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)

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)

Does rationality require imprecise credences? Many hold that it does: imprecise evidence requires correspondingly imprecise credences. I argue that this is false. The imprecise view faces the same arbitrariness worries that were meant to motivate it in the first place. It faces these worries because it incorporates a certain idealization. But doing away with this idealization effectively collapses the imprecise view into a particular kind of precise view. On this alternative, our attitudes should reflect a (...) kind of normative uncertainty: uncertainty about what to believe. This view refutes the claim that precise credences are inappropriately informative or committal. Some argue that indeterminate evidential support requires imprecise credences; but I argue that indeterminate evidential support instead places indeterminate requirements on credences, and is compatible with the claim that rational credences may always be precise. (shrink)

This article explores the main similarities and differences between Derek Parfit’s notion of imprecise comparability and a related notion I have proposed of parity. I argue that the main difference between imprecise comparability and parity can be understood by reference to ‘the standard view’. The standard view claims that 1) differences between cardinally ranked items can always be measured by a scale of units of the relevant value, and 2) all rankings proceed in terms of the trichotomy of (...) ‘better than’, ‘worse than’, and ‘equally good’. Imprecise comparability, which can be understood in terms of the more familiar notions of cardinality and incommensurability, rejects only the first claim while parity rejects both claims of the standard view. -/- I then argue that insofar as those attracted to imprecise comparability assume that all rankings are trichotomous, as Parfit appears to, the view should be rejected. This is because imprecise equality is not a form of equality but is a sui generis ‘fourth’ basic way in which items can be ranked. We should, I argue, understand imprecise equality as parity, and imprecise comparability as entailing ‘tetrachotomy’ – that if two items are comparable, one must better than, worse than, equal to, or on a par with the other. Thus those attracted to the idea that cardinality can be imprecise should abandon trichotomy and accept parity and tetrachotomy instead. -/- Finally, I illustrate the difference between Parfit’s trichotomous notion of imprecise comparability and parity by examining how each notion might be employed in different solutions to the problem posed by the Repugnant Conclusion in population ethics. I suggest that parity provides the arguably more ecumenical solution to the problem. (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)

This paper is a discussion note on Isaacs et al. (2022), who have claimed to offer a new motivation for imprecise probabilities, based on the mathematical phenomenon of non-measurability. In this note, I clarify some consequences of their proposal. In particular, I show that if their proposal is applied to a bounded 3-dimensional space, then they have to reject at least one of the following: (i) If A is at most as probable as B and B is at most (...) as probable as C, then A is at most as probable as C. (ii) Let A ∩ C = B ∩ C = ∅. A is at most as probable as B iff (A ∪ C) is at most as probable as (B ∪ C). But rejecting either statement seems unattractive. (shrink)

Many have argued that a rational agent's attitude towards a proposition may be better represented by a probability range than by a single number. I show that in such cases an agent will have unstable betting behaviour, and so will behave in an unpredictable way. I use this point to argue against a range of responses to the ‘two bets’ argument for sharp probabilities.

This chapter explores the topic of imprecise probabilities as it relates to model validation. IP is a family of formal methods that aim to provide a better representationRepresentation of severe uncertainty than is possible with standard probabilistic methods. Among the methods discussed here are using sets of probabilities to represent uncertainty, and using functions that do not satisfy the additvity property. We discuss the basics of IP, some examples of IP in computer simulation contexts, possible interpretations of the IP (...) framework and some conceptual problems for the approach. We conclude with a discussion of IP in the context of model validation. (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)

Bayesians often confuse insistence that probability judgment ought to be indeterminate (which is incompatible with Bayesian ideals) with recognition of the presence of imprecision in the determination or measurement of personal probabilities (which is compatible with these ideals). The confusion is discussed and illustrated by remarks in a recent essay by R. C. Jeffrey.

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)

Recently, Derek Parfit has offered a novel solution to the “Repugnant Conclusion” that compared with the existence of many people whose quality of life would be very high, there is some much larger number of people whose existence would be better but whose lives would be barely worth living. On this solution, qualitative differences between two populations will often entail that the populations are merely “imprecisely” comparable. According to Parfit, this fact allows us to avoid the Repugnant Conclusion without violating (...) the transitivity of better than. In this paper, I argue that Parfit’s view nevertheless implies two objectionable conclusions. The first is an alternative version of the Repugnant Conclusion that, Parfit suggests, may not be all that repugnant. The second is a revised version of the first that is nearly identical to the Repugnant Conclusion. I conclude that Parfit’s view offers no escape from repugnance. (shrink)

A number of recent arguments purport to show that imprecise credences are incompatible with accuracy-first epistemology. If correct, this conclusion suggests a conflict between evidential a...

Elga (2010) argues that no plausible decision rule governs action with imprecise credences. I follow Moss (2015a) in claiming that the solution to Elga’s challenge is found in the philosophy of mind, not in devising a special new decision rule. Moss suggests that in decision situations that involve imprecise credences, we must identify with a precise credence, but she says little about identification. By reflecting on the common conception of identification and on what is necessary for Moss’s solution (...) to succeed, I argue that identifying with a precise credence is fundamentally accepting (in the sense of Bratman 1992; Cohen 1989) a proposition about probabilities. The norm on action with imprecise credences is then a special case of the general norm on action and acceptance. I delineate a number of attractive features of this position. (shrink)

Much recent philosophical attention has been devoted to the prospects of the Best System Analysis of chance for yielding high-level chances, including statistical mechanical and special science chances. But a foundational worry about the BSA lurks: there don’t appear to be uniquely correct measures of the degree to which a system exhibits theoretical virtues, such as simplicity, strength, and fit. Nor does there appear to be a uniquely correct exchange rate at which the theoretical virtues trade off against one another (...) in the determination of an overall best system. I argue that there’s no robustly best system for our world – no system that comes out best under every reasonable measure of the theoretical virtues and exchange rate between them – but rather a set of ‘tied-for-best’ systems: a set of very good systems, none of which is robustly best. Among the tied-for-best systems are systems that entail differing high-level probabilities. I argue that the advocate of the BSA should conclude that the high-level chances for our world are imprecise. (shrink)

This article considers the extent to which Bayesian networks with imprecise probabilities, which are used in statistics and computer science for predictive purposes, can be used to represent causal structure. It is argued that the adequacy conditions for causal representation in the precise context—the Causal Markov Condition and Minimality—do not readily translate into the imprecise context. Crucial to this argument is the fact that the independence relation between random variables can be understood in several different ways when the (...) joint probability distribution over those variables is imprecise, none of which provides a compelling basis for the causal interpretation of imprecise Bayes nets. I conclude that there are serious limits to the use of imprecise Bayesian networks to represent causal structure. (shrink)

Contrary to the common-sense view and positivist aspirations, scientific concepts are often imprecise. Many of these concepts are ambiguous, vague, or have an under-specified meaning. In this paper, I discuss how imprecise concepts promote integration in biology and thus benefit science. Previous discussions of this issue focus on the concepts of molecular gene and evolutionary novelty. The concept of molecular gene helps biologists integrate explanatory practices, while the notion of evolutionary novelty helps them integrate research questions into an (...) interdisciplinary problem New directions in the philosophy of science, Springer, Dordrecht, 2014). In what follows, I compare molecular gene and evolutionary novelty to another imprecise concept, namely biological lineage. This concept promotes two other types of scientific integration: it helps biologists integrate theoretical principles and methodologies into different areas of biology. The concept of biological lineage facilitates these types of integration because it is broad and under-specified in ways that the concepts of molecular gene and evolutionary novelty are not. Hence, I use the concept of biological lineage as a case study to reveal types of integration that have been overlooked by philosophers. This case study also shows that even very imprecise concepts can be beneficial to scientific practice. (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)

Randomized controlled clinical trials play an important role in the development of new medical therapies. There is, however, an ethical issue surrounding the use of randomized treatment allocation when the patient is suffering from a life threatening condition and requires immediate treatment. Such patients can only benefit from the treatment they actually receive and not from the alternative therapy, even if it ultimately proves to be superior. We discuss a novel new way to analyse data from such clinical trials based (...) on the use of the recently developed theory of imprecise probabilities. This work draws an explicit distinction between the related but nevertheless distinct questions of inference and decision in clinical trials. The traditional question of scientific interest asks 'Which treatment offers the greater chance of success?' and is the primary reason for conducting the clinical trial. The question of decision concerns the welfare of the patients in the clinical trial, asking whether the accumulated evidence favours one treatment over the other to such an extent that the next patient should decline randomization and instead express a preference for one treatment. Consideration of the decision question within the framework of imprecise probabilities leads to a mathematical definition of equipoise and a method for governing the randomization protocol of a clinical trial. This paper describes in detail the protocol for the conduct of clinical trials based on this new method of analysis, which is illustrated in a retrospective analysis of data from a clinical trial comparing the anti-emetic drugs ondansetron and droperidol in the treatment of postoperative nausea and vomiting. The proposed methodology is compared quantitatively using computer simulation studies with conventional clinical trial designs and is shown to maintain high statistical power with reduced sample sizes, at the expense of a high type I error rate that we argue is irrelevant in some specific circumstances. Particular emphasis is placed on describing the type of medical conditions and treatment comparisons where the new methodology is expected to provide the greatest benefit. (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)

Many have claimed that epistemic rationality sometimes requires us to have imprecise credal states (i.e. credal states representable only by sets of credence functions) rather than precise ones (i.e. credal states representable by single credence functions). Some writers have recently argued that this claim conflicts with accuracy-centered epistemology, i.e., the project of justifying epistemic norms by appealing solely to the overall accuracy of the doxastic states they recommend. But these arguments are far from decisive. In this essay, we prove (...) some new results, which show that there is little hope for reconciling the rationality of credal imprecision with accuracy-centered epistemology. (shrink)

The field of of imprecise probability has matured, in no small part because of Teddy Seidenfeld’s decades of original scholarship and essential contributions to building and sustaining the ISIPTA community. Although the basic idea behind imprecise probability is (at least) 150 years old, a mature mathematical theory has only taken full form in the last 30 years. Interest in imprecise probability during this period has also grown, but many of the ideas that the mature theory serves can (...) be difficult to apprehend to those new to the subject. Although these fundamental ideas are common knowledge in the ISIPTA community, they are expressed, when they are expressed at all, obliquely, over the course of years with students and colleagues. -/- A single essay cannot convey the store of common knowledge from any research community, let alone the ISIPTA community. But, this essay nevertheless is an attempt to guide those familiar with the basic Bayesian framework to appreciate some of the elegant and powerful ideas that underpin the contemporary theory of lower previsions, which is the theory that most people associate with the term ‘imprecise probabilities’. (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)

Impermissivists hold that an agent with a given body of evidence has at most one rationally permitted attitude that she should adopt towards any particular proposition. Permissivists deny this, often motivating permissivism by describing scenarios that pump our intuitions that the agent could reasonably take one of several attitudes toward some proposition. We criticize the following impermissivist response: while it seems like any of that range of attitudes is permissible, what is actually required is the single broad attitude that encompasses (...) all of these single attitudes. While this might seem like an easy way to win over permissivists, we argue that this impermissivist response leads to an indefensible epistemology; permissive intuitions are not so easily co-opted. (shrink)

The paper, analyses the role of measurable concepts in deductive explanation. It is shown that such concepts are, although imprecise in a defined sense, exact in that neutral candidates to them do not arise. An analysis is given of the way in which imprecision is related to generalisation, and it is shown how imprecise concepts are incorporated in testable deductive explanations.

Physical theories often characterize their observables with real number precision. Many non-fundamental theories do so needlessly: they are more precise than they need to be to capture the physical matters of fact about their observables. A natural expectation is that a truly fundamental theory will require its full precision in order to exhaustively capture all of the fundamental physical matters of fact. I argue against this expectation and I show that we do not have good reason to expect that the (...) standard of precision set by successful theories, or even by a truly fundamental theory, will match the granularity of the physical facts. (shrink)

Two compelling principles, the Reasonable Range Principle and the Preservation of Irrelevant Evidence Principle, are necessary conditions that any response to peer disagreements ought to abide by. The Reasonable Range Principle maintains that a resolution to a peer disagreement should not fall outside the range of views expressed by the peers in their dispute, whereas the Preservation of Irrelevant Evidence Principle maintains that a resolution strategy should be able to preserve unanimous judgments of evidential irrelevance among the peers. No standard (...) Bayesian resolution strategy satisfies the PIE Principle, however, and we give a loss aversion argument in support of PIE and against Bayes. The theory of imprecise probability allows one to satisfy both principles, and we introduce the notion of a set-based credal judgment to frame and address a range of subtle issues that arise in peer disagreements. (shrink)

The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution, 410–414, [45]; Bordley Management Science, 28, 1137–1148, [5]; Genest et al. The Annals of Statistics, 487–501, [21]; Genest and Zidek Statistical Science, 114–135, [23]; Mongin Journal of Economic Theory, 66, 313–351, [46]; Clemen and (...) Winkler Risk Analysis, 19, 187–203, [7]; Dietrich and List [14]; Herzberg Theory and Decision, 1–19, [28]). We argue that this assumption is not always in order. We show how to extend the canonical mathematical framework for pooling to cover pooling with imprecise probabilities by employing set-valued pooling functions and generalizing common pooling axioms accordingly. As a proof of concept, we then show that one IP construction satisfies a number of central pooling axioms that are not jointly satisfied by any of the standard pooling recipes on pain of triviality. Following Levi, 3–11, [39]), we also argue that IP models admit of a much better philosophical motivation as a model of rational consensus. (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)

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)

In his entry on "Quantum Logic and Probability Theory" in the Stanford Encyclopedia of Philosophy, Alexander Wilce (2012) writes that "it is uncontroversial (though remarkable) the formal apparatus quantum mechanics reduces neatly to a generalization of classical probability in which the role played by a Boolean algebra of events in the latter is taken over the 'quantum logic' of projection operators on a Hilbert space." For a long time, Patrick Suppes has opposed this view (see, for example, the paper collected (...) in Suppes and Zanotti (1996). Instead of changing the logic and moving from a Boolean algebra to a non-Boolean algebra, one can also 'save the phenomena' by weakening the axioms of probability theory and work instead with upper and lower probabilities. However, it is fair to say that despite Suppes' efforts upper and lower probabilities are not particularly popular in physics as well as in the foundations of physics, at least so far. Instead, quantum logic is booming again, especially since quantum information and computation became hot topics. Interestingly, however, imprecise probabilities are becoming more and more popular in formal epistemology as recent work by authors such as James Joye (2010) and Roger White (2010) demonstrates. (shrink)

Suppose you can save one group of people or a larger group of different people, but you cannot save both groups. Are you morally required, ceteris paribus, to save the larger group? Some say, “No.” Far more say, without qualification, “Yes.” But some say, “It depends on the sizes of the groups.” In this paper, I argue that an attractive moral principle that seems on its face to support the second answer in fact supports a version of the third. In (...) the process, I defend some revisionary claims about how the lives and deaths of different people compare evaluatively to one another. The most important of these for my purposes is the claim that the deaths of different people are on a par, other things being equal. (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)

An examination of topics involved in statistical reasoning with imprecise probabilities. The book discusses assessment and elicitation, extensions, envelopes and decisions, the importance of imprecision, conditional previsions and coherent statistical models.

This essay gives an account of epistemic deference for agents with imprecise credences. I look at the two main imprecise deference principles in the literature, known as Identity Reflection and Pointwise Reflection (Moss, 2021). I show that Pointwise Reflection is strictly weaker than Identity Reflection, and argue that, if you are certain you will update by conditionalisation, you should defer to your future self according to Identity Reflection. Then I give a more general justification for Pointwise and Identity (...) Reflection from the assumption that you defer to someone whenever you consider their doxastic state to be better than yours, in the sense of leading to better decision-making. (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)

According to van Fraassen, inference to the best explanation (IBE) is incompatible with Bayesianism. To argue to the contrary, many philosophers have suggested hybrid models of scientific reasoning with both explanationist and probabilistic elements. This paper offers another such model with two novel features. First, its Bayesian component is imprecise. Second, the domain of credence functions can be extended.

Current diagnostic criteria for schizophrenia place emphasis on delusions and hallucinations, whereas the classical descriptions of schizophrenia by Kraepelin and Bleuler emphasized disorganization and impoverishment of mental activity. Despite the availability of antipsychotic medication for treating delusions and hallucinations, many patients continue to experience persisting disability. Improving treatment requires a better understanding of the processes leading to persisting disability. We recently introduced the term classical schizophrenia to describe cases with disorganized and impoverished mental activity, cognitive impairment and predisposition to persisting (...) disability. Recent evidence reveals that a polygenic score indicating risk for schizophrenia predicts severity of the features of classical schizophrenia: disorganization, and to a lesser extent, impoverishment of mental activity and cognitive impairment. Current understanding of brain function attributes a cardinal role to predictive coding: the process of generating models of the world that are successively updated in light of confirmation or contradiction by subsequent sensory information. It has been proposed that abnormalities of these predictive processes account for delusions and hallucinations. Here we examine the evidence provided by electrophysiology and fMRI indicating that imprecise predictive coding is the core pathological process in classical schizophrenia, accounting for disorganization, psychomotor poverty and cognitive impairment. Functional imaging reveals aberrant brain activity at network hubs engaged during encoding of predictions. We discuss the possibility that frequent prediction errors might promote excess release of the neurotransmitter, dopamine, thereby accounting for the occurrence of episodes of florid psychotic symptoms including delusions and hallucinations in classical schizophrenia. While the predictive coding hypotheses partially accounts for the time-course of classical schizophrenia, the overall body of evidence indicates that environmental factors also contribute. We discuss the evidence that chronic inflammation is a mechanism that might link diverse genetic and environmental etiological factors, and contribute to the proposed imprecision of predictive coding. (shrink)

Can we extend accuracy-based epistemic utility theory to imprecise credences? There's no obvious way of proceeding: some stipulations will be necessary for either (i) the notion of accuracy or (ii) the epistemic decision rule. With some prima facie plausible stipulations, imprecise credences are always required. With others, they’re always impermissible. Care is needed to reach the familiar evidential view of imprecise credence: that whether precise or imprecise credences are required depends on the character of one's evidence. (...) I propose an epistemic utility theoretic defense of a common view about how evidence places demands on imprecise credence: that your spread of credence should cover the range of chance hypotheses left open by your evidence. I argue that objections to the form of epistemic utility theoretic argument that I use will extend to the standard motivation for epistemically mandatory imprecise credences. (shrink)

Unspecific evidence calls for imprecise credence. My aim is to vindicate this thought. First, I will pin down what it is that makes one's imprecise credences more or less epistemically valuable. Then I will use this account of epistemic value to delineate a class of reasonable epistemic scoring rules for imprecise credences. Finally, I will show that if we plump for one of these scoring rules as our measure of epistemic value or utility, then a popular family (...) of decision rules recommends imprecise credences. In particular, a range of Hurwicz criteria, which generalise the Maximin decision rule, recommend imprecise credences. If correct, the moral is this: an agent who adopts precise credences, rather than imprecise ones, in the face of unspecific and incomplete evidence, goes wrong by gambling with the epistemic utility of her doxastic state in too risky a fashion. Precise credences represent an overly risky epistemic bet, according to the Hurwicz criteria. (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 special issue of the International Journal of Approximate Reasoning grew out of the 8th International Symposium on Imprecise Probability: Theories and Applications. The symposium was organized by the Society for Imprecise Probability: Theories and Applications at the Université de Technologie de Compiègne in July 2013. The biennial ISIPTA meetings are well established among international conferences on generalized methods for uncertainty quantification. The first ISIPTA took place in Gent in 1999, followed by meetings in Cornell, Lugano, Carnegie Mellon, (...) Prague, Durham and Innsbruck. Compiègne proved to be a very nice location for ISIPTA 2013, offering wonderful opportunities for collaborations and discussions, as well as sightseeing places such as its imperial palace. (shrink)

Those who model doxastic states with a set of probability functions, rather than a single function, face a pressing challenge: can they provide a plausible decision theory compatible with their view? Adam Elga and others claim that they cannot, and that the set of functions model should be rejected for this reason. This paper aims to answer this challenge. The key insight is that the set of functions model can be seen as an instance of the supervaluationist approach to vagueness (...) more generally. We can then generate our decision theory by applying the general supervaluationist semantics to decision-theoretic claims. The result: if an action is permissible according to all functions in the set, it’s determinately permissible; if impermissible according to all, determinately impermissible; and – crucially – if permissible according to some, but not all, it’s indeterminate whether it’s permissible. This proposal handles with ease some difficult cases ) on which alternative decision theories falter. One reason this view has been overlooked in the literature thus far is that all parties to the debate presuppose that an acceptable decision theory must classify each action as either permissible or impermissible. But I will argue that this thought is misguided. Seeing the set of functions model as an instance of supervaluationism provides a compelling motivation for the claim that there can be indeterminacy in the rationality of some actions. (shrink)