Does the strength of a particular belief depend upon the significance we attach to it? Do we move from one context to another, remaining in the same doxastic state concerning p yet holding a stronger belief that p in one context than in the other? For that to be so, a doxastic state must have a certain sort of context-sensitive complexity. So the question is about the nature of belief states, as we understand them, or as we (...) think a theory should model them. I explore the idea and how it relates to work on imprecise probabilities and second-order confidence. (shrink)

We argue, in the spirit of some of Jean-Yves Jaffray's work, that explicitly incorporating the information, however imprecise, available to the decision maker is relevant, feasible, and fruitful. In particular, we show that it can lead us to know whether the decision maker has wrong beliefs and whether it matters or not, that it makes it possible to better model and analyze how the decision maker takes into account new information, even when this information is not an event and (...) finally that it is crucial when attempting to identify and measure the decision maker's attitude toward imprecise information. (shrink)

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

We propose a method for estimating subjective beliefs, viewed as a subjective probability distribution. The key insight is to characterize beliefs as a parameter to be estimated from observed choices in a well-defined experimental task and to estimate that parameter as a random coefficient. The experimental task consists of a series of standard lottery choices in which the subject is assumed to use conventional risk attitudes to select one lottery or the other and then a series of betting choices in (...) which the subject is presented with a range of bookies offering odds on the outcome of some event that the subject has a belief over. Knowledge of the risk attitudes of subjects conditions the inferences about subjective beliefs. Maximum simulated likelihood methods are used to estimate a structural model in which subjects employ subjective beliefs to make bets. We present evidence that some subjective probabilities are indeed best characterized as probability distributions with non-zero variance. (shrink)

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)

The received model of degrees of belief represents them as probabilities. Over the last half century, many philosophers have been convinced that this model fails because it cannot make room for the idea that an agent’s degrees of belief should respect the available evidence. In its place they have advocated a model that represents degrees of belief using imprecise probabilities (sets of probability functions). This paper presents a model of degrees of belief based on Dempster–Shafer (...) belief functions and then presents arguments for belief functions over imprecise probabilities as a model of evidence-respecting degrees of belief. The arguments cover three kinds of issue: theoretical virtues (simplicity, interpretability and flexibility); motivations; and problem cases (dilation and belief inertia). (shrink)

Philosophy and Phenomenological Research, Volume 103, Issue 3, Page 620-638, November 2021.

Some Bayesians have suggested that beliefs based on ambiguous or incomplete evidence are best represented by families of probability functions. I spend the first half of this essay outlining one version of this imprecise model of belief, and spend the second half defending the model against recent objections, raised by Roger White and others, which concern the phenomenon of probabilistic dilation. Dilation occurs when learning some definite fact forces a person’s beliefs about an event to shift from a (...) sharp, point-valued subjective probability to an imprecise spread of probabilities. Some commentators find dilation disturbing, both from an epistemic and a decision-theoretic perspective, and place the blame on the use of sets of probabilities to model opinion. These reactions are based on an overly narrow conception of imprecise belief states which assumes that we know everything there is to know about a person’s doxastic attitudes once we have identified the spreads of values for her imprecise credences. Once we recognize that the imprecise model has the resources to characterize a much richer family of doxastic attitudes than this, we will see that White’s charges of epistemological and decision theoretic incoherence are unfounded. (shrink)

In formal modelling, it is essential that models be supplied with an interpretative story: there must be a clear and coherent account of how the formal model relates to the phenomena it is supposed to model. The traditional representation of degrees of belief as mathematical probabilities comes with a clear and simple interpretative story. This paper argues that the model of degrees of belief as imprecise probabilities (sets of probabilities) lacks a workable interpretation. The standard interpretative story (...) given in the literature is shown to lead to unacceptable results -- and, it is argued, there is no way for imprecise probabilists to restrict, replace or finesse this story so as either to avoid or to be able to live with the consequences. Thus the imprecise probabilist lacks a viable account of how a set of probability functions models a belief state: a story about which properties of the model correspond to facts about the thing modelled and how exactly we are to extract information about an agent's belief state from a set of probabilities. (shrink)

Do imprecise beliefs lead to worse decisions under uncertainty? This BJPS Short Reads article provides an informal introduction to our use of agent-based modelling to investigate this question. We explain the strengths of imprecise probabilities for modelling evidential states. We explain how we used an agent-based model to investigate the relative performance of Imprecise Bayesian reasoners against a standard Bayesian who has precise credences. We found that the very features of Imprecise Bayesianism which give it representational (...) strengths also cause relative underperformance in this decision problem. We explain the practical relevance of this research to applications of Bayesian reasoning in areas like artificial intelligence. (shrink)

Jim Joyce argues for two amendments to probabilism. The first is the doctrine that credences are rational, or not, in virtue of their accuracy or “closeness to the truth” (1998). The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (2010). We argue that both amendments cannot be satisfied simultaneously. To do so, we employ a (slightly-generalized) impossibility theorem of Seidenfeld, Schervish, and Kadane (2012), who (...) show that there is no strictly proper scoring rule for imprecise probabilities. -/- The question then is what should give way. Joyce, who is well aware of this no-go result, thinks that a quantifiability constraint on epistemic accuracy should be relaxed to accommodate imprecision. We argue instead that another Joycean assumption — called strict immodesty— should be rejected, and we prove a representation theorem that characterizes all “mildly” immodest measures of inaccuracy. (shrink)

How should we make decisions when we do not know the relevant physical probabilities? In these ambiguous situations, we cannot use our knowledge to determine expected utilities or payoffs. The traditional Bayesian answer is that we should create a probability distribution using some mix of subjective intuition and objective constraints. Imprecise Bayesians argue that this approach is inadequate for modelling ambiguity. Instead, they represent doxastic states using credal sets. Generally, insofar as we are more uncertain about the physical probability (...) of an event, there is more divergence in the credal set. Hence, their approach can represent these ambiguities via the extent of the divergence. Imprecise Bayesianism has mostly been advocated for its epistemological features. In this article, we examine its properties for decision-making. We develop a model for comparing standard and Imprecise Bayesianism by testing their performances in a classic decision problem. We find that the representational tools of Imprecise Bayesianism also cause it to underperform in our tests. This issue has been overlooked, because previous research on Imprecise Bayesianism has not utilised agent-based modelling to provide information about its performance in the short-run. Overall, we reveal the Ambiguity Dilemma for Imprecise Bayesianism: To what extent should one value representational power or decision-making performance? (shrink)

The usage of imprecise probabilities has been advocated in many domains: A number of philosophers have argued that our belief states should be “imprecise” in response to certain sorts of evidence, and imprecise probabilities have been thought to play an important role in disciplines such as artificial intelligence, climate science, and engineering. In this paper I’m interested in the question of whether the usage of imprecise probabilities can be given a practical motivation (a motivation based (...) on practical rather than epistemic, or alethic concerns). My aim is to challenge the central motivation for using imprecise probabilities in decision-making that has been offered in the literature: the idea that, in at least some contexts, it’s desirable to be ambiguity averse. If I succeed, this will show that we need to reconsider whether there are good reasons to use imprecise probabilities in contexts in which making good decisions is what's of primary concern. (shrink)

The generalized Bayes’ rule (GBR) can be used to conduct ‘quasi-Bayesian’ analyses when prior beliefs are represented by imprecise probability models. We describe a procedure for deriving coherent imprecise probability models when the event space consists of a finite set of mutually exclusive and exhaustive events. The procedure is based on Walley’s theory of upper and lower prevision and employs simple linear programming models. We then describe how these models can be updated using Cozman’s linear programming formulation of (...) the GBR. Examples are provided to demonstrate how the GBR can be applied in practice. These examples also illustrate the effects of prior imprecision and prior-data conflict on the precision of the posterior probability distribution. (shrink)

Wilcox proposed an argument against imprecise probabilities and for the principle of indifference based on a thought experiment where he argues that it is very intuitive to feel that one’s confidence in drawing a ball of a given colour out of an unknown urn should decrease while the number of potential colours in the urn increases. In my response to him, I argue that one’s intuitions may be unreliable because it is very hard to truly feel completely ignorant in (...) such a situation. I further argue that Wilcox must also account for the conflicting intuition that it is absurd to have to feel completely convinced that a specific claim about reality is true _in the absence of any evidence_ in order to avoid being irrational. It is dubious that this intuition is considerably less universal and strongly-held than Wilcox’s own intuition. Finally, I point out that even if Wilcox’s intuition were to be universally shared among members of our biological species, it is far from being clear that someone refusing to let that intuition dictate his or her beliefs would be irrational. For all these reasons, I believe that Wilcox was not successful in proving that philosophers and scientists representing uncertainty through imprecise probabilities are violating the principles of rationality. (shrink)

Understanding probabilities as something other than point values has often been motivated by the need to find more realistic models for degree of belief, and in particular the idea that degree of belief should have an objective basis in “statistical knowledge of the world.” I offer here another motivation growing out of efforts to understand how chance evolves as a function of time. If the world is “chancy” in that there are non-trivial, objective, physical probabilities at the macro-level, (...) then the chance of an event e that happens at a given time is \ until it happens. But whether the chance of e goes to one continuously or not is left open. Discontinuities in such chance trajectories can have surprising and troubling consequences for probabilistic analyses of causation and accounts of how events occur in time. This, coupled with the compelling evidence for quantum discontinuities in chance’s evolution, gives rise to a “continuity bind” with respect to chance probability trajectories. I argue that a viable option for circumventing the continuity bind is to understand the probabilities “imprecisely,” that is, as intervals rather than point values. I then develop and motivate an alternative kind of continuity appropriate for interval-valued chance probability trajectories. (shrink)

Orthodox Bayesian decision theory requires an agent’s beliefs representable by a real-valued function, ideally a probability function. Many theorists have argued this is too restrictive; it can be perfectly reasonable to have indeterminate degrees of belief. So doxastic states are ideally representable by a set of probability functions. One consequence of this is that the expected value of a gamble will be imprecise. This paper looks at the attempts to extend Bayesian decision theory to deal with such cases, (...) and concludes that all proposals advanced thus far have been incoherent. A more modest, but coherent, alternative is proposed. Keywords: Imprecise probabilities, Arrow’s theorem. (shrink)

The basic Bayesian model of credence states, where each individual’s belief state is represented by a single probability measure, has been criticized as psychologically implausible, unable to represent the intuitive distinction between precise and imprecise probabilities, and normatively unjustifiable due to a need to adopt arbitrary, unmotivated priors. These arguments are often used to motivate a model on which imprecise credal states are represented by sets of probability measures. I connect this debate with recent work in Bayesian (...) cognitive science, where probabilistic models are typically provided with explicit hierarchical structure. Hierarchical Bayesian models are immune to many classic arguments against single-measure models. They represent grades of imprecision in probability assignments automatically, have strong psychological motivation, and can be normatively justified even when certain arbitrary decisions are required. In addition, hierarchical models show much more plausible learning behavior than flat representations in terms of sets of measures, which—on standard assumptions about update—rule out simple cases of learning from a starting point of total ignorance. (shrink)

There is a trade-off between specificity and accuracy in existing models of belief. Descriptions of agents in the tripartite model, which recognizes only three doxastic attitudes—belief, disbelief, and suspension of judgment—are typically accurate, but not sufficiently specific. The orthodox Bayesian model, which requires real-valued credences, is perfectly specific, but often inaccurate: we often lack precise credences. I argue, first, that a popular attempt to fix the Bayesian model by using sets of functions is also inaccurate, since it requires (...) us to have interval-valued credences with perfectly precise endpoints. We can see this problem as analogous to the problem of higher order vagueness. Ultimately, I argue, the only way to avoid these problems is to endorse Insurmountable Unclassifiability. This principle has some surprising and radical consequences. For example, it entails that the trade-off between accuracy and specificity is in-principle unavoidable: sometimes it is simply impossible to characterize an agent’s doxastic state in a way that is both fully accurate and maximally specific. What we can do, however, is improve on both the tripartite and existing Bayesian models. I construct a new model of belief—the minimal model—that allows us to characterize agents with much greater specificity than the tripartite model, and yet which remains, unlike existing Bayesian models, perfectly accurate. (shrink)

Our ordinary assertions are often imprecise, insofar as the way we represent things as being only approximates how things are in the actual world. The phenomenon of assertoric imprecision raises a challenge to standard accounts of both the norm of assertion and the connection between semantics and the objects of assertion. After clarifying these problems in detail, I develop a framework for resolving them. Specifically, I argue that the phenomenon of assertoric imprecision motivates a rejection of the widely held (...) belief that a semantic theory for a language associates a single semantic value with each of the simple and complex expressions of that language, relative to the contexts in which they occur. Instead, I propose that we adopt a framework I call semantic pluralism. (shrink)

There is currently much discussion about how decision making should proceed when an agent's degrees of belief are imprecise; represented by a set of probability functions. I show that decision rules recently discussed by Sarah Moss, Susanna Rinard and Rohan Sud all suffer from the same defect: they all struggle to rationalize diachronic ambiguity aversion. Since ambiguity aversion is among the motivations for imprecise credence, this suggests that the search for an adequate imprecise decision rule is (...) not yet over. (shrink)

This paper considers a puzzling conflict between two positions that are each compelling: it is irrational for an agent to pay to avoid `free' evidence before making a decision, and rational agents may have imprecise beliefs and/or desires. Indeed, we show that Good's theorem concerning the invariable choice-worthiness of free evidence does not generalise to the imprecise realm, given the plausible existing decision theories for handling imprecision. A key ingredient in the analysis, and a potential source of controversy, (...) is the general approach taken for resolving sequential decision problems { we make explicit what the key alternatives are and defend our own approach. Furthermore, we endorse a resolution of the aforementioned puzzle { we privilege decision theories that merely permit avoiding free evidence over decision theories for which avoiding free evidence is uniquely admissible. Finally, we situate this particular result about free evidence within the broader `dynamic-coherence' literature. (shrink)

Many philosophers regard the imprecise credence framework as a more realistic model of probabilistic inferences with imperfect empirical information than the traditional precise credence framework. Hence, it is surprising that the literature lacks any discussion on how to update one’s imprecise credences when the given evidence itself is imprecise. To fill this gap, I consider two updating principles. Unfortunately, each of them faces a serious problem. The first updating principle, which I call “generalized conditionalization,” sometimes forces an (...) agent to change her imprecise degrees of belief even though she does not have new evidence. The second updating principle, which I call “the generalized dynamic Keynesian model,” may result in a very precise credal state although the agent does not have sufficiently strong evidence to justify such an informative doxastic state. This means that it is much more difficult to come up with an acceptable updating principle for the imprecise credence framework than one might have thought it would be. (shrink)

Ambiguity occurs insofar as a reasoner lacks information about the relevant physical probabilities. There are objections to the application of standard Bayesian inductive logic and decision theory in contexts of significant ambiguity. A variety of alternative frameworks for reasoning under ambiguity have been proposed. Two of the most prominent are Imprecise Bayesianism and Dempster–Shafer theory. We compare these inductive logics with respect to the Ambiguity Dilemma, which is a problem that has been raised for Imprecise Bayesianism. We develop (...) an agent-based model comparison that isolates the difference between the two inductive logics in their updating methods. We find that Dempster–Shafer theory does not avoid the Ambiguity Dilemma. We discuss the implications of this result. (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 I investigate an alternative to imprecise probabilism. Imprecise probabilism is a popular revision of orthodox Bayesianism: while the orthodox Bayesian claims that a rational agent’s belief-state can be represented by a single credence function, the imprecise probabilist claims instead that a rational agent’s belief-state can be represented by a set of such functions. The alternative that I put forward in this paper is to claim that the expression ‘credence’ is vague, and then (...) apply the theory of supervaluationism to sentences containing this expression. This gives us a viable alternative to imprecise probabilism, and I end by comparing the two accounts. I show that supervaluationism has a simpler way of handling sentences relating the belief-states of two different people, or of the same person at two different times; that both accounts may have the resources to develop plausible decision theories; and finally that the supervaluationist can accommodate higher-order vagueness in a way that is not available to the imprecise probabilist. (shrink)

A number of Bayesians claim that, if one has no evidence relevant to a proposition P, then one's credence in P should be spread over the interval [0, 1]. Against this, I argue: first, that it is inconsistent with plausible claims about comparative levels of confidence; second, that it precludes inductive learning in certain cases. Two motivations for the view are considered and rejected. A discussion of alternatives leads to the conjecture that there is an in-principle limitation on formal representations (...) of belief: they cannot be both fully accurate and maximally specific. (shrink)

Rational credence should be coherent in the sense that your attitudes should not leave you open to a sure loss. Rational credence should be such that you can learn when confronted with relevant evidence. Rational credence should not be sensitive to irrelevant differences in the presentation of the epistemic situation. We explore the extent to which orthodox probabilistic approaches to rational credence can satisfy these three desiderata and find them wanting. We demonstrate that an imprecise probability approach does better. (...) Along the way we shall demonstrate that the problem of “belief inertia” is not an issue for a large class of IP credences, and provide a solution to van Fraassen’s box factory puzzle. (shrink)

According to the Imprecise Credence Framework (ICF), a rational believer's doxastic state should be modelled by a set of probability functions rather than a single probability function, namely, the set of probability functions allowed by the evidence ( Joyce [2005] ). Roger White ( [2010] ) has recently given an arresting argument against the ICF, which has garnered a number of responses. In this article, I attempt to cast doubt on his argument. First, I point out that it's not (...) an argument against the ICF per se , but an argument for the Principle of Indifference. Second, I present an argument that's analogous to White's. I argue that if White's premises are true, the premises of this argument are too. But the premises of my argument entail something obviously false. Therefore, White's premises must not all be true. (shrink)

Whilst Bayesian epistemology is widely regarded nowadays as our best theory of knowledge, there are still a relatively large number of incompatible and competing approaches falling under that umbrella. Very recently, Wallmann and Williamson wrote an interesting article that aims at showing that a subjective Bayesian who accepts the principal principle and uses a known physical chance as her degree of belief for an event A could end up having incoherent or very implausible beliefs if she subjectively chooses the (...) probability of an event F for which she has much poorer evidence. They also argued that their own version of objective Bayesianism is completely immune to that challenge. In this article, after having presented the strongest version of Wallmann’s and Williamson’s argument, I will show that if successful, it has far-reaching consequences and would not only invalidate moderate subjective Bayesianism and imprecise probalism but also a form of objective Bayesianism that relies on conditionalisation, the principal principle, reference classes, and the principle of indifference applied to the most basic partitions. I then argue that their argument can be defeated by adding the rule that it is always irrational to choose a probability that can be computed from the known probabilities associated to one’s other beliefs. I finally argue that the authors’ main intuition that probabilities have different degrees of reliability favours imprecise Bayesianism over precise Bayesianism. (shrink)

We propose a model of uncertain belief. This models coherent beliefs by a filter, ????, on the set of probabilities. That is, it is given by a collection of sets of probabilities which are closed under supersets and finite intersections. This can naturally capture your probabilistic judgements. When you think that it is more likely to be sunny than rainy, we have{????|????(????????????????????)>????(????????????????????)}∈????. When you think that a gamble ???? is desirable, we have {????|Exp????[????]>0}∈????. It naturally extends the model of (...) credal sets; and we will show it captures all the expressive power of the desirable gambles model. It also captures the expressive power of sets of desirable gamble sets (with a mixing axiom, but no Archimadean axiom). (shrink)

Unlike other classical arguments for the existence of God, Pascal’s Wager provides a pragmatic rationale for theistic belief. Its most popular version says that it is rationally mandatory to choose a way of life that seeks to cultivate belief in God because this is the option of maximum expected utility. Despite its initial attractiveness, this long-standing argument has been subject to various criticisms by many philosophers. What is less discussed, however, is the rationality of this choice in situations (...) where the decision-makers are confronted with greater uncertainty. In this paper, I examine the imprecise version of Pascal’s Wager: those scenarios where an agent’s credence that God exists is imprecise or vague rather than precise. After introducing some technical background on imprecise probabilities, I apply five different principles for decision-making to two cases of state uncertainty. In the final part of the paper, I argue that it is not rationally permitted to include zero as the lower probability of God’s existence. Although the conditions for what makes an act uniquely optimal vary significantly across those principles, I also show how the option of wagering for God can defeat any mixed strategy under two distinct interpretations of salvation. (shrink)

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

This guide accompanies the following article: Nikolaj Nottelmann, ‘Belief‐Desire Explanation’. Philosophy Compass Vol/Iss : 1–10. doi: 10.1111/j.1747‐9991.2011.00446.xAuthor’s Introduction“Belief‐desire explanation” is short‐hand for a type of action explanation that appeals to a set of the agent’s mental states consisting of 1. Her desire to ψ and 2. Her belief that, were she to φ, she would promote her ψ‐ing. Here, to ψ could be to eat an ice cream, and to φ could be to walk to the ice (...) cream vendor. Adherents of belief‐desire explanation, often labelled “Humeans”, standardly assume that appeals to such belief‐desire pairs sufficiently explain many human and animal actions, and also that all actions are explainable thus, at least in so far as they are guided by the agent’s intentions. Humeans take their lead from David Hume’s famous dictum that “Reason...is only to be the slave of the passions, and can never pretend to any other office than to serve and obey them.” In its original context, this passage from the Treatise is naturally taken to convey the thesis that mental states subservient to epistemic rationality – such as beliefs – are never in themselves sufficient to motivate action. Thus, an appeal to an agent’s beliefs is never in itself sufficient to lay bare her motivations and explain her actions, but must be supplemented by an appeal to “passions” such as desires. Many philosophers, so‐called Anti‐Humeans, have sharply disagreed. Some have pointed to certain beliefs with alleged motivational force in isolation from desires, most commonly evaluative beliefs. Others have argued that belief‐desire psychology fails to cut up mental space in a way fruitful to action explanation. Instead, only appeals to other types of mental state will adequately explain many types of intentional action. The debate for and against Humeanism is a highly complex one, which is likely to persist along with any general interest in the theory of action explanation.Author RecommendsHume, David. A Treatise of Human Nature. 2nd ed. Edited and with an Analytical Index, by L. A. Selby‐Bigge. Oxford: Oxford University Press, 1978.Part III. Sect. III. of the Treatise is the classical source of the Humean view. Any in‐depth understanding of contemporary Humeanism must take it as its starting point.Stroud, Barry. Hume. London: Routledge, 1977.This is an excellent introductory text. Chap. VII treats on Humeanism and the key part of the Treatise listed above.Smith, Michael. ‘The Humean Theory of Motivation.’Mind 96.381 : 36–61.This is an authoritative modern account of Humeanism. Even if a bit imprecise in some regards, the text is lucidly written and nicely captures the structure of the debate over Humeanism.Schaefer‐Landau, Russ. Moral Realism. A Defence. Oxford: Clarendon Press, 2003.Chapt. 5 contains another fine, more recent, introduction to Humeanism and the typical arguments for and against it. This introduction is particularly recommendable in virtue of its clarity and comprehensiveness.Ratcliffe, Matthew. Rethinking Commonsense Psychology. A Critique of Folk Psychology, Theory of Mind and Simulation. New York: Palgrave Macmillan, 2007.This monograph treats on a very wide number of subjects pertaining to action explanation and harbours many highly controversial theses. Still, it is a refreshing eye‐opener re the immense complexity of the topic of action explanation and the great variety of such explanations in our folk practices. On my view Ratcliffe makes plausible the view that neither our folk practices nor our scientific practices single out a unique model of action explanation as the only appropriate one. Rather our practices of action explanation constitute a rather motley family. The consequence of this to the debates over Humeanism is obvious: The combatants must get clear on the exact models of action explanation within which they discuss the place of belief‐desire references instead of pretending to fight over action explanation in general.Gendler, Tamar Szabó. ‘Alief and Belief.’Journal of Philosophy 105 : 634–63.This paper, together with Gendler’s contemporary sister paper ‘Alief in Action ’, is an engaging proponent of the view that belief‐desire psychology and its associated practice of Human action explanations gets psychological reality radically wrong. Gendler presents a number of cases where, allegedly, relevant human actions are only explicable by appeal to a type of mental state, which Gendler dubs “alief”. Aliefs are neither beliefs nor desires; but share certain characteristics with both.Online MaterialsSample SyllabusWeek I: David Hume’s viewHume, Treatise, Part III. Sect III.Stroud: Hume, Chapt. VII.Week II: Modern HumeanismSmith, ‘The Humean Theory of Motivation’.Nottelmann, ‘Belief‐Desire Explanation’.Week III: Modern Humeanism continued: The Dialectics of the DebateSchaefer‐Landau, ‘Motivational Humeanism’.Week IV: Intention, Agency and CausationDavidson, Donald. ‘Actions, Reasons, and Causes’ & ‘Freedom to Act’, both in: Essays on Actions and Events. Oxford: Clarendon Press, 1980.Week V: Modern Anti‐Humeanism, The Neo‐Kantian VersionScanlon, T. M. What we Owe to Each Other. Cambridge, MA: The Belknap Press, 1998, Chapt. 1. ‘Reasons’.Week VI: Modern Anti‐Humeanism, The Cognitive Science VersionGendler, Tamar Szabó. ‘Alief and Belief’, supplemented with excerpts of her ‘Alief in Action ’. Mind and Language 23.5 : 552–85.Focus Questions1 Which kinds of explanation do belief‐desire explanations belong to?2 In so far as belief‐desire explanations provide causal explanation of action, how are we to understand the causal nexus between belief‐desire pairs and successful agency?3 How are we to understand the notions of belief and desire as appealed to in belief‐desire explanations? Are they even conceptually distinct from the concept of a belief‐desire explanation of human action?4 May evaluative judgments such as moral judgments motivate and/or rationalize action in isolation from accompanying distinct co‐native states of the agent?5 Are certain types of intentional action better explained with sole reference to mental states different from belief as well as desire? (shrink)

I focus my discussion on the well-known Ellsberg paradox. I find good normative reasons for incorporating non-precise belief, as represented by sets of probabilities, in an Ellsberg decision model. This amounts to forgoing the completeness axiom of expected utility theory. Provided that probability sets are interpreted as genuinely indeterminate belief, such a model can moreover make the “Ellsberg choices” rationally permissible. Without some further element to the story, however, the model does not explain how an agent may come (...) to have unique preferences for each of the Ellsberg options. Levi holds that the extra element amounts to innocuous secondary “risk” or security considerations that are used to break ties when more than one option is rationally permissible. While I think a lexical choice rule of this kind is very plausible, I argue that it involves a greater break with xpected utility theory than mere violation of the ordering axiom. (shrink)

_The Pragmatic Mind_ is a study of the pragmatism of Emerson, James, and Peirce and its overlooked relevance for the neopragmatism of thinkers like Richard Rorty, Stanley Cavell, Stanley Fish, and Cornel West. Arguing that the "original" pragmatists are too-often cited casually and imprecisely as mere precursors to this contemporary group of American intellectuals, Mark Bauerlein explores the explicit consequences of the earlier group’s work for current debates among and around the neopragmatists. Bauerlein extracts from Emerson, James, and Peirce an (...) intellectual focus that can be used to advance the broad social and academic reforms that the new pragmatists hail. He claims that, in an effort to repudiate the phony universalism of much contemporary theory, the new generation of theorists has ignored the fact that its visions of pragmatic action are grounded in this "old" school, not just in a way of _doing_ things but also in a way of _thinking_ about things. In other words, despite its inclination to regard psychological questions as irrelevant, Bauerlein shows that the pragmatic method demands a pragmatic mind—that is, a concept of cognition, judgment, habit, and belief. He shows that, in fact, such a concept of mind does exist, in the work of the "old" pragmatists. (shrink)

This paper presents a formalism that combines useful properties of both logic and probabilities. Like logic, the formalism admits qualitative sentences and provides symbolic machinery for deriving deductively closed beliefs and, like probability, it permits us to express if-then rules with different levels of firmness and to retract beliefs in response to changing observations. Rules are interpreted as order-of-magnitude approximations of conditional probabilities which impose constraints over the rankings of worlds. Inferences are supported by a unique priority ordering on rules (...) which is syntactically derived from the knowledge base. This ordering accounts for rule interactions, respects specificity considerations and facilitates the construction of coherent states of beliefs. Practical algorithms are developed and analyzed for testing consistency, computing rule ordering, and answering queries. Imprecise observations are incorporated using qualitative versions of Jeffrey's rule and Bayesian updating, with the result that coherent belief revision is embodied naturally and tractably. Finally, causal rules are interpreted as imposing Markovian conditions that further constrain world rankings to reflect the modularity of causal organizations. These constraints are shown to facilitate reasoning about causal projections, explanations, actions and change. (shrink)

It is a consequence of both Kennedy and McNally’s typology of the scale structures of gradable adjectives and Kennedy’s economy principle that an object is clean just in case its degree of cleanness is maximal. So they jointly predict that the sentence ‘Both towels are clean, but the red one is cleaner than the blue one’ is a contradiction. Surely, one can account for the sentence’s assertability by saying that the first instance of ‘clean’ is used loosely: since ‘clean’ pragmatically (...) conveys the property of being close to maximally clean rather than the property of being maximally clean, the sentence as a whole conveys a consistent proposition. I challenge this semantics–pragmatics package by considering the sentence ‘Mary believes that both towels are clean but that the red one is cleaner than the blue one’. We can certainly use this sentence to attribute a coherent belief to Mary: One of its readings says that she believes that the towels are clean by a contextually salient standard ; the other says that she believes that the towels are clean by her own standard. I argue that Kennedy’s semantics–pragmatics package can’t deliver those readings, and propose that we drop the economy principle and account for those readings semantically by assigning to the belief sentence two distinct truth conditions. I consider two ways to deliver those truth-conditions. The first one posits world-variables in the sentence’s logical form and analyzes those truth-conditions as resulting from two binding possibilities of those variables. The second one proposes that the threshold function introduced by the phonologically null morpheme pos is shiftable in belief contexts. (shrink)

Imprecise probabilities are often modelled with representors, or sets of probability functions. In the recent literature, two ways of interpreting representors have emerged as especially prominent: vagueness interpretations, according to which each probability function in the set represents how the agent's beliefs would be if any vagueness were precisified away; and comparativist interpretations, according to which the set represents those comparative confidence relations that are common to all probability functions therein. I argue that these interpretations have some important limitations. (...) I also propose an alternative—the functional interpretation—according to which representors are best interpreted by reference to the roles they play in the theories that make use of them. (shrink)

It is a prevalent, if not popular, thesis in the metaphysics of belief that facts about an agent’s beliefs depend entirely upon facts about that agent’s underlying credal state. Call this thesis ‘credal reductivism’ and any view that endorses this thesis a ‘credal reductivist view’. An adequate credal reductivist view will accurately predict both when belief occurs and which beliefs are held appropriately, on the basis of credal facts alone. Several well-known—and some lesser known—objections to credal reductivism turn (...) on the inability of standard credal reductivist views to get the latter, normative, results right. This paper presents and defends a novel credal reductivist view according to which belief is a type of “imprecise credence” that escapes these objections by including an extreme credence of 1. (shrink)

Forty years ago, Bayesian philosophers were just catching a new wave of technical innovation, ushering in an era of scoring rules, imprecise credences, and infinitesimal probabilities. Meanwhile, down the hall, Gettier’s 1963 paper [28] was shaping a literature with little obvious interest in the formal programs of Reichenbach, Hempel, and Carnap, or their successors like Jeffrey, Levi, Skyrms, van Fraassen, and Lewis. And how Bayesians might accommodate the discourses of full belief and knowledge was but a glimmer in (...) the eye of Isaac Levi. Forty years later, scoring rules, imprecise credences, and infinitesimal probabilities are all the rage. And the formal and “informal” traditions are increasingly coming together as Bayesian arguments spill over into debates about the foundations of empirical knowledge, skepticism, and more. Relatedly, Bayesian interest in full belief and knowledge has never been greater. Much more besides has happened in the last forty years of Bayesian philosophy, .. (shrink)

On an attractive, naturalistically respectable theory of intentionality, mental contents are a form of measurement system for representing behavioral and psychological dispositions. This chapter argues that a consequence of this view is that the content/attitude distinction is measurement system relative. As a result, there is substantial arbitrariness in the content/attitude distinction. Whether some measurement of mental states counts as characterizing the content of mental states or the attitude is not a question of empirical discovery but of theoretical utility. If correct, (...) this observation has ramifications in the theory of rationality. Some epistemologists and decision theorists have argued that imprecise credences are rationally impermissible, while others have argued that precise credences are rationally impermissible. If the measure theory of mental content is correct, however, then neither imprecise credences nor precise credences can be rationally impermissible. (shrink)

In vice epistemology, bad epistemic outcomes, such as maintaining false beliefs, are interpreted as indicators of blameworthy irrationality. Conversely, a growing trend in philosophical psychology advocates for environmentalist explanations, suggesting these outcomes emerge because rational cognitive processes of faultless individuals falter due to polluted environmental inputs. Building on concrete examples, I first offer a systematic analysis of the relative explanatory merits of that environmentalist project. I then use this analysis to advance the rationality debate, which has recently been identified as (...) stagnating due to an observational equivalence between environmentalist and vice accounts. Although the conceptual imprecision of vice epistemology has frequently been critiqued, the framework developed here reveals that environmentalism is (also) unable to meet various theoretical desiderata. I show why this is so and argue that, to make progress, environmentalism needs a more substantive conception of epistemic rationality. To this end, I propose that a closer engagement with questions of cognitive agency – how rational creatures can “make up” their minds about what to believe – could enable the necessary progress. (shrink)

Moss (2018) argues that rational agents are best thought of not as having degrees of belief in various propositions but as having beliefs in probabilistic contents, or probabilistic beliefs. Probabilistic contents are sets of probability functions. Probabilistic belief states, in turn, are modeled by sets of probabilistic contents, or sets of sets of probability functions. We argue that this Mossean framework is of considerable interest quite independently of its role in Moss’ account of probabilistic knowledge or her semantics (...) for epistemic modals and probability operators. It is an extremely general model of uncertainty. Indeed, it is at least as general and expressively powerful as every other current imprecise probability framework, including lower probabilities, lower previsions, sets of probabilities, sets of desirable gambles, and choice functions. In addition, we partially answer an important question that Moss leaves open, viz., why should rational agents have consistent probabilistic beliefs? We show that an important subclass of Mossean believers avoid Dutch bookability iff they have consistent probabilistic beliefs. (shrink)

It is well known that classical, aka ‘sharp’, Bayesian decision theory, which models belief states as single probability functions, faces a number of serious difficulties with respect to its handling of agnosticism. These difficulties have led to the increasing popularity of so-called ‘imprecise’ models of decision-making, which represent belief states as sets of probability functions. In a recent paper, however, Adam Elga has argued in favour of a putative normative principle of sequential choice that he claims to (...) be borne out by the sharp model but not by any promising incarnation of its imprecise counterpart. After first pointing out that Elga has fallen short of establishing that his principle is indeed uniquely borne out by the sharp model, I cast aspersions on its plausibility. I show that a slight weakening of the principle is satisfied by at least one, but interestingly not all, varieties of the imprecise model and point out that Elga has failed to motivate his stronger commitment. (shrink)

It is natural to think of precise probabilities as being special cases of imprecise probabilities, the special case being when one’s lower and upper probabilities are equal. I argue, however, that it is better to think of the two models as representing two different aspects of our credences, which are often vague to some degree. I show that by combining the two models into one model, and understanding that model as a model of vague credence, a natural interpretation arises (...) that suggests a hypothesis concerning how we can improve the accuracy of aggregate credences. I present empirical results in support of this hypothesis. I also discuss how this modeling interpretation of imprecise probabilities bears upon a philosophical objection that has been raised against them, the so-called inductive learning problem. (shrink)

Calibration inductive logics are based on accepting estimates of relative frequencies, which are used to generate imprecise probabilities. In turn, these imprecise probabilities are intended to guide beliefs and decisions — a process called “calibration”. Two prominent examples are Henry E. Kyburg's system of Evidential Probability and Jon Williamson's version of Objective Bayesianism. There are many unexplored questions about these logics. How well do they perform in the short-run? Under what circumstances do they do better or worse? What (...) is their performance relative to traditional Bayesianism? -/- In this article, we develop an agent-based model of a classic binomial decision problem, including players based on variations of Evidential Probability and Objective Bayesianism. We compare the performances of these players, including against a benchmark player who uses standard Bayesian inductive logic. We find that the calibrated players can match the performance of the Bayesian player, but only with particular acceptance thresholds and decision rules. Among other points, our discussion raises some challenges for characterising “cautious” reasoning using imprecise probabilities. Thus, we demonstrate a new way of systematically comparing imprecise probability systems, and we conclude that calibration inductive logics are surprisingly promising for making decisions. (shrink)

The evidence that we get from peer disagreement is especially problematic from a Bayesian point of view since the belief revision caused by a piece of such evidence cannot be modelled along the lines of Bayesian conditionalisation. This paper explains how exactly this problem arises, what features of peer disagreements are responsible for it, and what lessons should be drawn for both the analysis of peer disagreements and Bayesian conditionalisation as a model of evidence acquisition. In particular, it is (...) pointed out that the same characteristic of evidence from disagreement that explains the problems with Bayesian conditionalisation also suggests an interpretation of suspension of belief in terms of imprecise probabilities. (shrink)