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)

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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.

It is tempting to think that, if a person's beliefs are coherent, they are also likely to be true. This truth conduciveness claim is the cornerstone of the popular coherence theory of knowledge and justification. Erik Olsson's new book is the most extensive and detailed study of coherence and probable truth to date. Setting new standards of precision and clarity, Olsson argues that the value of coherence has been widely overestimated. Provocative and readable, Against Coherence will make stimulating reading for (...) epistemologists and anyone with a serious interest in truth. (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)

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)

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)

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)

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..

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)

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)

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)

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)

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)

We wish to give a precise formulation of the intuitive concept: The degree to which the known facts support a given hypothesis.

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.

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)

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.

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)

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.

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)

Charles S. Peirce argued that, besides deduction and induction, there is a third mode of inference which he called " hypothesis " or " abduction." He characterized abduction as reasoning " from effect to cause," and as " the operation of adopting an explanatory hypothesis." Peirce ' s ideas about abduction, which are related also to historically earlier accounts of heuristic reasoning, have been seen as providing a logic of scientific discovery. Alternatively, abduction is interpreted as giving reasons for pursuing (...) a hypothesis. Inference to the best explanation has also been regarded as an important mode of justification, both in everyday life, detective stories, and science. In particular, scientific realism has been defended by an abductive nomiracle argument, while the critics of realism have attempted to show that this appeal to abduction is question - begging, circular, or incoherent. This paper approaches these issues by distinguishing weaker and stronger forms of abduction, and by showing how these types of inferences can be given Peircean and Bayesian probabilistic reconstructions. (shrink)

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

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)

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)

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)

In The Structure of Empirical Knowledge , Laurence BonJour argues that coherence among a set of empirical beliefs can provide justification for those beliefs, in the sense of rendering them likely to be true. He also repudiates all forms of foundationalism for empirical beliefs, including what he calls "weak foundationalism" (the weakest form of foundationalism he can find). In the following, I will argue that coherence cannot provide any justification for our beliefs in the manner BonJour suggests unless some form (...) of foundational justification is assumed. In other words, the argument that BonJour gives in favor of the thesis that coherence provides a kind of justification succeeds if and only if some beliefs have (at least weak) foundational justification. (shrink)

(new version: 10/30/07). Click here to download the companion Mathematica 6 notebook that goes along with this paper.

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)

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)

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.

In this paper I consider whether there is a measure of coherence that could be rightly claimed to generalize the notion of logical equivalence. I show that Fitelson’s (2003) proposal to that effect encounters some serious difficulties. Furthermore, there is reason to believe that no mutual-support measure could ever be suitable for the formalization of coherence as generalized logical equivalence. Instead, it appears that the only plausible candidate for such a measure is one of relative overlap. The measure I propose (...) in this paper is quite similar to Olsson’s (2002) proposal but differs from it by not being susceptible to the type of counterexample that Bovens and Hartmann (2003) have devised against it. (shrink)

In a seminar with the title “Deduction and Induction in the Sciences”, it is intriguing to ask the following questions: Is there a third type of inference besides deduction and induction? Does this third type of inference play a significant role within scientific inquiry? A positive answer to both of these questions was advocated by Charles S. Peirce throughout his career, even though his opinions changed in important ways during the fifty years between 1865 and 1914. Peirce called the third (...) kind of inference “hypothesis”, “abduction”, or “retroduction”.1 In this paper, I shall follow Peirce’s steps in discussing abduction by analyzing its logical form , its role in science , and the grounds of its validity . We shall see that Peirce’s discussion is more insightful than many recent attempts to analyze abductive inference. Still, recently some progress has been made in the treatment of abduction within the Bayesian theory of epistemic probability and truth-approximation . The results of this work support the view of scientific realism: abduction or inference to the best explanation , combined with empirical and experimental testing of scientific theories, is the best method of seeking informative truths in science. (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.

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.