Bayesian Reasoning

This paper is about a tension between two theses. The first is Value of Evidence: roughly, the thesis that it is always rational for an agent to gather and use cost-free evidence for making decisions. The second is Rationality of Imprecision: the thesis that an agent can be rationally required to adopt doxastic states that are imprecise, i.e., not representable by a single credence function. While others have noticed this tension, I offer a new diagnosis of it. I show that (...) it arises when an agent with an imprecise doxastic state engages in an unreflective inquiry, an inquiry where they revise their beliefs using an updating rule that doesn't satisfy a weak reflection principle. In such an unreflective inquiry, certain synchronic norms of instrumental rationality can make it instrumentally irrational for an agent to gather and use cost-free evidence. I then go on to propose a diachronic norm of instrumental rationality that preserves Value of Evidence in unreflective inquiries. This, I suggest, may help us reconcile this thesis with Rationality of Imprecision. (shrink)

We are often justified in acting on the basis of evidential confirmation. I argue that such evidence supports belief in non-quantificational generic generalizations, rather than universally quantified generalizations. I show how this account supports, rather than undermines, a Bayesian account of confirmation. Induction from confirming instances of a generalization to belief in the corresponding generic is part of a reasoning instinct that is typically (but not always) correct, and allows us to approximate the predictions that formal epistemology would make.

Bayesians standardly claim that there is rational pressure for agents’ credences to cohere across time because they face bad (epistemic or practical) consequences if they fail to diachronically cohere. But as David Christensen has pointed out, groups of individual agents also face bad consequences if they fail to interpersonally cohere, and there is no general rational pressure for one agent's credences to cohere with another’s. So it seems that standard Bayesian arguments may prove too much. Here, we agree with Christensen (...) that there is no general rational pressure to diachronically cohere, but we argue that there are particular cases in which there is rational pressure to diachronically cohere, as well as particular cases in which interpersonal probabilistic coherence is rationally required. More generally, we suggest that Bayesian arguments for coherence apply whenever a collection (of agents or time slices) has a shared dimension of value and an ability to coordinate their actions in a range of cases relevant to that value. Typically, this shared value and ability to coordinate is very strong across the time slices of one human being, and very weak across different human beings, but there are special cases where these can switch—i.e., some groups of humans will have as much reason for their beliefs to cohere across a particular range of cases as the time slices of one human usually do, but some time slices of a human will have as much freedom to differ in their beliefs from the others as the members of a group usually do. (shrink)

In this article, I will provide a critical overview of the form of non-deductive reasoning commonly known as “Inference to the Best Explanation” (IBE). Roughly speaking, according to IBE, we ought to infer the hypothesis that provides the best explanation of our evidence. In section 2, I survey some contemporary formulations of IBE and highlight some of its putative applications. In section 3, I distinguish IBE from C.S. Peirce’s notion of abduction. After underlining some of the essential elements of IBE, (...) the rest of the entry is organized around an examination of various problems that IBE confronts, along with some extant attempts to address these problems. In section 4, I consider the question of when a fact requires an explanation, since presumably IBE applies only in cases where some explanation is called for. In section 5, I consider the difficult question of how we ought to understand IBE in light of the fact that among philosophers, there is significant disagreement about what constitutes an explanation. In section 6, I consider different strategies for justifying the truth-conduciveness of the explanatory virtues, e.g., simplicity, unification, scope, etc., criteria which play an indispensable role in any given application of IBE. In section 7, I survey some of the most recent literature on IBE, much of which consists of investigations of the status of IBE from the standpoint of the Bayesian philosophy of science. (shrink)

We argue that social deliberation may increase an agent’s confidence and credence under certain circumstances. An agent considers a proposition H and assigns a probability to it. However, she is not fully confident that she herself is reliable in this assignment. She then endorses H during deliberation with another person, expecting him to raise serious objections. To her surprise, however, the other person does not raise any objections to H. How should her attitudes toward H change? It seems plausible that (...) she should increase the credence she assigns to H and, at the same time, increase the reliability she assigns to herself concerning H. A Bayesian model helps us to investigate under what conditions, if any, this is rational. (shrink)

Tenenbaum and Griffiths (2001) have proposed that their Bayesian model of generalisation unifies Shepard’s (1987) and Tversky’s (1977) similarity-based explanations of two distinct patterns of generalisation behaviours by reconciling them under a single coherent task analysis. I argue that this proposal needs refinement: instead of unifying the heterogeneous notion of psychological similarity, the Bayesian approach unifies generalisation by rendering the distinct patterns of behaviours informationally relevant. I suggest that generalisation as a Bayesian inference should be seen as a complement to, (...) instead of a replacement of, similarity-based explanations. Furthermore, I show that the unificatory powers of the Bayesian model of generalisation can contribute to the selection of one of these models of psychological similarity. (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)

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”. 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 Analysis, 73:659–668, 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 Philosophy of Science, 84:359–368,. 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”, 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)

I argue that normative formal epistemology (NFE) is best understood as modelling, in the sense that this is the reconstruction of its methodology on which NFE is doing best. I focus on Bayesianism and show that it has the characteristics of modelling. But modelling is a scientific enterprise, while NFE is normative. I thus develop an account of normative models on which they are idealised representations put to normative purposes. Normative assumptions, such as the transitivity of comparative credence, are characterised (...) as modelling idealisations motivated normatively. I then survey the landscape of methodological options: what might formal epistemologists be up to? I argue the choice is essentially binary: modelling or theorising. If NFE is theorising it is doing very poorly: generating false claims with no clear methodology for separating out what is to be taken seriously. Modelling, by contrast, is a successful methodology precisely suited to the management of useful falsehoods. Regarding NFE as modelling is not costless, however. First, our normative inferences are less direct and are muddied by the presence of descriptive idealisations. Second, our models are purpose-specific and limited in their scope. I close with suggestions for how to adapt our practice. (shrink)

Scientific realism driven by inference to the best explanation (IBE) takes empirically confirmed objects to exist,independent,paceempiricism, of whether those objects are observable or not. This kind of realism, it has beenclaimed, does not need probabilistic reasoning to justify the claim that these objects exist. But I show that thereare scientific contexts in which a non-probabilistic IBE-driven realism leads to a puzzle. Since IBE can be appliedin scientific contexts in which empirical confirmation has not yet been reached, realists will in these (...) contexts becommitted to the existence of empirically unconfirmed objects. As a consequence of such commitments, becausethey lack probabilistic features, the possible empirical confirmation of those objects is epistemically redundantwith respect to realism. (shrink)

One is occasionally reminded of Foucault's proclamation in a 1970 interview that "perhaps, one day this century will be known as Deleuzian." Less often is one compelled to update and restart with a supplementary counter-proclamation of the mathematician, David Lindley: "the twenty-first century would be a Bayesian era..." The verb tenses of both are conspicuous. // To critically attend to what is today often feared and demonized, but also revered, deployed, and commonly referred to as algorithm(s), one cannot avoid the (...) mathematical and philosophical legacies of probability. // But attending to these probabilistic or Bayesian legacies must include an undeniable theological legacy in which they remain entangled. // We are not, today, discovering quirky theological metaphors in contemporary technics. It's the other way around. The technologies are mere metaphors of past theologies. (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)

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

Debunking arguments in ethics contend that our moral beliefs have dubious evolutionary, cultural, or psychological origins – hence concluding that we should doubt such beliefs. Debates about debunking are often couched in coarse-grained terms – about whether our moral beliefs are justified or not, for instance. In this paper, I propose a more detailed Bayesian analysis of debunking arguments, which proceeds in the fine-grained framework of rational confidence. Such analysis promises several payoffs: it highlights how debunking arguments don’t affect all (...) agents, but rather only those agents who updated on their intuitions using a specific range of evidentiary weights; it underscores how the debunkers shouldn’t conclude that we should reduce confidence beyond some threshold, but rather only that we should reduce confidence by some amount; and it proposes a method of integrating different kinds of evidence – about the kinds of epistemic flaws at play, about the different possible origins of our moral beliefs, about the background normative assumptions we’re entitled to make – in order to arrive at a rational moral credence in light of debunking. (shrink)

Evidentialists say that a necessary condition of sound epistemic reasoning is that our beliefs reflect only our evidence. This thesis arguably conflicts with standard Bayesianism, due to the importance of prior probabilities in the latter. Some evidentialists have responded by modelling belief-states using imprecise probabilities (Joyce 2005). However, Roger White (2010) and Aron Vallinder (2018) argue that this Imprecise Bayesianism is incompatible with evidentialism due to “inertia”, where Imprecise Bayesian agents become stuck in a state of ambivalence towards hypotheses. Additionally, (...) escapes from inertia apparently only create further conflicts with evidentialism. This dilemma gives a reason for evidentialist imprecise probabilists to look for alternatives without inertia. I shall argue that Henry E. Kyburg’s approach offers an evidentialist-friendly imprecise probability theory without inertia, and that its relevant anti-inertia features are independently justified. I also connect the traditional epistemological debates concerning the “ethics of belief” more systematically with formal epistemology than has been hitherto done. (shrink)

In this paper, we ask: how should an agent who has incoherent credences update when they learn new evidence? The standard Bayesian answer for coherent agents is that they should conditionalize; however, this updating rule is not defined for incoherent starting credences. We show how one of the main arguments for conditionalization, the Dutch strategy argument, can be extended to devise a target property for updating plans that can apply to them regardless of whether the agent starts out with coherent (...) or incoherent credences. The main idea behind this extension is that the agent should avoid updating plans that increase the possible sure loss from Dutch strategies. This happens to be equivalent to avoiding updating plans that increase incoherence according to a distance-based incoherence measure. (shrink)

In a recent paper, Pettigrew (2021) reports a generalization of the celebrated accuracy-dominance theorem due to Predd et al. (2009). But Pettigrew’s proof is incorrect. I will explain the mistakes and provide a correct proof.

English abstract: This paper discusses the delicate relationship between traditional epistemology and the increasingly influential probabilistic (or ‘Bayesian’) approach to epistemology. The paper introduces some of the key ideas of probabilistic epistemology, including credences or degrees of belief, Bayes’ theorem, conditionalization, and the Dutch Book argument. The tension between traditional and probabilistic epistemology is brought out by considering the lottery and preface paradoxes as they relate to rational (binary) belief and credence respectively. It is then argued that this tension can (...) be alleviated by rejecting the requirement that rational (binary) beliefs must be consistent and closed under logical entailment. Instead, it is suggested that this logical requirement applies to a different type of binary propositional attitude, viz. acceptance. (shrink)

One of the most difficult problems in the foundations of physics is what gives rise to the arrow of time. Since the fundamental dynamical laws of physics are (essentially) symmetric in time, the explanation for time's arrow must come from elsewhere. A promising explanation introduces a special cosmological initial condition, now called the Past Hypothesis: the universe started in a low-entropy state. Unfortunately, in a universe where there are many copies of us (in the distant ''past'' or the distant ''future''), (...) the Past Hypothesis is not enough; we also need to postulate self-locating (de se) probabilities. However, I show that we can similarly use self-locating probabilities to strengthen its rival---the Fluctuation Hypothesis, leading to in-principle empirical underdetermination and radical epistemological skepticism. The underdetermination is robust in the sense that it is not resolved by the usual appeal to 'empirical coherence' or 'simplicity.' That is a serious problem for the vision of providing a completely scientific explanation of time's arrow. (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)

While practitioners think highly of randomized studies, some philosophers argue that there is no epistemic reason to randomize. Here I show that their arguments do not entail their conclusion. Moreover, I provide novel reasons for randomizing in the context of interventional studies. The overall discussion provides a unified framework for assessing baseline balance, one that holds for interventional and observational studies alike. The upshot: practitioners’ strong preference for randomized studies can be defended in some cases, while still offering a nuanced (...) approach to evidence-appraisal, one where not all non-randomized studies are treated equally. (shrink)

In this paper, I offer a conceptual framework for understanding and evaluating personal identity claims. I analyze ontological and political properties of personal identity separately, arguing that their conceptual (if not practical) separation is necessary for a proper evaluation of different identity claims. I use probability theory to bypass some of the logical difficulties in conceptualizing personal identity and discuss a case of transitional identification. Finally, I outline the guidelines for a justified liberal policy of recognition.

This paper defends a novel sceptical response to the fine-tuning argument for the existence of God (FTA). According to this response, even if FTA can establish, what I call, the confirmation proposition: ‘fine-tuning confirms the God hypothesis’, there is no reason to think that a strengthening of FTA can establish the evidence-favouring proposition: ‘fine-tuning favours the God hypothesis over its competitors’. My argument is that, any criteria for the explanation of fine-tuning that permit us to take the God hypothesis seriously (...) ought to make us sceptical that fine-tuning favours the God hypothesis over its competitors. As taking the God hypothesis seriously requires us to give a fair hearing to all sorts of non-theistic explanations, including the so-called weird sorts of atheism. (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, M. 1997. “Probability and Coherence Justification.” Southern Journal of Philosophy 35: 463–72, Olsson, E. 2002. “What is the Problem of Coherence and Truth?” Journal of Philosophy XCIX : 246–72, Olsson, E. 2005. Against Coherence: Truth, Probability, and Justification. Oxford University Press., Bovens, L., and S. Hartmann. 2003. Bayesian Epistemology. Oxford University Press, 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)

Why do we use epistemic modals like 'might'? According to Factualism, the function of 'might' is to exchange information about state-of-affairs in the modal universe. As an alternative to Factualism, this paper offers a game-theoretic rationale for epistemic possibility operators in a Bayesian setting. The background picture is one whereby communication facilitates coordination, but coordination could fail if there's too much uncertainty, since the players' ability to share a belief is undermined. However, 'might' and related expressions can be used to (...) reveal one's uncertainty, and exploit this to coordinate despite the lack of a common epistemic ground. The final result is a way to articulate a non-Factualist view of epistemic possibility modals that builds on their standard semantics. (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)

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)

A prominent pillar of Bayesian philosophy is that, relative to just a few constraints, priors “wash out” in the limit. Bayesians often appeal to such asymptotic results as a defense against charges of excessive subjectivity. But, as Seidenfeld and coauthors observe, what happens in the short run is often of greater interest than what happens in the limit. They use this point as one motivation for investigating the counterintuitive short run phenomenon of dilation since, it is alleged, “dilation contrasts with (...) the asymptotic merging of posterior probabilities reported by Savage (1954) and by Blackwell and Dubins (1962)” (Herron et al., 1994). A partition dilates an event if, relative to every cell of the partition, uncertainty concerning that event increases. The measure of uncertainty relevant for dilation, however, is not the same measure that is relevant in the context of results concerning whether priors wash out or “opinions merge.” Here, we explicitly investigate the short run behavior of the metric relevant to merging of opinions. As with dilation, it is possible for uncertainty (as gauged by this metric) to increase relative to every cell of a partition. We call this phenomenon distention. It turns out that dilation and distention are orthogonal phenomena. (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)

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)

Recent objections to epistemic permissivism have a metaepistemic flavor. Impermissivists argue that their view best accounts for connections between rationality, planning and deference. Impermissivism is also taken to best explain the value of rational belief and normative assessment. These objections pose a series of metaepistemic explanatory challenges for permissivism. In this paper, I illustrate how permissivists might meet their explanatory burdens by developing two permissivist metaepistemic views which fare well against the explanatory challenges.

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.