One of the most important questions in epistemology and the philosophy of science is: what is a good theory and when is a theory better than another theory, given some observational data? The coherentist‟s answer would be the following twofold conjecture: A theory is a good theory given some observational data iff that theory coheres with the observational data and a theory is better than another theory given some observational data iff the first theory coheres more with the observational data (...) than the second theory. In this paper we show that this answer is a good answer. More precisely, we argue that the coherence measures of Olsson and Shogenji are good measures for the purpose of comparing and evaluating theories, i.e. assessing theories. We do so by clarifying the sufficient and necessary conditions every assessment function must satisfy for being a good measure of the goodness of theories. Afterwards we will show that the coherence measures of Olsson and Shogenji are indeed good assessment functions for assessing theories. (shrink)

This book defends the view that any adequate account of rational decision making must take a decision maker's beliefs about causal relations into account. The early chapters of the book introduce the non-specialist to the rudiments of expected utility theory. The major technical advance offered by the book is a 'representation theorem' that shows that both causal decision theory and its main rival, Richard Jeffrey's logic of decision, are both instances of a more general conditional decision theory. The book solves (...) a long-standing problem for Jeffrey's theory by showing for the first time how to obtain a unique utility and probability representation for preferences and judgements of comparative likelihood. The book also contains a major new discussion of what it means to suppose that some event occurs or that some proposition is true. The most complete and robust defence of causal decision theory available. (shrink)

The problem addressed in this paper is “the main epistemic problem concerning science”, viz. “the explication of how we compare and evaluate theories [...] in the light of the available evidence” (van Fraassen, BC, 1983, Theory comparison and relevant Evidence. In J. Earman (Ed.), Testing scientific theories (pp. 27–42). Minneapolis: University of Minnesota Press). Sections 1– 3 contain the general plausibility-informativeness theory of theory assessment. In a nutshell, the message is (1) that there are two values a theory should exhibit: (...) truth and informativeness—measured respectively by a truth indicator and a strength indicator; (2) that these two values are conflicting in the sense that the former is a decreasing and the latter an increasing function of the logical strength of the theory to be assessed; and (3) that in assessing a given theory by the available data one should weigh between these two conflicting aspects in such a way that any surplus in informativeness succeeds, if the shortfall in plausibility is small enough. Particular accounts of this general theory arise by inserting particular strength indicators and truth indicators. In Section 4 the theory is spelt out for the Bayesian paradigm of subjective probabilities. It is then compared to incremental Bayesian confirmation theory. Section 4 closes by asking whether it is likely to be lovely. Section 5 discusses a few problems of confirmation theory in the light of the present approach. In particular, it is briefly indicated how the present account gives rise to a new analysis of Hempel’s conditions of adequacy for any relation of confirmation (Hempel, CG, 1945, Studies in the logic of comfirmation. Mind, 54, 1–26, 97–121.), differing from the one Carnap gave in § 87 of his Logical foundations of probability (1962, Chicago: University of Chicago Press). Section 6 adresses the question of justification any theory of theory assessment has to face: why should one stick to theories given high assessment values rather than to any other theories? The answer given by the Bayesian version of the account presented in section 4 is that one should accept theories given high assessment values, because, in the medium run, theory assessment almost surely takes one to the most informative among all true theories when presented separating data. The concluding section 7 continues the comparison between the present account and incremental Bayesian confirmation theory. (shrink)

In this paper we show that the coherence measures of Olsson (J Philos 94:246–272, 2002), Shogenji (Log Anal 59:338–345, 1999), and Fitelson (Log Anal 63:194–199, 2003) satisfy the two most important adequacy requirements for the purpose of assessing theories. Following Hempel (Synthese 12:439–469, 1960), Levi (Gambling with truth, New York, A. A. Knopf, 1967), and recently Huber (Synthese 161:89–118, 2008) we require, as minimal or necessary conditions, that adequate assessment functions favor true theories over false theories and true and informative (...) theories over true but uninformative theories. We then demonstrate that the coherence measures of Olsson, Shogenji, and Fitelson satisfy these minimal conditions if we confront the hypotheses with a separating sequence of observational statements. In the concluding remarks we set out the philosophical relevance, and limitations, of the formal results. Inter alia, we discuss the problematic implications of our precondition that competing hypotheses must be confronted with a separating sequence of observational statements, which also leads us to discuss theory assessment in the context of scientific antirealism. (shrink)

Fitelson (1999) demonstrates that the validity of various arguments within Bayesian confirmation theory depends on which confirmation measure is adopted. The present paper adds to the results set out in Fitelson (1999), expanding on them in two principal respects. First, it considers more confirmation measures. Second, it shows that there are important arguments within Bayesian confirmation theory and that there is no confirmation measure that renders them all valid. Finally, the paper reviews the ramifications that this "strengthened problem of measure (...) sensitivity" has for Bayesian confirmation theory and discusses whether it points at pluralism about notions of confirmation. (shrink)

We discuss the probabilistic analysis of explanatory power and prove a representation theorem for posterior ratio measures recently advocated by Schupbach and Sprenger. We then prove a representation theorem for an alternative class of measures that rely on the notion of relative probability distance. We end up endorsing the latter, as relative distance measures share the properties of posterior ratio measures that are genuinely appealing, while overcoming a feature that we consider undesirable. They also yield a telling result concerning formal (...) accounts of explanatory power versus inductive confirmation, thereby bridging our discussion to a so-called no-miracle argument. (shrink)

This article introduces and defends a probabilistic measure of the explanatory power that a particular explanans has over its explanandum. To this end, we propose several intuitive, formal conditions of adequacy for an account of explanatory power. Then, we show that these conditions are uniquely satisfied by one particular probabilistic function. We proceed to strengthen the case for this measure of explanatory power by proving several theorems, all of which show that this measure neatly corresponds to our explanatory intuitions. Finally, (...) we briefly describe some promising future projects inspired by our account. (shrink)

APA PsycNET abstract: This is the first volume of a two-volume work on Probability and Induction. Because the writer holds that probability logic is identical with inductive logic, this work is devoted to philosophical problems concerning the nature of probability and inductive reasoning. The author rejects a statistical frequency basis for probability in favor of a logical relation between two statements or propositions. Probability "is the degree of confirmation of a hypothesis (or conclusion) on the basis of some given evidence (...) (or premises)." Furthermore, all principles and theorems of inductive logic are analytic, and the entire system is to be constructed by means of symbolic logic and semantic methods. This means that the author confines himself to the formalistic procedures of word and symbol systems. The resulting sentence or language structures are presumed to separate off logic from all subjectivist or psychological elements. Despite the abstractionism, the claim is made that if an inductive probability system of logic can be constructed it will have its practical application in mathematical statistics, and in various sciences. 16-page bibliography. (PsycINFO Database Record (c) 2016 APA, all rights reserved). (shrink)

Nozick analyzes fundamental issues, such as the identity of the self, knowledge and skepticism, free will, the foundations of ethics, and the meaning of life.

Described by the philosopher A.J. Ayer as a work of 'great originality and power', this book revolutionized contemporary thinking on science and knowledge. Ideas such as the now legendary doctrine of 'falsificationism' electrified the scientific community, influencing even working scientists, as well as post-war philosophy. This astonishing work ranks alongside The Open Society and Its Enemies as one of Popper's most enduring books and contains insights and arguments that demand to be read to this day.

Philosophically, one of the most important questions in the enterprise termed confirmation theory is this: Why should one stick to well confirmed theories rather than to any other theories? This paper discusses the answers to this question one gets from absolute and incremental Bayesian confirmation theory. According to absolute confirmation, one should accept ''absolutely well confirmed'' theories, because absolute confirmation takes one to true theories. An examination of two popular measures of incremental confirmation suggests the view that one should stick (...) to incrementally well confirmed theories, because incremental confirmation takes one to (the most) informative (among all) true theories. However, incremental confirmation does not further this goal in general. I close by presenting a necessary and sufficient condition for revealing the confirmational structure in almost every world when presented separating data. (shrink)

In three recent papers, Wayne Myrvold and Timothy McGrew have developed Bayesian accounts of the virtue of unification. In his account, McGrew demonstrates that, ceteris paribus, a hypothesis that unifies its evidence will have a higher posterior probability than a hypothesis that does not. Myrvold, on the other hand, offers a specific measure of unification that can be applied to individual hypotheses. He argues that one must account for this measure in order to calculate correctly the degree of confirmation that (...) a hypothesis receives from its evidence. Using the probability calculus, I prove that the two accounts of unification require the same underlying inequality; thus, McGrew and Myrvold have accounted for unification in fundamentally identical probabilistic terms. I then evaluate five putative counterexamples to this account and show that these examples, far from disqualifying it, serve to clarify our notion of unification by disentangling it from a host of other concepts. (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)

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)

The old evidence problem affects any probabilistic confirmation measure based on comparing pr(H/E) and pr(H). The article argues for the following points: (1) measures based on likelihood ratios also suffer old evidence difficulties; (2) the less-discussed synchronic old evidence problem is, in an important sense, the most acute; (3) prominent attempts to solve or dissolve the synchronic problem fail; (4) a little-discussed variant of the standard measure avoids the problem, in an appealing way; and (5) this measure nevertheless reveals a (...) different problem for probabilistic confirmation measures, a problem that is unlikely to lend itself to formal solution. (shrink)

Recently, in attempting to account for explanatory reasoning in probabilistic terms, Bayesians have proposed several measures of the degree to which a hypothesis explains a given set of facts. These candidate measures of "explanatory power" are shown to have interesting normative interpretations and consequences. What has not yet been investigated, however, is whether any of these measures are also descriptive of people’s actual explanatory judgments. Here, I present my own experimental work investigating this question. I argue that one measure in (...) particular is an accurate descriptor of explanatory judgments. Then, I discuss some interesting implications of this result for both the epistemology and the psychology of explanatory reasoning. (shrink)

According to Bayesian confirmation theory, evidence E (incrementally) confirms (or supports) a hypothesis H (roughly) just in case E and H are positively probabilistically correlated (under an appropriate probability function Pr). There are many logically equivalent ways of saying that E and H are correlated under Pr. Surprisingly, this leads to a plethora of non-equivalent quantitative measures of the degree to which E confirms H (under Pr). In fact, many non-equivalent Bayesian measures of the degree to which E confirms (or (...) supports) H have been proposed and defended in the literature on inductive logic. I provide a thorough historical survey of the various proposals, and a detailed discussion of the philosophical ramifications of the differences between them. I argue that the set of candidate measures can be narrowed drastically by just a few intuitive and simple desiderata. In the end, I provide some novel and compelling reasons to think that the correct measure of degree of evidential support (within a Bayesian framework) is the (log) likelihood ratio. The central analyses of this research have had some useful and interesting byproducts, including: (i ) a new Bayesian account of (confirmationally) independent evidence, which has applications to several important problems in con- firmation theory, including the problem of the (confirmational) value of evidential diversity, and (ii ) novel resolutions of several problems in Bayesian confirmation theory, motivated by the use of the (log) likelihood ratio measure, including a reply to the Popper-Miller critique of probabilistic induction, and a new analysis and resolution of the problem of irrelevant conjunction (a.k.a., the tacking problem). (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)

A common methodological adage holds that diverse evidence better confirms a hypothesis than does the same amount of similar evidence. Proponents of Bayesian approaches to scientific reasoning such as Horwich, Howson and Urbach, and Earman claim to offer both a precise rendering of this maxim in probabilistic terms and an explanation of why the maxim should be part of the methodological canon of good science. This paper contends that these claims are mistaken and that, at best, Bayesian accounts of diverse (...) evidence are crucially incomplete. This failure should lend renewed force to a long-neglected global worry about Bayesian approaches. (shrink)

A Bayesian account of the virtue of unification is given. On this account, the ability of a theory to unify disparate phenomena consists in the ability of the theory to render such phenomena informationally relevant to each other. It is shown that such ability contributes to the evidential support of the theory, and hence that preference for theories that unify the phenomena need not, on a Bayesian account, be built into the prior probabilities of theories.

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)

In this influential study of central issues in the philosophy of science, Paul Horwich elaborates on an important conception of probability, diagnosing the failure of previous attempts to resolve these issues as stemming from a too-rigid conception of belief. Adopting a Bayesian strategy, he argues for a probabilistic approach, yielding a more complete understanding of the characteristics of scientific reasoning and methodology. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Colin Howson, illuminating its (...) enduring importance and relevance to philosophical enquiry, this engaging work has been revived for a new generation of readers. (shrink)

Sections 1 through 3 present all of the main ideas behind the probabilistic logic of evidential support. For most readers these three sections will suffice to provide an adequate understanding of the subject. Those readers who want to know more about how the logic applies when the implications of hypotheses about evidence claims (called likelihoods) are vague or imprecise may, after reading sections 1-3, skip to section 6. Sections 4 and 5 are for the more advanced reader who wants a (...) detailed understanding of some telling results about how this logic may bring about convergence to the truth. (shrink)

Plausibly, when we adopt a probabilistic standpoint any measure Cb of the degree to which evidence e confirms hypothesis h relative to background knowledge b should meet these five desiderata: Cb > 0 when P > P < 0 when P < P; Cb = 0 when P = P. Cb is some function of the values P and P assume on the at most sixteen truth-functional combinations of e and h. If P < P and P = P then (...) Cb ≤ Cb; if P = P and P < P then Cb ≥ Cb. Cb – Cb is fully determined by Cb and Cbe – Cbe; if Cb = 0 then Cb + Cbe = 0. If P = P then Cb = Cb. (shrink)

Contemporary Bayesian confirmation theorists measure degree of (incremental) confirmation using a variety of non-equivalent relevance measures. As a result, a great many of the arguments surrounding quantitative Bayesian confirmation theory are implicitly sensitive to choice of measure of confirmation. Such arguments are enthymematic, since they tacitly presuppose that certain relevance measures should be used (for various purposes) rather than other relevance measures that have been proposed and defended in the philosophical literature. I present a survey of this pervasive class of (...) Bayesian confirmation-theoretic enthymemes, and a brief analysis of some recent attempts to resolve the problem of measure sensitivity. (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)

Andrew Wayne discusses some recent attempts to account, within a Bayesian framework, for the "common methodological adage" that "diverse evidence better confirms a hypothesis than does the same amount of similar evidence". One of the approaches considered by Wayne is that suggested by Howson and Urbach and dubbed the "correlation approach" by Wayne. This approach is, indeed, incomplete, in that it neglects the role of the hypothesis under consideration in determining what diversity in a body of evidence is relevant diversity. (...) In this paper, it is shown how this gap can be filled, resulting in a more satisfactory account of the evidential role of diversity of evidence. In addition, it is argued that Wayne's criticism of the correlation approach does not indicate a serious flaw in the approach. (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)

This comprehensive discussion of the problem of rational belief develops the subject on the pattern of Bayesian decision theory. The analogy with decision theory introduces philosophical issues not usually encountered in logical studies and suggests some promising new approaches to old problems."We owe Professor Levi a debt of gratitude for producing a book of such excellence. His own approach to inductive inference is not only original and profound, it also clarifies and transforms the work of his predecessors. In short, the (...) book deserves to become a classic....There is a great deal of interest in the book besides these basic matters [forumlating rules of acceptance]. Some of the most interesting chapters are those that examine the implications of such rules. The discussions of probability, generalization, and various forms of inference are brilliant and enlightening. Indeed, the problems and methods elaborated by Professor Levi in his book serve as a new foundation for the study of inductive inference."--Keith Lehrer, Nous"Levi's book is an extremely interesting report on 'tentative and speculative first steps' toward a decision-theoretic approach to inductive inference....Professor Levi is to be congratulated on his ingenious development and application of this approach...."--Richard C. Jeffrey, The Journal of Philosophy. (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..

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)