This paper discusses the nature and the status of inference to the best explanation. We outline the foundational role given IBE by its defenders and the arguments of critics who deny it any place at all ; argue that, on the two main conceptions of explanation, IBE cannot be a foundational inference rule ; sketch an account of IBE that makes it contextual and dependent on substantive empirical assumptions, much as simplicity seems to be ; show how that account avoids (...) the critics ' complaints and leaves IBE an important role ; and sketch how our account can clarify debates over IBE in arguments for scientific realism. (shrink)

Epistemologists and philosophers of science have often attempted to express formally the impact of a piece of evidence on the credibility of a hypothesis. In this paper we will focus on the Bayesian approach to evidential support. We will propose a new formal treatment of the notion of degree of confirmation and we will argue that it overcomes some limitations of the currently available approaches on two grounds: (i) a theoretical analysis of the confirmation relation seen as an extension of (...) logical deduction and (ii) an empirical comparison of competing measures in an experimental inquiry concerning inductive reasoning in a probabilistic setting. (shrink)

In a 1994 ANALYSIS article Peter Klein and Ted Warfield show that an epistemically more coherent set of beliefs often has a smaller unconditional probability of joint truth than some of its less coherent subsets. They conclude that epistemic justification, as understood in one version of a coherence theory of justification, is not truth conducive. After getting clear about what truth conduciveness requires, I show that their argument does not tell against BonJour's coherence theory.

The best extant statement of the epistemic regress problem makes assumptions that are too strong. An improved version assumes only that that reasons require support, that no proposition is supported only by endless regresses of reasons, and that some proposition is supported. These assumptions are individually plausible but jointly inconsistent. Attempts to explain support by means of unconceptualized sensations, contextually immunized propositions, endless regresses, and holistic coherence all require either additional reasons or an external condition on support that is arbitrary (...) from the believer's own point of view. (shrink)

The objects of credence are the entities to which credences are assigned for the purposes of a successful theory of credence. I use cases akin to Frege's puzzle to argue against referentialism about credence : the view that objects of credence are determined by the objects and properties at which one's credence is directed. I go on to develop a non-referential account of the objects of credence in terms of sets of epistemically possible scenarios.

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)

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)

The coherentist theory of justification provides a response to the sceptical challenge: even though the independent processes by which we gather information about the world may be of dubious quality, the internal coherence of the information provides the justification for our empirical beliefs. This central canon of the coherence theory of justification is tested within the framework of Bayesian networks, which is a theory of probabilistic reasoning in artificial intelligence. We interpret the independence of the information gathering processes (IGPs) in (...) terms of conditional independences, construct a minimal sufficient condition for a coherence ranking of information sets and assess whether the confidence boost that results from receiving information through independent IGPs is indeed a positive function of the coherence of the information set. There are multiple interpretations of what constitute IGPs of dubious quality. Do we know our IGPs to be no better than randomization processes? Or, do we know them to be better than randomization processes but not quite fully reliable, and if so, what is the nature of this lack of full reliability? Or, do we not know whether they are fully reliable or not? Within the latter interpretation, does learning something about the quality of some IGPs teach us anything about the quality of the other IGPs? The Bayesian-network models demonstrate that the success of the coherentist canon is contingent on what interpretation one endorses of the claim that our IGPs are of dubious quality. (shrink)

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. (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)

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)

Metaphysicians speak of laws of nature in terms of necessity and universality; scientists, in terms of symmetry and invariance. In this book van Fraassen argues that no metaphysical account of laws can succeed. He analyzes and rejects the arguments that there are laws of nature, or that we must believe there are, and argues that we should disregard the idea of law as an adequate clue to science. After exploring what this means for general epistemology, the author develops the empiricist (...) view of science as a construction of models to represent the phenomena. (shrink)

This book examines the philosophical conception of abductive reasoning as developed by Charles S. Peirce, the founder of American pragmatism. It explores the historical and systematic connections of Peirce's original ideas and debates about their interpretations. Abduction is understood in a broad sense which covers the discovery and pursuit of hypotheses and inference to the best explanation. The analysis presents fresh insights into this notion of reasoning, which derives from effects to causes or from surprising observations to explanatory theories. The (...) author outlines some logical and AI approaches to abduction as well as studies various kinds of inverse problems in astronomy, physics, medicine, biology, and human sciences to provide examples of retroductions and abductions. The discussion covers also everyday examples with the implication of this notion in detective stories, one of Peirce’s own favorite themes. The author uses Bayesian probabilities to argue that explanatory abduction is a method of confirmation. He uses his own account of truth approximation to reformulate abduction as inference which leads to the truthlikeness of its conclusion. This allows a powerful abductive defense of scientific realism. This up-to-date survey and defense of the Peircean view of abduction may very well help researchers, students, and philosophers better understand the logic of truth-seeking. (shrink)

Probabilistic models have much to offer to philosophy. We continually receive information from a variety of sources: from our senses, from witnesses, from scientific instruments. When considering whether we should believe this information, we assess whether the sources are independent, how reliable they are, and how plausible and coherent the information is. Bovens and Hartmann provide a systematic Bayesian account of these features of reasoning. Simple Bayesian Networks allow us to model alternative assumptions about the nature of the information sources. (...) Measurement of the coherence of information is a controversial matter: arguably, the more coherent a set of information is, the more confident we may be that its content is true, other things being equal. The authors offer a new treatment of coherence which respects this claim and shows its relevance to scientific theory choice. Bovens and Hartmann apply this methodology to a wide range of much discussed issues regarding evidence, testimony, scientific theories, and voting. Bayesian Epistemology is an essential tool for anyone working on probabilistic methods in philosophy, and has broad implications for many other disciplines. (shrink)

A central problem facing a probabilistic approach to the problem of induction is the difficulty of sufficiently constraining prior probabilities so as to yield the conclusion that induction is cogent. The Principle of Indifference, according to which alternatives are equiprobable when one has no grounds for preferring one over another, represents one way of addressing this problem; however, the Principle faces the well-known problem that multiple interpretations of it are possible, leading to incompatible conclusions. I propose a partial solution to (...) the latter problem, drawing on the notion of explanatory priority. The resulting synthesis of Bayesian and inference-to-best-explanation approaches affords a principled defense of prior probability distributions that support induction. (shrink)

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Niiniluoto has offered an incisive and comprehensive review of the recent debates about abduction. There is little on which I disagree with him. So, in this commentary, I shall try to cast some doubts to the attempts to render Inference to the Best Explanation within a Bayesian framework.

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 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)

Inference to the Best Explanation (IBE) and Bayesianism are our two most prominent theories of scientific inference. Are they compatible? Van Fraassen famously argued that they are not, concluding that IBE must be wrong since Bayesianism is right. Writers since then, from both the Bayesian and explanationist camps, have usually considered van Fraassen’s argument to be misguided, and have plumped for the view that Bayesianism and IBE are actually compatible. I argue that van Fraassen’s argument is actually not so misguided, (...) and that it causes more trouble for compatibilists than is typically thought. Bayesianism in its dominant, subjectivist form, can only be made compatible with IBE if IBE is made subservient to conditionalization in a way that robs IBE of much of its substance and interest. If Bayesianism and IBE are to be fit together, I argue, a strongly objective Bayesianism is the preferred option. I go on to sketch this objectivist, IBE-based Bayesianism, and offer some preliminary suggestions for its development. (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)

This paper considers how explanatory factors can play a role in our ampliative inferential practices. Van Fraassen has argued that there is no possible rational rule that governs ampliative inferences and includes weightings for explanatory beauty. In opposition to van Fraassen, Douven has argued that ampliative inferential rules that include weightings for explanatory factors can be rationally followed. There is, however, a crucial difficulty with Douven's approach: applying the ampliative rule that he suggests leads into irrational belief states. A way (...) to remove the difficulties with Douven's account is suggested. The implications of rationally including explanatory factors in ampliative inferences are then considered. Introduction The proposed interpretations Van Fraassen's justification of the Bayesian approach A rational non-Bayesian interpretation? Further restrictions on D(A,B) Conclusion. (shrink)

This target article presents a new computational theory of explanatory coherence that applies to the acceptance and rejection of scientific hypotheses as well as to reasoning in everyday life, The theory consists of seven principles that establish relations of local coherence between a hypothesis and other propositions. A hypothesis coheres with propositions that it explains, or that explain it, or that participate with it in explaining other propositions, or that offer analogous explanations. Propositions are incoherent with each other if they (...) are contradictory, Propositions that describe the results of observation have a degree of acceptability on their own. An explanatory hypothesis is acccpted if it coheres better overall than its competitors. The power of the seven principles is shown by their implementation in a connectionist program called ECHO, which treats hypothesis evaluation as a constraint satisfaction problem. Inputs about the explanatory relations are used to create a network of units representing propositions, while coherende and incoherence relations are encoded by excitatory and inbihitory links. ECHO provides an algorithm for smoothly integrating theory evaluation based on considerations of explanatory breadth, simplicity, and analogy. It has been applied to such important scientific cases as Lovoisier's argument for oxygen against the phlogiston theory and Darwin's argument for evolution against creationism, and also to cases of legal reasoning. The theory of explanatory coherence has implications for artificial intelligence, psychology, and philosophy. (shrink)

This article is a response to Elijah Millgram's argument that my characterization of coherence as constraint satisfaction is inadequate for philosophical purposes because it provides no guarantee that the most coherent theory available will be true. I argue that the constraint satisfaction account of coherence satisfies the philosophical, computational, and psychological prerequisites for the development of epistemological and ethical theories.

This paper provides a computational characterization of coherence that applies to a wide range of philosophical problems and psychological phenomena. Maximizing coherence is a matter of maximizing satisfaction of a set of positive and negative constraints. After comparing five algorithms for maximizing coherence, we show how our characterization of coherence overcomes traditional philosophical objections about circularity and truth.

Some philosophers, most notably Hempel and Salmon, have tried to reduce explanation to probability by proposing analyses of explanation in probabilistic terms. Hempel claims, roughly, that a hypothesis H explains a datum D if and only if the conditional probability P is close to 1. It is well known that such an account fails in cases where H is irrelevant for D. Even though it is highly likely that Tom will not become pregnant, given that he regularly takes his wife’s (...) birth control pills, the latter does not explain the former. Neither does an idea work which is in the proximity of Salmon’s, namely, that H explains D if and only if P > P. Suppose Susan swallows a pound of arsenic in order to commit suicide. Shortly after, however, she dies because she is run over by a bus. The probability of dying, given that one ingests a pound of arsenic, is usually higher than the prior probability of dying. Nonetheless, it is not the arsenic but the collision with the bus which explains Susan’s death. The aforementioned objections are directed against …. (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.

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)

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)

In this paper we make three points about justification of propositions by coherence “from scratch”, where pieces of evidence that are coherent have no individual credibility. First, we argue that no matter how many pieces of evidence are coherent, and no matter what relation we take coherence to be, coherence does not make independent pieces of evidence with no individual credibility credible. Second, we show that an intuitively plausible informal reasoning for justification by coherence from scratch is deficient since it (...) relies on an understanding of “individual credibility” inappropriate for justification from scratch. Third, we show that coherence, when it is recurrent, can make independent sources of evidence with no individual credibility credible. We describe specifically a case in which the same group of independent witnesses with no individual credibility repeatedly produce reports that are in agreement with each other, and their reports become credible as a result. (shrink)

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. (shrink)

The success of Bovens and Hartmann’s recent “impossibility result” against Bayesian Coherentism relies upon the adoption of a specific set of ceteris paribus conditions. In this paper, I argue that these conditions are not clearly appropriate; certain proposed coherence measures motivate different such conditions and also call for the rejection of at least one of Bovens and Hartmann’s conditions. I show that there exist sets of intuitively plausible ceteris paribus conditions that allow one to sidestep the impossibility result. This shifts (...) the debate from the merits of the impossibility result itself to the underlying choice of ceteris paribus conditions. (shrink)

A measure of coherence is said to be reliability conducive if and only if a higher degree of coherence (as measured) results in a higher likelihood that the witnesses are reliable. Recently, it has been proved that several coherence measures proposed in the literature are reliability conducive in a restricted scenario (Olsson and Schubert 2007, Synthese 157:297–308). My aim is to investigate which coherence measures turn out to be reliability conducive in the more general scenario where it is any finite (...) number of witnesses that give equivalent reports. It is shown that only the so-called Shogenji measure is reliability conducive in this scenario. I take that to be an argument for the Shogenji measure being a fruitful explication of coherence. (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)

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)

If a subject’s belief system is inconsistent, does it follow that the subject’s beliefs (all of them) are unjustified? It seems not. But, coherentist theories of justification (at least some of them) imply otherwise, and so, it seems, are open to counterexample. This is the “Problem of Justified Inconsistent Beliefs”. I examine two main versions of the Problem of Justified Inconsistent Beliefs, and argue that coherentists can give at least a promising line of response to each of them.

Andrew Cling presents a new version of the epistemic regress problem, and argues that intuitionist foundationalism, social contextualism, holistic coherentism, and infinitism fail to solve it. Cling’s discussion is quite instructive, and deserving of careful consideration. But, I argue, Cling’s discussion is not in all respects decisive. I argue that Cling’s dilemma argument against holistic coherentism fails.

Traditionally, philosophers have focused mostly on the logical template of inference. The paradigm-case has been deductive inference, which is topic-neutral and context-insensitive. The study of deductive rules has engendered the search for the Holy Grail: syntactic and topic-neutral accounts of all prima facie reasonable inferential rules. The search has hoped to find rules that are transparent and algorithmic, and whose following will just be a matter of grasping their logical form. Part of the search for the Holy Grail has been (...) to show that the so-called scientific method can be formalised in a topic-neutral way. We are all familiar with Carnap’s inductive logic, or Popper’s deductivism or the Bayesian account of scientific method. (shrink)

This paper develops and defends a coherentist account of reasons. I develop three core ideas for this defense: a distinction between basic reasons and noninferential justification, the plausibility of the neglected argument against first philosophy, and an emergent account of reasons. These three ideas form the backbone for a credible coherentist view of reasons. I work toward this account by formulating and explaining the basic reasons dilemma. This dilemma reveals a wavering attitude that coherentists have had toward basic reasons. More (...) importantly, the basic reasons dilemma focuses our attention on the central problems that afflict coherentist views of basic beliefs. By reflecting on the basic reasons dilemma, I formulate three desiderata that any viable coherentist account of basic beliefs must satisfy. I argue that the account on offer satisfies these desiderata. (shrink)