ON THE COHERENCE OF HIGHER‐ORDER BELIEFS

Let us by ‘first‐order beliefs’ mean beliefs about the world, such as the belief that it will rain tomorrow, and by ‘second‐order beliefs’ let us mean beliefs about the reliability of first‐order, belief‐forming processes. In formal epistemology, coherence has been studied, with much ingenuity and precision, for sets of first‐order beliefs. However, to the best of our knowledge, sets including second‐order beliefs have not yet received serious attention in that literature. In informal epistemology, by contrast, sets of the latter kind play an important role in some respectable coherence theories of knowledge and justification. In this paper, we extend the formal treatment of coherence to second‐order beliefs. Our main conclusion is that while extending the framework to second‐order beliefs sheds doubt on the generality of the notorious impossibility results for coherentism, another problem crops up that might be no less damaging to the coherentist project: facts of coherence turn out to be epistemically accessible only to agents who have a good deal of insight into matters external to their own belief states.     

Coherence and Conservatism in the Dynamics of Belief

In this paper I discuss the foundations of a formal theory of coherent and conservative belief change that is (a) suitable to be used as a method for constructing iterated changes of belief, (b) sensitive to the history of earlier belief changes, and (c) independent of any form of dispositional coherence. I review various ways to conceive the relationship between the beliefs actually held by an agent and her belief change strategies (that also deal with potential belief sets), show the problems they suffer from, and suggest that belief states should be represented by unary revision functions that take sequences of inputs. Three concepts of coherence implicit in current theories of belief change are distinguished: synchronic, diachronic and dispositional coherence. Diachronic coherence is essentially identified with what is known as conservatism in epistemology. The present paper elaborates on the philosophical motivation of the general framework; formal details and results are provided in a companion paper.     

Probabilistic Measures of Coherence and the Problem of Belief Individuation

Coherentism in epistemology has long suffered from lack of formal and quantitative explication of the notion of coherence. One might hope that probabilistic accounts of coherence such as those proposed by Lewis, Shogenji, Olsson, Fitelson, and Bovens and Hartmann will finally help solve this problem. This paper shows, however, that those accounts have a serious common problem: the problem of belief individuation. The coherence degree that each of the accounts assigns to an information set (or the verdict it gives as to whether the set is coherent tout court) depends on how beliefs (or propositions) that represent the set are individuated. Indeed, logically equivalent belief sets that represent the same information set can be given drastically different degrees of coherence. This feature clashes with our natural and reasonable expectation that the coherence degree of a belief set does not change unless the believer adds essentially new information to the set or drops old information from it; or, to put it simply, that the believer cannot raise or lower the degree of coherence by purely logical reasoning. None of the accounts in question can adequately deal with coherence once logical inferences get into the picture. Toward the end of the paper, another notion of coherence that takes into account not only the contents but also the origins (or sources) of the relevant beliefs is considered. It is argued that this notion of coherence is of dubious significance, and that it does not help solve the problem of belief individuation.     

The Diachronic Coherence of Ungraded Beliefs

This paper works within a model of ungraded belief that characterizes epistemic states as logically closed and consistent sets of sentences. The aim of this paper is to discuss three diachronic coherence conditions for such beliefs. These coherence conditions are formulated in terms of the reasoner's present beliefs about how his present beliefs will evolve in the future, for instance, in response to different pieces of future evidence.     

Coherence in Epistemology and Belief Revision*

A general theory of coherence is proposed, in which systemic and relational coherence are shown to be interdefinable. When this theory is applied to sets of sentences, it turns out that logical closure obscures the distinctions that are needed for a meaningful analysis of coherence. It is concluded that references to “all beliefs” in coherentist phrases such as “all beliefs support each other” have to be modified so that merely derived beliefs are excluded. Therefore, in order to avoid absurd conclusions, coherentists have to accept a weak version of epistemic priority, that sorts out merely derived beliefs. Furthermore, it is shown that in belief revision theory, coherence cannot be adequately represented by logical closure, but has to be represented separately. *Contribution to “Seven Bridges”     

Implications of the Dutch Book: Following Ramsey��s axioms

The Dutch Book Argument shows that an agent will lose surely in a gamble (a Dutch Book is made) if his degrees of belief do not satisfy the laws of the probability. Yet a question arises here: What does the Dutch Book imply? This paper firstly argues that there exists a utility function following Ramsey’s axioms. And then, it explicates the properties of the utility function and degree of belief respectively. The properties show that coherence in partial beliefs for Subjective Bayesianism means that the degree of belief, representing a belief ordering, satisfies the laws of probability, and that coherence in preferences means that the preferences are represented by expected utilities. A coherent belief ordering and a utility scale induce a coherent preference ordering; a coherent preference ordering induces a coherent belief ordering which can be uniquely represented by a degree-of-belief function. The preferences (values) and beliefs are both incoherent or disordered if a Dutch Book is made.     

The Role of Sensory Experience in Epistemic Justification: a Problem for Coherentism

The author argues that coherence views of justification, in spite of their crucial insight into the interpenetration of our beliefs, neglect a key constraint on justification: they are unable to accommodate the epistemic significance of experience. Epistemic justification is not just a function of our beliefs and their interrelations. Both, beliefs and experiences, are relevant to the justification of an empirical belief. Experience is not itself a form of belief or disposition to believe; it cannot be analyzed in doxastic terms. And, yet, nondoxastic experiences play a justificatory role, not merely a causal role. The positive epistemic status of a perceptual belief depends upon being appeared to in appropriate ways. It is important that, for an ordinary perceptual belief to be justified, one does not have to believe that one is appeared to in these ways. It is the experiences themselves, the ways of being appeared to, not our beliefs about them, that are required for justification.     

A localist solution to the regress of epistemic justification

Guided by an account of the norms governing justificatory conversations, I propose that person-level epistemic justification is a matter of possessing a certain ability: the ability to provide objectively good reasons for one's belief by drawing upon considerations which one responsibly and correctly takes there to be no reason to doubt. On this view, justification requires responsible belief and is also objectively truth-conducive. The foundationalist doctrine of immediately justified beliefs is rejected, but so too is the thought that coherence in one's total belief system is sufficient, or indeed necessary, for justification. The problem of the regress is solved by exploiting the ‘localist’ idea that in order to possess the ability to justify any given belief, one only needs to be in a position to draw upon appropriate justified background beliefs to provide good reasons for holding the belief; one needn't be able to defend the relevant background beliefs, and so on, all at one sitting.     

Justified inference

This paper proposes a general account of the epistemological significance of inference. This account rests on the assumption that the concept of a ??justified?? belief or inference is a normative concept. It also rests on a conception of belief that distinguishes both (a) between conditional and unconditional beliefs and (b) between enduring belief states and mental events of forming or reaffirming a belief, and interprets all of these different kinds of belief as coming in degrees. Conceptions of ??rational coherence?? and ??competent inference?? are then formulated, in terms of the undefeated instances of certain rules of inference. It is proposed that (non-accidental) rational coherence is a necessary and sufficient condition of justified enduring belief states, while competent inference always results in a justified mental event of some kind. This proposal turns out to tell against the view that there are any non-trivial cases of ??warrant transmission failure??. Finally, it is explained how these proposals can answer the objections that philosophers have raised against the idea that justified belief is ??closed?? under competent inference.     

An Impossibility Result for Coherence Rankings

If we receive information from multiple independent and partially reliable information sources, then whether we are justified to believe these information items is affected by how reliable the sources are, by how well the information coheres with our background beliefs and by how internally coherent the information is. We consider the following question. Is coherence a separable determinant of our degree of belief, i.e. is it the case that the more coherent the new information is, the more justified we are in believing the new information, ceteris paribus? We show that if we consider sets of information items of any size (Holism), and if we assume that there exists a coherence Ordering over such sets and that coherence is a function of the probability distribution over the propositions in such sets (Probabilism), then Separability fails to hold.     

My beliefs about your beliefs: a case study in theory of mind and epistemic logic

We model three examples of beliefs that agents may have about other agents’ beliefs, and provide motivation for this conceptualization from the theory of mind literature. We assume a modal logical framework for modelling degrees of belief by partially ordered preference relations. In this setting, we describe that agents believe that other agents do not distinguish among their beliefs (‘no preferences’), that agents believe that the beliefs of other agents are in part as their own (‘my preferences’), and the special case that agents believe that the beliefs of other agents are exactly as their own (‘preference refinement’). This multi-agent belief interaction is frame characterizable. We provide examples for introspective agents. We investigate which of these forms of belief interaction are preserved under three common forms of belief revision.     

Ethnodoxy: How Popular Ideologies Fuse Religious and Ethnic Identities

Popular beliefs conflating ethnic identities with particular faiths can lead to marginalization of religiously and ethnically “other” and fuel ethnoreligious conflict even in secularized societies. Despite their importance to ethnoreligious conflict and coexistence, ideological conflations of faith and ethnos have previously received little scholarly attention. We fill the gap by introducing the concept of ethnodoxy: a collectively held belief system that rigidly links a group's ethnic identity to its dominant faith. We theorize this phenomenon at three levels: macro (the interplay between religion and ethnonational identities), micro (construction of ethnoreligious identities and imagined communities viewed from a social identity theory perspective), and meso (the nature and functions of popular ideologies and religiosities). Subsequently, ethnodoxy is conceptualized as an ideal‐typical syndrome of six component beliefs. We further operationalize and verify the concept using representative national survey data from Russia. Findings show ethnodoxy's extent, coherence, dimensionality, and associations with religious and ethnic intolerance.     

Heterophenomenology: Heavy-handed sleight-of-hand

We argue that heterophenomenology both over- and under-populates the intentional realm. For example, when one is involved in coping, one’s mind does not contain beliefs. Since the heterophenomenologist interprets all intentional commitment as belief, he necessarily overgenerates the belief contents of the mind. Since beliefs cannot capture the normative aspect of coping and perceiving, any method, such as heterophenomenology, that allows for only beliefs is guaranteed not only to overgenerate beliefs but also to undergenerate other kinds of intentional phenomena.     

Two routes to perspective: Simulation and rule‐use as approaches to mentalizing

We review evidence relating to children's ability to acknowledge false beliefs within a simulation account according to which our focus is set by default to the world as we know it: hence, our current beliefs assume salience over beliefs that do not fall into this category. The model proposes that the ease with which we imaginatively shift from this default depends on the salience of our current belief, relative to the salience of the belief that is being simulated. However, children do use a rule‐based approach for mentalizing in some contexts, which has the advantage of protecting them from the salience of their own belief. Rule‐based mentalizing judgements might be faster, cognitively easier and less prone to error, relative to simulation‐based judgements that are much influenced by salience. We propose that although simulation is primary, rule‐based approaches develop as a shortcut; we thus grow from individuals capable of using only simulation into individuals capable of both techniques.     

Individual Differences in Commitment to Value‐Based Beliefs and the Amplification of Perceived Belief Dissimilarity Effects

The commitment to beliefs (CTB) framework (Maxwell‐Smith & Esses, 2012) proposes that there are individual differences in the extent to which people generally follow beliefs that are a reflection of their values. The current research hypothesized that CTB would amplify the effects of perceived belief dissimilarity or incompatibility, such that individuals higher in CTB would display more pronounced reactions to belief‐relevant groups, events, or individuals seen as incompatible with their value‐based beliefs. We tested our hypothesis in three studies that assessed participants' CTB and their perceptions of belief dissimilarity or incompatibility with regard to other religious groups (Study 1), political parties during a national election (Study 2), and their romantic partner (Study 3). CTB amplified the effects of perceived belief dissimilarity or incompatibility on people's biases toward other religious groups, voting intentions and behavior in a national election, and their evaluative and behavioral responses toward their romantic partner. These results collectively suggest that perceptions of belief dissimilarity or incompatibility are particularly important cues for individuals with higher levels of CTB as they encounter other people or events that are relevant to their beliefs.     

Diverse Supernatural Portfolios: Certitude,Exclusivity, and the Curvilinear Relationship Between Religiosity and Paranormal Beliefs

Studies have attempted to understand the association between more conventional supernatural (religious) beliefs and practices and less conventional “paranormal” supernatural beliefs. Some have posited that the two comprise incompatible cultural spheres and belief systems, while others have argued that supernatural religious beliefs are “small steps” toward less conventional paranormal views (such as belief in astrology and telekinesis). We build upon recent scholarship outlining a more nuanced, nonlinear relationship between religiosity and paranormal beliefs by identifying a specific niche of believers who are particularly likely to dabble in unconventional supernatural beliefs. Strong believers in the paranormal tend to be characterized by a nonexclusive spiritualist worldview, as opposed to materialist or exclusive religious outlooks. Paranormal believers tend to be characterized by moderate levels of religious belief and practice, and low levels of ideological exclusivity. In general, the relationship between more conventional religiosity and paranormal beliefs is best conceptualized as curvilinear.     

Stratified Belief Bases Revision with Argumentative Inference

We propose a revision operator on a stratified belief base, i.e., a belief base that stores beliefs in different strata corresponding to the value an agent assigns to these beliefs. Furthermore, the operator will be defined as to perform the revision in such a way that information is never lost upon revision but stored in a stratum or layer containing information perceived as having a lower value. In this manner, if the revision of one layer leads to the rejection of some information to maintain consistency, instead of being withdrawn it will be kept and introduced in a different layer with lower value. Throughout this development we will follow the principle of minimal change, being one of the important principles proposed in belief change theory, particularly emphasized in the AGM model. Regarding the reasoning part from the stratified belief base, the agent will obtain the inferences using an argumentative formalism. Thus, the argumentation framework will decide which information prevails when sentences of different layers are used for entailing conflicting beliefs. We will also illustrate how inferences are changed and how the status of arguments can be modified after a revision process.     

Resource Bounded Belief Revision

The AGM paradigm for belief revision provides a very elegant and powerful framework for reasoning about idealized agents. The paradigm assumes that the modeled agent is a perfect reasoner with infinite memory. In this paper we propose a framework to reason about non-ideal agents that generalizes the AGM paradigm. We first introduce a structure to represent an agent's belief states that distinguishes different status of beliefs according to whether or not they are explicitly represented, whether they are currently active and whether they are fully accepted or provisional. Then we define a set of basic operations that change the status of beliefs and show how these operations can be used to model agents with different capacities. We also show how different operations of belief change described in the literature can be seen as special cases of our theory.