Tom Stoneham put forward an argument purporting to show that coherentists are, under certain conditions, committed to the conjunction fallacy. Stoneham considers this argument a reductio ad absurdum of any coherence theory of justification. I argue that Stoneham neglects the distinction between degrees of confirmation and degrees of probability. Once the distinction is in place, it becomes clear that no conjunction fallacy has been committed.

Can some evidence confirm a conjunction of two hypotheses more than it confirms either of the hypotheses separately? We show that it can, moreover under conditions that are the same for ten different measures of confirmation. Further we demonstrate that it is even possible for the conjunction of two disconfirmed hypotheses to be confirmed by the same evidence.

The conjunction fallacy has been a key topic in debates on the rationality of human reasoning and its limitations. Despite extensive inquiry, however, the attempt of providing a satisfactory account of the phenomenon has proven challenging. Here, we elaborate the suggestion (first discussed by Sides et al., 2001) that in standard conjunction problems the fallacious probability judgments experimentally observed are typically guided by sound assessments of confirmation relations, meant in terms of contemporary Bayesian confirmation theory. Our main formal result is (...) a confirmation-theoretic account of the conjuntion fallacy which is proven robust (i.e., not depending on various alternative ways of measuring degrees of confirmation). The proposed analysis is shown distinct from contentions that the conjunction effect is in fact not a fallacy and is compared with major competing explanations of the phenomenon, including earlier references to a confirmation-theoretic account. (shrink)

Crupi et al. (2008) offer a confirmation-theoretic, Bayesian account of the conjunction fallacy—an error in reasoning that occurs when subjects judge that Pr( h 1 & h 2 | e ) > Pr( h 1 | e ). They introduce three formal conditions that are satisfied by classical conjunction fallacy cases, and they show that these same conditions imply that h 1 & h 2 is confirmed by e to a greater extent than is h 1 alone. Consequently, they suggest (...) that people are tracking this confirmation relation when they commit conjunction fallacies. I offer three experiments testing the merits of Crupi et al.’s account specifically and confirmation-theoretic accounts of the conjunction fallacy more generally. The results of Experiment 1 show that, although Crupi et al.’s conditions do seem to be causally linked to the conjunction fallacy, they are not necessary for it; there exist cases that do not meet their three conditions in which subjects still tend to commit the fallacy. The results of Experiments 2 and 3 show that Crupi et al.’s conditions, and those offered by other confirmation-theoretic accounts of the fallacy, are not sufficient for the fallacy either; there exist cases that meet all three of CFT’s conditions in which subjects do not tend to commit the fallacy. Additionally, these latter experiments show that such confirmation-theoretic conditions are at best only weakly causally relevant to the presence of the conjunction fallacy. Given these findings, CFT’s account specifically, and any general confirmation-theoretic account more broadly, falls short of offering a satisfying explanation of the presence of the conjunction fallacy. (shrink)

Bayesian epistemology addresses epistemological problems with the help of the mathematical theory of probability. It turns out that the probability calculus is especially suited to represent degrees of belief (credences) and to deal with questions of belief change, confirmation, evidence, justification, and coherence. Compared to the informal discussions in traditional epistemology, Bayesian epis- temology allows for a more precise and fine-grained analysis which takes the gradual aspects of these central epistemological notions into account. Bayesian epistemology therefore complements traditional epistemology; it (...) does not re- place it or aim at replacing it. (shrink)

The probabilistic support relation is known to violate transitivity. But over the years, philosophers have identified various conditions under which it does not, most notably screening-off and weak screening-off. In this short discussion note, I wish to highlight another condition that, unfortunately, is often neglected in the literature. This condition is due to Mary Hesse who recognized its transitivity-ensuring property long before other conditions entered the stage. I show that her condition is logically independent of screening-off and weak screening-off, but (...) that, just like the two aforementioned, it entails the recently proposed very weak screening-off condition due to Jeanne Peijnenburg and David Atkinson. (shrink)

As is well known, implication is transitive but probabilistic support is not. Eells and Sober, followed by Shogenji, showed that screening off is a sufficient constraint for the transitivity of probabilistic support. Moreover, this screening off condition can be weakened without sacrificing transitivity, as was demonstrated by Suppes and later by Roche. In this paper we introduce an even weaker sufficient condition for the transitivity of probabilistic support, in fact one that can be made as weak as one wishes. We (...) explain that this condition has an interesting property: it shows that transitivity is retained even though the Simpson paradox reigns. We further show that by adding a certain restriction the condition can be turned into one that is both sufficient and necessary for transitivity. (shrink)

This paper investigates the logic of reasons. Its aim is to provide an analysis of the sentences of the form ‘p is a reason for q’ that yields a coherent account of their logical properties. The idea that we will develop is that ‘p is a reason for q’ is acceptable just in case a suitably defined relation of incompatibility obtains between p and ¬q. As we will suggest, a theory of reasons based on this idea can solve three challenging (...) puzzles that concern, respectively, contraposing reasons, conflicting reasons, and supererogatory reasons, and opens a new perspective on some classical issues concerning non-deductive inferences. (shrink)

As is well known, implication is transitive but probabilistic support is not. Eells and Sober, followed by Shogenji, showed that screening off is a sufficient constraint for the transitivity of probabilistic support. Moreover, this screening off condition can be weakened without sacrificing transitivity, as was demonstrated by Suppes and later by Roche. In this paper we introduce an even weaker sufficient condition for the transitivity of probabilistic support, in fact one that can be made as weak as one wishes. We (...) explain that this condition has an interesting property: it shows that transitivity is retained even though the Simpson paradox reigns. We further show that by adding a certain restriction the condition can be turned into one that is both sufficient and necessary for transitivity. (shrink)

We model scientific theories as Bayesian networks. Nodes carry credences and function as abstract representations of propositions within the structure. Directed links carry conditional probabilities and represent connections between those propositions. Updating is Bayesian across the network as a whole. The impact of evidence at one point within a scientific theory can have a very different impact on the network than does evidence of the same strength at a different point. A Bayesian model allows us to envisage and analyze the (...) differential impact of evidence and credence change at different points within a single network and across different theoretical structures. (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)

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)

Barnett provides an interesting new challenge for Dogmatist accounts of perceptual justification. The challenge is that such accounts, by accepting that a perceptual experience can provide a distinctive kind of boost to one’s credences, would lead to a form of diachronic irrationality in cases where one has already learnt in advance that one will have such an experience. I show that this challenge rests on a misleading feature of using the 0–1 interval to express probabilities and show that if we (...) switch to using Odds or Log-Odds, the misleading appearance that there is only ‘a little room’ for one’s credences to increase evaporates. Moreover, there are familiar, independent reasons for taking the Log-Odds scale to provide a clearer picture of the confirmatory effect of evidence. Thus the Dogmatist can after all escape the charge of diachronic irrationality. (shrink)

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.”.

Analyses of the Sleeping Beauty Problem are polarised between those advocating the “1/2 view” (“halfers”) and those endorsing the “1/3 view” (“thirders”). The disagreement concerns the evidential relevance of self-locating information. Unlike halfers, thirders regard self-locating information as evidentially relevant in the Sleeping Beauty Problem. In the present study, we systematically manipulate the kind of information available in different formulations of the Sleeping Beauty Problem. Our findings indicate that patterns of judgment on different formulations of the Sleeping Beauty Problem do (...) not fit either the “1/2 view” or the “1/3 view.” Human reasoners tend to acknowledge self-locating evidence as relevant, but discount its weight significantly. Accordingly, self-locating information may trigger more cautious judgments of confirmation than familiar kinds of statistical evidence. We also discuss how these results can advance the debate by providing a more nuanced and empirically grounded account or explication of the evidential impact of self-locating information. (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 paper evaluates four different qualitative (probabilistic) accounts to coherence with a focus on structural properties (symmetries, asymmetries, and transitivity). It is shown that while coherence is not transitive on any of these accounts, there are screening-off conditions that render coherence transitive. In a second step, an array of quantitative (probabilistic) accounts to coherence is considered. The upshot is that extant measures differ considerably with respect to a number of symmetry constraints.

The paper investigates measures of explanatory power and how to define the inference schema “Inference to the Best Explanation”. It argues that these measures can also be used to quantify the systematic power of a hypothesis and the inference schema “Inference to the Best Systematization” is defined. It demonstrates that systematic power is a fruitful criterion for theory choice and IBS is truth-conducive. It also shows that even radical Bayesians must admit that systemic power is an integral component of Bayesian (...) reasoning. Finally, the paper puts the achieved results in perspective with van Fraassen’s famous criticism of IBE. (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)

Robustness is often presented as a guideline for distinguishing the true or real from mere appearances or artifacts. Most of recent discussions of robustness have focused on the kind of derivational robustness analysis introduced by Levins, while the related but distinct idea of robustness as multiple accessibility, defended by Wimsatt, has received less attention. In this paper, I argue that the latter kind of robustness, when properly understood, can provide justification for ontological commitments. The idea is that we are justified (...) in believing that things studied by science are real insofar as we have robust evidence for them. I develop and analyze this idea in detail, and based on concrete examples show that it plays an important role in science. Finally, I demonstrate how robustness can be used to clarify the debate on scientific realism and to formulate new arguments. (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)

Is evidential support transitive? The answer is negative when evidential support is understood as confirmation so that X evidentially supports Y if and only if p(Y | X) > p(Y). I call evidential support so understood “support” (for short) and set out three alternative ways of understanding evidential support: support-t (support plus a sufficiently high probability), support-t* (support plus a substantial degree of support), and support-tt* (support plus both a sufficiently high probability and a substantial degree of support). I also (...) set out two screening-off conditions (under which support is transitive): SOC1 and SOC2. It has already been shown that support-t is non-transitive in the general case (where it is not required that SOC1 holds and it is not required that SOC2 holds), in the special case where SOC1 holds, and in the special case where SOC2 holds. I introduce two rather weak adequacy conditions on support measures and argue that on any support measure meeting those conditions it follows that neither support-t* nor support-tt* is transitive in the general case, in the special case where SOC1 holds, or in the special case where SOC2 holds. I then relate some of the results to Douven’s evidential support theory of conditionals along with a few rival theories. (shrink)

The current state of inductive logic is puzzling. Survey presentations are recurrently offered and a very rich and extensive handbook was entirely dedicated to the topic just a few years ago [23]. Among the contributions to this very volume, however, one finds forceful arguments to the effect that inductive logic is not needed and that the belief in its existence is itself a misguided illusion , while other distinguished observers have eventually come to see at least the label as “slightly (...) antiquated” .What seems not to have lost any of its currency is the problem which inductive logic is meant to address. Inference from limited ascertained information to uncertain hypotheses is ubiquitous in learning, prediction and discovery. The logical insight that such kind of inference is fallible m .. (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)

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.

We show that as a chain of confirmation becomes longer, confirmation dwindles under screening-off. For example, if E confirms H1, H1 confirms H2, and H1 screens off E from H2, then the degree to which E confirms H2 is less than the degree to which E confirms H1. Although there are many measures of confirmation, our result holds on any measure that satisfies the Weak Law of Likelihood. We apply our result to testimony cases, relate it to the Data-Processing Inequality (...) in information theory, and extend it in two respects so that it covers a broader range of cases. (shrink)

Recently there have been several attempts in formal epistemology to develop an adequate probabilistic measure of coherence. There is much to recommend probabilistic measures of coherence. They are quantitative and render formally precise a notion—coherence—notorious for its elusiveness. Further, some of them do very well, intuitively, on a variety of test cases. Siebel, however, argues that there can be no adequate probabilistic measure of coherence. Take some set of propositions A, some probabilistic measure of coherence, and a probability distribution such (...) that all the probabilities on which A’s degree of coherence depends (according to the measure in question) are defined. Then, the argument goes, the degree to which A is coherent depends solely on the details of the distribution in question and not at all on the explanatory relations, if any, standing between the propositions in A. This is problematic, the argument continues, because, first, explanation matters for coherence, and, second, explanation cannot be adequately captured solely in terms of probability. We argue that Siebel’s argument falls short. (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)

In this thesis, I give a metascientific account of causality in medicine. I begin with two historical cases of causal discovery. These are the discovery of the causation of Burkitt’s lymphoma by the Epstein-Barr virus, and of the various viral causes suggested for cervical cancer. These historical cases then support a philosophical discussion of causality in medicine. This begins with an introduction to the Russo- Williamson thesis (RWT), and discussion of a range of counter-arguments against it. Despite these, I argue (...) that the RWT is historically workable, given a small number of modifications. I then expand Russo and Williamson’s account. I first develop their suggestion that causal relationships in medicine require some kind of evidence of mechanism. I begin with a number of accounts of mechanisms and produce a range of consensus features of them. I then develop this consensus position by reference to the two historical case studies with an eye to their operational competence. In particular, I suggest that it is mechanistic models and their representations which we are concerned with in medicine, rather than the mechanism as it exists in the world. -/- I then employ these mechanistic models to give an account of the sorts of evidence used in formulating and evaluating causal claims. Again, I use the two human viral oncogenesis cases to give this account. I characterise and distinguish evidence of mechanism from evidence of difference-making, and relate this to mechanistic models. I then suggest the relationship between types of evidence presents us with a means of tackling the reference-class problem. This sets the scene for the final chapter. Here, I suggest the manner in which these two different classes of evidence become integrated is also reflected in the way that developing research programmes change as their associated causal claims develop. (shrink)

Among Bayesian confirmation theorists, several quantitative measures of the degree to which an evidential proposition E confirms a hypothesis H have been proposed. According to one popular recent measure, s, the degree to which E confirms H is a function of the equation P(H|E) − P(H|~E). A consequence of s is that when we have two evidential propositions, E1 and E2, such that P(H|E1) = P(H|E2), and P(H|~E1) ≠ P(H|~E2), the confirmation afforded to H by E1 does not equal the (...) confirmation afforded to H by E2. I present several examples that demonstrate the unacceptability of this result, and conclude that we should reject s (and other measures that share this feature) as a measure of confirmation. (shrink)

Coherentism maintains that coherent beliefs are more likely to be true than incoherent beliefs, and that coherent evidence provides more confirmation of a hypothesis when the evidence is made coherent by the explanation provided by that hypothesis. Although probabilistic models of credence ought to be well-suited to justifying such claims, negative results from Bayesian epistemology have suggested otherwise. In this essay we argue that the connection between coherence and confirmation should be understood as a relation mediated by the causal relationships (...) among the evidence and a hypothesis, and we offer a framework for doing so by fitting together probabilistic models of coherence, confirmation, and causation. We show that the causal structure among the evidence and hypothesis is sometimes enough to determine whether the coherence of the evidence boosts confirmation of the hypothesis, makes no difference to it, or even reduces it. We also show that, ceteris paribus, it is not the coherence of the evidence that boosts confirmation, but rather the ratio of the coherence of the evidence to the coherence of the evidence conditional on a hypothesis. (shrink)

Abstract Recent criticisms of intuition from experimental philosophy and elsewhere have helped undermine the authority of traditional conceptual analysis. As the product of more empirically informed philosophical methodology, this result is compelling and philosophically salutary. But the negative critiques rarely suggest a positive alternative. In particular, a normative account of concept determination—how concepts should be characterized—is strikingly absent from such work. Carnap's underappreciated theory of explication provides such a theory. Analyses of complex concepts in empirical sciences illustrates and supports this (...) claim, and counteracts the charge explication is only suitable for highly mathematical, axiomatic contexts. Explication is also defended against the influential criticism it is “philosophically unilluminating”. Content Type Journal Article Category Original paper in Philosophy of Science Pages 1-19 DOI 10.1007/s13194-011-0027-5 Authors James Justus, Philosophy Department, Florida State University and University of Sydney, Tallahassee, FL 32306, USA Journal European Journal for Philosophy of Science Online ISSN 1879-4920 Print ISSN 1879-4912. (shrink)

Bayesianism provides a rich theoretical framework, which lends itself rather naturally to the explication of various “contrastive” and “non-contrastive” concepts. In this (brief) discussion, I will focus on issues involving “contrastivism”, as they arise in some of the recent philosophy of science, epistemology, and cognitive science literature surrounding Bayesian confirmation theory.

Confirmation of a hypothesis by evidence can be measured by one of the so far known incremental measures of confirmation. As we show, incremental measures can be formally defined as the measures of confirmation satisfying a certain small set of basic conditions. Moreover, several kinds of incremental measure may be characterized on the basis of appropriate structural properties. In particular, we focus on the so-called Matthew properties: we introduce a family of six Matthew properties including the reverse Matthew effect; we (...) further prove that incremental measures endowed with reverse Matthew effect are possible; finally, we shortly consider the problem of the plausibility of Matthew properties. (shrink)

This paper describes a formal measure of epistemic justification motivated by the dual goal of cognition, which is to increase true beliefs and reduce false beliefs. From this perspective the degree of epistemic justification should not be the conditional probability of the proposition given the evidence, as it is commonly thought. It should be determined instead by the combination of the conditional probability and the prior probability. This is also true of the degree of incremental confirmation, and I argue that (...) any measure of epistemic justification is also a measure of incremental confirmation. However, the degree of epistemic justification must meet an additional condition, and all known measures of incremental confirmation fail to meet it. I describe this additional condition as well as a measure that meets it. The paper then applies the measure to the conjunction fallacy and proposes an explanation of the fallacy. (shrink)

The conjunction fallacy has been a key topic in debates on the rationality of human reasoning and its limitations. Despite extensive inquiry, however, the attempt to provide a satisfactory account of the phenomenon has proved challenging. Here we elaborate the suggestion (first discussed by Sides, Osherson, Bonini, & Viale, 2002) that in standard conjunction problems the fallacious probability judgements observed experimentally are typically guided by sound assessments of _confirmation_ relations, meant in terms of contemporary Bayesian confirmation theory. Our main formal (...) result is a confirmation-theoretic account of the conjunction fallacy, which is proven _robust_ (i.e., not depending on various alternative ways of measuring degrees of confirmation). The proposed analysis is shown distinct from contentions that the conjunction effect is in fact not a fallacy, and is compared with major competing explanations of the phenomenon, including earlier references to a confirmation-theoretic account. (shrink)

Can some evidence confirm a conjunction of two hypotheses more than it confirms either of the hypotheses separately? We show that it can, moreover under conditions that are the same for nine different measures of confirmation. Further we demonstrate that it is even possible for the conjunction of two disconfirmed hypotheses to be confirmed by the same evidence.

The concept of an evidential conditional _If A then C_ that can be defined by the conjunction of \(A>C\) and \(\lnot C > \lnot A\), where > is a conditional of the kind introduced by Stalnaker and Lewis, has recently been studied in a series of papers by Vincenzo Crupi and Andrea Iacona. In this paper I argue that Crupi and Iacona’s central idea that contraposition captures the idea of evidential support cannot be maintained. I give examples showing that contraposition (...) is neither necessary nor sufficient for a conditional’s antecedent supporting its consequent. Crupi and Iacona’s alternative account of evidential conditionals that is based on a probabilistic measure of evidential support cannot add to the credentials of their modal account, because both the theoretical role of contraposition and the resulting logic are different in this account. (shrink)

When we talk about the coherence of a story, we seem to think of how well its individual pieces fit together—how to explicate this notion formally, though? We develop a Bayesian network based coherence measure with implementation in _R_, which performs better than its purely probabilistic predecessors. The novelty is that by paying attention to the network structure, we avoid simply taking mean confirmation scores between all possible pairs of subsets of a narration. Moreover, we assign special importance to the (...) weakest links in a narration, to improve on the other measures’ results for logically inconsistent scenarios. We illustrate and investigate the performance of the measures in relation to a few philosophically motivated examples, and (more extensively) using the real-life example of the Sally Clark case. (shrink)

Biologists and philosophers of science have recently called for an extension of evolutionary theory. This so-called ‘extended evolutionary synthesis’ seeks to integrate developmental processes, extra-genetic forms of inheritance, and niche construction into evolutionary theory in a central way. While there is often agreement in evolutionary biology over the existence of these phenomena, their explanatory relevance is questioned. Advocates of EES posit that their perspective offers better explanations than those provided by ‘standard evolutionary theory’. Still, why this would be the case (...) is unclear. Usually, such claims assume that EES’s superior explanatory status arises from the pluralist structure of EES, its different problem agenda, and a growing body of evidence for the evolutionary relevance of developmental phenomena. However, what is usually neglected in this debate is a discussion of what the explanatory standards of EES actually are, and how they differ from prevailing standards in SET. In other words, what is considered to be a good explanation in EES versus SET? To answer this question, we present a theoretical framework that evaluates the explanatory power of different evolutionary explanations of the same phenomena. This account is able to identify criteria for why and when evolutionary explanations of EES are better than those of SET. Such evaluations will enable evolutionary biology to find potential grounds for theoretical integration. (shrink)

This article reveals one general scheme for creating counter examples to Bayesian confirmation theory. The reason of the problems is that: in daily life the degree of confirmation is affected not only by probability but also by some non-probabilistic factors, e.g., structural similarity, quantity of evidence, and marginal utility, while Bayesian confirmation theory considers only probabilities to measure the degree of confirmation. This article resolves these problems after some detail analyses, and proposes a new confirmation measure based on these factors.

Relative overlap measures of coherence have recently been shown to have two devastating properties: according to the plain relative overlap measure, the degree of coherence of any set of propositions cannot be increased by adding further propositions, and according to the refined relative overlap measure, no set can be more coherent than its most coherent two-element subset. This result has been taken to rule out relative overlap as a foundation for a probabilistic explication of coherence. The present paper shows that (...) this view is premature: we propose a relative overlap measure that does not fall victim to the two properties. The guiding idea is to employ a well-established recipe for the construction of coherence measures and to adapt it to the idea of relative overlap. We show that this new measure keeps up with, or even outperforms, former overlap measures in a set of desiderata for coherence measures and a collection of popular test cases. This result re-establishes relative overlap as a candidate for a proper formalization of coherence. (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)

The concepts of coherence and confirmation are closely intertwined: according to a prominent proposal coherence is nothing but mutual confirmation. Accordingly, it should come as no surprise that both are confronted with similar problems. As regards Bayesian confirmation measures these are illustrated by the problem of tacking by conjunction. On the other hand, Bayesian coherence measures face the problem of belief individuation. In this paper we want to outline the benefit of an approach to coherence and confirmation based on content (...) elements. It will be shown that the resulting concepts, called genuine coherence and genuine confirmation, can be used in order to solve the two mentioned problems. In a final section we present some results on degrees of genuine coherence and genuine confirmation. (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.