I shall offer some very plausible assumptions for the measure of confirmation and show that they imply that E confirms H relative to background K to degree f/PK), where f is a strictly increasing function. An additional assumption about how measures of confirmation combine then makes f be proportional to a logarithm.

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.”.

While Wilfrid Sellars’ philosophy is often depicted in an ahistorical fashion, this book explores the consequences of placing his work in its historical context. In order to show how Sellars’ early publications depend on contextual factors, Peter Olen reconstructs the conceptions of language, psychological, and social explanation that dominated American philosophy in the early 20th century. Because of Sellars’ differing explanations of language and behaviour, Olen argues that many of Sellars’ early commitments are incompatible with his later works. In the (...) course of doing so, Olen highlights problematic tensions between Sellars’ early and later conceptions of language, meta-philosophy, and normativity. Supplementing the main text is a collection of previously unpublished archival material from Wilfrid Sellars, Gustav Bergmann, Everett Hall, and other early 20th century philosophers. This text will be a useful resource to those with an interest in the history of American philosophy, the history of analytic philosophy, Wilfrid Sellars’ philosophy, and the myriad issues surrounding normativity and language. (shrink)

According to a widespread but implicit thesis in Bayesian confirmation theory, two confirmation measures are considered equivalent if they are ordinally equivalent—call this the “ordinal equivalence thesis”. I argue that adopting OET has significant costs. First, adopting OET renders one incapable of determining whether a piece of evidence substantially favors one hypothesis over another. Second, OET must be rejected if merely ordinal conclusions are to be drawn from the expected value of a confirmation measure. Furthermore, several arguments and applications of (...) confirmation measures given in the literature already rely on a rejection of OET. I also contrast OET with stronger equivalence theses and show that they do not have the same costs as OET. On the other hand, adopting a thesis stronger than OET has costs of its own, since a rejection of OET ostensibly implies that people’s epistemic states have a very fine-grained quantitative structure. However, I suggest that the normative upshot of the paper in fact has a conditional form, and that other Bayesian norms can also fruitfully be construed as having a similar conditional form. (shrink)

According to a widespread but implicit thesis in Bayesian confirmation theory, two confirmation measures are considered equivalent if they are ordinally equivalent—call this the “ordinal equivalence thesis” (OET). I argue that adopting OET has significant costs. First, adopting OET renders one incapable of determining whether a piece of evidence substantially favors one hypothesis over another. Second, OET must be rejected if merely ordinal conclusions are to be drawn from the expected value of a confirmation measure. Furthermore, several arguments and applications (...) of confirmation measures given in the literature already rely on a rejection of OET. I also contrast OET with stronger equivalence theses and show that they do not have the same costs as OET. On the other hand, adopting a thesis stronger than OET has costs of its own, since a rejection of OET ostensibly implies that people’s epistemic states have a very fine-grained quantitative structure. However, I suggest that the normative upshot of the paper in fact has a conditional form, and that other Bayesian norms can also fruitfully be construed as having a similar conditional form. (shrink)

Many generic sentences express stable inductive generalizations. Stable inductive generalizations are typically true for a causal reason. In this paper we investigate to what extent this is also the case for the generalizations expressed by generic sentences. More in particular, we discuss the possibility that many generic sentences of the form ‘ks have feature e’ are true because kind k have the causal power to ‘produce’ feature e. We will argue that such an analysis is quite close to a probabilistic (...) based analysis of generic sentences according to which ‘relatively many’ ks have feature e, and that, in fact, this latter type of analysis can be ‘grounded’ in terms of causal powers. We will argue, moreover, that the causal power analysis is sometimes preferred to a correlation-based analysis, because it takes the causal structure that gives rise to the probabilistic data into account. (shrink)

Inductive reasoning requires exploiting links between evidence and hypotheses. This can be done focusing either on the posterior probability of the hypothesis when updated on the new evidence or on the impact of the new evidence on the credibility of the hypothesis. But are these two cognitive representations equally reliable? This study investigates this question by comparing probability and impact judgments on the same experimental materials. The results indicate that impact judgments are more consistent in time and more accurate than (...) probability judgments. Impact judgments also predict the direction of errors in probability judgments. These findings suggest that human inductive reasoning relies more on estimating evidential impact than on posterior probability. (shrink)

According to influential accounts of scientific method, such as critical rationalism, scientific knowledge grows by repeatedly testing our best hypotheses. But despite the popularity of hypothesis tests in statistical inference and science in general, their philosophical foundations remain shaky. In particular, the interpretation of non-significant results—those that do not reject the tested hypothesis—poses a major philosophical challenge. To what extent do they corroborate the tested hypothesis, or provide a reason to accept it? Popper sought for measures of corroboration that could (...) adequately answer this question. According to Popper, corroboration is different from probability-raising, and grounded in the predictive success and testability of a hypothesis. As such, corroboration becomes an indicator of the scientific value of a hypothesis and guides our practical preferences over hypotheses that have been subjected to severe tests. This article proves two impossibility results for corroboration measures based on statistical relevance. The generality of these results shows that Popper’s qualitative characterization of corroboration must be misguided. I explore what a more promising and scientifically useful concept of corroboration could look like. (shrink)

Over the past years, a number of probabilistic measures of coherence have been proposed. As shown in the paper, however, many of them do not conform to the intuitition that equivalent testimonies are highly coherent, regardless of their prior probability.

It is shown that the probabilistic theories of coherence proposed up to now produce a number of counter-intuitive results. The last section provides some reasons for believing that no probabilistic measure will ever be able to adequately capture coherence. First, there can be no function whose arguments are nothing but tuples of probabilities, and which assigns different values to pairs of propositions {A, B} and {A, C} if A implies both B and C, or their negations, and if P(B)=P(C). But (...) such sets may indeed differ in their degree of coherence. Second, coherence is sensitive to explanatory relations between the propositions in question. Explanation, however, can hardly be captured solely in terms of probability. (shrink)

In “What price coherence?”, Klein and Warfield put forward a simple argument that triggered an extensive debate on the epistemic virtues of coherence. As is well-known, this debate yielded far-reaching impossibility results to the effect that coherence is not conducive to truth, even if construed in a ceteris paribus sense. A large part of the present paper is devoted to a re-evaluation of these results. As is argued, all explications of truth-conduciveness leave out an important aspect: while it might not (...) be the case that coherence is truth-conducive, it might be conducive to verisimilitude or epistemic utility. Unfortunately, it is shown that the answer for both these issues must be in the negative, again. Furthermore, we shift the focus from sets of beliefs to particular beliefs: as is shown, neither is any of the extant probabilistic measures of coherence truth-conducive on the level of particular beliefs, nor does weakening these measures to quasi-orderings establish the link between coherence and truth for an important amount of measures. All in all, the results in this paper cast a serious doubt on the approach of establishing a link between coherence and truth. Finally, recent arguments that shift the focus from the relationship between coherence and truth to the one between coherence and confirmation are assessed. (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)

One of the integral parts of Bayesian coherentism is the view that the relation of ‘being no less coherent than’ is fully determined by the probabilistic features of the sets of propositions to be ordered. In the last one and a half decades, a variety of probabilistic measures of coherence have been put forward. However, there is large disagreement as to which of these measures best captures the pre-theoretic notion of coherence. This paper contributes to the debate on coherence measures (...) by considering three classes of adequacy constraints. Various independence and dependence relations between the members of each class will be taken into account in order to reveal the ‘grammar’ of probabilistic coherence measures. Afterwards, existing proposals are examined with respect to this list of desiderata. Given that for purely mathematical reasons there can be no measure that satisfies all constraints, the grammar allows the coherentist to articulate an informed pluralist stance as regards probabilistic measures of coherence. (shrink)

The debate on probabilistic measures of coherence flourishes for about 15 years now. Initiated by papers that have been published around the turn of the millennium, many different proposals have since then been put forward. This contribution is partly devoted to a reassessment of extant coherence measures. Focusing on a small number of reasonable adequacy constraints I show that (i) there can be no coherence measure that satisfies all constraints, and that (ii) subsets of these adequacy constraints motivate two different (...) classes of coherence measures. These classes do not coincide with the common distinction between coherence as mutual support and coherence as relative set-theoretic overlap. Finally, I put forward arguments to the effect that for each such class of coherence measures there is an outstanding measure that outperforms all other extant proposals. One of these measures has recently been put forward in the literature, while the other one is based on a novel probabilistic measure of confirmation. (shrink)

Focused correlation compares the degree of association within an evidence set to the degree of association in that evidence set given that some hypothesis is true. A difference between the confirmation lent to a hypothesis by one evidence set and the confirmation lent to that hypothesis by another evidence set is robustly tracked by a difference in focused correlations of those evidence sets on that hypothesis, provided that all the individual pieces of evidence are equally, positively relevant to that hypothesis. (...) However, that result depends on a very strong equal relevance condition on individual pieces of evidence. In this essay, we prove tracking results for focused correlation analogous to Wheeler and Scheines’s results but for cases involving unequal relevance. Our result is robust as well, and we retain conditions for bidirectional tracking between incremental confirmation measures and focused correlation. (shrink)

Two recently popular metaphilosophical movements, formal philosophy and experimental philosophy, promote what seem to be conflicting methodologies. Nonetheless, I argue that the two can be mutually supportive. I propose an experimentally-informed variation on explication, a powerful formal philosophical tool introduced by Carnap. The resulting method, which I call “experimental explication,” provides the formalist with a means of responding to explication's gravest criticism. Moreover, this method introduces a philosophically salient, positive role for survey-style experiments while steering clear of several objections that (...) critics of “positive experimental philosophy” raise. Thus, it provides the experimentalist with a more defensible example of how empirical work can have positive philosophical import. For these reasons, experimental explication should appeal to experimental philosophers and formal philosophers alike. (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)

The proposition that Tweety is a bird coheres better with the proposition that Tweety has wings than with the proposition that Tweety cannot fly. This relationship of contrastive coherence is the focus of the present paper. Based on recent work in formal epistemology we consider various possibilities to model this relationship by means of probability theory. In a second step we consider different applications of these models. Among others, we offer a coherentist interpretation of the conjunction fallacy.

The disjunction problem and the distality problem each presents a challenge that any theory of mental content must address. Here we consider their bearing on purely probabilistic causal theories. In addition to considering these problems separately, we consider a third challenge—that a theory must solve both. We call this “the hard problem.” We consider 8 basic ppc theories along with 240 hybrids of them, and show that some can handle the disjunction problem and some can handle the distality problem, but (...) none can handle the hard problem. This is our main result. We then discuss three possible responses to that result, and argue that though the first two fail, the third has some promise. (shrink)

The disjunction problem and the distality problem each presents a challenge that any theory of mental content must address. Here we consider their bearing on purely probabilistic causal theories. In addition to considering these problems separately, we consider a third challenge—that a theory must solve both. We call this “the hard problem.” We consider 8 basic ppc theories along with 240 hybrids of them, and show that some can handle the disjunction problem and some can handle the distality problem, but (...) none can handle the hard problem. This is our main result. We then discuss three possible responses to that result, and argue that though the first two fail, the third has some promise. (shrink)

Preface. Almost fifty years ago, in 1948, when I was an undergraduate at Queens College in New York and a student of Carl G. Hempel's, I received from his hands an offprint of his now-classic but then just-published paper “Studies in the Logic of Explanation”, written in collaboration with Paul Oppenheim and then just published in Philosophy of Science.1 This paper greatly impressed me—and I was not alone. We have here one of those unusual publications that sets the agenda for (...) a whole generation of investigators. It set in train an enormous body of discussions and publications which shaped the course of deliberations about scientific explanation over the next decades—an effort to which my own work also made some contributions. However my present aim is not to consider what came out of the Hempel-Oppenheim paper but what went into it. I want, in sum, to consider the prehistory of that era of scientific explanation studies—and to look more closely at the background ramifications of this paper that launched a thousand others. (shrink)

In the course of theorising, it can be appropriate to replace one concept—a folk concept, or one drawn from an earlier stage of theorising—with a more precise counterpart. The best-known account of concept replacement is Rudolf Carnap’s ‘explication’. P.F. Strawson famously critiqued explication as a method in philosophy. As the critique is standardly construed, it amounts to the objection that explication is ‘irrelevant’, fails to be ‘illuminating’, or simply ‘changes the subject’. In this paper, I argue that this is an (...) unfair characterisation of Strawson’s critique, spelling out the critique in more detail and showing that, fully understood, it is not undermined by extant responses. In light of both the critique and extant responses, I close by making some substantive comments about what explication can, and cannot, be used to do in philosophy. (shrink)

There are some candidates that have been thought to measure the degree to which evidence incrementally confirms a hypothesis. This paper provides an argument for one candidate—the log-likelihood ratio measure. For this purpose, I will suggest a plausible requirement that I call the Requirement of Collaboration. And then, it will be shown that, of various candidates, only the log-likelihood ratio measure \(l\) satisfies this requirement. Using this result, Jeffrey conditionalization will be reformulated so as to disclose explicitly what determines new (...) credences after experience. (shrink)

What sort of evidence can confer the strongest support to a hypothesis? A natural answer is that the evidence entails the hypothesis. Roush (Tracking Truth: Knowledge, Evidence, and Science, Clarendon Press, Oxford, 2005) claims that the likelihood ratio measure of degree of incremental support can deliver this intuitively natural result, and regards it as unifying “[the] account of induction and deduction in the only way that makes sense” (p. 163). In this paper, we highlight a difficulty in the treatment of (...) this case, and question the great significance that is attached to this measure and its alleged capacity to accommodate the logicality requirement. We contrast the likelihood ratio measure with other measures (such as the Kemeny–Oppenheim measure and the difference measure), and argue that problems still emerge in light of tensions with plausible requirements for confirmation measures more generally. (shrink)

Preface. Almost fifty years ago, in 1948, when I was an undergraduate at Queens College in New York and a student of Carl G. Hempel's, I received from his hands an offprint of his now-classic but then just-published paper “Studies in the Logic of Explanation”, written in collaboration with Paul Oppenheim and then just published in Philosophy of Science.1 This paper greatly impressed me—and I was not alone. We have here one of those unusual publications that sets the agenda for (...) a whole generation of investigators. It set in train an enormous body of discussions and publications which shaped the course of deliberations about scientific explanation over the next decades—an effort to which my own work also made some contributions. However my present aim is not to consider what came out of the Hempel-Oppenheim paper but what went into it. I want, in sum, to consider the prehistory of that era of scientific explanation studies—and to look more closely at the background ramifications of this paper that launched a thousand others. (shrink)

Traditional views on philosophical methodology characterize our primary philosophical goal as production of a successful conceptual analysis. The notion of conceptual analysis, however, faces several challenges—from experimental philosophy to more traditional worries such as the paradox of analysis. This paper explores an alternate approach, commonly called conceptual engineering, which aims at recommending conceptual revisions. An important question for the conceptual engineer is as follows: what counts as a case of successful conceptual engineering? What sorts of revisions are permitted, and what (...) sorts are too revisionary? In this paper I examine ‘functional’ approaches to conceptual engineering, ultimately arguing for a ‘radical’ functionalism according to which even revisions which ‘change the subject’ are permitted, and successful re-engineering is constrained only by the requirement that continuity in needed functions of a pre-engineering concept be maintained somewhere in the postengineering conceptual scheme. I further argue that this approach suggests a heightened role, in metaphilosophical discourse, for a neglected epistemic goal—conceptual efficacy. (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)

Coherentism in epistemology has long suffered from lack of formal and quantitative explication of the notion of coherence. One might hope that probabilistic accounts of coherence such as those proposed by Lewis, Shogenji, Olsson, Fitelson, and Bovens and Hartmann will finally help solve this problem. This paper shows, however, that those accounts have a serious common problem: the problem of belief individuation. The coherence degree that each of the accounts assigns to an information set (or the verdict it gives as (...) to whether the set is coherent tout court) depends on how beliefs (or propositions) that represent the set are individuated. Indeed, logically equivalent belief sets that represent the same information set can be given drastically different degrees of coherence. This feature clashes with our natural and reasonable expectation that the coherence degree of a belief set does not change unless the believer adds essentially new information to the set or drops old information from it; or, to put it simply, that the believer cannot raise or lower the degree of coherence by purely logical reasoning. None of the accounts in question can adequately deal with coherence once logical inferences get into the picture. Toward the end of the paper, another notion of coherence that takes into account not only the contents but also the origins (or sources) of the relevant beliefs is considered. It is argued that this notion of coherence is of dubious significance, and that it does not help solve the problem of belief individuation. (shrink)

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 series of three behavioral experiments, we found a systematic distortion of probability judgments concerning elementary visual stimuli. Participants were briefly shown a set of figures that had two features (e.g., a geometric shape and a color) with two possible values each (e.g., triangle or circle and black or white). A figure was then drawn, and participants were informed about the value of one of its features (e.g., that the figure was a “circle”) and had to predict the value (...) of the other feature (e.g., whether the figure was “black” or “white”). We repeated this procedure for various sets of figures and, by varying the statistical association between features in the sets, we manipulated the probability of a feature given the evidence of another (e.g., the posterior probability of hypothesis “black” given the evidence “circle”) as well as the support provided by a feature to another (e.g., the impact, or confirmation, of evidence “circle” on the hypothesis “black”). Results indicated that participants’ judgments were deeply affected by impact, although they only should have depended on the probability distributions over the features, and that the dissociation between evidential impact and posterior probability increased the number of errors. The implications of these findings for lower and higher level cognitive models are discussed. (shrink)

Mark Siebel has presented a compelling argument against Branden Fitelson’s probabilistic measure of coherence. The present paper shows how Siebel’s argument can be strengthened and thereby extended to an argument against a huge class of coherence measures from the literature including William Roche’s average mutual firmness account, which has not been challenged up to now.

Over the years several non-equivalent probabilistic measures of coherence have been discussed in the philosophical literature. In this paper we examine these measures with respect to their empirical adequacy. Using test cases from the coherence literature as vignettes for psychological experiments we investigate whether the measures can predict the subjective coherence assessments of the participants. It turns out that the participants’ coherence assessments are best described by Roche’s coherence measure based on Douven and Meijs’ average mutual support approach and the (...) conditional probability. (shrink)

How can we determine the adequacy of a probabilistic coherence measure? A widely accepted approach to this question besides formulating adequacy constraints is to employ paradigmatic test cases consisting of a scenario providing a joint probability distribution over some specified set of propositions coupled with a normative coherence assessment for this set. However, despite the popularity of the test case approach, a systematic evaluation of the proposed test cases is still missing. This paper’s aim is to change this. Using a (...) custom written computer program for the necessary probabilistic calculations a large number of coherence measures in an extensive collection of test cases is examined. The result is a detailed overview of the test case performance of any probabilistic coherence measures proposed so far. It turns out that none of the popular coherence measures such as Shogenji’s, Glass’ and Olsson’s, Fitelson’s or Douven and Meijs’ but two rather unnoticed measures perform best. This, however, does not mean that the other measures can be rejected straightforwardly. Instead, the results presented here are to be understood as a contribution among others to the project of finding adequate probabilistic coherence measures. (shrink)

Changing weather conditions and barometer changes usually coincide. Accordingly, the propositions that my barometer falls and that the weather conditions deteriorate are quite coherent—especially under the assumption that there is a drop in atmospheric pressure. Nevertheless, scenarios like these involving common causes turn out to be highly problematic for a prominent class of probabilistic coherence measures, namely, those explicating coherence based on the idea of relevance-sensitivity. In this article, we show that none of these measures accords with the intuition that (...) in the light of a common cause, two propositions referring to the cause’s effects should turn out to be coherent. This result casts doubts on the view that these measures can be considered proper explications of the concept of coherence. 1Introduction2Relevance-Sensitive Coherence Measures3Common Causes, Screening-off, and Coherence4Discussion 4.1Multiple explications of coherence4.2Conditionalization versus set expansion5Conclusion. (shrink)

This paper presents a symmetry condition for probabilistic measures of confirmation which is weaker than commutativity symmetry, disconfirmation commutativity symmetry but also antisymmetry. It is based on the idea that for any value a probabilistic measure of confirmation can assign there is a corresponding case where degrees of confirmation are symmetric. It is shown that a number of prominent confirmation measures such as Carnap’s difference function, Rescher’s measure of confirmation, Gaifman’s confirmation rate and Mortimer’s inverted difference function do not satisfy (...) this condition and instead exhibit a previously unnoticed and rather puzzling behavior in certain cases of disconfirmation. This behavior also carries over to probabilistic measures of information change, causal strength, explanatory power and coherence. (shrink)

This paper raises a principled objection against the idea that Bayesian confirmation theory can be used to explain the conjunction fallacy. The paper demonstrates that confirmation-based explanations are limited in scope and can only be applied to cases of the fallacy of a certain restricted kind. In particular; confirmation-based explanations cannot account for the inverse conjunction fallacy, a more recently discovered form of the conjunction fallacy. Once the problem has been set out, the paper explores four different ways for the (...) confirmation theorist to come to terms with the problem, and argues that none of them are successful. (shrink)

Bandyopadhyay, Taper, and Brittan advance a measure of evidential support that first appeared in the statistical and philosophical literature four decades ago and have been extensively discussed since. I have argued elsewhere, however, that it is vulnerable to a simple counterexample. BTB claim that the counterexample is flawed because it conflates evidence with confirmation. In this reply, I argue that the counterexample stands, and is fatal to their theory.

To explain the phenomena in the world of our experience, to answer the question “why?” rather than only the question “what?”, is one of the foremost objectives of all rational inquiry; and especially, scientific research in its various branches strives to go beyond a mere description of its subject matter by providing an explanation of the phenomena it investigates. While there is rather general agreement about this chief objective of science, there exists considerable difference of opinion as to the function (...) and the essential characteristics of scientific explanation. In the present essay, an attempt will be made to shed some light on these issues by means of an elementary survey of the basic pattern of scientific explanation and a subsequent more rigorous analysis of the concept of law and of the logical structure of explanatory arguments. (shrink)

Two of the probabilistic measures of coherence discussed in this paper take probabilistic dependence into account and so depend on prior probabilities in a fundamental way. An example is given which suggests that this prior-dependence can lead to potential problems. Another coherence measure is shown to be independent of prior probabilities in a clearly defined sense and consequently is able to avoid such problems. The issue of prior-dependence is linked to the fact that the first two measures can be understood (...) as measures of coherence as striking agreement, while the third measure represents coherence as agreement. Thus, prior (in)dependence can be used to distinguish different conceptions of coherence. (shrink)

This paper presents a new argument for the likelihood ratio measure of confirmation by showing that one of the adequacy criteria used in another argument can be replaced by a more plausible and better supported criterion which is a special case of the weak likelihood principle. This new argument is also used to show that the likelihood ratio measure is to be preferred to a measure that has recently received support in the literature.

Reliabilism is an intuitive and attractive view about epistemic justification. However, it has many well-known problems. I offer a novel condition on reliabilist theories of justification. This method coherence condition requires that a method be appropriately tested by appeal to a subject’s other belief-forming methods. Adding this condition to reliabilism provides a solution to epistemic circularity worries, including the bootstrapping problem.

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..

outlined. This account is partly inspired by the work of C.S. Peirce. When we want to consider how degree of confirmation varies with changing I show that a large class of quantitative Bayesian measures of con-.

A Bayesian account of independent evidential support is outlined. This account is partly inspired by the work of C. S. Peirce. I show that a large class of quantitative Bayesian measures of confirmation satisfy some basic desiderata suggested by Peirce for adequate accounts of independent evidence. I argue that, by considering further natural constraints on a probabilistic account of independent evidence, all but a very small class of Bayesian measures of confirmation can be ruled out. In closing, another application of (...) my account to the problem of evidential diversity is also discussed. (shrink)

Experimental observations are often taken in order to assist in making a choice between relevant hypotheses ∼ H and H. The power of observations in this decision is here metrically defined by information-theoretic concepts and Bayes' theorem. The exact (or maximum power) of a new observation to increase or decrease Pr(H) the prior probability that H is true; the power of that observation to modify the total amount of uncertainty involved in the choice between ∼ H and H: the power (...) of a new observation to reduce uncertainty toward the ideal amount, zero; all these powers are systematically shown to be exact metrical functions of Pr(H) and Pr(o/H)/Pr(o)-1 where the numerator is the likelihood of the new observation given H, and the denominator is the "expectedness" of the observation. (shrink)