Enjoying great popularity in decision theory, epistemology, and philosophy of science, Bayesianism as understood here is fundamentally concerned with epistemically ideal rationality. It assumes a tight connection between evidential probability and ideally rational credence, and usually interprets evidential probability in terms of such credence. Timothy Williamson challenges Bayesianism by arguing that evidential probabilities cannot be adequately interpreted as the credences of an ideal agent. From this and his assumption that evidential probabilities cannot be interpreted (...) as the actual credences of human agents either, he concludes that no interpretation of evidential probabilities in terms of credence is adequate. I argue to the contrary. My overarching aim is to show on behalf of Bayesians how one can still interpret evidential probabilities in terms of ideally rational credence and how one can maintain a tight connection between evidential probabilities and ideally rational credence even if the former cannot be interpreted in terms of the latter. By achieving this aim I illuminate the limits and prospects of Bayesianism. (shrink)

This paper defends David Hume's "Of Miracles" from John Earman's (2000) Bayesian attack by showing that Earman misrepresents Hume's argument against believing in miracles and misunderstands Hume's epistemology of probable belief. It argues, moreover, that Hume's account of evidence is fundamentally non-mathematical and thus cannot be properly represented in a Bayesian framework. Hume's account of probability is show to be consistent with a long and laudable tradition of evidential reasoning going back to ancient Roman law.

NOTE: This paper is a reworking of some aspects of an earlier paper – ‘What else justification could be’ and also an early draft of chapter 2 of Between Probability and Certainty. I'm leaving it online as it has a couple of citations and there is some material here which didn't make it into the book (and which I may yet try to develop elsewhere). My concern in this paper is with a certain, pervasive picture of epistemic justification. On (...) this picture, acquiring justification for believing something is essentially a matter of minimising one’s risk of error – so one is justified in believing something just in case it is sufficiently likely, given one’s evidence, to be true. This view is motivated by an admittedly natural thought: If we want to be fallibilists about justification then we shouldn’t demand that something be certain – that we completely eliminate error risk – before we can be justified in believing it. But if justification does not require the complete elimination of error risk, then what could it possibly require if not its minimisation? If justification does not require epistemic certainty then what could it possibly require if not epistemic likelihood? When all is said and done, I’m not sure that I can offer satisfactory answers to these questions – but I will attempt to trace out some possible answers here. The alternative picture that I’ll outline makes use of a notion of normalcy that I take to be irreducible to notions of statistical frequency or predominance. (shrink)

Once upon a time, some thought that indicative conditionals could be effectively analyzed as material conditionals. Later on, an alternative theoretical construct has prevailed and received wide acceptance, namely, the conditional probability of the consequent given the antecedent. Partly following critical remarks recently ap- peared in the literature, we suggest that evidential support—rather than conditional probability alone—is key to understand indicative conditionals. There have been motivated concerns that a theory of evidential conditionals (unlike their more tra- (...) ditional counterparts) cannot generate a sufficiently interesting logical system. Here, we will describe results dispelling these worries. Happily, and perhaps surprisingly, appropriate technical variations of Ernst Adams’s classical approach allow for the construction of a logic of evidential conditionals with distinctive fea- tures, which is also well-behaved and reasonably strong. (shrink)

Evidential support is often equated with confirmation, where evidence supports hypothesis H if and only if it increases the probability of H. This article argues against this received view. As the author shows, support is a comparative notion in the sense that increase-in-probability is not. A piece of evidence can confirm H, but it can confirm alternatives to H to the same or greater degree; and in such cases, it is at best misleading to conclude that the (...) evidence supports H. The author puts forward an alternative view that defines support in terms of measures of degree of confirmation. The proposed view is both sufficiently comparative and able to accommodate the increase-in-probability aspect of support. The author concludes that the proposed measure-theoretic approach to support provides a superior alternative to the standard confirmatory approach. (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)

Many philosophers argue that Keynes’s concept of the “weight of arguments” is an important aspect of argument appraisal. The weight of an argument is the quantity of relevant evidence cited in the premises. However, this dimension of argumentation does not have a received method for formalisation. Kyburg has suggested a measure of weight that uses the degree of imprecision in his system of “Evidential Probability” to quantify weight. I develop and defend this approach to measuring weight. I illustrate (...) the usefulness of this measure by employing it to develop an answer to Popper’s Paradox of Ideal Evidence. (shrink)

Credences are beliefs about evidential probabilities. We give the view an assessment-sensitive formulation, show how it evades the standard objections, and give several arguments in support.

Is evidential support transitive? The answer is negative when evidential support is understood as confirmation so that X evidentially supports Y if and only if p(Y | X) > p(Y). I call evidential support so understood “support” (for short) and set out three alternative ways of understanding evidential support: support-t (support plus a sufficiently high probability), support-t* (support plus a substantial degree of support), and support-tt* (support plus both a sufficiently high probability and a (...) substantial degree of support). I also set out two screening-off conditions (under which support is transitive): SOC1 and SOC2. It has already been shown that support-t is non-transitive in the general case (where it is not required that SOC1 holds and it is not required that SOC2 holds), in the special case where SOC1 holds, and in the special case where SOC2 holds. I introduce two rather weak adequacy conditions on support measures and argue that on any support measure meeting those conditions it follows that neither support-t* nor support-tt* is transitive in the general case, in the special case where SOC1 holds, or in the special case where SOC2 holds. I then relate some of the results to Douven’s evidential support theory of conditionals along with a few rival theories. (shrink)

Probability can be used to measure degree of belief in two ways: objectively and subjectively. The objective measure is a measure of the rational degree of belief in a proposition given a set of evidential propositions. The subjective measure is the measure of a particular subject’s dispositions to decide between options. In both measures, certainty is a degree of belief 1. I will show, however, that there can be cases where one belief is stronger than another yet both (...) beliefs are plausibly measurable as objectively and subjectively certain. In ordinary language, we can say that while both beliefs are certain, one belief is more certain than the other. I will then propose second, non probabilistic dimension of measurement, which tracks this variation in certainty in such cases where the probability is 1. A general principle of rationality is that one’s subjective degree of belief should match the rational degree of belief given the evidence available. In this paper I hope to show that it is also a rational principle that the maximum stake size at which one should remain certain should match the rational weight of certainty given the evidence available. Neither objective nor subjective measures of certainty conform to the axioms of probability, but instead are measured in utility. This has the consequence that, although it is often rational to be certain to some degree, there is no such thing as absolute certainty. (shrink)

John Maynard Keynes’s A Treatise on Probability is the seminal text for the logical interpretation of probability. According to his analysis, probabilities are evidential relations between a hypothesis and some evidence, just like the relations of deductive logic. While some philosophers had suggested similar ideas prior to Keynes, it was not until his Treatise that the logical interpretation of probability was advocated in a clear, systematic and rigorous way. I trace Keynes’s influence in the philosophy of (...) probability through a heterogeneous sample of thinkers who adopted his interpretation. This sample consists of Frederick C. Benenson, Roy Harrod, Donald C. Williams, Henry E. Kyburg and David Stove. The ideas of Keynes prove to be adaptable to their diverse theories of probability. My discussion indicates both the robustness of Keynes’s probability theory and the importance of its influence on the philosophers whom I describe. I also discuss the Problem of the Priors. I argue that none of those I discuss have obviously improved on Keynes’s theory with respect to this issue. (shrink)

The epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object’s weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks what probabilities (...) are not determined in this way—these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the “problem of the priors.”. (shrink)

Reasoning from inconclusive evidence, or ‘induction’, is central to science and any applications we make of it. For that reason alone it demands the attention of philosophers of science. This Element explores the prospects of using probability theory to provide an inductive logic, a framework for representing evidential support. Constraints on the ideal evaluation of hypotheses suggest that overall support for a hypothesis is represented by its probability in light of the total evidence, and incremental support, or (...) confirmation, indicated by an increased probability given the evidence than otherwise. This proposal is shown to have the capacity to reconstruct many canons of the scientific method and inductive inference. Along the way, significant objections are discussed, such as the challenge from inductive scepticism and the objection that the probabilistic approach makes evidential support arbitrary. (shrink)

The article is a plea for ethicists to regard probability as one of their most important concerns. It outlines a series of topics of central importance in ethical theory in which probability is implicated, often in a surprisingly deep way, and lists a number of open problems. Topics covered include: interpretations of probability in ethical contexts; the evaluative and normative significance of risk or uncertainty; uses and abuses of expected utility theory; veils of ignorance; Harsanyi’s aggregation theorem; (...) population size problems; equality; fairness; giving priority to the worse off; continuity; incommensurability; nonexpected utility theory; evaluative measurement; aggregation; causal and evidential decision theory; act consequentialism; rule consequentialism; and deontology. (shrink)

Epistemic closure under known implication is the principle that knowledge of "p" and knowledge of "p implies q", together, imply knowledge of "q". This principle is intuitive, yet several putative counterexamples have been formulated against it. This paper addresses the question, why is epistemic closure both intuitive and prone to counterexamples? In particular, the paper examines whether probability theory can offer an answer to this question based on four strategies. The first probability-based strategy rests on the accumulation of (...) risks. The problem with this strategy is that risk accumulation cannot accommodate certain counterexamples to epistemic closure. The second strategy is based on the idea of evidential support, that is, a piece of evidence supports a proposition whenever it increases the probability of the proposition. This strategy makes progress and can accommodate certain putative counterexamples to closure. However, this strategy also gives rise to a number of counterintuitive results. Finally, there are two broadly probabilistic strategies, one based on the idea of resilient probability and the other on the idea of assumptions that are taken for granted. These strategies are promising but are prone to some of the shortcomings of the second strategy. All in all, I conclude that each strategy fails. Probability theory, then, is unlikely to offer the account we need. (shrink)

In this paper, I argue that Islamic theism is best explained by the hypothesis of Divine Commission, whereby Muhammad is viewed as being divinely commissioned to serve the overall salvific purposes of God. To this end, I present three observation reports relating to Islamic theism and evaluate HDC against an alternative hypothesis, the hypothesis of Non-Commission whereby Muhammad is not viewed as being divinely commissioned. I argue that the probability of the observation reports is greater on the assumption that (...) HDC is true than on the assumption that NC is true. Accordingly, this gives us reason to prefer HDC as a better explanation of Islamic theism. (shrink)

A common objection to probabilistic theories of causation is that there are prima facie causes that lower the probability of their effects. Among the many replies to this objection, little attention has been given to Mellor's (1995) indirect strategy to deny that probability-lowering factors are bona fide causes. According to Mellor, such factors do not satisfy the evidential, explanatory, and instrumental connotations of causation. The paper argues that the evidential connotation only entails an epistemically relativized form (...) of causal attribution, not causation itself, and that there are clear cases of explanation and instrumental reasoning that must appeal to negatively relevant factors. In the end, it suggests a more liberal interpretation of causation that restores its connotations. Una objeción común a las teorías probabilísticas de la causalidad es que aparentemente existen causas que disminuyen la probabilidad de sus efectos. Entre las muchas respuestas a esta objeción, se le ha dado poca atención a la estrategia indirecta de D. H. Mellor (1995) para negar que un factor que disminuya la probabilidad de un efecto sea una causa legítima. Según Mellor, tales factores no satisfacen las connotaciones evidenciales, explicativas e instrumentales de la causalidad. El artículo argumenta que la connotación evidencial sólo implica una forma epistémicamente relativizada de atribución causal y no la causalidad misma, y que hay casos claros de explicación y razonamiento instrumental que deben apelar a factores negativamente relevantes. Se sugiere una interpretación más liberal de la causalidad que reinstaura sus connotaciones. (shrink)

David Builes presents a paradox concerning how confident you should be that any given member of an infinite collection of fair coins landed heads, conditional on the information that they were all flipped and only finitely many of them landed heads. We argue that if you should have any conditional credence at all, it should be 1/2.

Many theories of rational action are predicated on the idea that what it is rational to do in a given situation depends, in part, on what it is rational to believe in that situation. In short: they treat epistemic rationality as explanatorily prior to practical rationality. If they are right in doing so, it follows, on pain of explanatory circularity, that epistemic rationality cannot itself be a form of practical rationality. Yet, many epistemologists have defended just such a view of (...) epistemic rationality. According to them, there is no such thing as a distinctively epistemic form of rationality which could be explanatorily prior to practical rationality. Rather, they maintain, there is just one form of rationality—practical rationality—of which epistemic rationality is a species. What to make of this conflict? The aim of this paper is to motivate a view about the relationship between epistemic and practical rationality which resolves the conflict in a way that should be attractive to both sides. The central idea is to ground both epistemic and practical rationality in an independently motivated notion of evidential probability which is itself to be understood in non-normative terms. Doing so, I argue, allows us to unify epistemic and practical rationality in a way that does justice to the idea that what it is rational to do depends, in part, on what it is rational to believe; and to do so in a way that avoids explanatory circularity. (shrink)

Many epistemologists are enamored with a defeat condition on knowledge. In this paper we present some implementation problems for defeatism, understood along either internalist or externalist lines. We then propose that one who accepts a knowledge norm of belief, according to which one ought to believe only what one knows, can explain away much of the motivation for defeatism. This is an important result, because on the one hand it respects the plausibility of the intuitions about defeat shared by many (...) in epistemology; but on the other hand, it obviates the need to provide a unified account of defeat which plays well with the most plausible views of how knowledge fits with evidential probability. (shrink)

The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” (...) probability. (shrink)

In his article, ‘What's Wrong with Tooley's Argument from Evil?’, Calum Miller's goal was to show that the evidential argument from evil that I have advanced is unsound, and in support of that claim, Miller set out three main objections. First, he argued that I had failed to recognize that the actual occurrence of an event can by itself, at least in principle, constitute good evidence that it was not morally wrong for God to allow events of the kind (...) in question. Miller's second objection was then that, in attempting to show that it is unlikely that God exists, I had failed to consider either positive arguments in support of the existence of God or possible theodicies, and thus that I was unjustified in drawing any conclusions concerning the probability that theism is true in the light of the total evidence available. Miller's third and final objection was that one of the approaches to logical probability that I employed – namely, that based upon a structure-description equiprobability principle, rather than a state-description equiprobability principle – was unsound since it has clearly unacceptable implications. In response, I argue that all three of Miller's objections are unsound. The third objection, however, is nevertheless important since it shows that my type of argument from evil cannot be based merely on the evils found in the world. One must also consider good states of affairs, and their relations to bad ones. I show, however, that that deficiency can be addressed in a completely satisfactory manner. (shrink)

This paper argues that we should assign certainty a central place in epistemology. While epistemic certainty played an important role in the history of epistemology, recent epistemology has tended to dismiss certainty as an unattainable ideal, focusing its attention on knowledge instead. I argue that this is a mistake. Attending to certainty attributions in the wild suggests that much of our everyday knowledge qualifies, in appropriate contexts, as certain. After developing a semantics for certainty ascriptions, I put certainty to explanatory (...) work. Specifically, I argue that by taking certainty as our central epistemic notion, we can shed light on a variety of important topics, including evidence and evidential probability, epistemic modals, and the normative constraints on credence and assertion. (shrink)

One thousand fair causally isolated coins will be independently flipped tomorrow morning and you know this fact. I argue that the probability, conditional on your knowledge, that any coin will land tails is almost 1 if that coin in fact lands tails, and almost 0 if it in fact lands heads. I also show that the coin flips are not probabilistically independent given your knowledge. These results are uncomfortable for those, like Timothy Williamson, who take these probabilities to play (...) a central role in their theorizing. (shrink)

Kierkegaard's pseudonym Johannes Climacus famously defines faith as a risky “venture” that requires “holding fast” to “objective uncertainty.” Yet puzzlingly, he emphasizes that faith requires resolute conviction and certainty. Moreover, Climacus claims that all beliefs about contingent propositions about the external world “exclude doubt” and “nullify uncertainty,” but also that uncertainty is “continually present” in these very same beliefs. This paper argues that these apparent contradictions can be resolved by interpreting Climacus as a belief‐credence dualist. That is, Climacus holds that (...) beliefs and credences (i.e., degrees of belief) are two irreducibly distinct types of mental states. Beliefs are resolutions that close inquiry, thereby excluding doubt and reflecting subjective certainty by disregarding the possibility of error. Credences, by contrast, reflect assessments of evidential probabilities, thereby encoding a recognition of “objective uncertainty” by acknowledging the possibility of error. In addition to solving a vexing interpretive puzzle and showing how Kierkegaard anticipates contemporary views about the nature of belief and credence, this paper demonstrates that Kierkegaard developed a sophisticated account of the nature of belief, doubt, and certainty that merits serious philosophical consideration. (shrink)

Say that two goals are normatively coincident just in case one cannot aim for one goal without automatically aiming for the other. While knowledge and justification are distinct epistemic goals, with distinct achievement conditions, this paper begins from the suggestion that they are nevertheless normatively coincident—aiming for knowledge and aiming for justification are one and the same activity. A number of surprising consequences follow from this—both specific consequences about how we can ascribe knowledge and justification in lottery cases and more (...) general consequences about the nature of justification and the relationship between justification and evidential probability. Many of these consequences turn out to be at variance with conventional, prevailing views. (shrink)

Evidential decision theory (EDT) says that the choiceworthiness of an option depends on its evidential connections to possible outcomes. Causal decision theory (CDT) holds that it depends on your beliefs about its causal connections. While Newcomb cases support CDT, Arif Ahmed has described examples that support EDT. A new account is needed to get all cases right. I argue that an option A's choiceworthiness is determined by the probability that a good outcome ensues at possible A‐worlds that (...) match actuality in the facts causally unaffected by your decision (the “unaffected facts”). Moreover, you should evaluate A on the assumption that A is compossible with the unaffected facts. This view entails that you should use EDT when evaluating A on the assumption that the unaffected facts determine your action, but use CDT when assessing A on the opposite assumption. A's choiceworthiness equals a weighted average of these conditional assessments. The weights are determined by your beliefs about whether the unaffected fact determine your action. This account gets both Newcomb and Ahmed cases right. According to an influential view, whether you take the unaffected facts to determine your action can make a difference to whether you can regard yourself as free and the action as being under your control. While my account is neutral on this issue, it entails that whether you take the unaffected facts to determine your action is important in a different way: it matters to whether you should follow EDT or CDT. (shrink)

The value of knowledge can vary in that knowledge of important facts is more valuable than knowledge of trivialities. This variation in the value of knowledge is mirrored by a variation in evidential standards. Matters of greater importance require greater evidential support. But all knowledge, however trivial, needs to be evidentially certain. So on one hand we have a variable evidential standard that depends on the value of the knowledge, and on the other, we have the invariant (...) standard of evidential certainty. This paradox in the concept of knowledge runs deep in the history of philosophy. We approach this paradox by proposing a bet settlement theory of knowledge. Degrees of belief can be measured by the expected value of a bet divided by stake size, with the highest degree of belief being probability 1, or certainty. Evidence sufficient to settle the bet makes the expectation equal to the stake size and therefore has evidential probability 1. This gives us the invariant evidential certainty standard for knowledge. The value of knowledge relative to a bet is given by the stake size. We propose that evidential probability can vary with stake size, so that evidential certainty at low stakes does not entail evidential certainty at high stakes. This solves the paradox by allowing that certainty is necessary for knowledge at any stakes, but that the evidential standards for knowledge vary according to what is at stake. We give a Stake Size Variation Principle that calculates evidential probability from the value of evidence and the stakes. Stake size variant degrees of belief are probabilistically coherent and explain a greater range of preferences than orthodox expected utility theory, namely the Ellsberg and Allais preferences. The resulting theory of knowledge gives an empirically adequate, rationally grounded, unified account of evidence, value and probability. (shrink)

According to Probability 1 Infallibilism (henceforth, Infallibilism), if one knows that p, then the probability of p given one’s evidence is 1. Jessica Brown (2018, 2013) has recently argued that Infallibilism leads to scepticism unless the infallibilist also endorses the claim that if one knows that p, then p is part of one’s evidence for p. By doing that, however, the infalliblist has to explain why it is infelicitous to cite p as evidence for itself. And yet, the (...) infallibilist doesn’t seem to have a satisfying explanation available. Call this the Infelicity Challenge for Probability 1 Infallibilism. By exploiting the distinction between the justifying and the motivating role of evidence, in this paper, I argue that, contrary to first appearances, the Infelicity Challenge doesn’t arise for Probability 1 Infallibilism. However, after anticipating and resisting two objections to my argument, I show that we can identify a different version of infallibilism which seems to face a problem that is even more serious than the Infelicity Challenge. (shrink)

A challenge faced by defenders of the precautionary principle is to clarify when the evidence that a harmful event might occur suffices to regard this prospect as a real possibility. Plausible versions of the principle must articulate some epistemic threshold, or de minimis requirement, which specifies when precautionary measures are justified. Critics have argued that formulating such a threshold is problematic in the context of the precautionary principle. First, this is because the precautionary principle appears to be ambiguous about the (...) distinction between risk and uncertainty: should the principle merely be invoked when evidential probabilities are absent, or also when probabilities have low epistemic credentials? Secondly, defenders of the precautionary principle face an aggregation puzzle: in judging whether or not the de minimis requirement has been met, how should first-order evidential probabilities and their second-order epistemic standing be aggregated? This article argues that the ambiguity can be resolved, and the epistemological puzzle can be solved. Focusing on decisions in the context of climate uncertainty, I advance a version of the precautionary principle that serves as a plausible decision rule, to be adopted in situations where its main alternative—cost–benefit analysis—does not deliver. (shrink)

This paper models knowledge in cases where an agent has multiple experiences over time. Using this model, we introduce a series of observations that undermine the pretheoretic idea that the evidential significance of experience depends on the extent to which that experience matches the world. On the basis of these observations, we model knowledge in terms of what is likely given the agent’s experience. An agent knows p when p is implied by her epistemic possibilities. A world is epistemically (...) possible when its probability given the agent’s experiences is not significantly lower than the probability of the actual world given that experience. (shrink)

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

The problem of evil is the most prominent argument against the existence of God. Skeptical theists contend that it is not a good argument. Their reasons for this contention vary widely, involving such notions as CORNEA, epistemic appearances, 'gratuitous' evils, 'levering' evidence, and the representativeness of goods. We aim to dispel some confusions about these notions, in particular by clarifying their roles within a probabilistic epistemology. In addition, we develop new responses to the problem of evil from both the phenomenal (...) conception of evidence and the knowledge-first view of evidence. (shrink)

Two key questions of normative decision theory are: 1) whether the probabilities relevant to decision theory are evidential or causal; and 2) whether agents should be risk-neutral, and so maximise the expected value of the outcome, or instead risk-averse (or otherwise sensitive to risk). These questions are typically thought to be independent---that our answer to one bears little on our answer to the other. But there is a surprising argument that they are not. In this paper, I show that (...) evidential decision theory implies risk neutrality, at least in moral decision-making and at least on plausible empirical assumptions. Take any risk-aversion-accommodating decision theory, apply it using the probabilities prescribed by evidential decision theory, and every verdict of moral betterness you reach will match those of expected value theory. (shrink)

Extreme Permissivism is the view that a body of evidence could rationally permit both the attitude of belief and disbelief towards a proposition. This paper puts forward a new argument against Extreme Permissivism, which improves on a similar style of argument due to Roger White (2005, 2014). White’s argument is built around the principle that the support relation between evidence and a hypothesis is objective: so that if evidence E makes it rational for an agent to believe a hypothesis H, (...) then E makes it rational to believe H, for all agents. In this paper, I construct a new argument against Extreme Permissivism that appeals to a logically weaker, less demanding view about evidential support, Relational Objectivity: whether a body of evidence E is more likely if H is true than if H is false is an objective matter and does not depend on how any agent interprets the relationship between E and H. Relational Objectivity is solely concerned with the conditional probabilities called likelihoods and does not put substantive constraints on an agent’s prior and posterior credences. For this reason, the presented argument avoids the standard permissivist criticism levelled against White’s argument. (shrink)

According to the knowledge view of evidence notoriously defended by Timothy Williamson (2000), for any subject, her evidence consists of all and only her propositional knowledge (E=K). Many have found (E=K) implausible. However, few have offered arguments against Williamson’s positive case for (E=K). In this paper, I propose an argument against Williamson’s positive case in favour of (E=K). Central to my argument is the possibility of the knowledge of necessary truths. I also draw some more general conclusions concerning theorizing about (...) evidence. (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)

Evidentialism and Reliabilism are two of the main contemporary theories of epistemic justification. Some authors have thought that the theories are not incompatible with each other, and that a hybrid theory which incorporates elements of both should be taken into account. More recently, other authors have argued that the resulting theory is well- placed to deal with fine-grained doxastic attitudes (credences). In this paper I review the reasons for adopting this kind of hybrid theory, paying attention to the case of (...) credences and the notion of probability involved in their treatment. I argue that the notion of probability in question can only be an epistemic (or evidential) kind of probability. I conclude that the resulting theory will be incompatible with Reliabilism in one important respect: it cannot deliver on the reductivist promise of Reliabilism. I also argue that attention to the justification of basic beliefs reveals limitations in the Evidentialist framework as well. The theory that results from the right combination of Evidentialism and Reliabilism, therefore, is neither Evidentialist nor Reliabilist. (shrink)

The epistemology of risk examines how risks bear on epistemic properties. A common framework for examining the epistemology of risk holds that strength of evidential support is best modelled as numerical probability given the available evidence. In this essay I develop and motivate a rival ‘relevant alternatives’ framework for theorising about the epistemology of risk. I describe three loci for thinking about the epistemology of risk. The first locus concerns consequences of relying on a belief for action, where (...) those consequences are significant if the belief is false. The second locus concerns whether beliefs themselves—regardless of action—can be risky, costly, or harmful. The third locus concerns epistemic risks we confront as social epistemic agents. I aim to motivate the relevant alternatives framework as a fruitful approach to the epistemology of risk. I first articulate a ‘relevant alternatives’ model of the relationship between stakes, evidence, and action. I then employ the relevant alternatives framework to undermine the motivation for moral encroachment. Finally, I argue the relevant alternatives framework illuminates epistemic phenomena such as gaslighting, conspiracy theories, and crying wolf, and I draw on the framework to diagnose the undue skepticism endemic to rape accusations. (shrink)

According to Jim Pryor’s dogmatism, when you have an experience with content p, you often have prima facie justification for believing p that doesn’t rest on your independent justification for believing any proposition. Although dogmatism has an intuitive appeal and seems to have an antisceptical bite, it has been targeted by various objections. This paper principally aims to answer the objections by Roger White according to which dogmatism is inconsistent with the Bayesian account of how evidence affects our rational credences. (...) If this were true, the rational acceptability of dogmatism would be seriously questionable. I respond that these objections don’t get off the ground because they assume that our experiences and our introspective beliefs that we have experiences have the same evidential force, whereas the dogmatist is uncommitted to this assumption. I also consider the question whether dogmatism has an antisceptical bite. I suggest that the answer turns on whether or not the Bayesian can determine the priors of hypotheses and conjectures on the grounds of their extra-empirical virtues. If the Bayesian can do so, the thesis that dogmatism has an antisceptical bite is probably false. (shrink)

The concept of burden of proof is used in a wide range of discourses, from philosophy to law, science, skepticism, and even in everyday reasoning. This paper provides an analysis of the proper deployment of burden of proof, focusing in particular on skeptical discussions of pseudoscience and the paranormal, where burden of proof assignments are most poignant and relatively clear-cut. We argue that burden of proof is often misapplied or used as a mere rhetorical gambit, with little appreciation of the (...) underlying principles. The paper elaborates on an important distinction between evidential and prudential varieties of burdens of proof, which is cashed out in terms of Bayesian probabilities and error management theory. Finally, we explore the relationship between burden of proof and several (alleged) informal logical fallacies. This allows us to get a firmer grip on the concept and its applications in different domains, and also to clear up some confusions with regard to when exactly some fallacies (ad hominem, ad ignorantiam, and petitio principii) may or may not occur. (shrink)

Likelihoodism is the view that the degree of evidential support should be analysed and measured in terms of likelihoods alone. The paper considers and responds to a popular criticism that a likelihoodist framework is too restrictive to guide belief. First, I show that the most detailed and rigorous version of this criticism, as put forward by Gandenberger (2016), is unsuccessful. Second, I provide a positive argument that a broadly likelihoodist framework can accommodate guidance for comparative belief, even when objectively (...) well-grounded prior probabilities are not available. As I show, the shift from non-relational to comparative probabilities opens up a new space for addressing the belief guidance problem for likelihoodism. (shrink)

The paper argues that knowledge is not closed under logical inference. The argument proceeds from the openness of evidential support and the dependence of empirical knowledge on evidence, to the conclusion that knowledge is open. Without attempting to provide a full-fledged theory of evidence, we show that on the modest assumption that evidence cannot support both a proposition and its negation, or, alternatively, that information that reduces the probability of a proposition cannot constitute evidence for its truth, the (...) relation of evidential support is not closed under known entailment. Therefore the evidence-for relation is deductively open regardless of whether evidence is probabilistic or not. Given even a weak dependence of empirical knowledge on evidence, we argue that empirical knowledge is also open. On this basis, we also respond to the strongest argument in support of knowledge closure. Finally, we present a number of significant benefits of our position, namely, offering a unified explanation for a range of epistemological puzzles. (shrink)

A popular account of luck, with a firm basis in common sense, holds that a necessary condition for an event to be lucky, is that it was suitably improbable. It has recently been proposed that this improbability condition is best understood in epistemic terms. Two different versions of this proposal have been advanced. According to my own proposal :361–377, 2010), whether an event is lucky for some agent depends on whether the agent was in a position to know that the (...) event would occur. And according to Stoutenburg :319–334, 2015, Synthese, 1–15, 2018), whether an event is lucky for an agent depends on whether the event was guaranteed or certain to occur in light of the agent’s evidence. In this paper, I argue that we should prefer the account in terms of knowledge over that in terms of evidential certainty. (shrink)

According to Agnosticism with a capital A, even if we don’t see how any reason we know of would justify God in permitting all the evil in the world and even if we lack evidential and non-evidential warrant for theism, we should not infer that there probably is no reason that would justify God. That’s because, under those conditions, we should be in doubt about whether the goods we know of constitute a representative sample of all the goods (...) there are, among relevantly similar things. In my "Epistemic Humility, Arguments from Evil, and Moral Skepticism" (2009), I defended Agnosticism against the charge that it leaves us in doubt about whether we are obligated to intervene to prevent horrific suffering we can prevent at no risk to ourselves. In his “Agnosticism, Skeptical Theism, and Moral Obligation” (2014), Stephen Maitzen argues that, in light of my defense, Agnosticism is at odds with commonsense morality’s insistence that we have an obligation to intervene in such cases. In the present essay, I argue that the moral principle Maitzen seems to impute to commonsense (it's hard to tell what principle he has in mind) is false and that a moral principle much more in keeping with commonsense is compatible with Agnosticism and my defense of it. Along the way, I mention multiple misrepresentations Maitzen makes of Agnosticism and my defense of it. (shrink)

According to the traditional Bayesian view of credence, its structure is that of precise probability, its objects are descriptive propositions about the empirical world, and its dynamics are given by conditionalization. Each of the three essays that make up this thesis deals with a different variation on this traditional picture. The first variation replaces precise probability with sets of probabilities. The resulting imprecise Bayesianism is sometimes motivated on the grounds that our beliefs should not be more precise than (...) the evidence calls for. 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 the first essay I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid without compromising the initial evidentialist motivation. The second variation replaces descriptive claims with moral claims as the objects of credence. I consider three standard arguments for probabilism with respect to descriptive uncertainty—representation theorem arguments, Dutch book arguments, and accuracy arguments—in order to examine whether such arguments can also be used to establish probabilism with respect to moral uncertainty. In the second essay, I argue that by and large they can, with some caveats. First, I don’t examine whether these arguments can be given sound non-cognitivist readings, and any conclusions therefore only hold conditional on cognitivism. Second, decision-theoretic representation theorems are found to be less convincing in the moral case, because there they implausibly commit us to thinking that intertheoretic comparisons of value are always possible. Third and finally, certain considerations may lead one to think that imprecise probabilism provides a more plausible model of moral epistemology. The third variation considers whether, in addition to conditionalization, agents may also change their minds by becoming aware of propositions they had not previously entertained, and therefore not previously assigned any probability. More specifically, I argue that if we wish to make room for reflective equilibrium in a probabilistic moral epistemology, we must allow for awareness growth. In the third essay, I sketch the outline of such a Bayesian account of reflective equilibrium. Given that this account gives a central place to awareness growth, and that the rationality constraints on belief change by awareness growth are much weaker than those on belief change by conditionalization, it follows that the rationality constraints on the credences of agents who are seeking reflective equilibrium are correspondingly weaker. (shrink)

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

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 work in Bayesian epistemology. This work shows that, under certain probabilistic conditions, coherence cannot increase the probability of the target claim. These theorems are taken to demonstrate that epistemic coherentism is untenable. To date no one has investigated how these results bear on different conceptions of coherence. I investigate this situation using Thagard’s ECHO model (...) of explanatory coherence. Thagard’s ECHO model provides a natural representation of the evidential significance of multiple independent reports. (shrink)

According to a captivating picture, epistemic justification is essentially a matter of epistemic or evidential likelihood. While certain problems for this view are well known, it is motivated by a very natural thought—if justification can fall short of epistemic certainty, then what else could it possibly be? In this paper I shall develop an alternative way of thinking about epistemic justification. On this conception, the difference between justification and likelihood turns out to be akin to the more widely recognised (...) difference between ceteris paribus laws and brute statistical generalisations. I go on to discuss, in light of this suggestion, issues such as classical and lottery-driven scepticism as well as the lottery and preface paradoxes. (shrink)

Conspiracy theories are often portrayed as unwarranted beliefs, typically supported by suspicious kinds of evidence. Yet contemporary work in Philosophy argues provisional belief in conspiracy theories is at the very least understandable---because conspiracies occur---and that if we take an evidential approach, judging individual conspiracy theories on their particular merits, belief in such theories turns out to be warranted in a range of cases. -/- Drawing on this work, I examine the kinds of evidence typically associated with conspiracy theories, and (...) show how the so-called evidential problems with conspiracy theories are also problems for the kinds of evidence put forward in support of other theories. As such, if there is a problem with the conspiracy theorist's use of evidence, it is one of principle: is the principle which guides the conspiracy theorist's use of evidence somehow in error? I argue that whatever we might think about conspiracy theories generally, there is no prima facie case for a scepticism of conspiracy theories based purely on their use of evidence. (shrink)