Bayesian epistemology tells us with great precision how we should move from prior to posterior beliefs in light of new evidence or information, but says little about where our prior beliefs come from. It offers few resources to describe some prior beliefs as rational or well-justified, and others as irrational or unreasonable. A different strand of epistemology takes the central epistemological question to be not how to change one’s beliefs in light of new evidence, but what reasons justify a (...) given set of beliefs in the first place. We offer an account of rational belief formation that closes some of the gap between Bayesianism and its reason-based alternative, formalizing the idea that an agent can have reasons for his or her (prior) beliefs, in addition to evidence or information in the ordinary Bayesian sense. Our analysis of reasons for belief is part of a larger programme of research on the role of reasons in rational agency (Dietrich and List, Nous, 2012a, in press; Int J Game Theory, 2012b, in press). (shrink)

The Sleeping Beauty problem has attracted considerable attention in the literature as a paradigmatic example of how self-locating uncertainty creates problems for the Bayesian principles of Conditionalization and Reflection. Furthermore, it is also thought to raise serious issues for diachronic Dutch Book arguments. I show that, contrary to what is commonly accepted, it is possible to represent the Sleeping Beauty problem within a standard Bayesian framework. Once the problem is correctly represented, the ‘thirder’ solution satisfies standard rationality principles, (...) vindicating why it is not vulnerable to diachronic Dutch Book arguments. Moreover, the diachronic Dutch Books against the ‘halfer’ solutions fail to undermine the standard arguments for Conditionalization. The main upshot that emerges from my discussion is that the disagreement between different solutions does not challenge the applicability of Bayesian reasoning to centered settings, nor the commitment to Conditionalization, but is instead an instance of the familiar problem of choosing the priors. (shrink)

Our universe seems to be miraculously fine-tuned for life. Multiverse theories have been proposed as an explanation for this on the basis of probabilistic arguments, but various authors have objected that we should consider our total evidence that this universe in particular has life in our inference, which would block the argument. The debate thus crucially hinges on how Bayesian background and evidence are distinguished and on how indexical or demonstrative terms are analysed. The aim of this article is (...) to take a step back and examine these various aspects of Bayesian reasoning and how they affect the arguments. The upshot is that there are reasons to resist the fine-tuning argument for the multiverse, but the “this-universe-objection” is not one of them. (shrink)

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as the Riemann hypothesis, have had to be considered in terms of the evidence for and against them. In recent decades, massive increases in computer power have permitted the gathering of huge amounts of numerical evidence, both for conjectures in pure mathematics and (...) for the behavior of complex applied mathematical models and statistical algorithms. Mathematics has therefore become (among other things) an experimental science (though that has not diminished the importance of proof in the traditional style). We examine how the evaluation of evidence for conjectures works in mathematical practice. We explain the (objective) Bayesian view of probability, which gives a theoretical framework for unifying evidence evaluation in science and law as well as in mathematics. Numerical evidence in mathematics is related to the problem of induction; the occurrence of straightforward inductive reasoning in the purely logical material of pure mathematics casts light on the nature of induction as well as of mathematical reasoning. (shrink)

A major open question in the borderlands between epistemology and philosophy of science concerns whether Bayesian updating and abductive inference are compatible. Some philosophers—most influentially Bas van Fraassen—have argued that they are not. Others have disagreed, arguing that abduction, properly understood, is indeed compatible with Bayesianism. Here we present two formal results that allow us to tackle this question from a new angle. We start by formulating what we take to be a minimal version of the claim that abduction (...) is a rational pattern of reasoning. We then show that this minimal abductivist principle, when combined with Bayesian updating by conditionalization, places surprisingly strong and controversial constraints on how we must measure explanatory power. The lesson is not that Bayesianism is definitely incompatible with abduction, but that both compatibilism and incompatibilism have hitherto unrecognized consequences. We end the paper by formulating these consequences in the form of a trilemma. (shrink)

Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis for (...) Bayesian reasoning with idealized models in science. (shrink)

The gambler’s fallacy is the tendency to expect random processes to switch more often than they actually do—for example, to think that after a string of tails, a heads is more likely. It’s often taken to be evidence for irrationality. It isn’t. Rather, it’s to be expected from a group of Bayesians who begin with causal uncertainty, and then observe unbiased data from an (in fact) statistically independent process. Although they converge toward the truth, they do so in an asymmetric (...) way—ruling out “streaky” hypotheses more quickly than “switchy” ones. As a result, the majority (and the average) exhibit the gambler’s fallacy. If they have limited memory, this tendency persists even with arbitrarily-large amounts of data. Indeed, such Bayesians exhibit a variety of the empirical trends found in studies of the gambler’s fallacy: they expect switches after short streaks but continuations after long ones; these nonlinear expectations vary with their familiarity with the causal system; their predictions depend on the sequence they’ve just seen; they produce sequences that are too switchy; and they exhibit greater rates of gambler’s reasoning when forming binary predictions than when forming probability estimates. In short: what’s been thought to be evidence for irrationality may instead be rational responses to limited data and memory. (shrink)

Gordon Belot has recently developed a novel argument against Bayesianism. He shows that there is an interesting class of problems that, intuitively, no rational belief forming method is likely to get right. But a Bayesian agent’s credence, before the problem starts, that she will get the problem right has to be 1. This is an implausible kind of immodesty on the part of Bayesians. My aim is to show that while this is a good argument against traditional, precise Bayesians, (...) the argument doesn’t neatly extend to imprecise Bayesians. As such, Belot’s argument is a reason to prefer imprecise Bayesianism to precise Bayesianism. (shrink)

Politics is rife with motivated cognition. People do not dispassionately engage with the evidence when they form political beliefs; they interpret it selectively, generating justifications for their desired conclusions and reasons why contrary evidence should be ignored. Moreover, research shows that epistemic ability (e.g. intelligence and familiarity with evidence) is correlated with motivated cognition. Bjørn Hallsson has pointed out that this raises a puzzle for the epistemology of disagreement. On the one hand, we typically think that epistemic ability in an (...) interlocutor gives us reason to downgrade our belief upon learning that we disagree. On the other hand, if our interlocutor is under the sway of motivated cognition, then we have reason to discount his opinion. In this paper, I argue that Hallsson's puzzle is solved by adopting a Bayesian approach to disagreement. If an interlocutor is under the sway of motivated cognition, his disagreement should not affect our beliefs--no matter his ability. Because we implicitly and to high accuracy know his beliefs before he reveals them to us, disagreement provides us with no new information on which to conditionalize. I advance a model which accommodates the motivated cognition dynamic and other key epistemic features of disagreement. (shrink)

According to [Bayesian] models” in cognitive neuroscience, says a recent textbook, “the human mind behaves like a capable data scientist”. Do they? That is to say, do such model show we are rational? I argue that Bayesian models of cognition, perhaps surprisingly, do not and indeed cannot, show that we are Bayesian-rational. The key reason is that such models appeal to approximations, a fact that carries significant implications. After outlining the argument, I critique two responses, seen in (...) recent cognitive neuroscience. One says that the mind can be seen as approximately Bayes-rational, while the other reconceives norms of rationality. (shrink)

Whereas Bayesians have proposed norms such as probabilism, which requires immediate and permanent certainty in all logical truths, I propose a framework on which credences, including credences in logical truths, are rational because they are based on reasoning that follows plausible rules for the adoption of credences. I argue that my proposed framework has many virtues. In particular, it resolves the problem of logical omniscience.

There is a distinction between merely having the right belief, and further basing that belief on the right reasons. Any adequate epistemology needs to be able to accommodate the basing relation that marks this distinction. However, trouble arises for Bayesianism. I argue that when we combine Bayesianism with the standard approaches to the basing relation, we get the result that no agent forms their credences in the right way; indeed, no agent even gets close. This is a serious problem, for (...) it prevents us from making epistemic distinctions between agents that are doing a reasonably good job at forming their credences and those that are forming them in clearly bad ways. I argue that if this result holds, then we have a problem for Bayesianism. However, I show how the Bayesian can avoid this problem by rejecting the standard approaches to the basing relation. By drawing on recent work on the basing relation, we can develop an account of the relation that allows us to avoid the result that no agent comes close to forming their credences in the right way. The Bayesian can successfully accommodate the basing relation. (shrink)

Bayesians often assume, suppose, or conjecture that for any reasonable explication of the notion of simplicity a prior can be designed that will enforce a preference for hypotheses simpler in just that sense. But it is shown here that there are simplicity-driven approaches to curve-fitting problems that cannot be captured within the orthodox Bayesian framework.

Much contemporary epistemology is informed by a kind of confirmational holism, and a consequent rejection of the assumption that all confirmation rests on experiential certainties. Another prominent theme is that belief comes in degrees, and that rationality requires apportioning one's degrees of belief reasonably. Bayesian confirmation models based on Jeffrey Conditionalization attempt to bring together these two appealing strands. I argue, however, that these models cannot account for a certain aspect of confirmation that would be accounted for in any (...) adequate holistic confirmation theory. I then survey the prospects for constructing a formal epistemology that better accommodates holistic insights. (shrink)

This paper shows how an efficient and parallel algorithm for inference in Bayesian Networks (BNs) can be built and implemented combining sparse matrix factorization methods with variable elimination algorithms for BNs. This entails a complete separation between a first symbolic phase, and a second numerical phase.

Although some previous studies have investigated the relationship between moral foundations and moral judgment development, the methods used have not been able to fully explore the relationship. In the present study, we used Bayesian Model Averaging (BMA) in order to address the limitations in traditional regression methods that have been used previously. Results showed consistency with previous findings that binding foundations are negatively correlated with post-conventional moral reasoning and positively correlated with maintaining norms and personal interest schemas. In (...) addition to previous studies, our results showed a positive correlation for individualizing foundations and post-conventional moral reasoning. Implications are discussed as well as a detailed explanation of the novel BMA method in order to allow others in the field of moral education to be able to use it in their own studies. (shrink)

The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning (...) by the ‘proportional syllogism’, or argument from frequencies, such as ‘nearly all aeroplane flights arrive safely, so my flight is very likely to arrive safely’. Such arguments raise the ‘problem of the reference class’, arising from the fact that an individual case may be a member of many different classes in which frequencies differ. For example, if 15 per cent of swans are black and 60 per cent of fauna in the zoo is black, what should I think about the likelihood of a swan in the zoo being black? The nature of the problem is explained, and legal cases where it arises are given. It is explained how recent work in data mining on the relevance of features for prediction provides a solution to the reference class problem. (shrink)

The paper investigates measures of explanatory power and how to define the inference schema “Inference to the Best Explanation”. It argues that these measures can also be used to quantify the systematic power of a hypothesis and the inference schema “Inference to the Best Systematization” is defined. It demonstrates that systematic power is a fruitful criterion for theory choice and IBS is truth-conducive. It also shows that even radical Bayesians must admit that systemic power is an integral component of (...) class='Hi'>Bayesian reasoning. Finally, the paper puts the achieved results in perspective with van Fraassen’s famous criticism of IBE. (shrink)

Several philosophers and psychologists have characterized belief in conspiracy theories as a product of irrational reasoning. Proponents of conspiracy theories apparently resist revising their beliefs given disconfirming evidence and tend to believe in more than one conspiracy, even when the relevant beliefs are mutually inconsistent. In this paper, we bring leading views on conspiracy theoretic beliefs closer together by exploring their rationality under a probabilistic framework. We question the claim that the irrationality of conspiracy theoretic beliefs stems from an (...) inadequate response to disconfirming evidence and internal incoherence. Drawing analogies to Lakatosian research programs, we argue that maintaining a core conspiracy belief can be Bayes-rational when it is embedded in a network of auxiliary beliefs, which can be revised to protect the more central belief from disconfirmation. We propose that the irrationality associated with conspiracy belief lies not in a flawed updating method, but in a failure to converge toward wellconfirmed, stable belief networks in the long run. This approach not only reconciles previously disjointed views, but also points toward more specific descriptions of why agents may be prone to adopting beliefs in conspiracy theories. (shrink)

Precognition is an anomaly in information transmission and interpretation. Extant literature suggests that paranormal beliefs and gender may have significant influences on this unknown information process. This study examines the effects of these two factors, including their interactions, on precognition performance by employing the Bayesian Mindsponge Framework (BMF) analytics. Using Bayesian analysis on secondary data of 60 participants, we found that men may have higher chances to score a hit in a precognition task compared to women. Interestingly, stronger (...) beliefs in the paranormal may decrease the success probability in performing precognition tasks. Considering the interactions between the two factors, the effect of paranormal beliefs on precognition task performance is stronger in men than women. Using mindsponge-based reasoning, we argue that paranormal beliefs may increase the interference of imagination in the reception of hypothetical precognitive information. Women tend to rely more on intuition, which may lessen the interference effect of imagination on hypothetical psi reception. Based on the findings, we suggest that researchers should be careful when assessing participants’ psi potential for experiments. We also demonstrate some advantages of utilizing the BMF in parapsychological research. (shrink)

My purpose in this paper is to argue for two separate, but related theses. The first is that contemporary analytic philosophy is incoherent. This is so, I argue, because its methods contain as an essential constituent a conception of intuition that cannot be rendered consistent with a key tenet of analytic philosophy unless we allow a Bayesian-subjectivist epistemology. I argue for this within a discussion of two theories of intuition: a classical account as proposed by Descartes and a modern (...) reliabilist account as proposed by Kornblith, maintaining that reliabilist accounts require a commitment to Bayesian subjectivism about probability. However, and this is the second thesis, Bayesian subjectivism is itself logically incoherent given two simple assumptions: (1) that some empirical propositions are known and (2) any proposition that is known is assigned a degree of subjective credence of 1. I establish this using a formal reductio proof. I argue for the first thesis in section 2 and for the second in section 3. The final section contains a summary and conclusion. (shrink)

Resource rationality may explain suboptimal patterns of reasoning; but what of “anti-Bayesian” effects where the mind updates in a direction opposite the one it should? We present two phenomena — belief polarization and the size-weight illusion — that are not obviously explained by performance- or resource-based constraints, nor by the authors’ brief discussion of reference repulsion. Can resource rationality accommodate them?

We construct a probabilistic coherence measure for information sets which determines a partial coherence ordering. This measure is applied in constructing a criterion for expanding our beliefs in the face of new information. A number of idealizations are being made which can be relaxed by an appeal to Bayesian Networks.

Scientific theories are used for a variety of purposes. For example, physical theories such as classical mechanics and electrodynamics have important applications in engineering and technology, and we trust that this results in useful machines, stable bridges, and the like. Similarly, theories such as quantum mechanics and relativity theory have many applications as well. Beyond that, these theories provide us with an understanding of the world and address fundamental questions about space, time, and matter. Here we trust that the answers (...) scientific theories give are reliable and that we have good reason to believe that the features of the world are similar to what the theories say about them. But why do we trust scientific theories, and what counts as evidence in favor of them? (shrink)

The paper discusses the notion of reasoning with comparative moral judgements (i.e judgements of the form “act a is morally superior to act b”) from the point of view of several meta-ethical positions. Using a simple formal result, it is argued that only a version of moral cognitivism that is committed to the claim that moral beliefs come in degrees can give a normatively plausible account of such reasoning. Some implications of accepting such a version of moral cognitivism (...) are discussed. (shrink)

All of us, including scientists, make judgments about what is true or false, probable or improbable. And in the process, we frequently appeal to concepts such as evidential support or explanation. Bayesian philosophers of science have given illuminating formal accounts of these concepts. This paper aims to follow in their footsteps, providing a novel formal account of various additional concepts: the likelihood-prior trade-off, successful accommodation of evidence, ad hocness, and, finally, consilience—sometimes also called “unification”. Using these accounts, I also (...) provide a new Bayesian analysis of how someone such as Charles Darwin hypothetically could have reasoned in favor of evolution over special creationism. Lastly, I explore how these accounts relate to other topics and accounts in philosophy, and I chart out some areas for further research. (shrink)

In a series of recent papers Stephen Kearns and Daniel Star argue that normative reasons to ϕ simply are evidence that one ought to ϕ, and suggest that “evidence” in this context is best understood in standard Bayesian terms. I contest this suggestion.

Aumann’s theorem states that no individual should agree to disagree under a range of assumptions. Political liberalism appears to presuppose these assumptions with the idealized conditions of public reason. We argue Aumann’s theorem demonstrates they nevertheless cannot be simultaneously held with what is arguably political liberalism’s most central tenet. That is, the tenet of reasonable pluralism, which implies we can rationally agree to disagree over conceptions of the good. We finish by elaborating a way of relaxing one of the theorem’s (...) axioms that arguably lends itself to a coherent account of political liberalism, namely the condition of indexical independence. (shrink)

The new paradigm in the psychology of reasoning draws on Bayesian formal frameworks, and some advocates of the new paradigm think of these formal frameworks as providing a computational-level theory of rational human inference. I argue that Bayesian theories should not be seen as providing a computational-level theory of rational human inference, where by “Bayesian theories” I mean theories that claim that all rational credal states are probabilistically coherent and that rational adjustments of degrees of belief (...) in the light of new evidence must be in accordance with some sort of conditionalization. The problems with the view I am criticizing can best be seen when we look at chains of inferences, rather than single-step inferences. Chains of inferences have been neglected almost entirely within the new paradigm. (shrink)

The justificatory force of empirical reasoning always depends upon the existence of some synthetic, a priori justification. The reasoner must begin with justified, substantive constraints on both the prior probability of the conclusion and certain conditional probabilities; otherwise, all possible degrees of belief in the conclusion are left open given the premises. Such constraints cannot in general be empirically justified, on pain of infinite regress. Nor does subjective Bayesianism offer a way out for the empiricist. Despite often-cited convergence theorems, (...) subjective Bayesians cannot hold that any empirical hypothesis is ever objectively justified in the relevant sense. Rationalism is thus the only alternative to an implausible skepticism. (shrink)

According to dogmatism, one may know a proposition by inferring it from a set of evidence even if one has no independent grounds for rejecting a skeptical hypothesis compatible with one’s evidence but incompatible with one’s conclusion. Despite its intuitive attractions, many philosophers have argued that dogmatism goes wrong because they have thought that it licenses Moorean reasoning — i.e., reasoning in which one uses the conclusion of an inference as a premise in an argument against a skeptical (...) hypothesis that would undermine that very inference. In this paper I defend dogmatism against this line of thought. To begin with, I argue that the common assumption that uncontroversial Bayesian principles suffice to show that Moorean reasoning is not cogent is false: for all that Bayesianism says on the matter, Moorean reasoning might be perfectly fine. Nevertheless, Moorean reasoning does seem intuitively defective. As I argue, however, this does not provide grounds for an argument against dogmatism, because — contrary to what many philosophers have thought — dogmatism need not license Moorean reasoning. On the contrary, as I argue, dogmatism predicts that Moorean reasoning suffers from a clearly identifiable defect. (shrink)

Bayesianism is the position that scientific reasoning is probabilistic and that probabilities are adequately interpreted as an agent's actual subjective degrees of belief, measured by her betting behaviour. Confirmation is one important aspect of scientific reasoning. The thesis of this paper is the following: if scientific reasoning is at all probabilistic, the subjective interpretation has to be given up in order to get right confirmation—and thus scientific reasoning in general. The Bayesian approach to scientific (...) class='Hi'>reasoning Bayesian confirmation theory The example The less reliable the source of information, the higher the degree of Bayesian confirmation Measure sensitivity A more general version of the problem of old evidence Conditioning on the entailment relation The counterfactual strategy Generalizing the counterfactual strategy The desired result, and a necessary and sufficient condition for it Actual degrees of belief The common knock-down feature, or ‘anything goes’ The problem of prior probabilities. (shrink)

The notion of an ideal reasoner has several uses in epistemology. Often, ideal reasoners are used as a parameter of (maximum) rationality for finite reasoners (e.g. humans). However, the notion of an ideal reasoner is normally construed in such a high degree of idealization (e.g. infinite/unbounded memory) that this use is unadvised. In this dissertation, I investigate the conditions under which an ideal reasoner may be used as a parameter of rationality for finite reasoners. In addition, I present and justify (...) the research program of computational epistemology, which investigates the parameter of maximum rationality for finite reasoners using computer simulations. (shrink)

Recent years have seen a surge in online collaboration between experts and amateurs on scientific research. In this article, we analyse the epistemological implications of these crowdsourced projects, with a focus on Zooniverse, the world’s largest citizen science web portal. We use quantitative methods to evaluate the platform’s success in producing large volumes of observation statements and high impact scientific discoveries relative to more conventional means of data processing. Through empirical evidence, Bayesian reasoning, and conceptual analysis, we show (...) how information and communication technologies enhance the reliability, scalability, and connectivity of crowdsourced e-research, giving online citizen science projects powerful epistemic advantages over more traditional modes of scientific investigation. These results highlight the essential role played by technologically mediated social interaction in contemporary knowledge production. We conclude by calling for an explicitly sociotechnical turn in the philosophy of science that combines insights from statistics and logic to analyse the latest developments in scientific research. (shrink)

An influential suggestion about the relationship between Bayesianism and inference to the best explanation holds that IBE functions as a heuristic to approximate Bayesian reasoning. While this view promises to unify Bayesianism and IBE in a very attractive manner, important elements of the view have not yet been spelled out in detail. I present and argue for a heuristic conception of IBE on which IBE serves primarily to locate the most probable available explanatory hypothesis to serve as a (...) working hypothesis in an agent’s further investigations. Along the way, I criticize what I consider to be an overly ambitious conception of the heuristic role of IBE, according to which IBE serves as a guide to absolute probability values. My own conception, by contrast, requires only that IBE can function as a guide to the comparative probability values of available hypotheses. This is shown to be a much more realistic role for IBE given the nature and limitations of the explanatory considerations with which IBE operates. (shrink)

A consistent finding in research on conditional reasoning is that individuals are more likely to endorse the valid modus ponens (MP) inference than the equally valid modus tollens (MT) inference. This pattern holds for both abstract task and probabilistic task. The existing explanation for this phenomenon within a Bayesian framework (e.g., Oaksford & Chater, 2008) accounts for this asymmetry by assuming separate probability distributions for both MP and MT. We propose a novel explanation within a computational-level Bayesian (...) account of reasoning according to which “argumentation is learning”. We show that the asymmetry must appear for certain prior probability distributions, under the assumption that the conditional inference provides the agent with new information that is integrated into the existing knowledge by minimizing the Kullback-Leibler divergence between the posterior and prior probability distribution. We also show under which conditions we would expect the opposite pattern, an MT-MP asymmetry. (shrink)

Background: Food fortification refers to the process of adding nutrients to foods during their production. It is a cost-effective strategy with well-documented health, economic, and social benefits. Food fortification practices in school meal programs need guidance and legal support from various national policies. Aim: This study aims to analyze how various national policies—such as those related to school feeding, nutrition, health, food safety, agriculture, and the private sector—associate with the implementation of in-school food fortification among countries with school meals programs. (...) Methods: The Bayesian Mindsponge Framework, combining the reasoning strengths of Mindsponge Theory and inference advantages of Bayesian analysis, was employed on a dataset of 126 government representatives who manage large-scale school meal programs in 126 different countries. Results: Findings showed that food safety policy and agriculture policy were positively and significantly associated with the in-school food fortification practices, while school feeding policy and private sector policy had ambiguous relationships with these practices. Nutrition policy and health policy had a significant negative association with food fortification practices among countries implementing school meal programs. Conclusions: Findings underscore the strong position of food safety policy and agriculture policy in guiding food fortification practices in school meal programs. There is a need to re-assess the implemented nutrition policy and health policy due to their significant negative associations with these practices. Enhancing and strengthening the school feeding policy and private sector policy may increase their potencies in giving positive impacts on in-school food fortification practices. (shrink)

Crispin Wright has given an explanation of how a first time warrant can fall short of transmitting across a known entailment. Formal epistemologists have struggled to turn Wright’s informal explanation into cogent Bayesian reasoning. In this paper, I analyse two Bayesian models of Wright’s account respectively proposed by Samir Okasha and Jake Chandler. I argue that both formalizations are unsatisfactory for different reasons, and I lay down a third Bayesian model that appears to me to capture (...) the valid kernel of Wright’s explanation. After this, I consider a recent development in Wright’s account of transmission failure. Wright suggests that his condition sufficient for transmission failure of first time warrant also suffices for transmission failure of supplementary warrant. I propose an interpretation of Wright’s suggestion that shield it from objections. I then lay down a fourth Bayesian framework that provides a simplified model of the unified explanation of transmission failure envisaged by Wright. (shrink)

Bayesian confirmation theory is our best formal framework for describing inductive reasoning. The problem of old evidence is a particularly difficult one for confirmation theory, because it suggests that this framework fails to account for central and important cases of inductive reasoning and scientific inference. I show that we can appeal to the fragmentation of doxastic states to solve this problem for confirmation theory. This fragmentation solution is independently well-motivated because of the success of fragmentation in solving (...) other problems. I also argue that the fragmentation solution is preferable to other solutions to the problem of old evidence. These other solutions are already committed to something like fragmentation, but suffer from difficulties due to their additional commitments. If these arguments are successful, Bayesian confirmation theory is saved from the problem of old evidence, and the argument for fragmentation is bolstered by its ability to solve yet another problem. (shrink)

A large body of work has demonstrated the utility of the Bayesian framework for capturing inference in both specialist and everyday contexts. However, the central tool of the framework, conditionalization via Bayes’ rule, does not apply directly to a common type of learning: the acquisition of conditional information. How should an agent change her beliefs on learning that “If A, then C”? This issue, which is central to both reasoning and argumentation, has recently prompted considerable research interest. In (...) this paper, we critique a prominent proposal and provide a new, alternative, answer. -/- . (shrink)

This research employs the Bayesian network modeling approach, and the Markov chain Monte Carlo technique, to learn about the role of lies and violence in teachings of major religions, using a unique dataset extracted from long-standing Vietnamese folktales. The results indicate that, although lying and violent acts augur negative consequences for those who commit them, their associations with core religious values diverge in the final outcome for the folktale characters. Lying that serves a religious mission of either Confucianism or (...) Taoism (but not Buddhism) brings a positive outcome to a character (βT_and_Lie_O= 2.23; βC_and_Lie_O= 1.47; βT_and_Lie_O= 2.23). A violent act committed to serving Buddhist missions results in a happy ending for the committer (βB_and_Viol_O= 2.55). What is highlighted here is a glaring double standard in the interpretation and practice of the three teachings: the very virtuous outcomes being preached, whether that be compassion and meditation in Buddhism, societal order in Confucianism, or natural harmony in Taoism, appear to accommodate two universal vices—violence in Buddhism and lying in the latter two. These findings contribute to a host of studies aimed at making sense of contradictory human behaviors, adding the role of religious teachings in addition to cognition in belief maintenance and motivated reasoning in discounting counterargument. (shrink)

Moral circles help define the boundaries of one’s moral consideration. One’s moral circle may provide insight into how one perceives or treats other entities. A data-driven model exploration was conducted to explore predictors and prediction models. Candidate predictors were built upon past research using moral foundations and political orientation. Moreover, we also employed additional moral psychological indicators, i.e., moral reasoning, moral identity, and empathy, based on prior research in moral development and education. We used model exploration methods, i.e., (...) class='Hi'>Bayesian model exploration, Bayesian model averaging, and elastic-net regression. The study successfully replicated past research supporting the relationship between moral foundations, political orientation, and the moral circle. Additional moral psychological constructs, such as post-conventional moral reasoning and moral identity, significantly predicted the moral circle width. The identified components of the moral circle were conceptually related to phronesis, i.e., practical wisdom. We discussed the educational implications of the findings, particularly those related to moral education focusing on phronesis cultivation, multiculturalism and global citizenship, and climate justice. (shrink)

There is a current debate about the extent to which Academic Freedom should be permitted in our universities. On the one hand, we have traditionalists who maintain that Academic Freedom should be unrestricted: people who have the appropriate qualifications and accomplishments should be allowed to develop theories about how the world is, or ought to be, as they see fit. On the other hand, we have post-traditional philosophers who argue against this degree of Academic Freedom. I consider a conservative version (...) of post-traditional philosophy that permits restrictions on Academic Freedom only if the following conditions are met, Condition 1: The dissemination of the results of a given research project R must cause significant harm to some people, especially to people from oppressed groups. Condition 2: Condition 1 must possess strong empirical support, and which accepts the following assumptions: (1) there is a world of objective facts that is, in principle, discoverable, (2) rational means are the means of discovering it and, (3) rational means requires strong empirical support. I define strong empirical support for an hypothesis h on evidence e in probabilistic terms, as a ratio of posterior to prior probabilities substantially exceeding 1. I now argue in favour of a research policy that accepts unrestricted Academic Freedom. My argument is that there is a formal and general quandary that arises within the standard theory of probability when we apply this account of empirical support to a set of possible causal hypotheses framed in such a way that the “reverse probabilities”, pr(e/h) are 1. I consider various possible ways to escape this quandary, none of which are without difficulties, concluding that a research policy allowing for unrestricted Academic Freedom is probably the best that we can hope for. (shrink)

We explored the relationship between 24 character strengths measured by the Global Assessment of Character Strengths (GACS), which was revised from the original VIA instrument, and moral functioning comprising postconventional moral reasoning, empathic traits and moral identity. Bayesian Model Averaging (BMA) was employed to explore the best models, which were more parsimonious than full regression models estimated through frequentist regression, predicting moral functioning indicators with the 24 candidate character strength predictors. Our exploration was conducted with a dataset collected (...) from 666 college students at a public university in the Southern United States. Results showed that character strengths as measured by GACS partially predicted relevant moral functioning indicators. Performance evaluation results demonstrated that the best models identified by BMA performed significantly better than the full models estimated by frequentist regression in terms of AIC, BIC, and cross-validation accuracy. We discuss theoretical and methodological implications of the findings for future studies addressing character strengths and moral functioning. (shrink)

Background: Overnutrition, undernutrition, and micronutrient deficiency present a major global public health challenge due to food insecurity. Micronutrient deficiencies are prevalent among children and result in impaired intellectual growth. Policy guidelines at the national level are essential for the success of micronutrient supplementation programs for children during school feeding. Aim: This study aims to analyze how various national policies guiding the school meal programs—such as those related to school feeding, nutrition, health, food safety, agriculture, and the private sector—associate with the (...) implementation of in-school micronutrient supplementation among countries with school meals programs. Methods: The Bayesian Mindsponge Framework, combining the reasoning strengths of Mindsponge Theory and inference advantages of Bayesian analysis, was employed on a dataset of 126 government representatives who manage large-scale school meal programs in 126 different countries. Results: Findings showed that school feeding policies were positively associated with in-school micronutrient supplementation, while nutrition policy had a negative association with these practices. Both associations were only moderately reliable. Policies on health, food safety, agriculture, and the private sector had ambiguous relationships with micronutrient supplementation among countries implementing school meal programs. Conclusions: Findings highlight the evidence of school feeding policy’s positive association with micronutrient supplementation in school meal programs, indicating effective policy guidance on these practices. There is a need to re-assess the implemented nutrition policy due to its negative association with these practices. Enhancing and strengthening the national policies on health, food safety, agriculture, and the private sector may increase their potencies in supporting in-school micronutrient supplementation among countries implementing school meal programs. (shrink)

Background: Food biofortification practices in agricultural sectors involve the process of employing biotechnology to enhance the nutritional content of crops during their growth process. Biofortification makes foods even more nutritious and highly functional for addressing malnutrition among children. These practices in farming industries need guidance and legal support from various national policies to support high-quality supplies of school meals fully. Aim: This study aims to analyze the association between various national policies and the implementation of food biofortification practices in agricultural (...) sectors among countries implementing school meal programs. Methods: The Bayesian Mindsponge Framework, combining the reasoning strengths of Mindsponge Theory and inference advantages of Bayesian analysis, was employed on a dataset of 126 government representatives who manage large-scale school meal programs in 126 different countries. Results: Findings showed that food safety policy was positively associated with food biofortification practices in agricultural sectors among countries implementing school meal programs. In contrast, nutrition policy had a significant negative association with these practices. Additionally, policies of school feeding, health, agriculture, and the private sector had unclear associations with food biofortification. Conclusions: Findings underscore the strong position of food safety policy in guiding food biofortification practices in agricultural sectors among countries implementing school meal programs. There is a need to re-assess the implemented nutrition policy due to its significant negative association with these practices. Enhancing and strengthening the policies of school feeding, health, agriculture, and the private sector may increase their potencies in giving positive impacts on food biofortification practices in agricultural sectors to ensure high-quality school meal supplies. (shrink)

In this paper we explore the absentminded driver problem using two different scenarios. In the first scenario we assume that the driver is capable of reasoning about his degree of absentmindedness before he hits the highway. This leads to a Savage-style model where the states are mutually exclusive and the act-state independence is in place. In the second we employ centred possibilities, by modelling the states (i.e. the events about which the driver is uncertain) as the possible final destinations (...) indexed by a time period. The optimal probability we find for continuing at an exit is different from almost all papers in the literature. In this scenario, act-state independence is still violated, but states are mutually exclusive and the driver arrives at his optimal choice probability via Bayesian updating. We show that our solution is the only one guaranteeing immunity from sure loss via a Dutch strategy, and that – despite initial appearances – it is time consistent. This raises important implications for the rationality of commitment in such scenarios. (shrink)

The framework of Solomonoff prediction assigns prior probability to hypotheses inversely proportional to their Kolmogorov complexity. There are two well-known problems. First, the Solomonoff prior is relative to a choice of Universal Turing machine. Second, the Solomonoff prior is not computable. However, there are responses to both problems. Different Solomonoff priors converge with more and more data. Further, there are computable approximations to the Solomonoff prior. I argue that there is a tension between these two responses. This is because computable (...) approximations to Solomonoff prediction do not always converge. (shrink)

ABSTRACT In the present study, I explore the relationship between purpose, which was measured by the Claremont Purpose Scale, and moral psychological indicators, moral reasoning, moral identity, and empathy. Purpose was quantified in terms of three subcomponents: meaning, goal, and beyond-the-self motivation. Moral reasoning was assessed in terms of utilization of postconventional moral reasoning. Moral identity was examined with two subscales: moral internalization, and symbolization. Among diverse subscales of empathy, I focused on empathic concern and perspective taking, (...) which have been reported to be strongly related to morality. To explore the best prediction models using the data, I employed Bayesian Model Selection and Bayesian regression analysis. In general, purpose was significantly predicted by most surveyed moral psychological indicators but not by moral symbolization. The best prediction model for beyond-the-self motivation included the most moral psychological indicator predictors including moral reasoning, which did not significantly predict other dependent variables. (shrink)

Under the independence and competence assumptions of Condorcet’s classical jury model, the probability of a correct majority decision converges to certainty as the jury size increases, a seemingly unrealistic result. Using Bayesian networks, we argue that the model’s independence assumption requires that the state of the world (guilty or not guilty) is the latest common cause of all jurors’ votes. But often – arguably in all courtroom cases and in many expert panels – the latest such common cause is (...) a shared ‘body of evidence’ observed by the jurors. In the corresponding Bayesian network, the votes are direct descendants not of the state of the world, but of the body of evidence, which in turn is a direct descendant of the state of the world. We develop a model of jury decisions based on this Bayesian network. Our model permits the possibility of misleading evidence, even for a maximally competent observer, which cannot easily be accommodated in the classical model. We prove that (i) the probability of a correct majority verdict converges to the probability that the body of evidence is not misleading, a value typically below 1; (ii) depending on the required threshold of ‘no reasonable doubt’, it may be impossible, even in an arbitrarily large jury, to establish guilt of a defendant ‘beyond any reasonable doubt’. (shrink)