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.”.

How should we reason in science? Jan Sprenger and Stephan Hartmann offer a refreshing take on classical topics in philosophy of science, using a single key concept to explain and to elucidate manifold aspects of scientific reasoning. They present good arguments and good inferences as being characterized by their effect on our rational degrees of belief. Refuting the view that there is no place for subjective attitudes in 'objective science', Sprenger and Hartmann explain the value of convincing evidence in terms (...) of a cycle of variations on the theme of representing rational degrees of belief by means of subjective probabilities (and changing them by Bayesian conditionalization). In doing so, they integrate Bayesian inference—the leading theory of rationality in social science—with the practice of 21st century science. Bayesian Philosophy of Science thereby shows how modeling such attitudes improves our understanding of causes, explanations, confirming evidence, and scientific models in general. It combines a scientifically minded and mathematically sophisticated approach with conceptual analysis and attention to methodological problems of modern science, especially in statistical inference, and is therefore a valuable resource for philosophers and scientific practitioners. (shrink)

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

This paper synthesizes confirmation by instances and confirmation by successful predictions, and thereby the Hempelian and the hypothetico-deductive traditions in confirmation theory. The merger of these two approaches is subsequently extended to the piecemeal confirmation of entire theories. It is then argued that this synthetic account makes a useful contribution from both a historical and a systematic perspective.

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

Probabilistic support is not transitive. There are cases in which x probabilistically supports y , i.e., Pr( y | x ) > Pr( y ), y , in turn, probabilistically supports z , and yet it is not the case that x probabilistically supports z . Tomoji Shogenji, though, establishes a condition for transitivity in probabilistic support, that is, a condition such that, for any x , y , and z , if Pr( y | x ) > Pr( y (...) ), Pr( z | y ) > Pr( z ), and the condition in question is satisfied, then Pr( z | x ) > Pr( z ). I argue for a second and weaker condition for transitivity in probabilistic support. This condition, or the principle involving it, makes it easier (than does the condition Shogenji provides) to establish claims of probabilistic support, and has the potential to play an important role in at least some areas of philosophy. (shrink)

Synchronic intertheoretic reductions are an important field of research in science. Arguably, the best model able to represent the main relations occurring in this kind of scientific reduction is the Nagelian account of reduction, a model further developed by Schaffner and nowadays known as the generalized version of the Nagel–Schaffner model. In their article, Dizadji-Bahmani, Frigg, and Hartmann specified the two main desiderata of a reduction á la GNS: confirmation and coherence. DFH first and, more rigorously, Tešic later analyse the (...) confirmatory relation between the reducing and the reduced theory in terms of Bayesian confirmation theory. The purpose of this article is to analyse and compare the degree of coherence between the two theories involved in the GNS before and after the reduction. For this reason, in the first section, I will be looking at the reduction of thermodynamics to statistical mechanics and use it as an example to describe the GNS. In the second section, I will introduce three coherence measures which will then be employed in the comparison. Finally, in the last two sections, I will compare the degrees of coherence between the reducing and the reduced theory before and after the reduction and use a few numerical examples to understand the relation between coherence and confirmation measures. (shrink)

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

Since our visual perception of physical things essentially involves our identifying objects by their colours, any theory of visual perception must contain some account of the colours of things. The central problem with colour has to do with relating our normal, everyday colour perceptions to what science, i.e. physics, teaches us about physical objects and their qualities. Although we perceive colours as categorical surface properties of things, colour perceptions are explained by introducing physical properties like reflectance profiles or dispositions to (...) cause certain experiences in normal human perceivers. Hence, it seems as if colours as they are experienced by us have no place in the physical world, because they are fundamentally different from the properties which we ascribe to physical objects in scientific accounts of colour perceptions. This special issue on perspectives on colour perception presents new suggestions to solve to this major problem. (shrink)

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)

Suppose a theory T entails hypotheses H and $$H'$$, neither of which entails the other. A number of authors have argued that a piece of evidence E “indirectly confirms” H when E confirms either T or $$H'$$. But there has been a protracted and unsettled debate about whether indirect confirmation is a sound inference procedure. Skeptics argue that the procedure employs conditions of confirmation that jointly lead to absurdity. Proponents argue that this criticism is unfounded or that its import is (...) exaggerated. I will argue that no side has the story quite right, and some have the story quite wrong. Indirect confirmation, as characterized above, is unsound, and a good chunk of this paper will be concerned with showing why most extant defenses of the procedure err. On the other hand, when certain probabilistic (in)dependence relations hold between T, H, and $$H'$$, indirect confirmation can work, for reasons that trace back to Reichenbach’s principle of the common cause. I illustrate these matters with some contemporary and historical examples, with a particular focus on Kepler’s use of data about mars’s elliptical orbit to justify a claim about earth’s. (shrink)

Philosophical discussions on causal inference in medicine are stuck in dyadic camps, each defending one kind of evidence or method rather than another as best support for causal hypotheses. Whereas Evidence Based Medicine advocates the use of Randomised Controlled Trials and systematic reviews of RCTs as gold standard, philosophers of science emphasise the importance of mechanisms and their distinctive informational contribution to causal inference and assessment. Some have suggested the adoption of a pluralistic approach to causal inference, and an inductive (...) rather than hypothetico-deductive inferential paradigm. However, these proposals deliver no clear guidelines about how such plurality of evidence sources should jointly justify hypotheses of causal associations. We here develop such guidelines by first giving a philosophical analysis of the underpinnings of Hill’s viewpoints on causality. We then put forward an evidence-amalgamation framework adopting a Bayesian net approach to model causal inference in pharmacology for the assessment of harms. Our framework accommodates a number of intuitions already expressed in the literature concerning the EBM vs. pluralist debate on causal inference, evidence hierarchies, causal holism, relevance, and reliability. (shrink)

Coherence is a key concept in many accounts of epistemic justification within ‘traditional’ analytic epistemology. Within formal epistemology, too, there is a substantial body of research on coherence measures. However, there has been surprisingly little interaction between the two bodies of literature. The reason is that the existing formal literature on coherence measure operates with a notion of belief system that is very different from—what we argue is—a natural Bayesian formalisation of the concept of belief system from traditional epistemology. Therefore, (...) formal epistemology has so far only been concerned with one particular—arguably not even very natural—way of formalising coherence of belief systems; it has by no means refuted the viability of coherentism. In contrast to the existing literature, we formalise belief systems as families of assignments of (conditional) degrees of belief (which may be compatible with several subjective probability measures). Within this framework, we propose a Bayesian formalisation of the thrust of BonJour’s coherence concept in The structure of empirical knowledge (Harvard University Press, Cambridge, 1985), using a combination of Bayesian confirmation theory and basic graph theory. In excursions, we introduce graded notions for both logical and probabilistic consistency of belief systems—the latter being based on certain geometrical structures induced by probabilistic belief systems. For illustration, we reconsider BonJour’s “ravens” challenge (op. cit., p. 95f.). Finally, potential objections to our proposed formal coherence notion are explored. (shrink)

This paper argues that a successful philosophical analysis of models and simulations must accommodate an account of mathematically rigorous results. Such rigorous results may be thought of as genuinely model-specific contributions, which can neither be deduced from fundamental theory nor inferred from empirical data. Rigorous results provide new indirect ways of assessing the success of models and simulations and are crucial to understanding the connections between different models. This is most obvious in cases where rigorous results map different models on (...) to one another. Not only does this put constraints on the extent to which performance in specific empirical contexts may be regarded as the main touchstone of success in scientific modelling, it also allows for the transfer of warrant across different models. Mathematically rigorous results can thus come to be seen as not only strengthening the cohesion between scientific strategies of modelling and simulation, but also as offering new ways of indirect confirmation. (shrink)

This book offers a comprehensive and accessible introduction to the epistemology of science. It not only introduces readers to the general epistemological discussion of the nature of knowledge, but also provides key insights into the particular nuances of scientific knowledge. No prior knowledge of philosophy or science is assumed by The Nature of Scientific Knowledge. Nevertheless, the reader is taken on a journey through several core concepts of epistemology and philosophy of science that not only explores the characteristics of the (...) scientific knowledge of individuals but also the way that the development of scientific knowledge is a particularly social endeavor. The topics covered in this book are of keen interest to students of epistemology and philosophy of science as well as science educators interested in the nature of scientific knowledge. In fact, as a result of its clear and engaging approach to understanding scientific knowledge The Nature of Scientific Knowledge is a book that anyone interested in scientific knowledge, knowledge in general, and any of a myriad of related concepts would be well advised to study closely. (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)

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)

Inductive Logic is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive (...) Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. (shrink)

This paper presents a systematic challenge to the viability of revisionary metaphysics. The challenge is to provide epistemic grounds on which one might justifiably believe that a revisionary-metaphysical theory in some area is more likely to be true than its competitors. I argue that upon close examination, the main candidates for providing such grounds — empirical evidence, intuition, and the theoretical virtues — all turn out to be unsatisfactory.