Bayesian Reasoning

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)

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)

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.

I give a critical overview of the volume, focusing my attention on the chapters that deal with the explanationist response to skepticism.

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)

This essay has two aims. The first is to correct an increasingly popular way of misunderstanding Belot's Orgulity Argument. The Orgulity Argument charges Bayesianism with defect as a normative epistemology. For concreteness, our argument focuses on Cisewski et al.'s recent rejoinder to Belot. The conditions that underwrite their version of the argument are too strong and Belot does not endorse them on our reading. A more compelling version of the Orgulity Argument than Cisewski et al. present is available, however---a point (...) that we make by drawing an analogy with de Finetti's argument against mandating countable additivity. Having presented the best version of the Orgulity Argument, our second aim is to develop a reply to it. We extend Elga's idea of appealing to finitely additive probability to show that the challenge posed by the Orgulity Argument can be met. (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.

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.

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)

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)

It is a commonplace in epistemology that credences should equal known chances. It is less clear, however, that conditional credences should do so, too. Following Ramsey, this paper proposes a counterfactual interpretation of conditional probability which provides a justification for this equality without relying on the Principal Principle. As a result, we obtain a refined view of Bayesian inference where both learning and supposing have a place.

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)

It is often argued that while biases routinely influence the generation of scientific theories (in the ‘context of discovery’), a subsequent rational evaluation of such theories (in the ‘context of justification’) 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)

According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Ian Hacking (1967), I develop a version of Bayesianism that permits logical ignorance. This includes an account of the synchronic norms that govern a logically ignorant individual at any given time, (...) as well as an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations. (shrink)

It is sometimes claimed that the Bayesian framework automatically implements Ockham’s razor—that conditionalizing on data consistent with both a simple theory and a complex theory more or less inevitably favours the simpler theory. It is shown here that the automatic razor doesn’t in fact cut it for certain mundane curve-fitting problems.

Chancy modus ponens is the following inference scheme: ‘probably φ’, ‘if φ, then ψ’, therefore, ‘probably ψ’. I argue that Chancy modus ponens is invalid in general. I further argue that the invalidity of Chancy modus ponens sheds new light on the alleged counterexample to modus ponens presented by McGee. I close by observing that, although Chancy modus ponens is invalid in general, we can recover a restricted sense in which this scheme of inference is valid.

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?

In recent years, permissivism—the claim that a body of evidence can rationalize more than one response—has enjoyed somewhat of a revival. But it is once again being threatened, this time by a host of new and interesting arguments that, at their core, are challenging the permissivist to explain why rationality matters. A version of the challenge that I am especially interested in is this: if permissivism is true, why should we expect the rational credences to be more accurate than the (...) irrational ones? My aim is to turn this challenge on its head and argue that, actually, those who deny permissivism will have a harder time responding to such a challenge than those who accept it. (shrink)

Orthodox Bayesianism is a highly idealized theory of how we ought to live our epistemic lives. One of the most widely discussed idealizations is that of logical omniscience: the assumption that an agent’s degrees of belief must be probabilistically coherent to be rational. It is widely agreed that this assumption is problematic if we want to reason about bounded rationality, logical learning, or other aspects of non-ideal epistemic agency. Yet, we still lack a satisfying way to avoid logical omniscience within (...) a Bayesian framework. Some proposals merely replace logical omniscience with a different logical idealization; others sacrifice all traits of logical competence on the altar of logical non-omniscience. We think a better strategy is available: by enriching the Bayesian framework with tools that allow us to capture what agents can and cannot infer given their limited cognitive resources, we can avoid logical omniscience while retaining the idea that rational degrees of belief are in an important way constrained by the laws of probability. In this paper, we offer a formal implementation of this strategy, show how the resulting framework solves the problem of logical omniscience, and compare it to orthodox Bayesianism as we know it. (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)

In this chapter I analyse an objection to phenomenal conservatism to the effect that phenomenal conservatism is unacceptable because it is incompatible with Bayesianism. I consider a few responses to it and dismiss them as misled or problematic. Then, I argue that this objection doesn’t go through because it rests on an implausible formalization of the notion of seeming-based justification. In the final part of the chapter, I investigate how seeming-based justification and justification based on one’s reflective belief that one (...) has a seeming interact with one another. (shrink)

In the biomedical context, policy makers face a large amount of potentially discordant evidence from different sources. This prompts the question of how this evidence should be aggregated in the interests of best-informed policy recommendations. The starting point of our discussion is Hunter and Williams’ recent work on an automated aggregation method for medical evidence. Our negative claim is that it is far from clear what the relevant criteria for evaluating an evidence aggregator of this sort are. What is the (...) appropriate balance between explicitly coded algorithms and implicit reasoning involved, for instance, in the packaging of input evidence? In short: What is the optimal degree of ‘automation’? On the positive side: We propose the ability to perform an adequate robustness analysis as the focal criterion, primarily because it directs efforts to what is most important, namely, the structure of the algorithm and the appropriate extent of automation. Moreover, where there are resource constraints on the aggregation process, one must also consider what balance between volume of evidence and accuracy in the treatment of individual evidence best facilitates inference. There is no prerogative to aggregate the total evidence available if this would in fact reduce overall accuracy. (shrink)

We conceptualize observation selection effects (OSEs) by considering how a shift from one process of observation to another affects discrimination-conduciveness, by which we mean the degree to which possible observations discriminate between hypotheses, given the observation process at work. OSEs in this sense come in degrees and are causal, where the cause is the shift in process, and the effect is a change in degree of discrimination-conduciveness. We contrast our understanding of OSEs with others that have appeared in the literature. (...) After describing conditions of adequacy that an acceptable measure of degree of discrimination-conduciveness must satisfy, we use those conditions of adequacy to evaluate several possible measures. We also discuss how the effect of shifting from one observation process to another might be measured. We apply our framework to several examples, including the ravens paradox and the phenomenon of publication bias. (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)

A Bayesian mind is, at its core, a rational mind. Bayesianism is thus well-suited to predict and explain mental processes that best exemplify our ability to be rational. However, evidence from belief acquisition and change appears to show that we do not acquire and update information in a Bayesian way. Instead, the principles of belief acquisition and updating seem grounded in maintaining a psychological immune system rather than in approximating a Bayesian processor.

Stochastic independence (SI) 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, hence a property that any theory on the foundations of probability should be able to account for. Bayesian decision theory, which is one such theory, appears to be wanting in this respect. In Savage's classic treatment, postulates on preferences under uncertainty are shown to entail a (...) subjective expected utility (SEU) representation, and this permits asserting only the existence and uniqueness of a subjective probability, regardless of its properties. What is missing is a preference postulate that would specifically connect with the SI property. The paper develops a version of Bayesian decision theory that fills this gap. In a framework of multiple sources of uncertainty, we introduce preference conditions that jointly entail the SEU representation and the property that the subjective probability in this representation treats the sources of uncertainty as being stochastically independent. We give two representation theorems of graded complexity to demonstrate the power of our preference conditions. Two sections of comments follow, one connecting the theorems with earlier results in Bayesian decision theory, and the other connecting them with the foundational discussion on SI in probability theory and the philosophy of probability. Appendices offer more technical material. (shrink)

Suppose that two competing norms, N1 and N2, can be identified such that a given person’s response can be interpreted as correct according to N1 but incorrect according to N2. Which of these two norms, if any, should one use to interpret such a response? In this paper we seek to address this fundamental problem by studying individual variation in the interpretation of conditionals by establishing individual profiles of the participants based on their case judgments and reflective attitudes. To investigate (...) the participants’ reflective attitudes we introduce a new experimental paradigm called the Scorekeeping Task. As a case study, we identify the participants who follow the Suppositional Theory of conditionals (N1) versus Inferentialism (N2) and investigate to what extent internally consistent competence models can be reconstructed for the participants on this basis. After extensive empirical investigations, an apparent reasoning error with and-to-if inferences was found in one of these two groups. The implications of this case study for debates on the proper role of normative considerations in psychology are discussed. (shrink)

Fading Foundations: Probability and the Regress Problem. By Atkinson David, Peijnenburg Jeanne.

Traditional Bayesianism requires that an agent’s degrees of belief be represented by a real-valued, probabilistic credence function. However, in many cases it seems that our evidence is not rich enough to warrant such precision. In light of this, some have proposed that we instead represent an agent’s degrees of belief as a set of credence functions. This way, we can respect the evidence by requiring that the set, often called the agent’s credal state, includes all credence functions that are in (...) some sense compatible with the evidence. One known problem for this evidentially motivated imprecise view is that in certain cases, our imprecise credence in a particular proposition will remain the same no matter how much evidence we receive. In this article I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid it without compromising the initial evidentialist motivation. _1_ Introduction _2_ Precision and Its Problems _3_ Imprecise Bayesianism and Respecting Ambiguous Evidence _4_ Local Belief Inertia _5_ From Local to Global Belief Inertia _6_ Responding to Global Belief Inertia _7_ Conclusion. (shrink)

I argue elsewhere (Roche 2014) that evidence of evidence is evidence under screening-off. Tal and Comesaña (2017) argue that my appeal to screening-off is subject to two objections. They then propose an evidence of evidence thesis involving the notion of a defeater. There is much to learn from their very careful discussion. I argue, though, that their objections fail and that their evidence of evidence thesis is open to counterexample.

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)

Accuracy-first accounts of rational learning attempt to vindicate the intuitive idea that, while rationally-formed belief need not be true, it is nevertheless likely to be true. To this end, they attempt to show that the Bayesian's rational learning norms are a consequence of the rational pursuit of accuracy. Existing accounts fall short of this goal, for they presuppose evidential norms which are not and cannot be vindicated in terms of the single-minded pursuit of accuracy. I propose an alternative account, according (...) to which learning experiences rationalize changes in the way you value accuracy, which in turn rationalize changes in belief. I show that this account is capable of vindicating the Bayesian's rational learning norms in terms of the single-minded pursuit of accuracy, so long as accuracy is rationally valued. (shrink)

Crispin Wright maintains that the architecture of perceptual justification is such that we can acquire justification for our perceptual beliefs only if we have antecedent justification for ruling out any sceptical alternative. Wright contends that this principle doesn’t elicit scepticism, for we are non-evidentially entitled to accept the negation of any sceptical alternative. Sebastiano Moruzzi has challenged Wright’s contention by arguing that since our non-evidential entitlements don’t remove the epistemic risk of our perceptual beliefs, they don’t actually enable us to (...) acquire justification for these beliefs. In this paper I show that Wright’s responses to Moruzzi are ineffective and that Moruzzi’s argument is validated by probabilistic reasoning. I also suggest that Wright cannot answer Moruzzi’s challenge without weakening the support available for his conception of the architecture of perceptual justification. (shrink)

This paper offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency. Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: change in the commitment to the reason, the reason’s sensitivity and selectivity to the claim, one’s prior commitment to the claim, and the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, and (...) may indeed serve to correct, the informal understanding and applications of the RSA criteria concerning their conceptual dependence, their function as update-thresholds, and their status as obligatory rather than permissive norms, but also show how these formal and informal normative approachs can in fact align. (shrink)

Bayesian confirmation theory is rife with confirmation measures. Many of them differ from each other in important respects. It turns out, though, that all the standard confirmation measures in the literature run counter to the so-called “Reverse Matthew Effect” (“RME” for short). Suppose, to illustrate, that H1 and H2 are equally successful in predicting E in that p(E | H1)/p(E) = p(E | H2)/p(E) > 1. Suppose, further, that initially H1 is less probable than H2 in that p(H1) < p(H2). (...) Then by RME it follows that the degree to which E confirms H1 is greater than the degree to which it confirms H2. But by all the standard confirmation measures in the literature, in contrast, it follows that the degree to which E confirms H1 is less than or equal to the degree to which it confirms H2. It might seem, then, that RME should be rejected as implausible. Festa (2012), however, argues that there are scientific contexts in which RME holds. If Festa’s argument is sound, it follows that there are scientific contexts in which none of the standard confirmation measures in the literature is adequate. Festa’s argument is thus interesting, important, and deserving of careful examination. I consider five distinct respects in which E can be related to H, use them to construct five distinct ways of understanding confirmation measures, which I call “Increase in Probability”, “Partial Dependence”, “Partial Entailment”, “Partial Discrimination”, and “Popper Corroboration”, and argue that each such way runs counter to RME. The result is that it is not at all clear that there is a place in Bayesian confirmation theory for RME. (shrink)

Data from medical research are typically summarized with various types of outcome measures. We present three arguments in favor of absolute over relative outcome measures. The first argument is from cognitive bias: relative measures promote the reference class fallacy and the overestimation of treatment effectiveness. The second argument is decision-theoretic: absolute measures are superior to relative measures for making a decision between interventions. The third argument is causal: interpreted as measures of causal strength, absolute measures satisfy a set of desirable (...) properties, but relative measures do not. Absolute outcome measures outperform relative measures on all counts. (shrink)

In this public debate with Philippe Deterre (research director in immunology at the CNRS) – held at l'Enclos Rey in Paris' 15th district during the biennial Conference of the Réseau Blaise Pascal in March 2017 –, I defended the usefulness of natural theology. I first clarify theology's nature and understanding, then I speak about a tradition that upheld the public and exterior knowledge of God, and make an effort to show the presence of a theme reminiscent of natural theology behind (...) attempts at the good life. I then ask whether natural theology would only exist for the Christian. In the reply to my opponent's own reaction, I insist on the incongruity of separating our knowledge of God from our knowledge of science's wonderful discoveries, I ask whether nature could be said to be crafty and "ingenious," and I conclude by building a case for the return of God in public conversation, as part of an effort that our world needs in terms of finding back its compass, and restoring an ideal of living rationally. (shrink)

to appear in Szabó Gendler, T. & J. Hawthorne (eds.) Oxford Studies in Epistemology volume 6 -/- We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? (...) And how do they relate to the individual credences assigned by the members of the particular group in question? According to the credal judgment aggregation principle, Linear Pooling, the credence function of a group should be a weighted average or linear pool of the credence functions of the individuals in the group. In this paper, I give an argument for Linear Pooling based on considerations of accuracy. And I respond to two standard objections to the aggregation principle. (shrink)

Given a few assumptions, the probability of a conjunction is raised, and the probability of its negation is lowered, by conditionalising upon one of the conjuncts. This simple result appears to bring Bayesian confirmation theory into tension with the prominent dogmatist view of perceptual justification – a tension often portrayed as a kind of ‘Bayesian objection’ to dogmatism. In a recent paper, David Jehle and Brian Weatherson observe that, while this crucial result holds within classical probability theory, it fails within (...) intuitionistic probability theory. They conclude that the dogmatist who is willing to take intuitionistic logic seriously can make a convincing reply to the Bayesian objection. In this paper, I argue that this conclusion is premature – the Bayesian objection can survive the transition from classical to intuitionistic probability, albeit in a slightly altered form. I shall conclude with some general thoughts about what the Bayesian objection to dogmatism does and doesn’t show. (shrink)

Bayesian confirmation theory is rife with confirmation measures. Zalabardo focuses on the probability difference measure, the probability ratio measure, the likelihood difference measure, and the likelihood ratio measure. He argues that the likelihood ratio measure is adequate, but each of the other three measures is not. He argues for this by setting out three adequacy conditions on confirmation measures and arguing in effect that all of them are met by the likelihood ratio measure but not by any of the other (...) three measures. Glass and McCartney, hereafter “G&M,” accept the conclusion of Zalabardo’s argument along with each of the premises in it. They nonetheless try to improve on Zalabardo’s argument by replacing his third adequacy condition with a weaker condition. They do this because of a worry to the effect that Zalabardo’s third adequacy condition runs counter to the idea behind his first adequacy condition. G&M have in mind confirmation in the sense of increase in probability: the degree to which E confirms H is a matter of the degree to which E increases H’s probability. I call this sense of confirmation “IP.” I set out four ways of precisifying IP. I call them “IP1,” “IP2,” “IP3,” and “IP4.” Each of them is based on the assumption that the degree to which E increases H’s probability is a matter of the distance between p and a certain other probability involving H. I then evaluate G&M’s argument in light of them. (shrink)

We argued that explanatoriness is evidentially irrelevant in the following sense: Let H be a hypothesis, O an observation, and E the proposition that H would explain O if H and O were true. Then our claim is that Pr = Pr. We defended this screening-off thesis by discussing an example concerning smoking and cancer. Climenhaga argues that SOT is mistaken because it delivers the wrong verdict about a slightly different smoking-and-cancer case. He also considers a variant of SOT, called (...) “SOT*”, and contends that it too gives the wrong result. We here reply to Climenhaga’s arguments and suggest that SOT provides a criticism of the widely held theory of inference called “inference to the best explanation”. (shrink)

Some modern cosmological models predict the appearance of Boltzmann Brains: observers who randomly fluctuate out of a thermal bath rather than naturally evolving from a low-entropy Big Bang. A theory in which most observers are of the Boltzmann Brain type is generally thought to be unacceptable, although opinions differ. I argue that such theories are indeed unacceptable: the real problem is with fluctuations into observers who are locally identical to ordinary observers, and their existence cannot be swept under the rug (...) by a choice of probability distributions over observers. The issue is not that the existence of such observers is ruled out by data, but that the theories that predict them are cognitively unstable: they cannot simultaneously be true and justifiably believed. (shrink)

There are many scientific and everyday cases where each of Pr and Pr is high and it seems that Pr is high. But high probability is not transitive and so it might be in such cases that each of Pr and Pr is high and in fact Pr is not high. There is no issue in the special case where the following condition, which I call “C1”, holds: H 1 entails H 2. This condition is sufficient for transitivity in high (...) probability. But many of the scientific and everyday cases referred to above are cases where it is not the case that H 1 entails H 2. I consider whether there are additional conditions sufficient for transitivity in high probability. I consider three candidate conditions. I call them “C2”, “C3”, and “C2&3”. I argue that C2&3, but neither C2 nor C3, is sufficient for transitivity in high probability. I then set out some further results and relate the discussion to the Bayesian requirement of coherence. (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.

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.

Defenders of Inference to the Best Explanation claim that explanatory factors should play an important role in empirical inference. They disagree, however, about how exactly to formulate this role. In particular, they disagree about whether to formulate IBE as an inference rule for full beliefs or for degrees of belief, as well as how a rule for degrees of belief should relate to Bayesianism. In this essay I advance a new argument against non-Bayesian versions of IBE. My argument focuses on (...) cases in which we are concerned with multiple levels of explanation of some phenomenon. I show that in many such cases, following IBE as an inference rule for full beliefs leads to deductively inconsistent beliefs, and following IBE as a non-Bayesian updating rule for degrees of belief leads to probabilistically incoherent degrees of belief. (shrink)

Dogmatism is sometimes thought to be incompatible with Bayesian models of rational learning. I show that the best model for updating imprecise credences is compatible with dogmatism.