In this paper we distinguish between various kinds of doxastic theories. One distinction is between informal and formal doxastic theories. AGM-type theories of belief change are of the former kind, while Hintikka’s logic of knowledge and belief is of the latter. Then we distinguish between static theories that study the unchanging beliefs of a certain agent and dynamic theories that investigate not only the constraints that can reasonably be imposed on the doxastic states of a rational agent but (...) also rationality constraints on the changes of doxastic state that may occur in such agents. An additional distinction is that between non-introspective theories and introspective ones. Non-introspective theories investigate agents that have opinions about the external world but no higher-order opinions about their own doxasticnstates. Standard AGM-type theories as well as the currently existing versions of Segerberg’s dynamic doxastic logic (DDL) are non-introspective. Hintikka-style doxastic logic is of course introspective but it is a static theory. Thus, the challenge remains to devise doxastic theories that are both dynamic and introspective. We outline the semantics for truly introspective dynamic doxastic logic, i.e., a dynamic doxastic logic that allows us to describe agents who have both the ability to form higher-order beliefs and to reflect upon and change their minds about their own (higher-order) beliefs. This extension of DDL demands that we give up the Preservation condition on revision. We make some suggestions as to how such a non-preservative revision operation can be constructed. We also consider extending DDL with conditionals satisfying the Ramsey test and show that Gärdenfors’ well-known impossibility result applies to such a framework. Also in this case, Preservation has to be given up. (shrink)

The theories of belief change developed within the AGM-tradition are not logics in the proper sense, but rather informal axiomatic theories of belief change. Instead of characterizing the models of belief and belief change in a formalized object language, the AGM-approach uses a natural language — ordinary mathematical English — to characterize the mathematical structures that are under study. Recently, however, various authors such as Johan van Benthem and Maarten de Rijke have suggested representing doxastic change (...) within a formal logical language: a dynamic modal logic. Inspired by these suggestions Krister Segerberg has developed a very general logical framework for reasoning about doxastic change: dynamic doxastic logic (DDL). This framework may be seen as an extension of standard Hintikka-style doxastic logic with dynamic operators representing various kinds of transformations of the agent's doxastic state. Basic DDL describes an agent that has opinions about the external world and an ability to change these opinions in the light of new information. Such an agent is non-introspective in the sense that he lacks opinions about his own belief states. Here we are going to discuss various possibilities for developing a dynamic doxastic logic for introspective agents: full DDL or DDL unlimited. The project of constructing such a logic is faced with difficulties due to the fact that the agent’s own doxastic state now becomes a part of the reality that he is trying to explore: when an introspective agent learns more about the world, then the reality he holds beliefs about undergoes a change. But then his introspective (higher-order) beliefs have to be adjusted accordingly. In the paper we shall consider various ways of solving this problem. (shrink)

We discuss various possibilities for developing a dynamic doxastic logic (DDL) for introspective agents: agents who have the ability to form higher-order beliefs. Such agents can reflect upon and change their minds about their own beliefs. The project of constructing such a logic, full DDL or DDL unlimited, is ridden with difficulties due to the fact that the agent's own doxastic state now becomes a part of the reality he is trying to explore. When an introspective agent learns (...) more about the world (and himself), the reality he holds beliefs about undergoes a change in its doxastic part, which means that his introspective beliefs have to be adjusted accordingly. (shrink)

Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed that (...) this problem generalizes: there exists no local function from degrees of belief to binary beliefs that satisfies some minimal conditions of rationality and non-triviality. “Locality” means that the binary belief in each proposition depends only on the degree of belief in that proposition, not on the degrees of belief in others. One might think that the impossibility can be avoided by dropping the assumption that binary beliefs are a function of degrees of belief. We prove that, even if we drop the “functionality” restriction, there still exists no local relation between degrees of belief and binary beliefs that satisfies some minimal conditions. Thus functionality is not the source of the impossibility; its source is the condition of locality. If there is any non-trivial relation between degrees of belief and binary beliefs at all, it must be a “holistic” one. We explore several concrete forms this “holistic” relation could take. (shrink)

Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three (...) usual operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations. (shrink)

This article provides a discussion of the principle of transmission of evidential support across entailment from the perspective of belief revision theory in the AGM tradition. After outlining and briefly defending a small number of basic principles of belief change, which include a number of belief contraction analogues of the Darwiche-Pearl postulates for iterated revision, a proposal is then made concerning the connection between evidential beliefs and belief change policies in rational agents. This proposal is found (...) to be suffcient to establish the truth of a much-discussed intuition regarding transmission failure. (shrink)

The problem of how to accommodate inconsistencies has attracted quite a number of researchers, in particular, in the area of database theory. The problem is also of concern in the study of belief change. For inconsistent beliefs are ubiquitous. However, comparatively little work has been devoted to discussing the problem in the literature of belief change. In this paper, I examine how adequate the AGM theory is as a logical framework for belief change involving inconsistencies. The technique (...) is to apply to Grove’s sphere system, a semantical representation of the AGM theory, logics that do not infer everything from contradictory premises, viz., paraconsistent logics. I use three paraconsistent logics and discuss three sphere systems that are based on them. I then examine the completeness of the postulates of the AGM theory with respect to the systems. At the end, I discuss some philosophical implications of the examination. (shrink)

I present a possible worlds semantics for a hyperintensional belief revision operator, which reduces the logical idealization of cognitive agents affecting similar operators in doxastic and epistemic logics, as well as in standard AGM belief revision theory. (Revised) belief states are not closed under classical logical consequence; revising by inconsistent information does not perforce lead to trivialization; and revision can be subject to ‘framing effects’: logically or necessarily equivalent contents can lead to different revisions. Such results are (...) obtained without resorting to non-classical logics, or to non-normal or impossible worlds semantics. The framework combines, instead, a standard semantics for propositional S5 with a simple mereology of contents. (shrink)

According to conciliatory views about the epistemology of disagreement, when epistemic peers have conflicting doxastic attitudes toward a proposition and fully disclose to one another the reasons for their attitudes toward that proposition (and neither has independent reason to believe the other to be mistaken), each peer should always change his attitude toward that proposition to one that is closer to the attitudes of those peers with which there is disagreement. According to pure higher-order evidence views, higher-order evidence for a (...) proposition always suffices to determine the proper rational response to disagreement about that proposition within a group of epistemic peers. Using an analogue of Arrow's Impossibility Theorem, I shall argue that no conciliatory and pure higher-order evidence view about the epistemology of disagreement can provide a true and general answer to the question of what disagreeing epistemic peers should do after fully disclosing to each other the (first-order) reasons for their conflicting doxastic attitudes. (shrink)

Standard models in epistemic game theory make strong assumptions about agents’ knowledge of their own beliefs. Agents are typically assumed to be introspectively omniscient: if an agent believes an event with probability p, she is certain that she believes it with probability p. This paper investigates the extent to which this assumption can be relaxed while preserving some standard epistemic results. Geanakoplos (1989) claims to provide an Agreement Theorem using the “truth” axiom, together with the property of balancedness, a significant (...) relaxation of introspective omniscience. I provide an example which shows that Geanakoplos’s statement is incorrect. I then introduce a new property, local balancedness, which allows us both to correct Geanakoplos’s result, and to extend it to cases where the truth axiom may fail. I exploit this general Agreement Theorem to provide novel epistemic conditions for correlated and Nash equilibrium, both of which relax the assumption of introspective omniscience. In all three cases, the results are also extended to infinite state spaces. (This is Chapter 5 of my 2014 Oxford DPhil (PhD) thesis.). (shrink)

In earlier papers (Lindström & Rabinowicz, 1989. 1990), we proposed a generalization of the AGM approach to belief revision. Our proposal was to view belief revision as a relation rather thanas a function on theories (or belief sets). The idea was to allow for there being several equally reasonable revisions of a theory with a given proposition. In the present paper, we show that the relational approach is the natural result of generalizing in a certain way an (...) approach to belief revision due to Adam Grove. In his (1988) paper, Grove presents two closely related modelings of functional belief revision, one in terms of a family of "spheres" around the agent's theory G and the other in terms of an epistemic entrenchment ordering of propositions. The "sphere"-terminology is natural when one looks upon theories and propositions as being represented by sets of possible worlds. Grove's spheres may be thought of as possible "fallback" theories relative to the agent's original theory: theories that he may reach by deleting propositions that are not "sufficiently" entrenched (according to standards of sufficient entrenchment of varying stringency). To put it differently, fallbacks are theories that are closed upwards under entrenchment The entrenchment ordering can be recovered from the family of fallbacks by the definition: A is at least as entrenched as B iff A belongs to every fallback to which B belongs. To revise a theory T with a proposition A, we go to the smallest sphere that contain A-worlds and intersect it with A. The relational notion of belief revision that we are interested in, results from weakening epistemic entrenchment by not assuming it to be connected. I.e., we want to allow that some propositions may be incomparable with respect to epistemic entrenchment. As a result, the family of fallbacks around a given theory will no longer have to be nested. This change opens up the possibility for several different ways of revising a theory with a given proposition. (shrink)

The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility. However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being always probabilistically coherent with infinitely precise degrees (...) of belief and full knowledge of all a priori truths. Ordinary subjects do not look very rational when compared to the kinds of agents usually talked about in decision theory. In this paper, I will develop an expected utility representation theorem aimed at the representation of those who are neither probabilistically coherent, logically omniscient, nor expected utility maximisers across the board—that is, agents who are frequently irrational. The agents in question may be deductively fallible, have incoherent credences, limited representational capacities, and fail to maximise expected utility for all but a limited class of gambles. (shrink)

Belief revision theory studies how an ideal doxastic agent should revise her beliefs when she receives new information. In part I I will first present the AGM theory of belief revision (Alchourrón & Gärdenfors & Makinson 1985). Then I will focus on the problem of iterated belief revisions.

Starting from the sixties of the past century theory change has become a main concern of philosophy of science. Two of the best known formal accounts of theory change are the post-Popperian theories of verisimilitude (PPV for short) and the AGM theory of belief change (AGM for short). In this paper, we will investigate the conceptual relations between PPV and AGM and, in particular, we will ask whether the AGM rules for theory change are effective means for approaching the (...) truth, i.e., for achieving the cognitive aim of science pointed out by PPV. First, the key ideas of PPV and AGM and their application to a particular kind of propositional theories - the so called "conjunctive propositions" - will be illustrated. Afterwards, we will prove that, as far as conjunctive propositions are concerned, AGM belief change is an effective tool for approaching the truth. (shrink)

The field of iterated belief change has focused mainly on revision, with the other main operator of AGM belief change theory, i.e. contraction, receiving relatively little attention. In this paper we extend the Harper Identity from single-step change to define iterated contraction in terms of iterated revision. Specifically, just as the Harper Identity provides a recipe for defining the belief set resulting from contracting A in terms of (i) the initial belief set and (ii) the (...) class='Hi'>belief set resulting from revision by ¬A, we look at ways to define the plausibility ordering over worlds resulting from contracting A in terms of (iii) the initial plausibility ordering, and (iv) the plausibility ordering resulting from revision by ¬A. After noting that the most straightforward such extension leads to a trivialisation of the space of permissible orderings, we provide a family of operators for combining plausibility orderings that avoid such a result. These operators are characterised in our domain of interest by a pair of intuitively compelling properties, which turn out to enable the derivation of a number of iterated contraction postulates from postulates for iterated revision. We finish by observing that a salient member of this family allows for the derivation of counterparts for contraction of some well known iterated revision operators, as well as for defining new iterated contraction operators. (shrink)

Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the work going on in our field—a (...) book would be needed for that. Instead, we have tried to select material that is of interest in its own right or exemplifies noteworthy features in interesting ways. Here are some themes that have guided us throughout the writing: • The back-and-forth between philosophy and modal logic. There has been a good deal of give-and-take in the past. Carnap tried to use his modal logic to throw light on old philosophical questions, thereby inspiring others to continue his work and still others to criticise it. He certainly provoked Quine, who in his turn provided—and continues to provide—a healthy challenge to modal logicians. And Kripke’s and David Lewis’s philosophies are connected, in interesting ways, with their modal logic. Analytic philosophy would have been a lot different without modal logic! • The interpretation problem. The problem of providing a certain modal logic with an intuitive interpretation should not be conflated with the problem of providing a formal system with a model-theoretic semantics. An intuitively appealing model-theoretic semantics may be an important step towards solving the interpretation problem, but only a step. One may compare this situation with that in probability theory, where definitions of concepts like ‘outcome space’ and ‘random variable’ are orthogonal to questions about “interpretations” of the concept of probability. • The value of formalisation. Modal logic sets standards of precision, which are a challenge to—and sometimes a model for—philosophy. Classical philosophical questions can be sharpened and seen from a new perspective when formulated in a framework of modal logic. On the other hand, representing old questions in a formal garb has its dangers, such as simplification and distortion. • Why modal logic rather than classical (first or higher order) logic? The idioms of modal logic—today there are many!—seem better to correspond to human ways of thinking than ordinary extensional logic. (Cf. Chomsky’s conjecture that the NP + VP pattern is wired into the human brain.) In his An Essay in Modal Logic (1951) von Wright distinguished between four kinds of modalities: alethic (modes of truth: necessity, possibility and impossibility), epistemic (modes of being known: known to be true, known to be false, undecided), deontic (modes of obligation: obligatory, permitted, forbidden) and existential (modes of existence: universality, existence, emptiness). The existential modalities are not usually counted as modalities, but the other three categories are exemplified in three sections into which this chapter is divided. Section 1 is devoted to alethic modal logic and reviews some main themes at the heart of philosophical modal logic. Sections 2 and 3 deal with topics in epistemic logic and deontic logic, respectively, and are meant to illustrate two different uses that modal logic or indeed any logic can have: it may be applied to already existing (non-logical) theory, or it can be used to develop new theory. (shrink)

One response to the problem of logical omniscience in standard possible worlds models of belief is to extend the space of worlds so as to include impossible worlds. It is natural to think that essentially the same strategy can be applied to probabilistic models of partial belief, for which parallel problems also arise. In this paper, I note a difficulty with the inclusion of impossible worlds into probabilistic models. Under weak assumptions about the space of worlds, most of (...) the propositions which can be constructed from possible and impossible worlds are in an important sense inexpressible; leaving the probabilistic model committed to saying that agents in general have at least as many attitudes towards inexpressible propositions as they do towards expressible propositions. If it is reasonable to think that our attitudes are generally expressible, then a model with such commitments looks problematic. (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)

Computer assisted theorem proving is an increasingly important part of mathematical methodology, as well as a long-standing topic in artificial intelligence (AI) research. However, the current generation of theorem proving software have limited functioning in terms of providing new proofs. Importantly, they are not able to discriminate interesting theorems and proofs from trivial ones. In order for computers to develop further in theorem proving, there would need to be a radical change in how the software functions. Recently, machine learning results (...) in solving mathematical tasks have shown early promise that deep artificial neural networks could learn symbolic mathematical processing. In this paper, I analyze the theoretical prospects of such neural networks in proving mathematical theorems. In particular, I focus on the question how such AI systems could be incorporated in practice to theorem proving and what consequences that could have. In the most optimistic scenario, this includes the possibility of autonomous automated theorem provers (AATP). Here I discuss whether such AI systems could, or should, become accepted as active agents in mathematical communities. (shrink)

Public health care interventions—regarding vaccination, obesity, and HIV, for example—standardly take the form of information dissemination across a community. But information networks can vary importantly between different ethnic communities, as can levels of trust in information from different sources. We use data from the Greater Pittsburgh Random Household Health Survey to construct models of information networks for White and Black communities--models which reflect the degree of information contact between individuals, with degrees of trust in information from various sources correlated with (...) positions in that social network. With simple assumptions regarding belief change and social reinforcement, we use those modeled networks to build dynamic agent-based models of how information can be expected to flow and how beliefs can be expected to change across each community. With contrasting information from governmental and religious sources, the results show importantly different dynamic patterns of belief polarization within the two communities. (shrink)

The very existence of society depends on the ability of its members to influence formatively the beliefs, desires, and actions of their fellows. In every sphere of social life, powerful human agents (whether individuals or institutions) tend to use coercion as a favorite shortcut to achieving their aims without taking into consideration the non-violent alternatives or the negative (unintended) consequences of their actions. This propensity for coercion is manifested in the doxastic sphere by attempts to shape people’s beliefs (and doubts) (...) while ignoring the essential characteristics of these doxastic states. I argue that evidential persuasion is a better route to influence people’s beliefs than doxastic coercion. Doxastic coercion perverts the belief-forming mechanism and undermines the epistemic and moral faculties both of coercers and coercees. It succeeds sporadically and on short-term. Moreover, its pseudo doxastic effects tend to disappear once the use of force ceases. In contrast to doxastic coercion, evidential persuasion produces lasting correct beliefs in accordance with proper standards of evidence. It helps people to reach the highest possible standards of rationality and morality. Evidential persuasion is based on the principles of symmetry and reciprocity in that it asks all persuaders to use for changing the beliefs of others only those means they used in forming their own beliefs respecting the freedom of will and assuming the standard of rationality. The arguments in favor of evidential persuasion have a firm theoretical basis that includes a conceptual clarification of the essential traits of beliefs. Belief is treated as a hypercomplex system governed by Leibniz’s law of continuity and the principle of self-organization. It appears to be a mixture consisting of a personal propositional attitude and physical objects and processes. The conceptual framework also includes a typology of believers according to the standards of evidence they assume. In this context, I present a weak version of Clifford’ ethical imperative. In the section dedicated to the prerequisites for changing beliefs, I show how doxastic agents can infuse premeditated or planned changes in the flow of endogenous changes in order to shape certain beliefs in certain desired forms. The possibility of changing some beliefs in a planned manner is correlated with a feedback doxastic (macro-mechanism) that produces a reaction when it is triggered by a stimulus. In relation with the two routes to influence beliefs, a response mechanism is worth taking into consideration – a mechanism governed to a significant extent by human conscience and human will, that appears to be complex, acquired, relatively detached from visceral or autonomic information processing, and highly variable in reactions. Knowing increasingly better this doxastic mechanism, we increase our chances to use evidential persuasion as an effective (although not time-efficient) method to mold people’s beliefs. (shrink)

I want to model a finite, fallible cognitive agent who imagines that p in the sense of mentally representing a scenario—a configuration of objects and properties—correctly described by p. I propose to capture imagination, so understood, via variably strict world quantifiers, in a modal framework including both possible and so-called impossible worlds. The latter secure lack of classical logical closure for the relevant mental states, while the variability of strictness captures how the agent imports information from actuality in the imagined (...) non-actual scenarios. Imagination turns out to be highly hyperintensional, but not logically anarchic. Section 1 sets the stage and impossible worlds are quickly introduced in Sect. 2. Section 3 proposes to model imagination via variably strict world quantifiers. Section 4 introduces the formal semantics. Section 5 argues that imagination has a minimal mereological structure validating some logical inferences. Section 6 deals with how imagination under-determines the represented contents. Section 7 proposes additional constraints on the semantics, validating further inferences. Section 8 describes some welcome invalidities. Section 9 examines the effects of importing false beliefs into the imagined scenarios. Finally, Sect. 10 hints at possible developments of the theory in the direction of two-dimensional semantics. (shrink)

What makes a choice hard? I discuss and criticize three common answers and then make a proposal of my own. Paradigmatic hard choices are not hard because of our ignorance, the incommensurability of values, or the incomparability of the alternatives. They are hard because the alternatives are on a par; they are comparable, but one is not better than the other, and yet nor are they equally good. So understood, hard choices open up a new way of thinking about what (...) it is to be a rational agent. (shrink)

‘Normative powers’ are capacities to create normative reasons by our willing or say-so. They are significant, because if we have them and exercise them, then sometimes the reasons we have are ‘up to us’. But such powers seem mysterious. How can we, by willing, create reasons? In this paper, I examine whether normative powers can be adequately explained normatively, by appeal to norms of a practice, normative principles, human interests, or values. Can normative explanations of normative powers explain how an (...) exercise of the will can afford us special freedom in determining our reasons? I argue that normative approaches to answering this question prove to be inadequate. To vindicate the thought that normative powers can make our reasons ‘up to us’, we need an altogether different approach to understanding them, one that is located not in the normative but in the metaphysical. I end the paper by sketching a metaphysical explanation of normative powers. This metaphysical defence of normative powers provides a window into a different, more agent-centered way of thinking about rational agency. (shrink)

This paper investigates two puzzles in practical reason and proposes a solution to them. First, sometimes, when we are practically certain that neither of two alternatives is better than or as good as the other with respect to what matters in the choice between them, it nevertheless seems perfectly rational to continue to deliberate, and sometimes the result of that deliberation is a conclusion that one alternative is better, where there is no error in one’s previous judgment. Second, there are (...) striking differences between rational agents – some rational agents have most reason to pursue careers on Wall Street while others have most reason to take up a career in teaching, or scuba diving, or working for political causes. These differences aren’t plausibly explained by ‘passive’ facts about our psychology or their causal interaction with our environment; instead, these facts seem in some sense to ‘express who we are’. But what is this sense? These puzzles disappear if we adopt a novel view about the source of the normativity of reasons – some reasons are given to us and others are reasons in virtue of an act of will. We make certain considerations reasons through an act of will and thus sometimes make it true through an act of agency that we have most reason to do one thing rather than another. (shrink)

We call our thoughts conscious, and we also say the same of our bodily sensations, perceptions and other sensory experiences. But thoughts and sensory experiences are very different phenomena, both from the point of view of their subject and in their functional or cognitive role. Does this mean, then, that there are very different kinds or varieties of consciousness? Philosophers do often talk about different kinds of consciousness: Christopher Hill, for example, claims that ‘it is customary to distinguish five forms (...) of consciousness’ (Hill 2009: 1). These are: agent consciousness, propositional consciousness, introspective consciousness, relational consciousness and phenomenal consciousness; to which Hill adds experiential consciousness, making six in total. (shrink)

This paper assesses five main empirical scientific arguments against the reliability of belief formation on the basis of introspecting phenomenal states. After defining ‘reliability’ and ‘introspection’, I discuss five arguments to the effect that phenomenal states are more elusive than we usually think: the argument on the basis of differences in introspective reports from differences in introspective measurements; the argument from differences in reports about whether or not dreams come in colours; the argument from the absence of (...) a correlation between visual imagery ability and the performance on certain cognitive tasks; the argument from our unawareness of our capacity of echolocation; the argument from inattentional blindness and change blindness. I argue that the experiments on which these arguments are based do not concern belief formation on the basis of introspection in the first place or fail to show that it is unreliable, even when limited to introspection of phenomenal states. (shrink)

In this article, I identify and critically examine 3 dogmas of normativity that support a commonly accepted ‘Passivist View' of rational agency. I raise some questions about these dogmas, suggest what we should believe in their place, and moot an alternative ‘Activist View' of what it is to be a rational agent that grows out of rejection of the 3 dogmas. Underwriting the dogmas and the Passivist View, I suggest, is a deeply held but mistaken assumption that the normative domain (...) is fundamentally akin to the nonnormative domain. Once we allow that the normative may be fundamentally unlike the nonnormative in certain key ways, a shift in our thinking about what it is to be rational becomes possible. I end by considering some implications of this paradigm shift in rationality from the passive to the active for various applied matters. (shrink)

On Hume’s account of motivation, beliefs and desires are very different kinds of propositional attitudes. Beliefs are cognitive attitudes, desires emotive ones. An agent’s belief in a proposition captures the weight he or she assigns to this proposition in his or her cognitive representation of the world. An agent’s desire for a proposition captures the degree to which he or she prefers its truth, motivating him or her to act accordingly. Although beliefs and desires are sometimes entangled, they play (...) very different roles in rational agency. In two classic papers (Lewis 1988, 1996), David Lewis discusses several challenges to this Humean picture, but ultimately rejects them. We think that his discussion of a central anti-Humean alternative – the desire-as-belief thesis – is in need of refinnement. On this thesis, the desire for proposition p is given by the belief that p is desirable. Lewis claims that ‘[e]xcept in trivial cases, [this thesis] collapses into contradiction’(Lewis 1996, p. 308). The problem, he argues, is that the thesis is inconsistent with the purportedly plausible requirement that one’s desire for a proposition should not change upon learning that the proposition is true; call this the invariance requirement. In this paper, we revisit Lewis’s argument. We show that, if one carefully distinguishes between non-evaluative and evaluative propositions, the desire-asbelief thesis can be rendered consistent with the invariance requirement. Lewis’s conclusion holds only under certain conditions: the desire-as-belief thesis conflicts with the invariance requirement if and only if there are certain correlations between non-evaluative and evaluative propositions. But when there are such correlations, we suggest, the invariance requirement loses its plausibility. Thus Lewis’s argument against the desire-as-belief thesis appears to be valid only in cases in which it is unsound. (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)

Belief revision theory studies how an ideal doxastic agent should revise her beliefs when she receives new information. In part I, I have first presented the AGM theory of belief revision. Then I have focused on the problem of iterated belief revisions. In part II, I will first present ranking theory (Spohn 1988). Then I will show how it solves the problem of iterated belief revisions. I will conclude by sketching two areas of future research.

This essay discusses the difficulty to reconcile two paradigms about beliefs: the binary or categorical paradigm of yes/no beliefs and the probabilistic paradigm of degrees of belief. The possibility for someone to hold both types of belief simultaneously is challenged by the lottery paradox, and more recently by a general impossibility theorem by Dietrich and List (2018, 2021). The nature, relevance, and implications of the tension are explained and assessed.

Veltman’s test semantics and developments thereof reject the canon about semantic contents and attitude ascriptions in favor of dynamic alternatives. According to these theories the semantic content of a sentence is not a proposition, but a context change potential (CCP). Similarly, beliefs are not taken to be relations between agents and propositions, but agents and CCPs. These deviations from the canon come at the cost of an elegant explanation about the correctness of belief. Standardly, it is taken that the (...) content of a belief is correct just in case the content of that belief is true. The proponent of the test semantics cannot appeal to this explanation since they hold that certain contents, namely epistemically modalized contents, do not express propositions, and are neither true nor false. After motivating the need for an account of the correctness of belief within the dynamic framework, I argue that the few extant accounts in the literature are unsatisfactory. A novel account is proposed that avoids the problems of competing views. (shrink)

According to the traditional Bayesian view of credence, its structure is that of precise probability, its objects are descriptive propositions about the empirical world, and its dynamics are given by conditionalization. Each of the three essays that make up this thesis deals with a different variation on this traditional picture. The first variation replaces precise probability with sets of probabilities. The resulting imprecise Bayesianism is sometimes motivated on the grounds that our beliefs should not be more precise than the evidence (...) calls for. One known problem for this evidentially motivated imprecise view is that in certain cases, our imprecise credence in a particular proposition will remain the same no matter how much evidence we receive. In the first essay I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid without compromising the initial evidentialist motivation. The second variation replaces descriptive claims with moral claims as the objects of credence. I consider three standard arguments for probabilism with respect to descriptive uncertainty—representation theorem arguments, Dutch book arguments, and accuracy arguments—in order to examine whether such arguments can also be used to establish probabilism with respect to moral uncertainty. In the second essay, I argue that by and large they can, with some caveats. First, I don’t examine whether these arguments can be given sound non-cognitivist readings, and any conclusions therefore only hold conditional on cognitivism. Second, decision-theoretic representation theorems are found to be less convincing in the moral case, because there they implausibly commit us to thinking that intertheoretic comparisons of value are always possible. Third and finally, certain considerations may lead one to think that imprecise probabilism provides a more plausible model of moral epistemology. The third variation considers whether, in addition to conditionalization, agents may also change their minds by becoming aware of propositions they had not previously entertained, and therefore not previously assigned any probability. More specifically, I argue that if we wish to make room for reflective equilibrium in a probabilistic moral epistemology, we must allow for awareness growth. In the third essay, I sketch the outline of such a Bayesian account of reflective equilibrium. Given that this account gives a central place to awareness growth, and that the rationality constraints on belief change by awareness growth are much weaker than those on belief change by conditionalization, it follows that the rationality constraints on the credences of agents who are seeking reflective equilibrium are correspondingly weaker. (shrink)

Bayesian epistemology tells us with great precision how we should move from prior to posterior beliefs in light of new evidence or information, but says little about where our prior beliefs come from. It offers few resources to describe some prior beliefs as rational or well-justified, and others as irrational or unreasonable. A different strand of epistemology takes the central epistemological question to be not how to change one’s beliefs in light of new evidence, but what reasons justify a given (...) set of beliefs in the first place. We offer an account of rational belief formation that closes some of the gap between Bayesianism and its reason-based alternative, formalizing the idea that an agent can have reasons for his or her (prior) beliefs, in addition to evidence or information in the ordinary Bayesian sense. Our analysis of reasons for belief is part of a larger programme of research on the role of reasons in rational agency (Dietrich and List, Nous, 2012a, in press; Int J Game Theory, 2012b, in press). (shrink)

A large body of work has demonstrated the utility of the Bayesian framework for capturing inference in both specialist and everyday contexts. However, the central tool of the framework, conditionalization via Bayes’ rule, does not apply directly to a common type of learning: the acquisition of conditional information. How should an agent change her beliefs on learning that “If A, then C”? This issue, which is central to both reasoning and argumentation, has recently prompted considerable research interest. In this paper, (...) we critique a prominent proposal and provide a new, alternative, answer. -/- . (shrink)

Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. (...) In this paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a ‘proper ordinal interval’ (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general. (shrink)

This paper begins with a puzzle regarding Lewis' theory of radical interpretation. On the one hand, Lewis convincingly argued that the facts about an agent's sensory evidence and choices will always underdetermine the facts about her beliefs and desires. On the other hand, we have several representation theorems—such as those of (Ramsey 1931) and (Savage 1954)—that are widely taken to show that if an agent's choices satisfy certain constraints, then those choices can suffice to determine her beliefs and desires. In (...) this paper, I will argue that Lewis' conclusion is correct: choices radically underdetermine beliefs and desires, and representation theorems provide us with no good reasons to think otherwise. Any tension with those theorems is merely apparent, and relates ultimately to the difference between how 'choices' are understood within Lewis' theory and the problematic way that they're represented in the context of the representation theorems. For the purposes of radical interpretation, representation theorems like Ramsey's and Savage's just aren't very relevant after all. (shrink)

“There is no use in trying,” said Alice; “one can’t believe impossible things.” “I dare say you haven’t had much practice,” said the Queen. “When I was your age, I always did it for half an hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast”. Lewis Carroll, Through the Looking Glass. -/- It is a rather common view among philosophers that one cannot, properly speaking, be said to believe, conceive, imagine, hope for, or seek (...) what is impossible. -/- Some philosophers, for instance George Berkeley and the early Wittgenstein, thought that logically contradictory propositions lack cognitive meaning (informational content) and cannot, therefore, be thought or believed. Philosophers who do not go as far as Berkeley and Wittgenstein in denying that impossible propositions or states of affairs are thinkable, may still claim that it is impossible to rationally believe an impossible proposition. On a classical “Cartesian” view of belief, belief is a purely mental state of the agent holding true a proposition p that she “grasps” and is directly acquainted with. But if the agent is directly acquainted with an impossible proposition, then, presumably, she must know that it is impossible. But surely no rational agent can hold true a proposition that she knows is impossible. Hence, no rational agent can believe an impossible proposition. Thus it seems that on the Cartesian view of propositional attitudes as inner mental states in which proposition are immediately apprehended by the mind, it is impossible for a rational agent to believe, imagine or conceive an impossible proposition. -/- Ruth Barcan Marcus (1983) has suggested that a belief attribution is defeated once it is discovered that the proposition, or state of affairs that is believed is impossible. According to her intuition, just as knowledge implies truth, belief implies possibility. -/- It is commonplace that people claim to believe propositions that later turn out to be impossible. According to Barcan Marcus, the correct thing to say in such a situation is not: I once believed that A but I don’t believe it any longer since I have come to realize that it is impossible that A. What one should say is instead: It once appeared to me that I believed that A, but I did not, since it is impossible that A. Thus, Barcan Marcus defends what we might call Alice’s thesis: Necessarily, for any proposition p and any subject x, if x believes p, then p is possible. -/- Alice’s thesis that it is impossible to hold impossible beliefs, seems to come into conflict with our ordinary practices of attributing beliefs. Consider a mathematical example. Some mathematicians believe that CH (the continuum hypothesis) is true and others believe that it is false. But if CH is true, then it is necessarily true; and if it is false, then it is necessarily false. Regardless of whether CH is true or false, the conclusion seems to be that there are mathematicians who believe impossible propositions. -/- Examples of apparent beliefs in impossible propositions outside of mathematics are also easy to come by. Consider, for example, Kripke’s (1999) story of the Frenchman Pierre who without realizing it has two different names ‘London’ and ‘Londres’ for the same city, London. After having arrived in London, Pierre may assent to ‘Londres is beautiful and London is not beautiful’ without being in any way irrational. It seems reasonably to infer from this that Pierre believes that Londres is beautiful and London is not beautiful. But since ‘Londres’ and ‘London’ are rigid designators for the same city, it seems to follow from this that Pierre believes the inconsistent proposition that we may express as ‘London is both beautiful and not beautiful’. (shrink)

The historical sensibility of Western modernity is best captured by the phrase “acting upon a story that we can believe.” Whereas the most famous stories of historians facilitated nation-building processes, philosophers of history told the largest possible story to act upon: history itself. When the rise of an overwhelming postwar skepticism about the modern idea of history discredited the entire enterprise, the historical sensibility of “acting upon a story that we can believe” fell apart to its constituents: action, story form, (...) and belief in a feasible future outcome. Its constituent parts are nevertheless still hold, either separately or in paired arrangements. First, believable stories are still told, but without an equally believable future outcome to facilitate. Second, in the shape of what I call the prospect of unprecedented change, there still is a feasible vision of a future (in prospects of technology and the Anthropocene), but it defies story form. And third, it is even possible to upon that feasible future, but such action aims at avoiding worst case scenarios instead of facilitating best outcomes. These are, I believe, features of an emerging postwar historical sensibility that the theory and philosophy of history is yet to understand. (shrink)

Christine Korsgaard bases her interpretation of personal identity upon the notion of moral agency and thereby refutes the Reductionist thesis of Derek Parfit. Korsgaard indicates that actions and choices, from the practical standpoint, must be viewed as having agents and choosers. This is what makes them our own actions and choices as well as contributes to the process of self-constitution. Personal identity manifested as the chooser of our desires and author of our actions can be viewed as the common denominator (...) between Korsgaard and Wang Yangming (王陽明). For liangzhi (良知) is none other than the agency that acts as the capacity for moral judgment and the motivation of performing moral actions. Given liangzhi is the authentic self that make laws for us, our true identities are exhibited in the performance of moral behaviors. Moreover, further engagement between the two sides reveals that Wang’s characterizations of liangzhi, particularly those of practical justification, law-embodying identity, and zhih –zhi (致知), can be seen as either a complement to practical standpoint argument or an approach of consummating self-constitution. (shrink)

We propose a dynamic hyperintensional logic of belief revision for non-omniscient agents, reducing the logical omniscience phenomena affecting standard doxastic/epistemic logic as well as AGM belief revision theory. Our agents don’t know all a priori truths; their belief states are not closed under classical logical consequence; and their belief update policies are such that logically or necessarily equivalent contents can lead to different revisions. We model both plain and conditional belief, then focus on dynamic (...) class='Hi'>belief revision. The key idea we exploit to achieve non-omniscience focuses on topic- or subject matter-sensitivity: a feature of belief states which is gaining growing attention in the recent literature. (shrink)

Interactions between an intelligent software agent and a human user are ubiquitous in everyday situations such as access to information, entertainment, and purchases. In such interactions, the ISA mediates the user’s access to the content, or controls some other aspect of the user experience, and is not designed to be neutral about outcomes of user choices. Like human users, ISAs are driven by goals, make autonomous decisions, and can learn from experience. Using ideas from bounded rationality, we frame these interactions (...) as instances of an ISA whose reward depends on actions performed by the user. Such agents benefit by steering the user’s behaviour towards outcomes that maximise the ISA’s utility, which may or may not be aligned with that of the user. Video games, news recommendation aggregation engines, and fitness trackers can all be instances of this general case. Our analysis facilitates distinguishing various subcases of interaction, as well as second-order effects that might include the possibility for adaptive interfaces to induce behavioural addiction, and/or change in user belief. We present these types of interaction within a conceptual framework, and review current examples of persuasive technologies and the issues that arise from their use. We argue that the nature of the feedback commonly used by learning agents to update their models and subsequent decisions could steer the behaviour of human users away from what benefits them, and in a direction that can undermine autonomy and cause further disparity between actions and goals as exemplified by addictive and compulsive behaviour. We discuss some of the ethical, social and legal implications of this technology and argue that it can sometimes exploit and reinforce weaknesses in human beings. (shrink)

This paper develops and explores a new framework for theorizing about the measurement and aggregation of well-being. It is a qualitative variation on the framework of social welfare functionals developed by Amartya Sen. In Sen’s framework, a social or overall betterness ordering is assigned to each profile of real-valued utility functions. In the qualitative framework developed here, numerical utilities are replaced by the properties they are supposed to represent. This makes it possible to characterize the measurability and interpersonal comparability of (...) well-being directly, without the use of invariance conditions, and to distinguish between real changes in well-being and merely representational changes in the unit of measurement. The qualitative framework is shown to have important implications for a range of issues in axiology and social choice theory, including the characterization of welfarism, axiomatic derivations of utilitarianism, the meaningfulness of prioritarianism, the informational requirements of variable-population ethics, the impossibility theorems of Arrow and others, and the metaphysics of value. (shrink)

Suppositions can be introduced in either the indicative or subjunctive mood. The introduction of either type of supposition initiates judgments that may be either qualitative, binary judgments about whether a given proposition is acceptable or quantitative, numerical ones about how acceptable it is. As such, accounts of qualitative/quantitative judgment under indicative/subjunctive supposition have been developed in the literature. We explore these four different types of theories by systematically explicating the relationships canonical representatives of each. Our representative qualitative accounts of indicative (...) and subjunctive supposition are based on the belief change operations provided by AGM revision and KM update respectively; our representative quantitative ones are offered by conditionalization and imaging. This choice is motivated by the familiar approach of understanding supposition as `provisional belief revision' wherein one temporarily treats the supposition as true and forms judgments by making appropriate changes to their other opinions. To compare the numerical judgments recommended by the quantitative theories with the binary ones recommended by the qualitative accounts, we rely on a suitably adapted version of the Lockean thesis. Ultimately, we establish a number of new results that we interpret as vindicating the often-repeated claim that conditionalization is a probabilistic version of revision, while imaging is a probabilistic version of update. (shrink)

Many philosophers claim that interesting forms of epistemic evaluation are insensitive to truth in a very specific way. Suppose that two possible agents believe the same proposition based on the same evidence. Either both are justified or neither is; either both have good evidence for holding the belief or neither does. This does not change if, on this particular occasion, it turns out that only one of the two agents has a true belief. Epitomizing this line of thought (...) are thought experiments about radically deceived “brains in vats.” It is widely and uncritically assumed that such a brain is equally justified as its normally embodied human “twin.” This “parity” intuition is the heart of truth-insensitive theories of core epistemological properties such as justification and rationality. Rejecting the parity intuition is considered radical and revisionist. In this paper, I show that exactly the opposite is true. The parity intuition is idiosyncratic and widely rejected. A brain in a vat is not justified and has worse evidence than its normally embodied counterpart. On nearly every ordinary way of evaluating beliefs, a false belief is significantly inferior to a true belief. Of all the evaluations studied here, only blamelessness is truth-insensitive. (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free (...) topology) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

Amalgamating evidence of different kinds for the same hypothesis into an overall confirmation is analogous, I argue, to amalgamating individuals’ preferences into a group preference. The latter faces well-known impossibility theorems, most famously “Arrow’s Theorem”. Once the analogy between amalgamating evidence and amalgamating preferences is tight, it is obvious that amalgamating evidence might face a theorem similar to Arrow’s. I prove that this is so, and end by discussing the plausibility of the axioms required for the theorem.

I argue for the unexceptionality of evidence about what rationality requires. Specifically, I argue that, as for other topics, one’s total evidence can sometimes support false beliefs about this. Despite being prima facie innocuous, a number of philosophers have recently denied this. Some have argued that the facts about what rationality requires are highly dependent on the agent’s situation and change depending on what that situation is like. (Bradley 2019). Others have argued that a particular subset of normative truths, those (...) concerning what epistemic rationality requires, have the special property of being ‘fixed points’—it is impossible to have total evidence that supports false belief about them. (Smithies 2012; Titelbaum 2015). Each of these kinds of exceptionality permits a solution to downstream theoretical problems that arise from the possibility of evidence supporting false belief about requirements of rationality. However, as I argue here, they incur heavy explanatory burdens that we should avoid. (shrink)