Bayesian Reasoning

How do multiple reasons combine to support a conclusion about what to do or believe? This question raises two challenges: (1) how can we represent the strength of a reason? (2) how do the strengths of multiple reasons combine?. Analogous challenges about confirmation have been answered using probabilistic tools. Can reductive and non-reductive theories of reasons use these tools to answer their challenges? Yes, or more exactly: Reductive theories can answer both challenges. Non-reductive theories, with the help of a (new?) (...) result in confirmation theory, can answer one and there are grounds for optimism that they can answer the other. (shrink)

In Unsettled Thoughts, Julia Staffel argues that non-ideal thinkers should seek to approximate ideal Bayesian rationality. She argues that the more rational you are, the more benefits of rationality you will enjoy. After summarizing Staffel’s main results, this paper looks more closely at two issues that arise later in the book: the relationship between Bayesian rationality and other kinds of rationality, and the role that outright belief plays in addition to credence. Ultimately, I argue that there are several roles that (...) outright belief might play, and I explore different ways that these roles for belief might fit together. (shrink)

For two ideally rational agents, does learning a finite amount of shared evidence necessitate agreement? No. But does it at least guard against belief polarization, the case in which their opinions get further apart? No. OK, but are rational agents guaranteed to avoid polarization if they have access to an infinite, increasing stream of shared evidence? No.

It is a widespread intuition that the coherence of independent reports provides a powerful reason to believe that the reports are true. Formal results by Huemer (1997), Olsson (2002, 2005), and Bovens and Hartmann (2003) prove that, under certain conditions, coherence cannot increase the probability of the target claim. These formal results, known as ‘the impossibility theorems’ have been widely discussed in the literature. They are taken to have significant epistemic upshot. In particular, they are taken to show that reports (...) must first individually confirm the target claim before the coherence of multiple reports offers any positive confirmation. In this paper, I dispute this epistemic interpretation. The impossibility theorems are consistent with the idea that the coherence of independent reports provides a powerful reason to believe that the reports are true even if the reports do not individually confirm prior to coherence. Once we see that the formal discoveries do not have this implication, we can recover a model of coherence justification consistent with Bayesianism and these results. This paper, thus, seeks to turn the tide of the negative findings for coherence reasoning by defending coherence as a unique source of confirmation. (shrink)

The topic of fake news has received increased attention from philosophers since the term became a favorite of politicians (Habgood-Coote 2016; Dentith 2016). Notably missing from the conversation, however, is a discussion of fake news and conspiracy theory media as a market. This paper will take as its starting point the account of noxious markets put forward by Debra Satz (2010), and will argue that there is a pro tanto moral reason to restrict the market for fake news. Specifically, we (...) begin with Satz’s argument that restricting a market may be required when i) that market inhibits citizens from being able to stand in an equal relationship with one another, and ii) this problem cannot be solved without such direct restrictions. Our own argument then proceeds in three parts: first, we argue that the market for fake news fits Satz’s description of a noxious market; second, we argue against explanations of the proliferation of fake news that are couched in terms of “epistemic vice”, and likewise argue against prescribing critical thinking education as a solution to the problem; finally, we conclude that, in the absence of other solutions to mitigate the noxious effects of the fake news market, we have a pro tanto moral reason to impose restrictions on this market. At the end of the paper, we consider one proposal to regulate the fake news market, which involves making social media outlets potentially liable in civil court for damages caused by the fake news hosted on their websites. (shrink)

A review of Gary Smith and Jay Cordes: The Phantom Pattern Problem: The Mirage of Big Data. New York: Oxford University Press, 2020.

Recent studies indicate that indicative conditionals like "If people wear masks, the spread of Covid-19 will be diminished" require a probabilistic dependency between their antecedents and consequents to be acceptable (Skovgaard-Olsen et al., 2016). But it is easy to make the slip from this claim to the thesis that indicative conditionals are acceptable only if this probabilistic dependency results from a causal relation between antecedent and consequent. According to Pearl (2009), understanding a causal relation involves multiple, hierarchically organized conceptual dimensions: (...) prediction, intervention, and counterfactual dependence. In a series of experiments, we test the hypothesis that these conceptual dimensions are differentially encoded in indicative and counterfactual conditionals. If this hypothesis holds, then there are limits as to how much of a causal relation is captured by indicative conditionals alone. Our results show that the acceptance of indicative and counterfactual conditionals can become dissociated. Furthermore, it is found that the acceptance of both is needed for accepting a causal relation between two co-occurring events. The implications that these findings have for the hypothesis above, and for recent debates at the intersection of the psychology of reasoning and causal judgment, are critically discussed. Our findings are consistent with viewing indicative conditionals as answering predictive queries requiring evidential relevance (even in the absence of direct causal relations). Counterfactual conditionals in contrast target causal relevance, specifically. Finally, we discuss the implications our results have for the yet unsolved question of how reasoners succeed in constructing causal models from verbal descriptions. (shrink)

Complex constraints like conditionals ('If A, then B') and probabilistic constraints ('The probability that A is p') pose problems for Bayesian theories of learning. Since these propositions do not express constraints on outcomes, agents cannot simply conditionalize on the new information. Furthermore, a natural extension of conditionalization, relative information minimization, leads to many counterintuitive predictions, evidenced by the sundowners problem and the Judy Benjamin problem. Building on the notion of a `paradigm shift' and empirical research in psychology and economics, I (...) argue that the model of hypothesis testing can explain how people learn complex, theory-laden propositions like conditionals and probability constraints. Theories are formalized as probability distributions over a set of possible outcomes and theory change is triggered by a constraint which is incompatible with the initial theory. This leads agents to consult a higher order probability function, or a 'prior over priors,' to choose the most likely alternative theory which satisfies the constraint. The hypothesis testing model is applied to three examples: learning a simple probabilistic constraint involving coin bias, the sundowners problem for conditional learning, and the Judy Benjamin problem for learning conditional probability constraints. (shrink)

McGrew & McGrew make a solid statistical case for the historicity of the resurrection. This article fills two lacunae in the argument given there, and repairs a conceptual error (making the first lacuna irrelevant in the process).

Why should we make our beliefs consistent or, more generally, probabilistically coherent? That it will prevent sure losses in betting and that it will maximize one’s chances of having accurate beliefs are popular answers. However, these justifications are self-centered, focused on the consequences of our coherence for ourselves. I argue that incoherence has consequences for others because it is liable to mislead others, to false beliefs about one’s beliefs and false expectations about one’s behavior. I argue that the moral obligation (...) of truthfulness thus constrains us to either conform to the logic our audience assumes we use, educate them in a new logic, or give notice that one will do neither. This does not show that probabilistic coherence is uniquely suited to making truthful communication possible, but I argue that classical probabilistic coherence is superior to other logics for maximizing efficiency in communication. (shrink)

According to the probabilistic relevance account of confirmation, E confirms H relative to background knowledge K just in case P(H/K&E) > P(H/K). This requires an inequality between the rational degree of belief in H determined relative to two bodies of total knowledge which are such that one (K&E) includes the other (K) as a proper part. In this paper, I argue that it is quite plausible that there are no two possible bodies of total knowledge for ideally rational agents meeting (...) this requirement. Hence, the positive relevance account may have to be rejected. (shrink)

In the process of scientific discovery, knowledge ampliation is pursued by means of non-deductive inferences. When ampliative reasoning is performed, probabilities cannot be assigned objectively. One of the reasons is that we face the problem of the unconceived alternatives: we are unable to explore the space of all the possible alternatives to a given hypothesis, because we do not know how this space is shaped. So, if we want to adequately account for the process of knowledge ampliation, we need to (...) develop an account of the process of scientific discovery which is not exclusively based on probability calculus. We argue that the analytic view of the method of science advocated by Cellucci is interestingly suited to this goal, since it rests on the concept of plausibility. In this perspective, in order to account for how probabilities are in fact assigned in uncertain contexts and knowledge ampliation is really pursued, we have to take into account plausibility-based considerations. (shrink)

The epistemology of self-locating belief concerns itself with how rational agents ought to respond to certain kinds of indexical information. I argue that those who endorse the thesis of Time-Slice Rationality ought to endorse a particular view about the epistemology of self-locating belief, according to which ‘essentially indexical’ information is never evidentially relevant to non-indexical matters. I close by offering some independent motivations for endorsing Time-Slice Rationality in the context of the epistemology of self-locating belief.

In this paper, I examine Cicero’s oft-neglected De Divinatione, a dialogue investigating the legitimacy of the practice of divination. First, I offer a novel analysis of the main arguments for divination given by Quintus, highlighting the fact that he employs two logically distinct argument forms. Next, I turn to the first of the main arguments against divination given by Marcus. Here I show, with the help of modern probabilistic tools, that Marcus’ skeptical response is far from the decisive, proto-naturalistic assault (...) on superstition that it is sometimes portrayed to be. Then, I offer an extended analysis of the second of the main arguments against divination given by Marcus. Inspired by Marcus’ second main argument, I formulate, explicate, and defend a substantive principle of scientific methodology that I call the “Ciceronian Causal-Nomological Requirement” (CCR). Roughly, this principle states that causal knowledge is essential for relying on correlations in predictive inference. Although I go on to argue that Marcus’ application of the CCR in his debate with Quintus is dialectically inadequate, I conclude that De Divinatione deserves its place in Cicero’s philosophical corpus, and that ultimately, its significance for the history and philosophy of science ought to be recognized. (shrink)

In this paper, I critically evaluate several related, provocative claims made by proponents of data-intensive science and “Big Data” which bear on scientific methodology, especially the claim that scientists will soon no longer have any use for familiar concepts like causation and explanation. After introducing the issue, in section 2, I elaborate on the alleged changes to scientific method that feature prominently in discussions of Big Data. In section 3, I argue that these methodological claims are in tension with a (...) prominent account of scientific method, often called “Inference to the Best Explanation” (IBE). Later on, in section 3, I consider an argument against IBE that will be congenial to proponents of Big Data, namely the argument due to Roche and Sober (2013) that “explanatoriness is evidentially irrelevant”. This argument is based on Bayesianism, one of the most prominent general accounts of theory-confirmation. In section 4, I consider some extant responses to this argument, especially that of Climenhaga (2017). In section 5, I argue that Roche and Sober’s argument does not show that explanatory reasoning is dispensable. In section 6, I argue that there is good reason to think explanatory reasoning will continue to prove indispensable in scientific practice. Drawing on Cicero’s oft-neglected De Divinatione, I formulate what I call the “Ciceronian Causal-nomological Requirement”, (CCR), which states roughly that causal-nomological knowledge is essential for relying on correlations in predictive inference. I defend a version of the CCR by appealing to the challenge of “spurious correlations”, chance correlations which we should not rely upon for predictive inference. In section 7, I offer some concluding remarks. (shrink)

This chapter presents a typology of the different kinds of inductive inferences we can draw from our evidence, based on the explanatory relationship between evidence and conclusion. Drawing on the literature on graphical models of explanation, I divide inductive inferences into (a) downwards inferences, which proceed from cause to effect, (b) upwards inferences, which proceed from effect to cause, and (c) sideways inferences, which proceed first from effect to cause and then from that cause to an additional effect. I further (...) distinguish between direct and indirect forms of downwards and upwards inferences. I then show how we can subsume canonical forms of inductive inference mentioned in the literature, such as inference to the best explanation, enumerative induction, and analogical inference, under this typology. Along the way, I explore connections with probability and confirmation, epistemic defeat, the relation between abduction and enumerative induction, the compatibility of IBE and Bayesianism, and theories of epistemic justification. (shrink)

In this critical notice, I focus my attention on the chapters that deal with the explanationist response to skepticism.

This develops a framework for second-order conditionalization on statements about one's own epistemic reliability. It is the generalization of the framework of "Second-Guessing" (2009) to the case where the subject is uncertain about her reliability. See also "Epistemic Self-Doubt" (2017).

When we get evidence that tells us our belief-forming mechanisms may not be reliable this presents a thorny set of questions about whether and how to revise our original belief. This article analyzes aspects of the problem and a variety of approaches to its solution.

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)

Our evidence can be about different subject matters. In fact, necessarily equivalent pieces of evidence can be about different subject matters. Does the hyperintensionality of ‘aboutness’ engender any hyperintensionality at the level of rational credence? In this paper, I present a case which seems to suggest that the answer is ‘yes’. In particular, I argue that our intuitive notions of independent evidence and inadmissible evidence are sensitive to aboutness in a hyperintensional way. We are thus left with a paradox. While (...) there is strong reason to think that rational credence cannot make such hyperintensional distinctions, our intuitive judgements about certain cases seem to demand that it does. (shrink)

In this paper, I argue that theories of perception that appeal to Helmholtz’s idea of unconscious inference (“Helmholtzian” theories) should be taken literally, i.e. that the inferences appealed to in such theories are inferences in the full sense of the term, as employed elsewhere in philosophy and in ordinary discourse. -/- In the course of the argument, I consider constraints on inference based on the idea that inference is a deliberate acton, and on the idea that inferences depend on the (...) syntactic structure of representations. I argue that inference is a personal-level but sometimes unconscious process that cannot in general be distinguished from association on the basis of the structures of the representations over which it’s defined. I also critique arguments against representationalist interpretations of Helmholtzian theories, and argue against the view that perceptual inference is encapsulated in a module. (shrink)

I defend an analog of probabilism that characterizes rationally coherent estimates for chances. Specifically, I demonstrate the following accuracy-dominance result for stochastic theories in the C*-algebraic framework: supposing an assignment of chance values is possible if and only if it is given by a pure state on a given algebra, your estimates for chances avoid accuracy-dominance if and only if they are given by a state on that algebra. When your estimates avoid accuracy-dominance (roughly: when you cannot guarantee that other (...) estimates would be more accurate), I say that they are sufficiently coherent. In formal epistemology and quantum foundations, the notion of rational coherence that gets more attention requires that you never allow for a sure loss (or “Dutch book”) in a given sort of betting game; I call this notion full coherence. I characterize when these two notions of rational coherence align, and I show that there is a quantum state giving estimates that are sufficiently coherent, but not fully coherent. (shrink)

Disagreement is a ubiquitous feature of human life, and philosophers have dutifully attended to it. One important question related to disagreement is epistemological: How does a rational person change her beliefs (if at all) in light of disagreement from others? The typical methodology for answering this question is to endorse a steadfast or conciliatory disagreement norm (and not both) on a priori grounds and selected intuitive cases. In this paper, I argue that this methodology is misguided. Instead, a thoroughgoingly Bayesian (...) strategy is what's needed. Such a strategy provides conciliatory norms in appropriate cases and steadfast norms in appropriate cases. I argue, further, that the few extant efforts to address disagreement in the Bayesian spirit are laudable but uncompelling. A modelling, rather than a functional, approach gets us the right norms and is highly general, allowing the epistemologist to deal with (1) multiple epistemic interlocutors, (2) epistemic superiors and inferiors (i.e. not just epistemic peers), and (3) dependence between interlocutors. (shrink)

A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non-public or even private information (learnt by not all or (...) just one individual), or to non-representable information (not representable by any event in the domain where credences are held). I pro- pose a taxonomy of six types of ‘group Bayesianism’. They differ in the information for which Bayesian revision of group credences is required: public representable information, private representable information, public non-representable information, etc. Six corre- sponding theorems establish how individual credences must (not) be aggregated to ensure group Bayesianism of any type, respectively. Aggregating through standard averaging is never permitted; instead, different forms of geometric averaging must be used. One theorem—that for public representable information—is essentially Russell et al.’s central result (with minor corrections). Another theorem—that for public non-representable information—fills a gap in the theory of externally Bayesian opinion pooling. (shrink)

I defend belief-credence dualism, the view that we have both beliefs and credences and both attitudes are equally fundamental. First, I explain belief, credence, and three views on their relationship. Then, I argue for dualism. I do so first by painting a picture of the mind on which belief and credence are two cognitive tools that we use for different purposes. Finally, I respond to two objections to dualism. I conclude that dualism is a promising view, and one that both (...) epistemologists and philosophers of mind should take seriously. (shrink)

In this paper, I offer an analysis of the radical disagreement over the adequacy of string theory. The prominence of string theory despite its notorious lack of empirical support is sometimes explained as a troubling case of science gone awry, driven largely by sociological mechanisms such as groupthink (e.g. Smolin 2006). Others, such as Dawid (2013), explain the controversy by positing a methodological revolution of sorts, according to which string theorists have quietly turned to nonempirical methods of theory assessment given (...) the technological inability to directly test the theory. The appropriate response, according to Dawid, is to acknowledge this development and widen the canons of acceptable scientific methods. As I’ll argue, however, the current situation in fundamental physics does not require either of these responses. Rather, as I’ll suggest, much of the controversy stems from a failure to properly distinguish the “context of justification” from the “context of pursuit”. Both those who accuse string theorists of betraying the scientific method and those who advocate an enlarged conception of scientific methodology objectionably conflate epistemic justification with judgements of pursuit-worthiness. Once we get clear about this distinction and about the different norms governing the two contexts, the current situation in fundamental physics becomes much less puzzling. After defending this diagnosis of the controversy, I’ll show how the argument patterns that have been posited by Dawid as constituting an emergent methodological revolution in science are better off if reworked as arguments belonging to the context of pursuit. (shrink)

It is widely thought in philosophy and elsewhere that parsimony is a theoretical virtue in that if T1 is more parsimonious than T2, then T1 is preferable to T2, other things being equal. This thesis admits of many distinct precisifications. I focus on a relatively weak precisification on which preferability is a matter of probability, and argue that it is false. This is problematic for various alternative precisifications, and even for Inference to the Best Explanation as standardly understood.

ABSTRACTIn this article, we discuss the benefits of Bayesian statistics and how to utilize them in studies of moral education. To demonstrate concrete examples of the applications of Bayesian statistics to studies of moral education, we reanalyzed two data sets previously collected: one small data set collected from a moral educational intervention experiment, and one big data set from a large-scale Defining Issues Test-2 survey. The results suggest that Bayesian analysis of data sets collected from moral educational studies can provide (...) additional useful statistical information, particularly that associated with the strength of evidence supporting alternative hypotheses, which has not been provided by the classical frequentist approach focusing on P-values. Finally, we introduce several practical guidelines pertaining to how to utilize Bayesian statistics, including the utilization of newly developed free statistical software, Jeffrey’s Amazing Statistics Program, and thresholding based on Bayes Factors, to scholars in the field of moral education. (shrink)

This article examines the effect of material evidence upon historiographic hypotheses. Through a series of successive Bayesian conditionalizations, I analyze the extended competition among several hypotheses that offered different accounts of the transition between the Bronze Age and the Iron Age in Palestine and in particular to the “emergence of Israel”. The model reconstructs, with low sensitivity to initial assumptions, the actual outcomes including a complete alteration of the scientific consensus. Several known issues of Bayesian confirmation, including the problem of (...) old evidence, the introduction and confirmation of novel theories and the sensitivity of convergence to uncertain and disputed evidence are discussed in relation to the model’s result and the actual historical process. The most important result is that convergence of probabilities and of scientific opinion is indeed possible when advocates of rival hypotheses hold similar judgment about the factual content of evidence, even if they differ sharply in their historiographic interpretation. This speaks against the contention that understanding of present remains is so irrevocably biased by theoretical and cultural presumptions as to make an objective assessment impossible. (shrink)

Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being silent about stochastic independence. From their current preference axioms, they can derive no more than the definitional properties of a probability measure. In a new framework of twofold uncertainty, we introduce preference axioms that entail not (...) only these definitional properties, but also the stochastic independence of the two sources of uncertainty. This goes some way towards filling a curious lacuna in Bayesian decision theory. (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed (...) by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

When visual attention is directed away from a stimulus, neural processing is weak and strength and precision of sensory data decreases. From a computational perspective, in such situations observers should give more weight to prior expectations in order to behave optimally during a discrimination task. Here we test a signal detection theoretic model that counter-intuitively predicts subjects will do just the opposite in a discrimination task with two stimuli, one attended and one unattended: when subjects are probed to discriminate the (...) unattended stimulus, they rely less on prior information about the probed stimulus’ identity. The model is in part inspired by recent findings that attention reduces trial-by-trial variability of the neuronal population response and that they use a common criterion for attended and unattended trials. In five different visual discrimination experiments, when attention was directed away from the target stimulus, subjects did not adjust their response bias in reaction to a change in stimulus presentation frequency despite being fully informed and despite the presence of performance feedback and monetary and social incentives. This indicates that subjects did not rely more on the priors under conditions of inattention as would be predicted by a Bayes-optimal observer model. These results inform and constrain future models of Bayesian inference in the human brain. (shrink)

Many epistemologists hold that an agent can come to justifiably believe that p is true by seeing that it appears that p is true, without having any antecedent reason to believe that visual impressions are generally reliable. Certain reliabilists think this, at least if the agent’s vision is generally reliable. And it is a central tenet of dogmatism (as described by Pryor (2000) and Pryor (2004)) that this is possible. Against these positions it has been argued (e.g. by Cohen (2005) (...) and White (2006)) that this violates some principles from probabilistic learning theory. To see the problem, let’s note what the dogmatist thinks we can learn by paying attention to how things appear. (The reliabilist says the same things, but we’ll focus on the dogmatist.) Suppose an agent receives an appearance that p, and comes to believe that p. Letting Ap be the proposition that it appears to the agent that p, and → be the material implication, we can say that the agent learns that p, and hence is in a position to infer Ap → p, once they receive the evidence Ap.1 This is surprising, because we can prove the following. (shrink)

Our aim here is to present a result that connects some approaches to justifying countable additivity. This result allows us to better understand the force of a recent argument for countable additivity due to Easwaran (2013). We have two main points. First, Easwaran’s argument in favor of countable additivity should have little persuasive force on those permissive probabilists who have already made their peace with violations of conglomerability. As our result shows, Easwaran’s main premise—the comparative principle—is strictly stronger than conglomerability. (...) Second, with the connections between the comparative principle and other probabilistic concepts clearly in view, we point out that opponents of countable additivity can still make a case that countable additivity is an arbitrary stopping point between finite and full additivity. (shrink)

The coherence of independent reports provides a strong reason to believe that the reports are true. This plausible claim has come under attack from recent results in Bayesian epistemology. Huemer (1997), Olsson (2002, 2005), and Bovens and Hartmann (2003) prove that, under certain probabilistic conditions, coherence cannot increase the probability of the target claim. These results are taken to demonstrate that epistemic coherentism is untenable. To date no one has investigated how these Bayesian results bear on different conceptions of coherence. (...) In this paper, I investigate these Bayesian results by using Paul Thagard’s ECHO model of explanatory coherence (Thagard (2000)). Thagard’s ECHO model provides a natural representation of the evidential significance of multiple independent reports. The ECHO model, in contrast to the Bayesian models, captures the power of coherence in a witness scenario. The conditions that Bayesian models found to be impossible, ECHO models naturally accommodate. This demonstrates that there are different formal tools for representing coherence. I close with a discussion of the differences between the Bayesian model and the ECHO model. (shrink)

Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only preference aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and combine individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs linearly, but achieves only static (...) rationality. Our characterisation of linear-geometric preference aggregation has two corollaries: a characterisation of linear aggregation of values (Harsanyi's Theorem) and a characterisation of geometric aggregation of beliefs. (shrink)

According to Crispin Wright, we have evidential justification for, or knowledge of, various propositions that we quotidianly accept only if we have antecedent justification for accepting general hinge propositions––called ‘cornerstones’––which cannot be evidentially supported. Wright contends that this doesn’t engender scepticism, for we are non-evidentially entitled to accept cornerstones. This paper focuses on the Leaching Worry––the concern that since the epistemic risk of accepting a cornerstone C without evidence for it is significantly high, the epistemic risk of accepting a proposition (...) P for which C is a cornerstone is also significantly high, to the effect that one cannot have evidential justification for, or knowledge that, P. We suggest that Wright’s original response to the Leaching Worry retains its strength if risk is construed in accordance with either of two non-orthodox (non-probabilistic) notions of risk, recently introduced by Duncan Pritchard (modal notion) and Philip Ebert, Martin Smith and Ian Durbach (normic notion). We concede, however, that Luca Moretti’s recent probabilistic version of the Leaching Worry isn't undercut by Wright's original response. We put forward two novel responses: revising the notion of significant epistemic risk originally adopted by Wright, or broadening the range of attitudes towards cornerstones that we are non-evidentially entitled to. (shrink)

It is often argued that while biases routinely influence the generation of scientific theories, a subsequent rational evaluation of such theories will ensure that biases do not affect which theories are ultimately accepted. Against this line of thought, this paper shows that the existence of certain kinds of biases at the generation-stage implies the existence of biases at the evaluation-stage. The key argumentative move is to recognize that a scientist who comes up with a new theory about some phenomena has (...) thereby gained an unusual type of evidence, viz. information about the space of theories that could be true of the phenomena. It follows that if there is bias in the generation of scientific theories in a given domain, then the rational evaluation of theories with reference to the total evidence in that domain will also be biased. (shrink)

Conditionalization is one of the central norms of Bayesian epistemology. But there are a number of competing formulations, and a number of arguments that purport to establish it. In this paper, I explore which formulations of the norm are supported by which arguments. In their standard formulations, each of the arguments I consider here depends on the same assumption, which I call Deterministic Updating. I will investigate whether it is possible to amend these arguments so that they no longer depend (...) on it. As I show, whether this is possible depends on the formulation of the norm under consideration. (shrink)

The Bayesian maxim for rational learning could be described as conservative change from one probabilistic belief or credence function to another in response to newinformation. Roughly: ‘Hold fixed any credences that are not directly affected by the learning experience.’ This is precisely articulated for the case when we learn that some proposition that we had previously entertained is indeed true (the rule of conditionalisation). But can this conservative-change maxim be extended to revising one’s credences in response to entertaining propositions or (...) concepts of which one was previously unaware? The economists Karni and Vierø (2013, 2015) make a proposal in this spirit. Philosophers have adopted effectively the same rule: revision in response to growing awareness should not affect the relative probabilities of propositions in one’s ‘old’ epistemic state. The rule is compelling, but only under the assumptions that its advocates introduce. It is not a general requirement of rationality, or so we argue. We provide informal counterexamples. And we show that, when awareness grows, the boundary between one’s ‘old’ and ‘new’ epistemic commitments is blurred. Accordingly, there is no general notion of conservative change in this setting. (shrink)

Health anxiety is, among other things, a response to a universal epistemological problem about whether changes in one’s body indicate serious illness, a problem that grows more challenging to the individual with age and with every advance in medical science, detection, and treatment. There is growing evidence that dysfunctional metacognitive beliefs – beliefs about thinking – are the driving factor, with dysfunctional substantive beliefs about the probability of illness a side‐effect, and that Metacognitive Therapy (MCT) is more effective than Cognitive (...) Behavioral Therapy (CBT). However, hypochondria is distinct from other forms of anxiety, I argue, in ways that make some reality‐checking techniques of CBT and MCT of limited usefulness. I propose a Re‐Calibration Technique (RCT) that complements these therapies by focusing on a metacognitive belief that has not been studied: the patient’s presumption of his own personal reliability in judging symptoms, an assumption exposed every time he disagrees with a doctor. I propose a technique whereby a patient keeps a long‐term register of every episode of alarm about symptoms and its resolution, possibly years later. When healthcare‐seeking impulses arise the patient then uses his own track record to re‐calibrate his confidence that medical attention is needed. The new technique allows one to improve self‐judgment about whether one has an illness or not by improving self‐knowledge of one’s own reliability. (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)

Peter Achinstein has argued at length and on many occasions that the view according to which evidential support is defined in terms of probability-raising faces serious counterexamples and, hence, should be abandoned. Proponents of the positive probabilistic relevance view have remained unconvinced. The debate seems to be in a deadlock. This paper is an attempt to move the debate forward and revisit some of the central claims within this debate. My conclusion here will be that while Achinstein may be right (...) that his counterexamples undermine probabilistic relevance views of what it is for e to be evidence that h, there is still room for a defence of a related probabilistic view about an increase in being supported, according to which, if p > p, then h is more supported given e than it is without e. My argument relies crucially on an insight from recent work on the linguistics of gradable adjectives. (shrink)

An important problem with machine learning is that when label number n>2, it is very difficult to construct and optimize a group of learning functions, and we wish that optimized learning functions are still useful when prior distribution P(x) (where x is an instance) is changed. To resolve this problem, the semantic information G theory, Logical Bayesian Inference (LBI), and a group of Channel Matching (CM) algorithms together form a systematic solution. MultilabelMultilabel A semantic channel in the G theory consists (...) of a group of truth functions or membership functions. In comparison with likelihood functions, Bayesian posteriors, and Logistic functions used by popular methods, membership functions can be more conveniently used as learning functions without the above problem. In Logical Bayesian Inference (LBI), every label’s learning is independent. For Multilabel learning, we can directly obtain a group of optimized membership functions from a big enough sample with labels, without preparing different samples for different labels. A group of Channel Matching (CM) algorithms are developed for machine learning. For the Maximum Mutual Information (MMI) classification of three classes with Gaussian distributions on a two-dimensional feature space, 2-3 iterations can make mutual information between three classes and three labels surpass 99% of the MMI for most initial partitions. For mixture models, the Expectation-Maxmization (EM) algorithm is improved and becomes the CM-EM algorithm, which can outperform the EM algorithm when mixture ratios are imbalanced, or local convergence exists. The CM iteration algorithm needs to combine neural networks for MMI classifications on high-dimensional feature spaces. LBI needs further studies for the unification of statistics and logic. (shrink)

Trust is defined as a belief of a human H (‘the trustor’) about the ability of an agent A (the ‘trustee’) to perform future action(s). We adopt here dispositionalism and internalism about trust: H trusts A iff A has some internal dispositions as competences. The dispositional competences of A are high-level metacognitive requirements, in the line of a naturalized virtue epistemology. (Sosa, Carter) We advance a Bayesian model of two (i) confidence in the decision and (ii) model uncertainty. To trust (...) A, H demands A to be self-assertive about confidence and able to self-correct its own models. In the Bayesian approach trust can be applied not only to humans, but to artificial agents (e.g. Machine Learning algorithms). We explain the advantage the metacognitive trust when compared to mainstream approaches and how it relates to virtue epistemology. The metacognitive ethics of trust is swiftly discussed. (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)

As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage’s postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To fill this (...) significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework. (shrink)

Intellectual progress involves forming a more accurate picture of the world. But it also figuring out which concepts to use for theorizing about the world. Bayesian epistemology has had much to say about the former aspect of our cognitive lives, but little if at all about the latter. I outline a framework for formulating questions about conceptual change in a broadly Bayesian framework. By enriching the resources of Epistemic Utility Theory with a more expansive conception of epistemic value, I offer (...) a picture of our cognitive economy on which adopting new conceptual tools can sometimes be epistemically rational. (shrink)