Hybrid belief aggregation addresses aggregation of individual probabilistic beliefs into collective binary beliefs. In line with the development of judgment aggregation theory, our research delves into the identification of precise agenda conditions associated with some key impossibility theorems in the context of hybrid belief aggregation. We determine the necessary and sufficient level of logical interconnection between the propositions in an agenda for some key impossibilities to arise. Specifically, we prove three characterization theorems (...) about hybrid belief aggregation: (i) Precisely the path-connected and pair-negatable agendas lead to the ‘oligarchy result’—only oligarchic rules satisfy universal domain, proposition-wise independence, respect for unanimity, and deductive closure of collective beliefs. (ii) Precisely the negation-connected agendas lead to the ‘triviality result’—only unanimity rules satisfy those conditions as well as anonymity. (iii) Precisely the blocked agendas lead to the ‘non-existence result’—no rules satisfy those conditions as well as completeness and consistency of collective beliefs. Furthermore, we compare these novel findings with existing agenda-theoretic characterization theorems in the domains of judgment aggregation and belief binarization. (shrink)

This paper addresses how multiple individual credences on logically related issues should be aggregated into collective binary beliefs. We call this binarizing belief aggregation. It is vulnerable to dilemmas such as the discursive dilemma or the lottery paradox: proposition-wise independent aggregation can generate inconsistent or not deductively closed collective judgments. Addressing this challenge using the familiar axiomatic approach, we introduce general conditions on a binarizing belief aggregation rule, including rationality conditions on individual inputs and collective (...) outputs, and determine which rules (if any) satisfy different combinations of these conditions. Furthermore, we analyze similarities and differences between our proofs and other related proofs in the literature and conclude that the problem of binarizing belief aggregation is a free-standing aggregation problem not reducible to judgment aggregation or probabilistic opinion pooling. (shrink)

How do opinion diversity and belief polarisation affect epistemic group decision-making, particularly if decisions must be made without delay and on the basis of permissive evidence? In an agent-based model, we track the consistency of group opinions aggregated through sentence-wise majority voting. Simulations on the model reveal that high opinion diversity, but not polarisation, incurs a significant inconsistency risk. These results indicate that epistemic group decisions based on permissive evidence can be particularly difficult for diverse groups. The results also (...) improve our understanding of what can reasonably be expected of expert groups, and where expert advice might have limits. (shrink)

The debate on the epistemology of disagreement has so far focused almost exclusively on cases of disagreement between individual persons. Yet, many social epistemologists agree that at least certain kinds of groups are equally capable of having beliefs that are open to epistemic evaluation. If so, we should expect a comprehensive epistemology of disagreement to accommodate cases of disagreement between group agents, such as juries, governments, companies, and the like. However, this raises a number of fundamental questions concerning what it (...) means for groups to be epistemic peers and to disagree with each other. In this paper, we explore what group peer disagreement amounts to given that we think of group belief in terms of List and Pettit’s ‘belief aggregation model’. We then discuss how the so-called ‘equal weight view’ of peer disagreement is best accommodated within this framework. The account that seems most promising to us says, roughly, that the parties to a group peer disagreement should adopt the belief that results from applying the most suitable belief aggregation function for the combined group on all members of the combined group. To motivate this view, we test it against various intuitive cases, derive some of its notable implications, and discuss how it relates to the equal weight view of individual peer disagreement. (shrink)

The paper is devoted to such a unique phenomenon of so-called written or fixed folklore, as Ukrainian epigraphic rushnyks containing a specific verbal formula “I was embroidering the towel with a sincere hand and praying to God for fate and godsend” which were popular at the end of the 19th and the first half of the 20th century. Considering the communication of these towels according to the well-known multimodal scheme, the author states that such rushnyks with inscriptions could use all (...) five modes (spatial, visual, linguistic, aural, and gestural one), having already become not quite rushnyks in its traditional sense. On the one hand, these embroidered towels functioned as drawings or open books (locating on the wall with two hanging ends). On the other hand, they also could be gifted for the road, thus symbolizing the path, as it was typical for more traditional and older samples. Concerning modern interpretation of these towels, hybrid beliefs and identities are frequently connected with them. In addition, the article claims that rushnyks’ inscriptions, functioning simultaneously in several roles (in particular, they could be both embroidered and sung), provoke us to develop more deeply the theory of speech acts in linguistic pragmatics. (shrink)

Strong epistemic anti-individualism—i.e., the claim that knowledge can be irreducibly social—is increasingly debated within mainstream and social epistemology. Most existing approaches attempt to argue for the view on the basis of aggregative analyses, which focus on the way certain groups aggregate the epistemic attitudes of their members. Such approaches are well motivated, given that many groups to which we often ascribe group knowledge—such as juries and committees—operate in this way. Yet another way that group knowledge can be generated is on (...) the basis of epistemic collaborations, such as scientific research teams and Transactive Memory Systems. To produce knowledge, epistemic collaborations rely heavily on the mutual interactions of their group members. This is a distinctive feature of epistemic collaborations that renders them resistant to aggregative analyses. To accommodate this kind of group knowledge, the paper combines virtue reliabilism with the hypothesis of distributed cognition in order to introduce the hybrid approach of distributed virtue reliabilism. On this view, beliefs produced by epistemic collaborations entertain positive epistemic standing in virtue of the mutual interactions of their group members; this positive epistemic standing is a collective property; epistemic collaborations qualify as epistemic group agents; collaborative knowledge is a special kind of group knowledge, motivating strong epistemic anti-individualism in a distinctive way. (shrink)

Binarizing belief aggregation tackles the problem of aggregating individuals’ probabilistic beliefs on logically connected propositions into the group’s binary beliefs. One common approach to associating probabilistic beliefs with binary beliefs would be applying thresholds to probabilities. This paper aims to introduce and classify a range of threshold-based binarizing belief aggregation rules while characterizing them based on different forms of monotonicity and other properties.

The aggregation of individual judgments on logically interconnected propositions into a collective decision on the same propositions is called judgment aggregation. Literature in social choice and political theory has claimed that judgment aggregation raises serious concerns. For example, consider a set of premises and a conclusion where the latter is logically equivalent to the former. When majority voting is applied to some propositions (the premises) it may give a different outcome than majority voting applied to another set (...) of propositions (the conclusion). This problem is known as the discursive dilemma (or paradox). The discursive dilemma is a serious problem since it is not clear whether a collective outcome exists in these cases, and if it does, what it is like. Moreover, the two suggested escape-routes from the paradox—the so-called premise-based procedure and the conclusion-based procedure—are not, as I will show, satisfactory methods for group decision-making. In this paper I introduce a new aggregation procedure inspired by an operator defined in artificial intelligence in order to merge belief bases. The result is that we do not need to worry about paradoxical outcomes, since these arise only when inconsistent collective judgments are not ruled out from the set of possible solutions. (shrink)

We introduce a new operator – belief fusion– which aggregates the beliefs of two agents, each informed by a subset of sources ranked by reliability. In the process we definepedigreed belief states, which enrich standard belief states with the source of each piece of information. We note that the fusion operator satisfies the invariants of idempotence, associativity, and commutativity. As a result, it can be iterated without difficulty. We also define belief diffusion; whereas fusion generally produces (...) a belief state with more information than is possessed by either of its two arguments, diffusion produces a state with less information. Fusion and diffusion are symmetric operators, and together define a distributive lattice. Finally, we show that AGM revision can be viewed as fusion between a novice and an expert. (shrink)

What is the relationship between degrees of belief and binary beliefs? Can the latter be expressed as a function of the former—a so-called “belief-binarization rule”—without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from the perspective of judgment-aggregation theory. Although some formal similarities between belief binarization and judgment aggregation have been noted before, the connection between the two problems has not yet been studied in full generality. (...) In this paper, we seek to fill this gap. The paper is organized around a baseline impossibility theorem, which we use to map out the space of possible solutions to the belief-binarization problem. Our theorem shows that, except in limiting cases, there exists no belief-binarization rule satisfying four initially plausible desiderata. Surprisingly, this result is a direct corollary of the judgment-aggregation variant of Arrow’s classic impossibility theorem in social choice theory. (shrink)

We introduce a new operator – belief fusion– which aggregates the beliefs of two agents, each informed by a subset of sources ranked by reliability. In the process we definepedigreed belief states, which enrich standard belief states with the source of each piece of information. We note that the fusion operator satisfies the invariants of idempotence, associativity, and commutativity. As a result, it can be iterated without difficulty. We also define belief diffusion; whereas fusion generally produces (...) a belief state with more information than is possessed by either of its two arguments, diffusion produces a state with less information. Fusion and diffusion are symmetric operators, and together define a distributive lattice. Finally, we show that AGM revision can be viewed as fusion between a novice and an expert. (shrink)

In this paper we explore the relation between three areas: judgment aggregation, belief merging and social choice theory. Judgment aggregation studies how to aggregate individual judgments on logically interconnected propositions into a collective decision on the same propositions. When majority voting is applied to some propositions it may however give a different outcome than majority voting applied to another set of propositions. Starting from this so-called doctrinal paradox, the paper surveys the literature on judgment aggregation, and (...) shows that the application of a well known belief merging operator can dissolve the paradox. Finally, the use of distances is shown to establish a link between belief merging and preference aggregation in social choice theory. (shrink)

When a group of agents attempts to reach an agreement on certain issues, it is usually desirable that the resulting consensus be as close as possible to the original judgments of the individuals. However, when these judgments are logically connected to further beliefs, the notion of closeness should also take into account to what extent the individuals would have to revise their entire belief set to reach an agreement. In this work, we present a model for generation of agreement (...) with respect to a given agenda which allows individual epistemic entrenchment to influence the value of the consensus. While the postulates for the transformation function and their construction resemble those of AGM belief revision, the notion of an agenda is adapted from the theory of judgment aggregation. This allows our model to connect both frameworks. (shrink)

One important trend in the debate over expressivism and cognitivism is the emergence of ‘hybrid’ or ‘ecumenical’ theories. According to such theories, moral sentences express both beliefs, as cognitivism has it, and desire-like states, as expressivism has it. One may wonder, though, whether the hybrid move is as novel as its advocates seem to take it to be—or whether it simply leads us back to the conceptions of early expressivists, such as Charles Stevenson or Richard Hare. Michael Ridge (...) has recently argued that we ought not to see Hare as a hybrid expressivist because Hare’s approach allows for moral sentences that do not express any descriptive beliefs at all. Yet, Ridge’s reading has been challenged by John Eriksson, who even goes as far as to claim that modern hybrid expressivists should follow in Hare’s footsteps because it is Hare’s framework that actually provides a solution to the so-called ‘Frege-Geach problem’. In the present paper, I first want to show that we can defend Eriksson’s reading with regard to the official version of Hare’s theory. I will, secondly, argue that, in line with what we may take to be Ridge’s critical perspective on Hare, this official version faces serious difficulties, resulting from the possibility of unknown speaker standards. Thirdly, I will demonstrate that a modern reconstruction of Hare in terms of what I will refer to as ‘de dicto beliefs’, though in principle possible, will not allow us to solve the ‘Frege-Geach problem’. (shrink)

Betting methods, of which de Finetti's Dutch Book is by far the most well-known, are uncertainty modelling devices which accomplish a twofold aim. Whilst providing an interpretation of the relevant measure of uncertainty, they also provide a formal definition of coherence. The main purpose of this paper is to put forward a betting method for belief functions on MV-algebras of many-valued events which allows us to isolate the corresponding coherence criterion, which we term coherence in the aggregate. Our framework (...) generalises the classical Dutch Book method. (shrink)

The article proceeds upon the assumption that the beliefs and degrees of belief of rational agents satisfy a number of constraints, including: consistency and deductive closure for belief sets, conformity to the axioms of probability for degrees of belief, and the Lockean Thesis concerning the relationship between belief and degree of belief. Assuming that the beliefs and degrees of belief of both individuals and collectives satisfy the preceding three constraints, I discuss what further constraints (...) may be imposed on the aggregation of beliefs and degrees of belief. Some possibility and impossibility results are presented. The possibility results suggest that the three proposed rationality constraints are compatible with reasonable aggregation procedures for belief and degree of belief. (shrink)

The main aim of the present paper is to use a proof system for hybrid modal logic to formalize what are called false-belief tasks in cognitive psychology, thereby investigating the interplay between cognition and logical reasoning about belief. We consider two different versions of the Smarties task, involving respectively a shift of perspective to another person and to another time. Our formalizations disclose that despite this difference, the two versions of the Smarties task have exactly the same (...) underlying logical structure. We also consider the Sally-Anne task, having a more complicated logical structure, presupposing a “principle of inertia” saying that a belief is preserved over time, unless there is belief to the contrary. (shrink)

Judgment aggregation is naturally applied to the modeling of collective attitudes. In the individual case, we represent agents as having not just beliefs, but also as supporting them with reasons. Can the Judgment Aggregation help model a concept of collective reason? I argue that the resources of the standard judgment aggregation framework are insufficiently general. I develop a generalization of the framework that improves along this dimension. In the new framework, new aggregation rules become available, as (...) well as a natural account of collective reasons. (shrink)

In the paper (Braüner, 2014) we were concerned with logical formalizations of the reasoning involved in giving correct responses to the psychological tests called the Sally-Anne test and the Smarties test, which test children’s ability to ascribe false beliefs to others. A key feature of the formal proofs given in that paper is that they explicitly formalize the perspective shift to another person that is required for figuring out the correct answers – you have to put yourself in another person’s (...) shoes, so to speak, to give the correct answer. We shall in the present paper be concerned with what happens when answers are given that are not correct. The typical incorrect answers indicate that children failing false-belief tests have problems shifting to a perspective different from their own, to be more precise, they simply reason from their own perspective. Based on this hypothesis, we in the present paper give logical formalizations that in a systematic way model the typical incorrect answers. The remarkable fact that the incorrect answers can be derived using logically correct rules indicates that the origin of the mistakes does not lie in the children’s logical reasoning, but rather in a wrong interpretation of the task. (shrink)

Neural language models (NLMs) are susceptible to producing inconsistent output. This paper proposes a new diagnosis as well as a novel remedy for NLMs' incoherence. We train NLMs on synthetic text corpora that are created by simulating text production in a society. For diagnostic purposes, we explicitly model the individual belief systems of artificial agents (authors) who produce corpus texts. NLMs, trained on those texts, can be shown to aggregate the judgments of individual authors during pre-training according to sentence-wise (...) vote ratios (roughly, reporting frequencies), which inevitably leads to so-called discursive dilemmas: aggregate judgments are inconsistent even though all individual belief states are consistent. As a remedy for such inconsistencies, we develop a self-training procedure—inspired by the concept of reflective equilibrium—that effectively reduces the extent of logical incoherence in a model's belief system, corrects global mis-confidence, and eventually allows the model to settle on a new, epistemically superior belief state. Thus, social choice theory helps to understand why NLMs are prone to produce inconsistencies; epistemology suggests how to get rid of them. (shrink)

Most non-consequentialists “let the numbers count” when one can save either a lesser or greater number from equal or similar harm. But they are wary of doing so when one can save either a small number from grave harm or instead a very large number from minor harm. Limited aggregation is an approach that reconciles these two commitments. It is motivated by a powerful idea: our decision whom to save should respect each person who has a claim to our (...) help, including those whom we fail to save. However, it has recently been argued that it is open to decisive objections. I develop a new limitedly aggregative view:Hybrid Balance Relevant Claims. This view is well grounded in the reasons we have to be skeptical of aggregation and resolves all recent challenges by paying careful attention to the rationale for limited aggregation. (shrink)

How can the propositional attitudes of several individuals be aggregated into overall collective propositional attitudes? Although there are large bodies of work on the aggregation of various special kinds of propositional attitudes, such as preferences, judgments, probabilities and utilities, the aggregation of propositional attitudes is seldom studied in full generality. In this paper, we seek to contribute to filling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation and prove (...) two new theorems. Our first theorem simultaneously characterizes some prominent aggregation rules in the cases of probability, judgment and preference aggregation, including linear opinion pooling and Arrovian dictatorships. Our second theorem abstracts even further from the specific kinds of attitudes in question and describes the properties of a large class of aggrega tion rules applicable to a variety of belief-like attitudes. Our approach integrates some previously disconnected areas of investigation. (shrink)

As the ongoing literature on the paradoxes of the Lottery and the Preface reminds us, the nature of the relation between probability and rational acceptability remains far from settled. This article provides a novel perspective on the matter by exploiting a recently noted structural parallel with the problem of judgment aggregation. After offering a number of general desiderata on the relation between finite probability models and sets of accepted sentences in a Boolean sentential language, it is noted that a (...) number of these constraints will be satisfied if and only if acceptable sentences are true under all valuations in a distinguished non-empty set W. Drawing inspiration from distance-based aggregation procedures, various scoring rule based membership conditions for W are discussed and a possible point of contact with ranking theory is considered. The paper closes with various suggestions for further research. (shrink)

How can the propositional attitudes of several individuals be aggregated into overall collective propositional attitudes? Although there are large bodies of work on the aggregation of various special kinds of propositional attitudes, such as preferences, judgments, probabilities and utilities, the aggregation of propositional attitudes is seldom studied in full generality. In this paper, we seek to contribute to filling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation and prove (...) two new theorems. Our first theorem simultaneously characterizes some prominent aggregation rules in the cases of probability, judgment and preference aggregation, including linear opinion pooling and Arrovian dictatorships. Our second theorem abstracts even further from the specific kinds of attitudes in question and describes the properties of a large class of aggregation rules applicable to a variety of belief-like attitudes. Our approach integrates some previously disconnected areas of investigation. (shrink)

The theory of belief revision and merging has recently been applied to judgement aggregation. In this paper I argue that judgements are best aggregated by merging the evidence on which they are based, rather than by directly merging the judgements themselves. This leads to a threestep strategy for judgement aggregation. First, merge the evidence bases of the various agents using some method of belief merging. Second, determine which degrees of belief one should adopt on the (...) basis of this merged evidence base, by applying objective Bayesian theory. Third, determine which judgements are appropriate given these degrees of belief by applying a decision-theoretic account of rational judgement formation. (shrink)

Michael Ridge presents an original expressivist theory of normative judgments--Ecumenical Expressivism--which offers distinctive treatments of key problems in metaethics, semantics, and practical reasoning. He argues that normative judgments are hybrid states partly constituted by ordinary beliefs and partly constituted by desire-like states.

This paper is a survey of recent ‘hybrid’ approaches to metaethics, according to which moral sentences, in some sense or other, express both beliefs and desires. I try to show what kinds of theoretical issues come up at the different choice points we encounter in developing such a view, to raise some problems and explain where they come from, and to begin to get a sense for what the payoff of such views can be, and what they will need (...) to do in order to earn that payoff. (shrink)

We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then shown (...) to be represented by a linear transformation of the representations of the individual preorders. Further Pareto conditions on the social preorder correspond to positivity conditions on the transformation. When all the Pareto conditions hold and the population is finite, the social preorder is represented by a sum of individual preorder representations. We provide two applications. The first yields an extremely general version of Harsanyi's social aggregation theorem. The second generalizes a classic result about linear opinion pooling. (shrink)

Judgment aggregation studies how collective opinions arise from the aggregation of individual ones. This article surveys a variety of aggregation rules (possible ways of aggregating individual judgments into collective ones). Aggregation by majority opinion is known to satisfy some but not all the desiderata for an aggregation rule. More general impossibility results show that not all the natural desiderata can be satisfied by a single aggregation rule. To interpret these results, we focus here on (...) some applications of judgment aggregation models in Epistemology. In particular, we explore their possible role in an account of collective belief and collective reason. The focus on these applications allows us to give precise answers concerning which of the natural desiderata must be abandoned. (shrink)

Disagreement is a pervasive feature of human discourse and a crucial force in shaping our social reality. From mundane squabbles about matters of taste to high-stakes disputes about law and public policy, the way we express and navigate disagreement plays a central role in both our personal and political lives. Legal discourse, in particular, is rife with disagreement - it is the very bread and butter of courtroom argument and legal scholarship alike. Consider a debate between two legal philosophers, Ronald (...) and Herbert, about the Eighth Amendment of the U.S. Constitution, which prohibits ‘cruel and unusual punishment’. Ronald asserts: ‘It is the law that capital punishment is prohibited’. In response, Herbert states: ‘It is not the law that capital punishment is prohibited’. We intuitively think Ronald and Herbert are disagreeing, which reveals in the fact that they are licensed to use ex¬pressions like no (it isn’t) and nuh-uh when responding to their opponent’s claim. But despite the ubiquity and significance of legal disagreement, its precise nature remains elusive. This chapter discusses what exactly is going on when two people disagree about what the law requires, and how can hybrid theory may answer this question. (shrink)

In this paper, we explore how we should aggregate the degrees of belief of a group of agents to give a single coherent set of degrees of belief, when at least some of those agents might be probabilistically incoherent. There are a number of ways of aggregating degrees of belief, and there are a number of ways of fixing incoherent degrees of belief. When we have picked one of each, should we aggregate first and then fix, (...) or fix first and then aggregate? Or should we try to do both at once? And when do these different procedures agree with one another? In this paper, we focus particularly on the final question. (shrink)

There are many reasons we might want to take the opinions of various individuals and pool them to give the opinions of the group they constitute. If all the individuals in the group have probabilistic opinions about the same propositions, there is a host of pooling functions we might deploy, such as linear or geometric pooling. However, there are also cases where different members of the group assign probabilities to different sets of propositions, which might overlap a lot, a little, (...) or not at all. There are far fewer proposals for how to proceed in these cases, and those there are have undesirable features. I begin by considering four proposals and arguing that they don't work. Then I'll describe my own proposal, which is intended to cover the situation in which we want to pool the individual opinions in order to ascribe an opinion to the group considered as an agent in its own right. (shrink)

: In recent literature supporting a hybrid view between metaethical cognitivism and noncognitivist expressivism, much has been made of an analogy between moral terms and pejoratives. The analogy is based on the plausible idea that pejorative slurs are used to express both a descriptive belief and a negative attitude. The analogy looks promising insofar as it encourages the kinds of features we should want from a hybrid expressivist view for moral language. But the analogy between moral terms (...) and pejorative slurs is also problematic. In this paper, I argue for two main ways in which we should distinguish between two different types of pejorative terms: slurs, on the one hand, and what I call general pejorative terms, on the other. I examine the problems with the analogy between slurs and moral terms and conclude that general pejorative terms like ‘jerk’ are a better candidate on which to model the potential dual-use behavior of moral terms. So if hybrid theorists are looking for a dual-use model for moral language, they should be careful to base their analogies on general pejoratives, rather than slurs. (shrink)

This paper addresses the problem of judgment aggregation in science. How should scientists decide which propositions to assert in a collaborative document? We distinguish the question of what to write in a collaborative document from the question of collective belief. We argue that recent objections to the application of the formal literature on judgment aggregation to the problem of judgment aggregation in science apply to the latter, not the former question. The formal literature has introduced various (...) desiderata for an aggregation procedure. Proposition-wise majority voting emerges as a procedure that satisfies all desiderata which represent norms of science. An interesting consequence is that not all collaborating scientists need to endorse every proposition asserted in a collaborative document. (shrink)

Philosophers should consider a hybrid meta-ethical theory that includes elements of both moral expressivism and moral error theory. Proponents of such an expressivist-error theory hold that all moral utterances are either expressions of attitudes or expressions of false beliefs. Such a hybrid theory has two advantages over pure expressivism, because hybrid theorists can offer a more plausible account of the moral utterances that seem to be used to express beliefs, and hybrid theorists can provide a simpler (...) solution to the Frege-Geach problem. The hybrid theory has three advantages over pure error theory, because hybrid theorists can offer a more plausible account of the moral utterances that seem to be used to express attitudes, hybrid theorists can more easily explain moral motivation, and hybrid theorists can avoid the implausible claim that all moral discourse is radically mistaken. Accordingly, such a hybrid theory should be more attractive than pure expressivism or pure error theory to philosophers who are skeptical about moral facts and truth. (shrink)

The merging/fusion of belief/data collections in propositional logic form is a topic that has received due attention within the domains of database and AI research. A distinction can be made between two types of scenarios to which the process of merging can be applied. In the first type, the collections represent preferences, such as the voting choices of a group of people, that need to be aggregated so as to give a consistent result that in some way best represents (...) the collective judgement of the group. In the second type, the collections represent factual data that is to be aggregated with an aim of obtaining a result that maximises factual correctness. After introducing a general framework for belief merging via some prominent literature on the topic, this paper then introduces and considers a method for belief merging with the second type of scenario in mind. Its suitability is corroborated by demonstrating how it can be seen as a special case of a merging procedure that combines aggregation of probabilities and maximisation of expected truthlikeness. (shrink)

Hybrid theories are metaethical theories concerning the content of sentences about moral value. These theories claim that sentences with ethical content express two kinds of mental state. One state is an affect‐like state. The other is a belief‐like state. The expressed affect‐like state will involve a moral attitude of some kind, such as approval, but it is not part of the truth‐conditions of the sentence. We can divide hybridists into two kinds.

A common starting point for ‘going hybrid’ is the thought that moral discourse somehow combines belief and desire-like aspects, or is both descriptive and expressive. Hybrid meta-ethical theories aim to give an account of moral discourse that is sufficiently sensitive to both its cognitive and its affective, or descriptive and expressive, dimensions. They hold at least one of the following: moral thought: moral judgements have belief and desire-like aspects or elements; moral language: moral utterances both ascribe (...) properties and express desire-like attitudes. This entry concerns hybrid theories of moral language. The main division within such theories is between those treating the expression of desire-like attitudes as semantic and those treating it as pragmatic. This entry exclusively focuses on pragmatic forms of and examines the prospects for treating moral attitude expression as working via certain standard pragmatic mechanisms. I explain these mechanisms, outline the properties that standardly define them, and test to see whether moral attitude expression matches them. At the end, I briefly explain a more minimal pragmatic alternative. The main conclusions are that we should disregard presupposition and conventional implicature views and that the most plausible options for a pragmatic hybrid view are a generalised conversational implicature view and a more minimal pragmatic view. (shrink)

Epistemic expressivists maintain, to a first approximation, that epistemic assertions express non-cognitive mental states, like endorsements, valuations, or pro-attitudes, rather than cognitive mental states such as beliefs. Proponents of epistemic expressivism include Chrisman, Gibbard, Field, Kappel, and Ridge, among others. In this paper, I argue for an alternative view to epistemic expressivism. The view I seek to advocate is inspired by hybrid expressivist theories about moral judgments, Copp Oxford studies in metaethics, 2009), Finlay, Strandberg ). According to these (...) class='Hi'>hybrid views, moral judgments express semantically cognitive or representational states and pragmatically convey the speaker’s non-cognitive mental states via implicatures. I will argue that a particular version of this view can reasonably be extended to epistemic judgments and that it has several advantages over its expressivist and cognitivist competitors. In particular, I will try to show that there exist certain phenomena in the epistemic domain that seem to be best accounted for by expressivist theories of epistemic judgments. However, a version of hybrid expressivism that maintains that epistemic judgments convey the attributor’s non-cognitive mental states via generalized conversational implicatures is able to account for these phenomena just as well without running afoul of the main problems that have been identified for different versions of epistemic expressivism. (shrink)

Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only preference aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and combine individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs linearly, but (...) achieves only static rationality. Our characterisation of linear-geometric preference aggregation has two corollaries: a characterisation of linear aggregation of values (Harsanyi's Theorem) and a characterisation of geometric aggregation of beliefs. (shrink)

The problem of how to rationally aggregate probability measures occurs in particular when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and when an individual whose belief system is compatible with several probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory. We investigate this problem by first recalling some negative results from preference (...) and judgment aggregation theory which show that the aggregate of several probability measures should not be conceived as the probability measure induced by the aggregate of the corresponding expected utility preferences. We describe how McConway’s :410–414, 1981) theory of probabilistic opinion pooling can be generalised to cover the case of the aggregation of infinite profiles of finitely additive probability measures, too; we prove the existence of aggregation functionals satisfying responsiveness axioms à la McConway plus additional desiderata even for infinite electorates. On the basis of the theory of propositional-attitude aggregation, we argue that this is the most natural aggregation theory for probability measures. Our aggregation functionals for the case of infinite electorates are neither oligarchic nor integral-based and satisfy a weak anonymity condition. The delicate set-theoretic status of integral-based aggregation functionals for infinite electorates is discussed. (shrink)

The use of aggregated quality of life estimatesin the formation of public policy and practiceguidelines raises concerns about the moralrelevance of variability in values inpreferences for health care. This variabilitymay reflect unique and deeply held beliefs thatmay be lost when averaged with the preferencesof other individuals. Feminist moral theorieswhich argue for attention to context andparticularity underline the importance ofascertaining the extent to which differences inpreferences for health states revealinformation which is morally relevant toclinicians and policymakers. To facilitatethese considerations, we present (...) an empiricalstudy of preferences for the timing andoccurrence of health states associated withhormone replacement therapy (HRT). Sixteenwomen between the ages of 45 and 55 wereenrolled in this pilot study. Theirpreferences regarding five health statesassociated with HRT (menopausal symptoms, sideeffects of HRT, breast cancer, myocardialinfarction, and osteoporosis) were assessed inquantitative terms known as utilities. Twostandard methods, the visual analog scale (VAS) and the standard gamble (SG), were used toassess utility and time preference (calculatedas a discount rate). The wide variability ofresponses underlines the importance oftailoring health care to individual women'spreferences. Policy guidelines whichincorporate utility analysis must recognize thenormative limitations of aggregatedpreferences, and the moral relevance ofindividual conceptions of health. (shrink)

Judgment-aggregation theory has always focused on the attainment of rational collective judgments. But so far, rationality has been understood in static terms: as coherence of judgments at a given time, defined as consistency, completeness, and/or deductive closure. This paper asks whether collective judgments can be dynamically rational, so that they change rationally in response to new information. Formally, a judgment aggregation rule is dynamically rational with respect to a given revision operator if, whenever all individuals revise their judgments (...) in light of some information (a learnt proposition), then the new aggregate judgments are the old ones revised in light of this information, i.e., aggregation and revision commute. We prove an impossibility theorem: if the propositions on the agenda are non-trivially connected, no judgment aggregation rule with standard properties is dynamically rational with respect to any revision operator satisfying some basic conditions on revision. Our theorem is the dynamic-rationality counterpart of some well-known impossibility theorems for static rationality. We also explore how dynamic rationality might be achieved by relaxing some of the conditions on the aggregation rule and/or the revision operator. Notably, premise-based aggregation rules are dynamically rational with respect to so-called premise-based revision operators. (shrink)

What is it that we are doing when we make ethical claims and judgments, such as the claim that we morally ought to assist refugees? This dissertation introduces and defends a novel theory of ethical thought and discourse. I begin by identifying the surface features of ethical thought and discourse to be explained, including the realist and cognitivist (i.e. belief-like) appearance of ethical judgments, and the apparent close connection between making a sincere ethical judgment and being motivated to act (...) on it. I examine prominent attempts to explain these features, with a focus on recent ‘hybrid’ theories combining elements of expressivism and cognitivism. Despite their initial promise, I argue that extant hybrid theories are nevertheless committed to problematic semantic, metasemantic, or pragmatic assumptions. I then discuss what I take to be the strongest existing option, ethical neo-expressivism (Bar-On and Chrisman, 2009; Bar-On, Chrisman, and Sias, 2014), and develop it into an explicitly hybrid theory proposing that ethical judgments incorporate both motivationally-charged affective states and moral beliefs. I then supplement this account with a theory of the proper function (following Millikan, 1984) of ethical claims and judgments, arguing that they function simultaneously to track the morally salient features of social situations, and to coordinate our behavior around these features. Finally, I defend one of the cognitivist commitments of the theory – namely, that objective moral knowledge is possible – by applying recent work on the epistemology of fundamental or ‘core’ intellectual commitments (Lynch, 2012; Pritchard, 2016) to the moral realm. (shrink)

The Ostrogorski paradox and the discursive dilemma are seemingly unrelated paradoxes of aggregation. The former is discussed in traditional social choice theory, while the latter is at the core of the new literature on judgment aggregation. Both paradoxes arise when, in a group, each individual consistently makes a judgment, or expresses a preference, (in the form of yes or no) over specific propositions, and the collective outcome is in some respect inconsistent. While the result is logically inconsistent in (...) the case of the discursive paradox, it is not stable with respect to the level of aggregation in the case of the Ostrogorski paradox. In the following I argue that, despite these differences, the two problems have a similar structure. My conclusion will be twofold: on the one hand, the similarities between the paradoxes support the claim that these problems should be tackled using the same aggregation procedure; on the other hand, applying the same procedure to these paradoxes will help clarify the strengths and weaknesses of the aggregation method itself. More specifically, I will show that an operator defined in artificial intelligence to merge belief bases can deal with both paradoxes. (shrink)

This paper is about how to aggregate outside opinion. If two experts are on one side of an issue, while three experts are on the other side, what should a non-expert believe? Certainly, the non-expert should take into account more than just the numbers. But which other factors are relevant, and why? According to the view developed here, one important factor is whether the experts should have been expected, in advance, to reach the same conclusion. When the agreement of two (...) (or of twenty) thinkers can be predicted with certainty in advance, their shared belief is worth only as much as one of their beliefs would be worth alone. This expectational model of belief dependence can be applied whether we think in terms of credences or in terms of all-or-nothing beliefs. (shrink)

When one communicates that they are in pain, it is often assumed that the speaker is providing an assertion or report. Call this the cognitivist stance of pain utterances. Nevertheless, many sentential pain utterances seem to have both assertive and imperatival communicative content in virtue of expressing both the speaker's pain belief and the pain experience, respectively. I call this view hybrid expressivism about pain. In this paper, I take the imperativist idea of pain seriously and show that, (...) via an expression relation, pain utterances inherit the imperative and motivational force of the pain. A hybrid expressivist stance better explains why pain utterances often have the perlocutionary effect of eliciting care from others, and it can provide a new understanding of what it means to silence one's pain. (shrink)

Can hybridism about moral claims be made to work? I argue it can if we accept the conventional implicature approach developed in Barker (Analysis 2000). However, this kind of hybrid expressivism is only acceptable if we can make sense of conventional implicature, the kind of meaning carried by operators like ‘even’, ‘but’, etc. Conventional implictures are a form of pragmatic presupposition, which involves an unsaid mode of delivery of content. I argue that we can make sense of conventional implicatures, (...) but doing so requires we embrace a form of pure, non-hybrid expressivism. This is a cognitivist expressivism I have developed elsewhere. We need cognitivist expressivism to make sense of how we evaluate—judge as correct or incorrect—implicature-bearing sentences. Once we embraced the possibility of this pure expressivism, we might as well be pure expressivists about normative discourse too. I show how we can do that. The motivations for a specifically hybrid theory are dialectically undercut. (shrink)

In this text an overview is offered of some of the most significant categories of the demonic from the Mesopotamian beliefs – of hybridity and liminality – through some examples of the conceptions of the demons Pazuzu and Lamaštu. Firstly, the logicaldialectical relations of the sphere of the demonic as external and foreign, opposed to the homely, familiar and close sphere are sketched; as well as the relation of the demonic as terrifying and potentially menacing, as opposed to the ordered (...) civilized sphere with norms of conduct. Then, several representations of the concepts of Pazuzu as an ambivalent demon are listed – he is an evil fighting against evil, his nemesis, Lamaštu, and precisely because of the need for him to be efficient in his protective function, he has to be a horrifying, dangerous demon. This is shown through the descriptions of the available incantations and preserved rituals. The terrifying threat of Lamaštu against the most precious part of the communities – the new generations - through her snatching and destroying of the newborns, is shown through the representations of her hybridity and monstrosity, and mainly through the incantations for her removal and (permanent) expulsion. (shrink)