they show that these same conditions imply that h 1 & h 2 is confirmed by e to a greater extent than is h 1 alone. Consequently, they suggest (...) that people are tracking this confirmation relation when they commit conjunction fallacies. I offer three experiments testing the merits of Crupi et al.’s account specifically and confirmation-theoretic accounts of the conjunction fallacy more generally. The results of Experiment 1 show that, although Crupi et al.’s conditions do seem to be causally linked to the conjunction fallacy, they are not necessary for it; there exist cases that do not meet their three conditions in which subjects still tend to commit the fallacy. The results of Experiments 2 and 3 show that Crupi et al.’s conditions, and those offered by other confirmation-theoretic accounts of the fallacy, are not sufficient for the fallacy either; there exist cases that meet all three of CFT’s conditions in which subjects do not tend to commit the fallacy. Additionally, these latter experiments show that such confirmation-theoretic conditions are at best only weakly causally relevant to the presence of the conjunction fallacy. Given these findings, CFT’s account specifically, and any general confirmation-theoretic account more broadly, falls short of offering a satisfying explanation of the presence of the conjunction fallacy. (shrink)

Crupi and Tentori (2012) propose a condition of adequacy for any Bayesian measure of explanatory power, which they call Explanatory Justice. They criticize a measure recently defended by Schupbach and Sprenger(2011) for failing to satisfy this condition, and they offer a new explanatorily just measure of explanatory power. In this paper, we investigate Explanatory Justice’s merits as a condition of adequacy. We offer three arguments against this condition, thus supporitng the idea that a measure of explanatory power should rather be (...) unjust. Then, in order to ensure that the debate advances beyond a mere battle of intuitions, we offer some new results derived from the empirical study described in (Schupbach, 2011a). All of this strengthens the case for Schupbach and Sprenger’s measure while simultaneously posing new challenges to Crupi and Tentori’s alternative proposal. (shrink)

In a recent article, Graham Oppy offers a lucid and intriguing examination of William Paley's design argument. Oppy sets two goals for his article. First, he sets out to challenge the "almost universal assumption" that Paley's argument is inductive by revealing it actually to be a deductive argument. Second, he attempts to expose Paley's argument as manifestly poor when interpreted in this way. I will argue that Oppy is unsuccessful in accomplishing his first goal, leaving his second goal quite irrelevant. (...) Contrary to Oppy's interpretation, Paley's argument is best interpreted as an inference to the best explanation. (shrink)

Philosophers and psychologists are increasingly investigating the conditions under which multiple explanations are better in conjunction than they are individually. This book brings together leading scholars to provide an interdisciplinary and unified discussion of such "conjunctive explanations." The book starts with an introductory chapter expounding the notion of conjunctive explanation and motivating a multifaceted approach to its study. The remaining chapters are divided into three parts. Part I includes chapters on "The Nature of Conjunctive Explanations." Each chapter illustrates distinct ways (...) in which explanatory multiplicity is motivated by a careful study of the nature and concept of explanation. The second part ("Reasoning about Conjunctive Explanations") includes chapters on the epistemology and logic of conjunctive explanations. Here the contributors propose and evaluate various norms for reasoning correctly about and to conjunctive explanations. Part III concerns "The Psychology of Conjunctive Explanations," with contributions discussing conditions under which humans entertain and hold multiple explanations of single explananda simultaneously and the cognitive limitations and capacities for doing so. Conjunctive Explanations will be of interest to researchers and advanced students working on explanation in philosophy of science, epistemology, philosophical logic, and cognitive psychology. (shrink)

Formal epistemology is just what it sounds like: epistemology done with formal tools. Coinciding with the general rise in popularity of experimental philosophy, formal epistemologists have begun to apply experimental methods in their own work. In this entry, I survey some of the work at the intersection of formal and experimental epistemology. I show that experimental methods have unique roles to play when epistemology is done formally, and I highlight some ways in which results from formal epistemology have been used (...) fruitfully to advance epistemically‐relevant experimental work. The upshot of this brief, incomplete survey is that formal and experimental methods often constitute mutually informative means to epistemological ends. (shrink)

Marc Alspector-Kelly claims that Bas van Fraassen’s primary challenge to the scientific realist is for the realist to find a way to justify the use of some mode of inference that takes him from the world of observables to knowledge of the world of unobservables without thereby abandoning empiricism. It is argued that any effort to justify such an “inferential wand” must appeal either to synthetic a priori or synthetic a posteriori knowledge. This disjunction turns into a dilemma for the (...) empirically-minded realist as either disjunct leads to unwanted consequences. In this paper, I split the horns of this dilemma by arguing that the realist can justify one particular such mode of inference – abduction – without committing himself to rationalism. The realist may justify this mode of inference by appealing to the analytic a priori axioms of the probability calculus. I show that Peter Lipton’s tripartite defense of abduction constitutes such a method of justification. (shrink)

In, I put forward a “possibility result” for Bayesian Coherentism, showing that there exist plausible sets of ceteris paribus conditions that imply that coherence is truth-conducive. Against this result, Schubert argues that the specific ceteris paribus conditions I consider are “jointly inconsistent”. In this article, I prove to the contrary that these conditions can consistently be enforced while allowing degrees of coherence to vary. Next, I consider a related criticism, inspired by Olsson’s constraints on ceteris paribus conditions. This leads to (...) a general discussion of the principle that should guide one in choosing appropriately stringent ceteris paribus conditions.En planteo un “resultado de posibilidad” para el bayesianismo coherentista mostrando que existen conjuntos plausibles de condiciones ceteris paribus que implican que la coherencia conduce a la verdad. Schubert argumenta en contra de este resultado que las condiciones ceteris paribus que considero son “inconsistentes tomadas conjuntamente”. En este articulo demuestro, sin embargo, que estas condiciones pueden ser satisfechas permitiendo que los grados de coherencia varien. Abordo despues una critica relacionada con la anterior e inspirada en los requisitos impuestos por Olsson a las condiciones ceteris paribus. Eso lleva a una discusion general del principio, o principios, que deberia guiarnos para elegir unas condiciones ceterisparibus que sean apropiadas, es decir, que no sean ni muy restrictivas, ni demasiado laxas. (shrink)

Formal epistemology is just what it sounds like: epistemology done with formal tools. Coinciding with the general rise in popularity of experimental philosophy, formal epistemologists have begun to apply experimental methods in their own work. In this entry, I survey some of the work at the intersection of formal and experimental epistemology. I show that experimental methods have unique roles to play when epistemology is done formally, and I highlight some ways in which results from formal epistemology have been used (...) fruitfully to advance epistemically-relevant experimental work. The upshot of this brief, incomplete survey is that formal and experimental methods often constitute mutually informative means to epistemological ends. (shrink)

This entry provides a brief summary of the works of William Paley (1743–1805) that are of most interest and relevance to contemporary philosophy of religion.

There is an ongoing controversy in philosophy about the connection between explanation and inference. According to Bayesians, explanatory considerations should be given weight in determining which inferences to make, if at all, only insofar as doing so is compatible with Strict Conditionalization. Explanationists, on the other hand, hold that explanatory considerations can be relevant to the question of how much confidence to invest in our hypotheses in ways which violate Strict Conditionalization. The controversy has focused on normative issues. This paper (...) investigates experimentally the descriptive question of whether judgments of the explanatory goodness of hypotheses do play a role when people revise their degrees of belief in those hypotheses upon the receipt of new evidence. We present the results of three experiments that together strongly support the predictive superiority of the explanationist position. (shrink)

There has been a probabilistic turn in contemporary cognitive science. Far and away, most of the work in this vein is Bayesian, at least in name. Coinciding with this development, philosophers have increasingly promoted Bayesianism as the best normative account of how humans ought to reason. In this paper, we make a push for exploring the probabilistic terrain outside of Bayesianism. Non-Bayesian, but still probabilistic, theories provide plausible competitors both to descriptive and normative Bayesian accounts. We argue for this general (...) idea via recent work on explanationist models of updating, which are fundamentally probabilistic but assign a substantial, non-Bayesian role to explanatory considerations. (shrink)

This chapter develops and defends a formal epistemology of conjunctive explanation by determining the conditions under which multiple distinct explanations are better than one. The general approach is to identify an appropriate measure of explanatory goodness that can then be applied to conjunctive explanations. If a conjunctive explanation is to be preferred it needs to have greater explanatory virtue (e.g., power or scope) with respect to the evidence, but this explanatory gain is insufficient on its own. Given a conjunctive explanation’s (...) greater complexity, it also has a cost associated with it and so a balance needs to be struck between the gain and the cost. This is achieved by employing a Bayesian measure proposed by I. J. Good. This chapter explores some properties of this measure and its application to the epistemology of conjunctive explanation. In so doing, it addresses the general question of whether it is desirable to have more informative, less probable hypotheses when seeking good explanations. (shrink)

Cognitive approaches to religious phenomena have attracted considerable interdisciplinary attention since their emergence a couple of decades ago. Proponents offer explanatory accounts of the content and transmission of religious thought and behavior in terms of underlying cognition. A central claim is that the cross‐cultural recurrence and historical persistence of religion is attributable to the cognitive naturalness of religious ideas, i.e., attributable to the readiness, the ease, and the speed with which human minds acquire and process popular religious representations. In this (...) article, we primarily provide an introductory summary of foundational questions, assumptions, and hypotheses in this field, including some discussion of features distinguishing cognitive science approaches to religion from established psychological approaches. Relevant ethnographic and experimental evidence illustrate and substantiate core claims. Finally, we briefly consider the broader implications of these cognitive approaches for the appropriateness of ‘religion’ as an explanatorily useful category in the social sciences. (shrink)

Soon after the coronavirus disease 2019 (COVID‐19) pandemic outbreak, it became clear that vaccination will be the most useful tool to combat the disease. Despite the apparent safety and efficacy of the developed anti‐COVID‐19 vaccines, relatively high percentages of the population worldwide refused to get vaccinated, including many health workers and health students. The present cross‐sectional study examined the motives, attitudes, and personal characteristics of those who did not get vaccinated against COVID‐19 or vaccinated without complete willingness among nursing students (...) and nursing faculty members in Israel (n = 472). Results show that the vast majority of the study participants (97%) received at least one dose of the anti‐COVID‐19 vaccine. Nearly 37% of the participants indicated that they received the vaccine without complete willingness. As compared to faculty members, nursing students reported lower trust in the efficacy of the vaccine, perceived the COVID‐19 pandemic as a health threat to a lesser extent, exhibited lower institutional and personal trust, and had higher levels of posttraumatic stress disorder symptoms. Non‐Jewish participants were at risk of vaccinating without complete willingness. These findings underscore the need for developing evidence‐based strategies to promote the safety and efficacy of the anti‐COVID‐19 vaccines in nursing schools. (shrink)

In 2004 a survey was conducted in the member states of the European Union designed to gain greater insight into the views on control strategies for foot and mouth disease, classical swine fever, and avian influenza with respect to the epidemiological, economic and social-ethical consequences of each of these animal diseases. This article presents the results of the social-ethical survey. A selection of stakeholders from each member state was asked to prioritize issues for the prevention and control of these diseases. (...) A majority of stakeholders chose preventive measures as the preferred issue. An analysis was done to determine whether there were differences in views expressed by stakeholders from member states with a history of recent epidemics and ones without such a history, and whether there were regional differences. There were no differences between member states with or without a history of recent epidemics. There were indeed regional differences between the priority orders from Northern and Southern Europe on the one hand, and from Eastern Europe on the other. (shrink)

This article explores the effect of women’s movement into the labor market on the gender segregation of work, using the Current Population Survey from 1972 to 1993. The author includes as working those respondents who were “keeping house” and codes keeping house as an occupation. The results show higher estimates of gender segregation, and slightly steeper declines over time, than were seen in previous studies. Analysis of one-year longitudinal changes reveals less movement out of female-dominated occupations when keeping house is (...) included as an occupation. Finally, a decomposition of the segregation trend shows that the movement of women away from keeping house contributed as much to the overall decline in gender segregation as did the desegregation of paid occupations. The author concludes that the movement of women’s work from the household to the labor market has been a driving force in the changing nature of gender inequality. (shrink)

In this paper, we present and defend the theoretical framework of an empirical model to describe people’s fundamental moral attitudes (FMAs) to animals, the stratification of FMAs in society and the role of FMAs in judgment on the culling of healthy animals in an animal disease epidemic. We used philosophical animal ethics theories to understand the moral basis of FMA convictions. Moreover, these theories provide us with a moral language for communication between animal ethics, FMAs, and public debates. We defend (...) that FMA is a two-layered concept. The first layer consists of deeply felt convictions about animals. The second layer consists of convictions derived from the first layer to serve as arguments in a debate on animal issues. In a debate, the latter convictions are variable, depending on the animal issue in a specific context, time, and place. This variability facilitates finding common ground in an animal issue between actors with opposing convictions. (shrink)