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)

To understand something involves some sort of commitment to a set of propositions comprising an account of the understood phenomenon. Some take this commitment to be a species of belief; others, such as Elgin and I, take it to be a kind of cognitive policy. This paper takes a step back from debates about the nature of understanding and asks when this commitment involved in understanding is epistemically appropriate, or ‘acceptable’ in Elgin’s terminology. In particular, appealing to lessons from the (...) lottery and preface paradoxes, it is argued that this type of commitment is sometimes acceptable even when it would be rational to assign arbitrarily low probabilities to the relevant propositions. This strongly suggests that the relevant type of commitment is sometimes acceptable in the absence of epistemic justification for belief, which in turn implies that understanding does not require justification in the traditional sense. The paper goes on to develop a new probabilistic model of acceptability, based on the idea that the maximally informative accounts of the understood phenomenon should be optimally probable. Interestingly, this probabilistic model ends up being similar in important ways to Elgin’s proposal to analyze the acceptability of such commitments in terms of ‘reflective equilibrium’. (shrink)

This Open Access book addresses the age-old problem of infinite regresses in epistemology. How can we ever come to know something if knowing requires having good reasons, and reasons can only be good if they are backed by good reasons in turn? The problem has puzzled philosophers ever since antiquity, giving rise to what is often called Agrippa's Trilemma. The current volume approaches the old problem in a provocative and thoroughly contemporary way. Taking seriously the idea that good reasons are (...) typically probabilistic in character, it develops and defends a new solution that challenges venerable philosophical intuitions and explains why they were mistakenly held. Key to the new solution is the phenomenon of fading foundations, according to which distant reasons are less important than those that are nearby. The phenomenon takes the sting out of Agrippa's Trilemma; moreover, since the theory that describes it is general and abstract, it is readily applicable outside epistemology, notably to debates on infinite regresses in metaphysics. (shrink)

In everyday life and in science we acquire evidence of evidence and based on this new evidence we often change our epistemic states. An assumption underlying such practice is that the following EEE Slogan is correct: 'evidence of evidence is evidence' (Feldman 2007, p. 208). We suggest that evidence of evidence is best understood as higher-order evidence about the epistemic state of agents. In order to model evidence of evidence we introduce a new powerful framework for modelling epistemic states, Dyadic (...) Bayesianism. Based on this framework, we then discuss characterizations of evidence of evidence and argue for one of them. Finally, we show that whether the EEE Slogan holds, depends on the specific kind of evidence of evidence. (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)

According to an influential Enlightenment ideal, one shouldn't rely epistemically on other people's say-so, at least not if one is in a position to evaluate the relevant evidence for oneself. However, in much recent work in social epistemology, we are urged to dispense with this ideal, which is seen as stemming from a misguided focus on isolated individuals to the exclusion of groups and communities. In this paper, I argue that that an emphasis on the social nature of inquiry should (...) not lead us to entirely abandon the Enlightenment ideal of epistemically autonomous agents. Specifically, I suggest that it is an appropriate ideal for those who serve as experts in a given epistemic community, and develop a notion of expert acceptance to make sense of this. I go on to show that, all other things being equal, this kind of epistemic autonomy among experts makes their joint testimony more reliable, which in turn brings epistemic benefits both to laypeople and to experts in other fields. (shrink)

For two ideally rational agents, does learning a finite amount of shared evidence necessitate agreement? No. But does it at least guard against belief polarization, the case in which their opinions get further apart? No. OK, but are rational agents guaranteed to avoid polarization if they have access to an infinite, increasing stream of shared evidence? No.

It can be argued (cf. Dizadji‑Bahmani et al. 2010) that an increase in coherence is one goal that drives reductionist enterprises. Consequently, the question if or how well this goal is achieved can serve as an epistemic criterion for evaluating both a concrete case of a purported reduction and our model of reduction : what conditions on the model allow for an increase in coherence ? In order to answer this question, I provide an analysis of the relation between the (...) reduction and the coherence of two theories. The underlying model of reduction is a (generalised) Nagelian model (cf. Nagel 1970, Schaffner 1974, Dizadji‑Bahmani et al. 2010). For coherence, different measures have been put forward (e.g. Shogenji 1999, Olsson 2002, Fitelson 2003, Bovens & Hartmann 2003). However, since there are counterexamples to each proposed coherence measure, we should be careful that the analysis be sufficiently stable (in a sense to be specified). It will turn out that this can be done. (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.”.

According to the truth-conduciveness problem of coherentism, the coherence theory of justification can hardly show that coherentist justification is truth-conducive. This problem is generally conceived as the most recalcitrant problem with the coherence theory. The purpose of this paper is to show that it does not pose a serious problem for a certain version of coherentism, namely a Sellarsian explanatory coherence theory of justification combined with the deflationary theory of truth. On this version of coherentism, our epistemic goal is to (...) gradually improve our conceptual framework so as to maximize its explanatory coherence, and there is no substantial norm of truth independent of the norms of justification, so that we cannot evaluate the truth-conduciveness of a belief independently of the norms of justification. I argue that this version of coherentism can cope with the truth-conduciveness problem. (shrink)

According to the traditional requirement, formulated by William Whewell in his account of the “consilience of inductions” in 1840, a scientific hypothesis should have unifying power in the sense that it explains and predicts several mutually independent phenomena. Variants of this notion of consilience or unification include deductive, inductive, and approximate systematization. Inference from surprising phenomena to their theoretical explanations was called abduction by Charles Peirce. As a unifying theory is independently testable by new kinds of phenomena, it should also (...) receive confirmation from its empirical success. The study of the prospects of probabilistic Bayesianism to motivate this kind of criterion for abductive confirmation is shown to lead to two quite distinct conceptions of unification. (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)

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)

This paper discusses two senses in which a hypothesis may be said to unify evidence. One is the ability of the hypothesis to increase the mutual information of a set of evidence statements; the other is the ability of the hypothesis to explain commonalities in observed phenomena by positing a common origin for them. On Bayesian updating, it is only mutual information unification that contributes to the incremental support of a hypothesis by the evidence unified. This poses a challenge for (...) the view that explanation is a confirmatory virtue that contributes to such incremental support; its advocates must ground it in some relevant difference between humans and a Bayesian agent. (shrink)

Bayesian epistemology provides a formal framework within which concepts in traditional epistemology, in particular concepts relating to the justification of our beliefs, can be given precise definitions in terms of probability. The Bayesian approach has contributed clarity and precision to a number of traditional issues. A salient example is the recent embedding of the so-called coherentist theory of epistemic justification in a Bayesian framework shedding light on the relation between coherence and truth as well as on the concept of coherence (...) itself. Starting with the early work of Condorcet, the calculus of probability has proved to be a useful tool in the study of social aspects of knowledge as it is pursued in social epistemology. (shrink)

Two recently popular metaphilosophical movements, formal philosophy and experimental philosophy, promote what seem to be conflicting methodologies. Nonetheless, I argue that the two can be mutually supportive. I propose an experimentally-informed variation on explication, a powerful formal philosophical tool introduced by Carnap. The resulting method, which I call “experimental explication,” provides the formalist with a means of responding to explication's gravest criticism. Moreover, this method introduces a philosophically salient, positive role for survey-style experiments while steering clear of several objections that (...) critics of “positive experimental philosophy” raise. Thus, it provides the experimentalist with a more defensible example of how empirical work can have positive philosophical import. For these reasons, experimental explication should appeal to experimental philosophers and formal philosophers alike. (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)

It is often claimed that the greatest value of the Bayesian framework in cognitive science consists in its unifying power. Several Bayesian cognitive scientists assume that unification is obviously linked to explanatory power. But this link is not obvious, as unification in science is a heterogeneous notion, which may have little to do with explanation. While a crucial feature of most adequate explanations in cognitive science is that they reveal aspects of the causal mechanism that produces the phenomenon to be (...) explained, the kind of unification afforded by the Bayesian framework to cognitive science does not necessarily reveal aspects of a mechanism. Bayesian unification, nonetheless, can place fruitful constraints on causal–mechanical explanation. 1 Introduction2 What a Great Many Phenomena Bayesian Decision Theory Can Model3 The Case of Information Integration4 How Do Bayesian Models Unify?5 Bayesian Unification: What Constraints Are There on Mechanistic Explanation?5.1 Unification constrains mechanism discovery5.2 Unification constrains the identification of relevant mechanistic factors5.3 Unification constrains confirmation of competitive mechanistic models6 ConclusionAppendix. (shrink)

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)

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 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)

Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically (...) independent of F (for all F in a partition of the underlying state space) is sufficient to avoid dilation, but (2) stochastic independence is not the only independence concept at play within imprecise probability models. In this paper we give a simple characterization of dilation formulated in terms of deviation from stochastic independence, propose a measure of dilation, and distinguish between proper and improper dilation. Through this we revisit the most sensational examples of dilation, which play up independence between dilator and dilatee, and find the sensationalism undermined by either fallacious reasoning with imprecise probabilities or improperly constructed imprecise probability models. (shrink)

In der neueren Erkenntnistheorie wird der Bayesianismus immer populärer. In diesem Ansatz werden Überzeugungen mit Glaubensgraden versehen. Dazu möchte ich der Frage nachgehen, ob wir den klassischen Ansatz in der Erkennnistheorie mit seinen kategorischen Überzeugungen komplett durch einen bayesianischen mit einem probabilistischen Überzeugungssystem ersetzen könnten. Um das zu klären, rekonstruiere ich zunächst beide Modelle unserer Überzeugungssysteme und vergleiche sie dann im Hinblick darauf, wie leistungsfähig sie jeweils dafür sind, erkenntnistheoretische Probleme zu lösen und als Grundlage für Entscheidungen zu dienen. Dabei (...) zeigt sich eine gewisse Inkommensurabilität der beiden Ansätze und außerdem erweist sich keine der Konzeptionen als eindeutig überlegen. Deshalb argumentiere ich schließlich für eine bestimmte Hybridkonzeption aus beiden Ansätzen, die die Vorteile beider Konzeptionen vereinen kann. (shrink)

In recent decades, the concept of coherence has become one of the key concepts in philosophy. Although there is still no consensus about how to explicate coherence, it is widely accepted that the appearance of anomalies significantly lowers the coherence of a propositional or belief system. In this paper, the relationship between coherence and anomalies is analysed by looking at a specific case study from astronomy. It concerns anomalies that occurred in the first half of the twentieth century during the (...) attempt to develop a cosmic distance scale. These anomalies could not be removed until several decades after their appearance, which required a fundamental change in astronomical theory. During this process, the astronomical distance scale had to be adjusted by a factor of about 2. This paper focuses on the role that explanatory relations played with respect to the elimination of these anomalies. Thereby, special attention is paid to the explanatory work of astronomical theories or models that were not especially designed for this task. (shrink)

Some recent work in formal epistemology shows that “witness agreement” by itself implies neither an increase in the probability of truth nor a high probability of truth—the witnesses need to have some “individual credibility.” It can seem that, from this formal epistemological result, it follows that coherentist justification (i.e., doxastic coherence) is not truth-conducive. I argue that this does not follow. Central to my argument is the thesis that, though coherentists deny that there can be noninferential justification, coherentists do not (...) deny that there can be individual credibility. (shrink)

Coherentism maintains that coherent beliefs are more likely to be true than incoherent beliefs, and that coherent evidence provides more confirmation of a hypothesis when the evidence is made coherent by the explanation provided by that hypothesis. Although probabilistic models of credence ought to be well-suited to justifying such claims, negative results from Bayesian epistemology have suggested otherwise. In this essay we argue that the connection between coherence and confirmation should be understood as a relation mediated by the causal relationships (...) among the evidence and a hypothesis, and we offer a framework for doing so by fitting together probabilistic models of coherence, confirmation, and causation. We show that the causal structure among the evidence and hypothesis is sometimes enough to determine whether the coherence of the evidence boosts confirmation of the hypothesis, makes no difference to it, or even reduces it. We also show that, ceteris paribus, it is not the coherence of the evidence that boosts confirmation, but rather the ratio of the coherence of the evidence to the coherence of the evidence conditional on a hypothesis. (shrink)

A common objection to coherentism is that it cannot account for truth: it gives us no reason to prefer a true theory over a false one, if both theories are equally coherent. By extending Susan Haack's crossword metaphor, the authors argue that there could be circumstances under which this objection is untenable. Although these circumstances are remote, they are in full accordance with the most ambitious modern theories in physics. Coherence may perhaps be truth conducive.

I show that the two most devastating objections to Shogenji's formal account of coherence necessarily involve information sets of cardinality . Given this, I surmise that the problem with Shogenji's measure has more to do with his means of generalizing the measure than with the measure itself. I defend this claim by offering an alternative generalization of Shogenji's measure. This alternative retains the intuitive merits of the original measure while avoiding both of the relevant problems that befall it. In the (...) light of all of this, I suggest that there is new hope for Shogenji's analysis: Shogenji's early and influential attempt at measuring coherence, when generalized in a subset-sensitive way, is able to clear its most troubling objections. (shrink)

Coherentists on epistemic justification claim that all justification is inferential, and that beliefs, when justified, get their justification together (not in isolation) as members of a coherent belief system. Some recent work in formal epistemology shows that “individual credibility” is needed for “witness agreement” to increase the probability of truth and generate a high probability of truth. It can seem that, from this result in formal epistemology, it follows that coherentist justification is not truth-conducive, that it is not the case (...) that, under the requisite conditions, coherentist justification increases the probability of truth and generates a high probability of truth. I argue that this does not follow. (shrink)

In a famous experiment by Tversky and Kahneman (Psychol Rev 90:293–315, 1983), featuring Linda the bank teller, the participants assign a higher probability to a conjunction of propositions than to one of the conjuncts, thereby seemingly committing a probabilistic fallacy. In this paper, we discuss a slightly different example featuring someone named Walter, who also happens to work at a bank, and argue that, in this example, it is rational to assign a higher probability to the conjunction of suitably chosen (...) propositions than to one of the conjuncts. By pointing out the similarities between Tversky and Kahneman’s experiment and our example, we argue that the participants in the experiment may assign probabilities to the propositions in question in such a way that it is also rational for them to give the conjunction a higher probability than one of the conjuncts. (shrink)

This essay presents results about a deviation from independence measure called focused correlation . This measure explicates the formal relationship between probabilistic dependence of an evidence set and the incremental confirmation of a hypothesis, resolves a basic question underlying Peter Klein and Ted Warfield's ‘truth-conduciveness’ problem for Bayesian coherentism, and provides a qualified rebuttal to Erik Olsson's claim that there is no informative link between correlation and confirmation. The generality of the result is compared to recent programs in Bayesian epistemology (...) that attempt to link correlation and confirmation by utilizing a conditional evidential independence condition. Several properties of focused correlation are also highlighted. Introduction Correlation Measures 2.1 Standard covariance and correlation measures 2.2 The Wayne–Shogenji measure 2.3 Interpreting correlation measures 2.4 Correlation and evidential independence Focused Correlation Conclusion Appendix CiteULike Connotea Del.icio.us What's this? (shrink)

The impossibility results of Bovens and Hartmann (2003) and Olsson (2005) call into question the strength of the connection between coherence and truth. As part of the inquiry into this alleged link, I define a notion of degree of truth-conduciveness, relevant for measuring the usefulness of coherence measures as rules-of-thumb for assigning probabilities in situations of partial knowledge. I use the concept to compare the viability of some of the measures of coherence that have been suggested so far under different (...) circumstances. It turns out that all of these, including the prior, are just about equally good in cases of very little knowledge. Nevertheless, there are differences in when they are applicable, and they also depart more from each other when more knowledge is added. CiteULike Connotea Del.icio.us What's this? (shrink)

This paper describes a formal measure of epistemic justification motivated by the dual goal of cognition, which is to increase true beliefs and reduce false beliefs. From this perspective the degree of epistemic justification should not be the conditional probability of the proposition given the evidence, as it is commonly thought. It should be determined instead by the combination of the conditional probability and the prior probability. This is also true of the degree of incremental confirmation, and I argue that (...) any measure of epistemic justification is also a measure of incremental confirmation. However, the degree of epistemic justification must meet an additional condition, and all known measures of incremental confirmation fail to meet it. I describe this additional condition as well as a measure that meets it. The paper then applies the measure to the conjunction fallacy and proposes an explanation of the fallacy. (shrink)

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)

Can some evidence confirm a conjunction of two hypotheses more than it confirms either of the hypotheses separately? We show that it can, moreover under conditions that are the same for nine different measures of confirmation. Further we demonstrate that it is even possible for the conjunction of two disconfirmed hypotheses to be confirmed by the same evidence.

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..

Meijs and Douven (2005) present an interesting pair of alleged counterexamples and an algorithm to generate such counter-examples to our criterion for a coherence quasi-ordering over information sets as outlined in our 2003a and 2003b accounts. We agree that our criterion does not always provide an ordering when we would intuitively say that one set is more coherent than the other. Nonetheless, we think that our criterion can be salvaged.

Recent works in epistemology show that the claim that coherence is truth conducive – in the sense that, given suitable ceteris paribus conditions, more coherent sets of statements are always more probable – is dubious and possibly false. From this, it does not follows that coherence is a useless notion in epistemology and philosophy of science. Dietrich and Moretti (Philosophy of science 72(3): 403–424, 2005) have proposed a formal of account of how coherence is confirmation conducive—that is, of how the (...) coherence of a set of statements facilitates the confirmation of such statements. This account is grounded in two confirmation transmission properties that are satisfied by some of the measures of coherence recently proposed in the literature. These properties explicate everyday and scientific uses of coherence. In his paper, I review the main findings of Dietrich and Moretti (2005) and define two evidence-gathering properties that are satisfied by the same measures of coherence and constitute further ways in which coherence is confirmation conducive. At least one of these properties vindicates important applications of the notion of coherence in everyday life and in science. (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)

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)

Bayesian epistemology addresses epistemological problems with the help of the mathematical theory of probability. It turns out that the probability calculus is especially suited to represent degrees of belief (credences) and to deal with questions of belief change, confirmation, evidence, justification, and coherence. Compared to the informal discussions in traditional epistemology, Bayesian epis- temology allows for a more precise and fine-grained analysis which takes the gradual aspects of these central epistemological notions into account. Bayesian epistemology therefore complements traditional epistemology; it (...) does not re- place it or aim at replacing it. (shrink)

The impossibility results of Bovens and Hartmann (2003, Bayesian epistemology. Oxford: Clarendon Press) and Olsson (2005, Against coherence: Truth, probability and justification. Oxford: Oxford University Press.) show that the link between coherence and probability is not as strong as some have supposed. This paper is an attempt to bring out a way in which coherence reasoning nevertheless can be justified, based on the idea that, even if it does not provide an infallible guide to probability, it can give us an (...) indication thereof. It is further shown that this actually is the case, for several of the coherence measures discussed in the literature so far. We also discuss how this affects the possibility to use coherence as a means of epistemic justification. (shrink)

Most foundationalists allow that relations of coherence among antecedently justified beliefs can enhance their overall level of justification or warrant. In light of this, some coherentists ask the following question: if coherence can elevate the epistemic status of a set of beliefs, what prevents it from generating warrant entirely on its own? Why do we need the foundationalist’s basic beliefs? I address that question here, drawing lessons from an instructive series of attempts to reconstruct within the probability calculus the classical (...) problem of independent witnesses who corroborate each other’s testimony. Starred section headings indicate sections omitted here, but available on the author’s USC website. (shrink)

Can some evidence confirm a conjunction of two hypotheses more than it confirms either of the hypotheses separately? We show that it can, moreover under conditions that are the same for ten different measures of confirmation. Further we demonstrate that it is even possible for the conjunction of two disconfirmed hypotheses to be confirmed by the same evidence.