The debate on probabilistic measures of coherence flourishes for about 15 years now. Initiated by papers that have been published around the turn of the millennium, many different proposals have since then been put forward. This contribution is partly devoted to a reassessment of extant coherence measures. Focusing on a small number of reasonable adequacy constraints I show that (i) there can be no coherence measure that satisfies all constraints, and that (ii) subsets of (...) these adequacy constraints motivate two different classes of coherence measures. These classes do not coincide with the common distinction between coherence as mutual support and coherence as relative set-theoretic overlap. Finally, I put forward arguments to the effect that for each such class of coherence measures there is an outstanding measure that outperforms all other extant proposals. One of these measures has recently been put forward in the literature, while the other one is based on a novel probabilistic measure of confirmation. (shrink)

It is shown that the probabilistic theories of coherence proposed up to now produce a number of counter-intuitive results. The last section provides some reasons for believing that no probabilistic measure will ever be able to adequately capture coherence. First, there can be no function whose arguments are nothing but tuples of probabilities, and which assigns different values to pairs of propositions {A, B} and {A, C} if A implies both B and C, or their negations, (...) and if P(B)=P(C). But such sets may indeed differ in their degree of coherence. Second, coherence is sensitive to explanatory relations between the propositions in question. Explanation, however, can hardly be captured solely in terms of probability. (shrink)

Two of the probabilistic measures of coherence discussed in this paper take probabilistic dependence into account and so depend on prior probabilities in a fundamental way. An example is given which suggests that this prior-dependence can lead to potential problems. Another coherence measure is shown to be independent of prior probabilities in a clearly defined sense and consequently is able to avoid such problems. The issue of prior-dependence is linked to the fact that the first (...) two measures can be understood as measures of coherence as striking agreement, while the third measure represents coherence as agreement. Thus, prior (in)dependence can be used to distinguish different conceptions of coherence. (shrink)

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. (shrink)

Is logical consistency required for a set of beliefs or propositions to be categorically coherent? An affirmative answer is often assumed by mainstream epistemologists, and yet it is unclear why. Cases like the lottery and the preface call into question the assumption that beliefs must be consistent in order to be epistemically rational. And thus it is natural to wonder why all inconsistent sets of propositions are incoherent. On the other hand, Easwaran and Fitelson have shown that particular kinds of (...) inconsistency entail the epistemically ‘irrationality’ of holding certain sets of beliefs. In cases of the latter kind of inconsistency, it seems more reasonable to insist that such sets of beliefs or propositions are categorically incoherent. What the precise relationship is between coherence and consistency depends on the nature of the coherence relation. We shall examine recent attempts to explicate the coherence relation in terms of probabilistic measures of confirmation or agreement to see what they can teach us about the relationship between coherence and consistency. We shall show that some probabilistic measures of coherence allow for inconsistent sets to be categorically coherent, while satisfying plausible epistemic rationality constraints. Other probabilistic measures of coherence impose very strong logical consistency requirements, and some measures are tolerant of most forms of inconsistency. As we try to understand what distinguishes coherence measures in this respect, we will also draw some important lessons about Bayesian confirmation measures and differences in the way that they treat contradictory propositions. (shrink)

In recent years, some authors have proposed quantitative measures of the coherence of sets of propositions. Such probabilistic measures of coherence (PMCs) are, in general terms, functions that take as their argument a set of propositions (along with some probability distribution) and yield as their value a number that is supposed to represent the degree of coherence of the set. In this paper, I introduce a minimal constraint on PMC theories, the weak stability principle, (...) and show that any correct, coherent, and complete PMC cannot satisfy it. As a matter of fact, the argument offered in this paper can be applied to any coherence theory that uses a priori procedures. I briefly explore some consequences of this fact. (shrink)

Coherence is a property of propositions hanging together or dovetailing with each other. About two decades ago, formal epistemologists started to engage in the project of explicating the seemingly elusive concept of coherence by means of probability theory. Since then, a plethora of coherence measures have been discussed in the literature. In this paper, we propose a general framework for coherence measures that encompasses the different frameworks of deviation measures, overlap measures and (...) mutual support measures of coherence. Above that we show that some of the new measures that can be obtained outperform existing coherence measures in important respects. (shrink)

How can we determine the adequacy of a probabilistic coherence measure? A widely accepted approach to this question besides formulating adequacy constraints is to employ paradigmatic test cases consisting of a scenario providing a joint probability distribution over some specified set of propositions coupled with a normative coherence assessment for this set. However, despite the popularity of the test case approach, a systematic evaluation of the proposed test cases is still missing. This paper’s aim is to change (...) this. Using a custom written computer program for the necessary probabilistic calculations a large number of coherence measures in an extensive collection of test cases is examined. The result is a detailed overview of the test case performance of any probabilistic coherence measures proposed so far. It turns out that none of the popular coherence measures such as Shogenji’s, Glass’ and Olsson’s, Fitelson’s or Douven and Meijs’ but two rather unnoticed measures perform best. This, however, does not mean that the other measures can be rejected straightforwardly. Instead, the results presented here are to be understood as a contribution among others to the project of finding adequate probabilistic coherence measures. (shrink)

Bayesian Coherence Theory of Justification or, for short, Bayesian Coherentism, is characterized by two theses, viz. (i) that our degree of confidence in the content of a set of propositions is positively affected by the coherence of the set, and (ii) that coherence can be characterized in probabilistic terms. There has been a longstanding question of how to construct a measure of coherence. We will show that Bayesian Coherentism cannot rest on a single measure of (...) coherence, but requires a vector whose components exhaustively characterize the coherence properties of the set. Our degree of confidence in the content of the information set is a function of the reliability of the sources and the components of the coherence vector. The components of this coherence vector are weakly but not strongly separable, which blocks the construction of a single coherence measure. (shrink)

Tomoji Shogenji is generally assumed to be the first author to have presented a probabilistic measure of coherence. Interestingly, Rudolf Carnap in his Logical Foundations of Probability discussed a function that is based on the very same idea, namely his well-known relevance measure. This function is largely neglected in the coherence literature because it has been proposed as a measure of evidential support and still is widely conceived as such. The aim of this paper is therefore to (...) investigate Carnap’s measure regarding its plausibility as a candidate for a probabilistic measure of coherence by comparing it to Shogenji’s. It turns out that both measures satisfy and violate the same adequacy constraints, despite not being ordinally equivalent exhibit a strong correlation with each other in a Monte Carlo simulation and perform similarly in a series of test cases for probabilistic coherence measures. (shrink)

A measure of coherence is said to be truth conducive if and only if a higher degree of coherence (as measured) results in a higher likelihood of truth. Recent impossibility results strongly indicate that there are no (non-trivial) probabilistic coherence measures that are truth conducive. Indeed, this holds even if truth conduciveness is understood in a weak ceteris paribus sense (Bovens & Hartmann, 2003, Bayesian epistemology. New York, Oxford: Oxford University Press; Olsson, 2005, Against (...) class='Hi'>coherence: Truth probability and justification. Oxford: Oxford University Press). This raises the problem of how coherence could nonetheless be an epistemically important property. Our proposal is that coherence may be linked in a certain way to reliability. We define a measure of coherence to be reliability conducive if and only if a higher degree of coherence (as measured) results in a higher probability that the information sources are reliable. Restricting ourselves to the most basic case, we investigate which coherence measures in the literature are reliability conducive. It turns out that, while a number of measures fail to be reliability conducive, except possibly in a trivial and uninteresting sense, Shogenji’s measure and several measures generated by Douven and Meijs’s recipe are notable exceptions to this rule. (shrink)

Let E be a set of n propositions E1, ..., En. We seek a probabilistic measure C(E) of the ‘degree of coherence’ of E. Intuitively, we want C to be a quantitative, probabilistic generalization of the (deductive) logical coherence of E. So, in particular, we require C to satisfy the following..

Coherence is the property of propositions hanging or fitting together. Intuitively, adding a proposition to a set of propositions should be compatible with either increasing or decreasing the set’s degree of coherence. In this paper we show that probabilistic coherence measures based on relative overlap are in conflict with this intuitive verdict. More precisely, we prove that according to the naive overlap measure it is impossible to increase a set’s degree of coherence by adding (...) propositions and that according to the refined overlap measure no set’s degree of coherence exceeds the degree of coherence of its maximally coherent subset. We also show that this result carries over to all other subset-sensitive refinements of the naive overlap measure. As both results stand in sharp contrast to elementary coherence intuitions, we conclude that extant relative overlap measures of coherence are inadequate. (shrink)

Over the years several non-equivalent probabilistic measures of coherence have been discussed in the philosophical literature. In this paper we examine these measures with respect to their empirical adequacy. Using test cases from the coherence literature as vignettes for psychological experiments we investigate whether the measures can predict the subjective coherence assessments of the participants. It turns out that the participants’ coherence assessments are best described by Roche’s coherence measure based on (...) Douven and Meijs’ average mutual support approach and the conditional probability. (shrink)

Bovens and Hartmann propose to analyze coherence as a confidence-boosting property. On the basis of this idea, they construct a new probabilistic theory of coherence. In this paper, I will attempt to show that the resulting measure of coherence clashes with some of the intuitions that motivate it. Also, I will try to show that this clash is not due to the view on coherence as a confidence-boosting property or to the general features of the (...) model that Bovens and Hartmann use to analyze coherence. It will turn out that there is at least one other measure that is similarly based on the concept of a confidence-boosting property, but does not have the same counterintuitive results. (shrink)

This paper presents a symmetry condition for probabilistic measures of confirmation which is weaker than commutativity symmetry, disconfirmation commutativity symmetry but also antisymmetry. It is based on the idea that for any value a probabilistic measure of confirmation can assign there is a corresponding case where degrees of confirmation are symmetric. It is shown that a number of prominent confirmation measures such as Carnap’s difference function, Rescher’s measure of confirmation, Gaifman’s confirmation rate and Mortimer’s inverted difference (...) function do not satisfy this condition and instead exhibit a previously unnoticed and rather puzzling behavior in certain cases of disconfirmation. This behavior also carries over to probabilistic measures of information change, causal strength, explanatory power and coherence. (shrink)

Relative overlap measures of coherence have recently been shown to have two devastating properties: according to the plain relative overlap measure, the degree of coherence of any set of propositions cannot be increased by adding further propositions, and according to the refined relative overlap measure, no set can be more coherent than its most coherent two-element subset. This result has been taken to rule out relative overlap as a foundation for a probabilistic explication of coherence. (...) The present paper shows that this view is premature: we propose a relative overlap measure that does not fall victim to the two properties. The guiding idea is to employ a well-established recipe for the construction of coherence measures and to adapt it to the idea of relative overlap. We show that this new measure keeps up with, or even outperforms, former overlap measures in a set of desiderata for coherence measures and a collection of popular test cases. This result re-establishes relative overlap as a candidate for a proper formalization of coherence. (shrink)

Over the past years, a number of probabilistic measures of coherence have been proposed. As shown in the paper, however, many of them do not conform to the intuitition that equivalent testimonies are highly coherent, regardless of their prior probability.

Changing weather conditions and barometer changes usually coincide. Accordingly, the propositions that my barometer falls and that the weather conditions deteriorate are quite coherent—especially under the assumption that there is a drop in atmospheric pressure. Nevertheless, scenarios like these involving common causes turn out to be highly problematic for a prominent class of probabilistic coherence measures, namely, those explicating coherence based on the idea of relevance-sensitivity. In this article, we show that none of these measures (...) accords with the intuition that in the light of a common cause, two propositions referring to the cause’s effects should turn out to be coherent. This result casts doubts on the view that these measures can be considered proper explications of the concept of coherence. 1Introduction2Relevance-Sensitive Coherence Measures3Common Causes, Screening-off, and Coherence4Discussion 4.1Multiple explications of coherence4.2Conditionalization versus set expansion5Conclusion. (shrink)

There is an emerging consensus in the literature on probabilistic coherence that such coherence cannot be truth conducive unless the information sources providing the cohering information are individually credible and collectively independent. Furthermore, coherence can at best be truth conducive in a ceteris paribus sense. Bovens and Hartmann have argued that there cannot be any measure of coherence that is truth conducive even in this very weak sense. In this paper, I give an alternative impossibility (...) proof. I provide a relatively detailed comparison of the two results, which turn out to be logically unrelated, and argue that my result answers a question raised by Bovens and Hartmann’s study. Finally, I discuss the epistemological ramifications of these findings and try to make plausible that a shift to an explanatory framework such as Thagard’s is unlikely to turn the impossibility into a possibility. (shrink)

One of the integral parts of Bayesian coherentism is the view that the relation of ‘being no less coherent than’ is fully determined by the probabilistic features of the sets of propositions to be ordered. In the last one and a half decades, a variety of probabilistic measures of coherence have been put forward. However, there is large disagreement as to which of these measures best captures the pre-theoretic notion of coherence. This paper contributes (...) to the debate on coherence measures by considering three classes of adequacy constraints. Various independence and dependence relations between the members of each class will be taken into account in order to reveal the ‘grammar’ of probabilistic coherence measures. Afterwards, existing proposals are examined with respect to this list of desiderata. Given that for purely mathematical reasons there can be no measure that satisfies all constraints, the grammar allows the coherentist to articulate an informed pluralist stance as regards probabilistic measures of coherence. (shrink)

Striving for a probabilistic explication of coherence, scholars proposed a distinction between agreement and striking agreement. In this paper I argue that only the former should be considered a genuine concept of coherence. In a second step the relation between coherence and reliability is assessed. I show that it is possible to concur with common intuitions regarding the impact of coherence on reliability in various types of witness scenarios by means of an agreement measure of (...) coherence. Highlighting the need to separate the impact of coherence and specificity on reliability it is finally shown that a recently proposed vindication of the Shogenji measure qua measure of coherence vanishes. (shrink)

Recently there have been several attempts in formal epistemology to develop an adequate probabilistic measure of coherence. There is much to recommend probabilistic measures of coherence. They are quantitative and render formally precise a notion—coherence—notorious for its elusiveness. Further, some of them do very well, intuitively, on a variety of test cases. Siebel, however, argues that there can be no adequate probabilistic measure of coherence. Take some set of propositions A, some (...) class='Hi'>probabilistic measure of coherence, and a probability distribution such that all the probabilities on which A’s degree of coherence depends (according to the measure in question) are defined. Then, the argument goes, the degree to which A is coherent depends solely on the details of the distribution in question and not at all on the explanatory relations, if any, standing between the propositions in A. This is problematic, the argument continues, because, first, explanation matters for coherence, and, second, explanation cannot be adequately captured solely in terms of probability. We argue that Siebel’s argument falls short. (shrink)

This paper considers an application of work on probabilistic measures of coherence to inference to the best explanation. Rather than considering information reported from different sources, as is usually the case when discussing coherence measures, the approach adopted here is to use a coherence measure to rank competing explanations in terms of their coherence with a piece of evidence. By adopting such an approach IBE can be made more precise and so a major (...) objection to this mode of reasoning can be addressed. Advantages of the coherence - based approach are pointed out by comparing it with several other ways to characterize ‘ best explanation ’ and showing that it takes into account their insights while overcoming some of their problems. The consequences of adopting this approach for IBE are discussed in the context of recent discussions about the relationship between IBE and Bayesianism. (shrink)

The debate on probabilistic measures of coherence has focused on evaluating sets of consistent propositions. In this paper we draw attention to the largely neglected question of whether such measures concur with intuitions on test cases involving inconsistent propositions and whether they satisfy general adequacy constraints on coherence and inconsistency. While it turns out that, for the vast majority of measures in their original shape, this question must be answered in the negative, we show (...) that it is possible to adapt many of them in order to improve their performance. (shrink)

In “What price coherence?”, Klein and Warfield put forward a simple argument that triggered an extensive debate on the epistemic virtues of coherence. As is well-known, this debate yielded far-reaching impossibility results to the effect that coherence is not conducive to truth, even if construed in a ceteris paribus sense. A large part of the present paper is devoted to a re-evaluation of these results. As is argued, all explications of truth-conduciveness leave out an important aspect: while (...) it might not be the case that coherence is truth-conducive, it might be conducive to verisimilitude or epistemic utility. Unfortunately, it is shown that the answer for both these issues must be in the negative, again. Furthermore, we shift the focus from sets of beliefs to particular beliefs: as is shown, neither is any of the extant probabilistic measures of coherence truth-conducive on the level of particular beliefs, nor does weakening these measures to quasi-orderings establish the link between coherence and truth for an important amount of measures. All in all, the results in this paper cast a serious doubt on the approach of establishing a link between coherence and truth. Finally, recent arguments that shift the focus from the relationship between coherence and truth to the one between coherence and confirmation are assessed. (shrink)

This paper aims to contribute to our understanding of the notion of coherence by explicating in probabilistic terms, step by step, what seem to be our most basic intuitions about that notion, to wit, that coherence is a matter of hanging or fitting together, and that coherence is a matter of degree. A qualitative theory of coherence will serve as a stepping stone to formulate a set of quantitative measures of coherence, each of (...) which seems to capture well the aforementioned intuitions. Subsequently it will be argued that one of those measures does better than the others in light of some more specific intuitions about coherence. This measure will be defended against two seemingly obvious objections. (shrink)

A coherent story is a story that fits together well. This notion plays a central role in the coherence theory of justification and has been proposed as a criterion for scientific theory choice. Many attempts have been made to give a probabilistic account of this notion. A proper account of coherence must not start from some partial intuitions, but should pay attention to the role that this notion is supposed to play within a particular context. Coherence (...) is a property of an information set that boosts our confidence that its content is true ceteris paribus when we receive information from independent and partially reliable sources. We construct a measure cr that relies on hypothetical sources with certain idealized characteristics. A maximally coherent information set, i.e. a set with equivalent propositions, affords a maximal confidence boost. cr is the ratio of the actual confidence boost over the confidence boost that we would have received, had the information been presented in the form of maximally coherent information, ceteris paribus. This measure is functionally dependent on the degree of reliability r of the sources. We use cr to construct a coherence quasi-ordering over information sets S and S’: S is no less coherent than S’ just in case c_r is not smaller than c_r for any value of the reliability parameter. We show that, on our account, the coherence of the story about the world gives us a reason to believe that the story is true and that the coherence of a scientific theory, construed as a set of models, is a proper criterion for theory choice. (shrink)

To remedy the lack of precision attached to the concept of coherence, a plethora of probabilistic measures has been developed. To broaden the perspective, we do not focus on the differences between these quantitative but the differences between qualitative approaches to coherence by comparing three probabilistic definitions for the relation denoted by ‘coheres with’. To reveal the different logics underlying these relations, we introduce a considerable number of formal properties and examine whether the given (...) class='Hi'>coherence relations possess them. Among these properties are not only the classics reflexivity, symmetry and transitivity, but also a variety of features that concern propositions containing negation, conjunction and disjunction, as well as features that concern inconsistency, entailment and equivalence. (shrink)

Coherence considerations play an important role in science and in everyday reasoning. However, it is unclear what exactly is meant by coherence of information and why we prefer more coherent information over less coherent information. To answer these questions, we first explore how to explicate the dazzling notion of ``coherence'' and how to measure the coherence of an information set. To do so, we critique prima facie plausible proposals that incorporate normative principles such as ``Agreement'' or (...) ``Dependence'' and then argue that the coherence of an information set is best understood as an indicator of the truth of the set under certain conditions. Using computer simulations, we then show that a new probabilistic measure of coherence that combines aspects of the two principles above, but without strictly satisfying either principle, performs particularly well in this regard. (shrink)

Stochastic forecasts in complex environments can benefit from combining the estimates of large groups of forecasters (“judges”). But aggregating multiple opinions faces several challenges. First, human judges are notoriously incoherent when their forecasts involve logically complex events. Second, individual judges may have specialized knowledge, so different judges may produce forecasts for different events. Third, the credibility of individual judges might vary, and one would like to pay greater attention to more trustworthy forecasts. These considerations limit the value of simple aggregation (...) methods like linear averaging. In this paper, a new algorithm is proposed for combining probabilistic assessments from a large pool of judges. Two measures of a judge’s likely credibility are introduced and used in the algorithm to determine the judge’s weight in aggregation. The algorithm was tested on a data set of nearly half a million probability estimates of events related to the 2008 U.S. presidential election (∼ 16000 judges). (shrink)

Why should coherence be an epistemic desideratum? One response is that coherence is truth-conducive: mutually coherent propositions are more likely to be true, ceteris paribus, than mutually incoherent ones. But some sets of propositions are more coherent, while others are less so. How could coherence be measured? Probabilistic measures of coherence exist; some are identical to probabilistic measures of confirmation, while others are extensions of such measures. Probabilistic measures of (...) coherence are fine when applicable, but many situations are so information-poor that the requisite probabilities cannot be determined. To measure coherence in these cognitively impoverished situations, this article proposes that the discussion be broadened to include plausibilistic measures of coherence. It shows how plausibilistic measures of coherence can be defined using plausibilistic measures of confirmation. It then illustrates how plausibilisic coherence can be measured in situations where probabilistic coherence cannot be determined. The coherence values obtained through the use of plausibilistic measures are often, though not always, comparable. The article also shows that coherence can be instantiated on different levels, one of which permits connections to inductive strength and deductive validity. (shrink)

It is argued that suitably trained neural language models exhibit key properties of epistemic agency: they hold probabilistically coherent and logically consistent degrees of belief, which they can rationally revise in the face of novel evidence. To this purpose, we conduct computational experiments with rankers: T5 models [Raffel et al. 2020] that are pretrained on carefully designed synthetic corpora. Moreover, we introduce a procedure for eliciting a model’s degrees of belief, and define numerical metrics that measure the extent to which (...) given degrees of belief violate (probabilistic, logical, and Bayesian) rationality constraints. While pretrained rankers are found to suffer from global inconsistency (in agreement with, e.g., [Jang et al. 2021]), we observe that subsequent self-training on auto-generated texts allows rankers to gradually obtain a probabilistically coherent belief system that is aligned with logical constraints. In addition, such self-training is found to have a pivotal role in rational evidential learning, too, for it seems to enable rankers to propagate a novel evidence item through their belief systems, successively re-adjusting individual degrees of belief. All this, we conclude, confirms the Rationality Hypothesis, i.e., the claim that suitable trained NLMs may exhibit advanced rational skills. We suggest that this hypothesis has empirical, yet also normative and conceptual ramifications far beyond the practical linguistic problems NLMs have originally been designed to solve. (shrink)

In his groundbreaking book, Against Coherence (2005), Erik Olsson presents an ingenious impossibility theorem that appears to show that there is no informative relationship between probabilistic measures of coherence and higher likelihood of truth. Although Olsson's result provides an important insight into probabilistic models of epistemological coherence, the scope of his negative result is more limited than generally appreciated. The key issue is the role conditional independence conditions play within the witness testimony model Olsson (...) uses to establish his result. Olsson maintains that his witness model yields charitable ceteris paribus conditions for any theory of probabilistic coherence. Not so. In fact, Olsson's model, like Bayesian witness models in general, selects a peculiar class of models that are in no way representative of the range of options available to coherence theorists. Recent positive results suggest that there is a way to develop a formal theory of coherence after all. Further, although Bayesian witness models are not conducive to the truth, they are conducive to reliability. (shrink)

This paper aims to reconcile (i) the intuitively plausible view that a higher degree of coherence among independent pieces of evidence makes the hypothesis they support more probable, and (ii) the negative results in Bayesian epistemology to the effect that there is no probabilistic measure of coherence such that a higher degree of coherence among independent pieces of evidence makes the hypothesis they support more probable. I consider a simple model in which the negative result appears (...) in a stark form: the prior probability of the hypothesis and the individual vertical relations between each piece of evidence and the hypothesis completely determine the conditional probability of the hypothesis given the total evidence, leaving no room for the lateral relation (such as coherence) among the pieces of evidence to play any role. Despite this negative result, the model also reveals that a higher degree of coherence is indirectly associated with a higher conditional probability of the hypothesis because a higher degree of coherence indicates stronger individual supports. This analysis explains why coherence appears truth-conducive but in such a way that it defeats the idea of coherentism since the lateral relation (such as coherence) plays no independent role in the confirmation of the hypothesis. (shrink)

Several philosophers propose probabilistic measures of how well a potential scientific explanation would explain the given evidence. These measures could elaborate “best” in “inference to the best explanation”. This paper argues that none of these measures succeeds. The paper considers the various rival explanations that scientists proposed for the parallelogram of forces. Scientists regarded various features of these proposals as making them more or less “lovely”. None of these probabilistic measures of loveliness can reflect (...) these features. The paper concludes by considering the kinds of probabilities that could reflect these features. (shrink)

When we talk about the coherence of a story, we seem to think of how well its individual pieces fit together—how to explicate this notion formally, though? We develop a Bayesian network based coherence measure with implementation in _R_, which performs better than its purely probabilistic predecessors. The novelty is that by paying attention to the network structure, we avoid simply taking mean confirmation scores between all possible pairs of subsets of a narration. Moreover, we assign special (...) importance to the weakest links in a narration, to improve on the other measures’ results for logically inconsistent scenarios. We illustrate and investigate the performance of the measures in relation to a few philosophically motivated examples, and (more extensively) using the real-life example of the Sally Clark case. (shrink)

Alongside science and law, argumentation is also of central importance in everyday life. But what characterizes a good argument? This question has occupied philosophers and psychologists for centuries. The theory of Bayesian argumentation is particularly suitable for clarifying it, because it allows us to take into account in a natural way the role of uncertainty, which is central to much argumentation. Moreover, it offers the possibility of measuring the strength of an argument in probabilistic terms. One way to do (...) this, implicit in much work, is to identify the strength of an argument with the degree to which the premises of the argument confirm the conclusion. We criticize this prima facie plausible proposal and suggest instead that the strength of an argument has something to do with how much the premises and the conclusion of the argument cohere with each other. This leads to a new probabilistic measure whose properties we examine in more detail. (shrink)

All extant purely probabilistic measures of explanatory power satisfy the following technical condition: if Pr(E | H1) > Pr(E | H2) and Pr(E | ∼H1) < Pr(E | ∼H2), then H1’s explanatory power with respect to E is greater than H2’s explanatory power with respect to E. We argue that any measure satisfying this condition faces three serious problems—the Problem of Temporal Shallowness, the Problem of Negative Causal Interactions, and the Problem of Nonexplanations. We further argue that many (...) such measures face a fourth problem—the Problem of Explanatory Irrelevance. (shrink)

This paper evaluates four different qualitative (probabilistic) accounts to coherence with a focus on structural properties (symmetries, asymmetries, and transitivity). It is shown that while coherence is not transitive on any of these accounts, there are screening-off conditions that render coherence transitive. In a second step, an array of quantitative (probabilistic) accounts to coherence is considered. The upshot is that extant measures differ considerably with respect to a number of symmetry constraints.

This thesis is a collection of three self-contained papers on related themes in the area of formal and social epistemology. The first paper explores the possibility of measuring the coherence of a set with multiplicative averaging. It has been pointed out that all the existing probabilistic measures of coherence are flawed for taking the relevance between a set of propositions as the primary factor which determines the coherence of the set. What I show in this (...) paper is that a group of measures, namely the confirmation-based ones, can be saved from this problem if we adopt a nonlinear averaging function to measure the coherence of a set. The second paper discusses how people should conciliate in disagreements. Some epistemologists take linear averaging as the only way of conciliating and claim that conciliating leads to fallacious results. In the paper, I show that the problem is not conciliating, but taking linear averaging as the only way to conciliate. Since there is no reason for us to insist on conciliating with linear averaging, we can adopt nonlinear averaging functions for conciliating and thereby avoid the formal deficiencies. The third paper focuses on the pragmatic results of taking conciliating as a general strategy in disagreements. There is a potential dilemma about conciliating: if everyone always conciliates, it is likely for an epistemic bubble to arise. If everyone refuses to conciliate, an epistemic echo chamber may appear. A possible way of solving the dilemma is to develop a diachronic strategy which tells people how to both conciliate and update their estimate of their interlocutors’ reliability. Although the three papers differ in the subject, they jointly offer some unifying reflections on the way we approach philosophical problems with formal tools. From 5 the first two papers, we see that a formal analysis of a philosophical position is incomplete if philosophers fail to consider a sufficiently wide range of formal tools. The third paper, on the contrary, shows that we should change the ordinary way of modelling a notion if required. This thesis concludes by proposing a pluralistic view of formal methods in formal epistemology. (shrink)

Recently, in attempting to account for explanatory reasoning in probabilistic terms, Bayesians have proposed several measures of the degree to which a hypothesis explains a given set of facts. These candidate measures of "explanatory power" are shown to have interesting normative interpretations and consequences. What has not yet been investigated, however, is whether any of these measures are also descriptive of people’s actual explanatory judgments. Here, I present my own experimental work investigating this question. I argue (...) that one measure in particular is an accurate descriptor of explanatory judgments. Then, I discuss some interesting implications of this result for both the epistemology and the psychology of explanatory reasoning. (shrink)

This paper provides a new approach to inference to the best explanation based on a new coherence measure for comparing how well hypotheses explain the evidence. It addresses a number of criticisms of the use of probabilistic measures in this context by Clark Glymour, including limitations of earlier work on IBE. Computer experiments are used to show that the new approach finds the truth with a high degree of accuracy in hypothesis selection tasks and that in some (...) cases its accuracy is greater than hypothesis selection based on maximizing posterior probability. Hence, by overcoming some of the problems with the previous approach, this work provides a more adequate defence of IBE and suggests that IBE not only tracks truth but also has practical advantages over the previous approach. Applications of the new approach to parameter estimation and model selection are also explored. (shrink)

Mark Siebel has presented a compelling argument against Branden Fitelson’s probabilistic measure of coherence. The present paper shows how Siebel’s argument can be strengthened and thereby extended to an argument against a huge class of coherence measures from the literature including William Roche’s average mutual firmness account, which has not been challenged up to now.

In this paper, we identify a new and mathematically well-defined sense in which the coherence of a set of hypotheses can be truth-conducive. Our focus is not, as usual, on the probability but on the confirmation of a coherent set and its members. We show that, if evidence confirms a hypothesis, confirmation is “transmitted” to any hypotheses that are sufficiently coherent with the former hypothesis, according to some appropriate probabilistic coherence measure such as Olsson’s or Fitelson’s measure. (...) Our findings have implications for scientific methodology, as they provide a formal rationale for the method of indirect confirmation and the method of confirming theories by confirming their parts. (shrink)

I develop a probabilistic account of coherence, and argue that at least in certain respects it is preferable to (at least some of) the main extant probabilistic accounts of coherence: (i) Igor Douven and Wouter Meijs’s account, (ii) Branden Fitelson’s account, (iii) Erik Olsson’s account, and (iv) Tomoji Shogenji’s account. Further, I relate the account to an important, but little discussed, problem for standard varieties of coherentism, viz., the “Problem of Justified Inconsistent Beliefs.”.

Brian Skyrms (1987, 1990, 1993, 1997) has discussed the role of dynamic coherence arguments in the theory of personal or subjective probability. In particular, Skryms (1997) both reviews and discusses the utility of martingale arguments in establishing the convergence of beliefs within the context of radical probabilism. The classical martingale converence theorem, however, assumes the countable additivity of the underlying probability measure; an assumption rejected by some subjectivists such as Bruno de Finetti (see, e.g., de Finetti 1930 and 1972). (...) This brief note has a very modest goal: to briefly consider the extent to which Skyrms’s argument can be extended to the finitely additive case. (shrink)