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.

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.

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.

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.

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)

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)

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.

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)

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)

We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

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)

How do we go about weighing evidence, testing hypotheses, and making inferences? The model of " inference to the best explanation " -- that we infer the hypothesis that would, if correct, provide the best explanation of the available evidence--offers a compelling account of inferences both in science and in ordinary life. Widely cited by epistemologists and philosophers of science, IBE has nonetheless remained little more than a slogan. Now this influential work has been thoroughly revised and updated, and features (...) a new introduction and two new chapters. Inference to the Best Explanation is an unrivaled exposition of a theory of particular interest in the fields both of epistemology and the philosophy of science. (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)

The most pressing difficulty coherentism faces is, I believe, the problem of justified inconsistent beliefs. In a nutshell, there are cases in which our beliefs appear to be both fully rational and justified, and yet the contents of the beliefs are inconsistent, often knowingly so. This fact contradicts the seemingly obvious idea that a minimal requirement for coherence is logical consistency. Here, I present a solution to one version of this problem.

Parsimony is a virtue of empirical theories. Is it also a virtue of philosophical theories? I review four contemporary accounts of the virtue of parsimony in empirical theorizing, and consider how each might apply to two prominent appeals to parsimony in the philosophical literature, those made on behalf of physicalism and on behalf of nominalism. None of the accounts of the virtue of parsimony extends naturally to either of these philosophical cases. This suggests that in typical philosophical contexts, ontological simplicity (...) has no evidential value. (shrink)

Recent work on inference to the best explanation has come to an impasse regarding the proper way to coordinate the theoretical virtues in explanatory inference with probabilistic confirmation theory, and in particular with aspects of Bayes's Theorem. I argue that the theoretical virtues are best conceived heuristically and that such a conception gives us the resources to explicate the virtues in terms of ceteris paribus theorems. Contrary to some Bayesians, this is not equivalent to identifying the virtues with likelihoods or (...) priors per se; the virtues may be more accessible epistemically than likelihoods or priors. I then prove a ceteris paribus theorem regarding theoretical consilience, use it to correct a recent application of Reichenbach's common cause principle, and apply it to a test case of scientific reasoning. Explanation and confirmation The heuristic conception of theoretical virtues Abduction and the accessibility of explanatory power Evidential and theoretical consilience A test case: gravitational lensing Conclusion Thus natural science appears completely to lose from sight the large and general questions; but all the more splendid is the success when, groping in the thicket of special questions, we suddenly find a small opening that allows a hitherto undreamt of outlook on the whole. (L. Boltzmann, Theoretical Physics and Philosophical Problems). (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)

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.

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)

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)

Bayesianism and Inference to the best explanation are two different models of inference. Recently there has been some debate about the possibility of “bayesianizing” IBE. Firstly I explore several alternatives to include explanatory considerations in Bayes’s Theorem. Then I distinguish two different interpretations of prior probabilities: “IBE-Bayesianism” and “frequentist-Bayesianism”. After detailing the content of the latter, I propose a rule for assessing the priors. I also argue that Freq-Bay: endorses a role for explanatory value in the assessment of scientific hypotheses; (...) avoids a purely subjectivist reading of prior probabilities; and fits better than IBE-Bayesianism with two basic facts about science, i.e., the prominent role played by empirical testing and the existence of many scientific theories in the past that failed to fulfil their promises and were subsequently abandoned. (shrink)

Most philosophers agree that abduction (in the sense of Inference to the Best Explanation) is a type of inference that is frequently employed, in some form or other, both in everyday and in scientific reasoning. However, the exact form as well as the normative status of abduction are still matters of controversy. This entry contrasts abduction with other types of inference; points at prominent uses of it, both in and outside philosophy; considers various more or less precise statements of it; (...) discusses its normative status; and highlights possible connections between abduction and Bayesian confirmation theory. (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)

Recent results in probability theory have cast doubt on the coherence theory of justification, allegedly showing that coherence cannot produce justification for beliefs in the absence of foundational justification, and that there can be no measure of coherence on which coherence is generally truth-conducive. I argue that the coherentist can reject some of the assumptions on which these theorems depend. Coherence can then be held to produce justification on its own, and truth-conducive measures of coherence can be constructed.

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)

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.

Earlier in this volume, Wesley Salmon has given a characteristically clear and trenchant critique of the account of non-demonstrative reasoning known by the slogan `Inference to the Best Explanation'. As a long-time fan of the idea that explanatory considerations are a guide to inference, I was delighted by the suggestion that Wes and I might work together on a discussion of the issues. In the event, this project has exceeded my high expectations, for in addition to the intellectual gain that (...) comes from the careful study of his essay, I have benefited enormously from the stream of illuminating emails and faxes that Wes has sent me during our collaboration. Doing philosophy together has been an education and a pleasure. Salmon's essay would place Inference to the Best Explanation beyond the pale of acceptable philosophical accounts of inference. According to Salmon, Inference to the Best Explanation has serious internal difficulties and compares very unfavourably with Bayesian approaches to these matters. My aim in the following remarks is irenic. I hope to show that a number of the claimed difficulties either are not really difficulties or are avoidable. In some cases, the avoidance will require a mild reinterpretation of the account that lies behind the slogan `Inference to the Best Explanation'; in others, it will require admitting limits to the scope of the account. For I accept at the outset that Inference to the Best Explanation cannot possibly be the whole story about the assessment of scientific hypotheses. For me, the interesting idea is simply that we sometimes decide how likely a hypothesis is to be correct in part by considering how good an explanation it would provide, if it were correct. This is the idea of explanatory considerations providing a guide to inference, and this is the idea that I will here promote. (shrink)

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)

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..

Several forms of symmetry in degrees of evidential support areconsidered. Some of these symmetries are shown not to hold in general. This has implications for the adequacy of many measures of degree ofevidential support that have been proposed and defended in the philosophical literature.

Van Fraassen (1989) argues that Inference to the Best Explanation is incoherent in the sense that adopting it as a rule for belief change will make one susceptible to a dynamic Dutch book. The present paper argues against this. A strategy is described that allows us to infer to the best explanation free of charge.

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)

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)

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)

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)

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)

An explanatory coherence theory of justification is sketched and then defended against a number of recent objections: conservatism and relativism; wild and crazy beliefs; reliability; warranted necessary falsehoods; basing; distant, unknown coherences; Sosa's “self- and present-abstracts”; and Bayesian impossibility results.

This paper applies a new theory of explanatory coherence to the early history of the idea of continental drift. The new theory consists of seven principles that establish coherence and incoherence relations among propositions. It has been implemented in a connectionist computer program called ECHO. Analysis of the arguments of Alfred Wegener, the first major proponent of continental drift, provided input to ECHO which evaluated the explanatory coherence of his hypotheses. ECHO has also been used to analyze the coherence of (...) the views of Wegener 's critics. The paper concludes by contrasting our explanatory coherence account of Wegener and his opposition with a decision-theoretic account recently offered by Ron Giere. (shrink)

Note: This is not an ad hoc change at all. It’s simply the natural thing say here – if one thinks of F as a generalization of classical logical entailment. The extra complexity I had in my original (incorrect) definition of F was there because I was foolishly trying to encode some non-classical, or “relavant” logical structure in F. I now think this is a mistake, and that I should go with the above, classical account of F. Arguments about relevance (...) logic need to be handled in a different way (and a different context!). And, besides, as Luca Moretti has shown (see below), the original definition of F cannot be the right basis for C ! OK, now on to C. (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)

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 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)