In addition to purely practical values, cognitive values also figure into scientific deliberations. One way of introducing cognitive values is to consider the cognitive value that accrues to the act of accepting a hypothesis. Although such values may have a role to play, such a role does not exhaust the significance of cognitive values in scientific decision-making. This paper makes a plea for consideration of epistemic value —that is, value attaching to a state of belief—and defends the notion of cognitive (...) epistemic value against some criticisms that have been raised. A stability requirement for epistemic value functions is argued for on the basis of considerations of diachronic coherence. This stability requirement is sufficient to obtain the Value of Learning Theorem, which says that the expected utility of cost-free learning cannot be negative. This holds also for cognitive epistemic values, provided that the stability requirement is met. (shrink)

Reasoning, defined as the production and evaluation of reasons, is a central process in science. The dominant view of reasoning, both in the psychology of reasoning and in the psychology of science, is of a mechanism with an asocial function: bettering the beliefs of the lone reasoner. Many observations, however, are difficult to reconcile with this view of reasoning; in particular, reasoning systematically searches for reasons that support the reasoner’s initial beliefs, and it only evaluates these reasons cursorily. By contrast, (...) reasoners are well able to evaluate others’ reasons: accepting strong arguments and rejecting weak ones. The argumentative theory of reasoning accounts for these traits of reasoning by postulating that the evolved function of reasoning is to argue: to find arguments to convince others and to change one’s mind when confronted with good arguments. Scientific reasoning, however, is often described as being at odds with such an argumentative mechanisms: scientists are supposed to reason objectively on their own, and to be pigheaded when their theories are challenged, even by good arguments. In this article, we review evidence showing that scientists, when reasoning, are subject to the same biases as are lay people while being able to change their mind when confronted with good arguments. We conclude that the argumentative theory of reasoning explains well key features of scientists’ reasoning and that differences in the way scientists and laypeople reason result from the institutional framework of science. (shrink)

Charles Peirce’s model of inquiry is supposed to demarcate appropriate methods of inquiry from specious ones. Cheryl Misak points out that Peirce’s explicit account fails, but can nevertheless be rescued by elements of his own system. While Misak’s criticism is a propos, her own attempt to fortify Peirce’s account does not succeed, as it falls prey to the same criticism she raises against Peirce’s explicit account. The account provided in this paper—the ‘open path’ alternative—draws from Peirce’s corollary to his “first (...) rule of reason”, that one should not block the road to inquiry. The ‘open path’ account is able to withstand Misak’s objections, and when combined with other aspects of Peirce’s work, shows us why the optimal way to conduct inquiry is to follow the path of greatest resistance. Inquiry, however, is rarely conducted in optimal conditions. Actual, constrained conditions of inquiry require a measure of economy in terms of what can be reasonably pursued and how. The question, then, is how to conduct our inquiries so that they are as nearly optimal as possible given actual constraints. As a working scientist, Peirce was acutely aware of the need to economize in research. Nicholas Rescher has recognized this issue’s significance for Peirce, and noted its neglect in discussions of Peirce’s work. One issue that has been largely neglected in the literature on Peirce is what specifically he recommends, based on considerations of economy, for how to go about gathering evidence. Kronz & McLaughlin points out that Peirce’s primary recommendation is that in gathering evidence relevant to a particular hypothesis we should test for empirical consequences that would not have been expected otherwise. The view that is developed in this paper is that economy in research, according to Peirce, follows the general line of his theory of inquiry. Peirce’s theory of inquiry implies that pursuit of truth requires maximizing resistance. I argue that his considerations about how to navigate within the constraints introduced in the context of actual research are also best understood as recommendations for maximizing resistance. (shrink)

I offer an account of ad hocness that explains why the adoption of an ad hoc auxiliary is accompanied by the disconfirmation of a hypothesis H. H must be conjoined with an auxiliary a′, which is improbable antecedently given H, while ~H does not have this disability. This account renders it unnecessary to require, for identifying ad hocness, that either a′ or H have a posterior probability less than or equal to 0.5; there are also other reasons for abandoning that (...) condition. I distinguish between formal ad hocness, which is bad in the probabilistic sense that it results in disconfirmation of H, and argumentative ad hocness, which actually involves bad reasoning on the part of a subject. The latter is what I call “not counting the cost.” This distinction allows us to see why the 0.5 condition appeared attractive in the first place. The concept of not counting the cost also has implications for other areas of research, including both a Bayesian concept of unfalsifiability and the classic epistemological question of the problem of the external world. (shrink)

A familiar adage in the philosophy of science is that general hypotheses are better supported by varied evidence than by uniform evidence. Several studies suggest that young children do not respect this principle, and thus suffer from a defect in their inductive methodology. We argue that the diversity principle does not have the normative status that psychologists attribute to it, and should be replaced by a simple rule of probability. We then report experiments designed to detect conformity to the latter (...) rule in children's inductive judgment. The results suggest that young children in both the United States and Taiwan are sensitive to the constraints imposed by the rule on judgments of probability and evidential strength. We conclude with a suggested reinterpretation of the thesis that children's inductive methodology qualifies them as “little scientists.”. (shrink)

Abstract Evidence that supports a theory may be available to the scientist who constructs the theory and used as a guide to that construction, or it may only be discovered in the course of testing the theory. The central claim of this essay is that information about whether the evidence was accommodated or predicted affects the rational degree of confidence one ought to have in the theory. Only when the evidence is accommodated is there some reason to believe that the (...) theoretical system was ?fudged? to fit the evidence in a way that weakens support. This weakening is an objective matter, but not one that can be conclusively determined by examining the contents of the theory and its logical relationship to the evidence. Consequently, there is less reason to believe a theory on the basis of that evidence when it is known that the evidence was accommodated than there would be if it was known instead that the same evidence had been predicted. (shrink)

According to Hitchcock and Sober’s argument from overfitting for weak predictivism, the fact that a theory accurately predicts a portion of its data is evidence that it has been formulated by balancing simplicity and goodness-of-fit rather than overfitting data. The core argument consists of two likelihood inequalities. In this paper I show that there is a surprising accommodation-friendly implication in their argument, and contend that it is beset by a substantial difficulty, namely, there is no good reason to think that (...) their second likelihood inequality is true. (shrink)

Varied evidence confirms more strongly than less varied evidence, ceteris paribus. This epistemological Variety of Evidence Thesis enjoys widespread intuitive support. We put forward a novel explication of one notion of varied evidence and the Variety of Evidence Thesis within Bayesian models of scientific inference by appealing to measures of entropy. Our explication of the Variety of Evidence Thesis holds in many of our models which also pronounce on disconfirmatory and discordant evidence. We argue that our models pronounce rightly. Against (...) a backdrop of failures of the Variety of Evidence Thesis, the intuitive case for the Variety of Evidence Thesis emerges strengthened. Our models do however not support the general case for the thesis since our explication of it fails to hold in certain cases. The parameter space of this failure is explored and an explanation for the failure is offered. (shrink)

Varied evidence for a hypothesis confirms it more strongly than less varied evidence, ceteris paribus. This epistemological Variety of Evidence Thesis enjoys long-standing widespread intuitive support. Recent literature has raised serious doubts that the correlational approach of explicating the thesis can vindicate it. By contrast, the eliminative approach due to Horwich vindicates the Variety of Evidence Thesis but only within a relatively narrow domain. I investigate the prospects of extending the eliminative approach to a larger domain by considering a larger (...) class of sensible explications of evidential variety. For a large subclass class of such explications I show how to construct cases in which the less diverse body of evidence for a hypothesis confirms more strongly. I hence argue that these prospects are dire since the eliminative approach widely fails to vindicate the thesis. (shrink)

Surprisingly, modified versions of the confirmation theory (Carnap and Hempel) and truth approximation theory (Popper) turn out to be smoothly sythesizable. The glue between the two appears to be the instrumentalist methodology, rather than that of the falsificationalist. The instrumentalist methodology, used in the separate, comparative evaluation of theories in terms of their successes and problems (hence, even if already falsified), provides in theory and practice the straight road to short-term empirical progress in science ( à la Laudan). It is (...) also argued that such progress is also functional for all kinds of truth approximation: observational, referential, and theoretical. This sheds new light on the long-term dynamics of science and hence on the relation between the main epistemological positions, viz., instrumentalism (Toulmin, Laudan), constructive empiricism (Van Fraassen), referential realism (Hacking, Cartwright), and theory realism of a non-essentialist nature (constructive realism à la Popper). Readership: Open minded philosophers and scientists. The book explains and justifies the scientist's intuition that the debate among philosophers about instrumentalism and realism has almost no practical consequences. (shrink)

I present a justification for the intution that more-varied data are more valuable than the same number of less-varied data by showing that the more-varied data help to improve the accuracy of our predictions.

This discussion centers on two desiderata: the role of measurement in information-gathering and physical interaction in scientific practice. By taking inspiration from van Fraassen’s view, we present a methodological account of perspectival measurement that addresses empirical practice where there is complex intervention, disagreeing results, and limited theory. The specific aim of our account is to provide a methodological prescription for developing measurement processes in the context of limited theory. The account should be useful to philosophers of science, who are interested (...) in the intersection between representation and intervention; scientists, who are interested in methodological suggestions for theory-development and reliability; and interdisciplinary researchers, who are interested in the intersections between the pandemic, built environments, and social processes. We apply the process-view of measurement to COVID-19, specifically, measuring replication in the SARS-CoV-2 virus. The aim is to show that our account tracks key elements—manipulation/intervention, independence, invariance, and theory-development—by organizing unfolding measurement processes. Additionally, we use our account to make prescriptive suggestions for measurement practice in the COVID-19 context by discussing the need to broaden measurement perspective on interaction, manipulation, and production. (shrink)

The concept of evidence is among the central concerns of epistemology broadly construed. As such, it has long engaged the intellectual energies of both philosophers of science and epistemologists of a more traditional variety. Here I briefly survey some of the more important ideas to have emerged from this tradition of reflection. I then look somewhat more closely at an issue that has recently come to the fore, largely as a result of Williamson's Knowledge and Its Limits: that of whether (...) one's evidence supervenes on one's non-factive mental states. (shrink)

According to one view about the rationality of belief, such rationality is ultimately nothing other than the rationality that one exhibits in taking the means to one’s ends. On this view, epistemic rationality is really a species or special case of instrumental rationality. In particular, epistemic rationality is instrumental rationality in the service of one’s distinctively cognitive or epistemic goals (perhaps: one’s goal of holding true rather than false beliefs). In my (2003), I dubbed this view the instrumentalist conception of (...) epistemic rationality. (shrink)

Orthodox Probabilists hold that an inquirer ought to harbor a precise degree of confidence in each hypothesis about which she is concerned. Modest Probabilism is one of a family doctrines inspired by the thought that Orthodox Probabilists are thereby demanding that an inquirer effect a precision that is often unwarranted by her evidence. The purpose of this essay is (i) to explain the particular way in which Modest Probabilism answers to this thought, and (ii) to address an alleged counterexample to (...) Modest Probabilism meant to offer proof that Modest Probabilism is no better than its orthodox predecessor at avoiding unwarranted precision. (shrink)

Is there a duty to respond to objections in order to present a good argument? Ralph Johnson argues that there is such a duty, which he refers to as the ‘dialectical tier’ of an argument. I deny the (alleged) duty primarily on grounds that it would exert too great a demand on arguers, harming argumentation practices. The valuable aim of responding to objections, which Johnson’s dialectical tier is meant to satisfy, can be achieved in better ways, as argumentation is a (...) social-epistemic activity. (shrink)

There are different Bayesian measures to calculate the degree of confirmation of a hypothesis H in respect of a particular piece of evidence E. Zalabardo (Analysis 69:630–635, 2009) is a recent attempt to defend the likelihood-ratio measure (LR) against the probability-ratio measure (PR). The main disagreement between LR and PR concerns their sensitivity to prior probabilities. Zalabardo invokes intuitive plausibility as the appropriate criterion for choosing between them. Furthermore, he claims that it favours the ordering of pairs evidence/hypothesis generated by (...) LR. We will argue, however, that the intuitive non-numerical example provided by Zalabardo does not show that prior probabilities do not affect the degree of confirmation. On account of this, we conclude that there is no compelling reason to endorse LR qua measure of degree of confirmation. On the other side, we should not forget some technicalities which still benefit PR. (shrink)

The adverse reaction to Hempel's 'ravens paradox' embodied in giving it that description is compared with the usual reaction of experimental subjects to the Wason selection task.

an observation to formulate a theory, it is no surprise that the resulting theory accurately captures that observation. However, when the theory makes a novel prediction—when it predicts an observation that was not used in its formulation—this seems to provide more substantial confirmation of the theory. This paper presents a new approach to the vexed problem of understanding the epistemic difference between prediction and accommodation. In fact, there are several problems that need to be disentangled; in all of them, the (...) key is the concept of overfitting. We float the hypothesis that accommodation is a defective methodology only when the methods used to accommodate the data fail to guard against the risk of overfitting. We connect our analysis with the proposals that other philosophers have made. We also discuss its bearing on the conflict between instrumentalism and scientific realism. Introduction Predictivisms—a taxonomy Observations Formulating the problem What might Annie be doing wrong? Solutions Observations explained Mayo on severe tests The miracle argument and scientific realism Concluding comments. (shrink)

Scientific theories are developed in response to a certain set of phenomena and subsequently evaluated, at least partially, in terms of the quality of fit between those same theories and appropriately distinctive phenomena. To differentiate between these two stages it is popular to describe the former as involving the accommodation of data and the latter as involving the prediction of data. Predictivism is the view that, ceteris paribus, correctly predicting data confers greater confirmation than successfully accommodating data. In this paper, (...) I take issue with a variety of predictivist theses, argue that their role for issues of confirmation is extremely limited, and attempt to account for the appeal that predictivism has enjoyed. Introduction Temporal Predictivism Heuristic Predictivism Weak Predictivism 4.1 Inference to better theories 4.2 Inference to better methods Arguments for Strong Heuristic Predictivism 5.1 Best explanations argument 5.2 Conditional support 5.3 Unique explanations Increased Explanatory Unification 6.1 Explaining what other theories can't 6.2 Contrived hypotheses 6.2 Strength and simplicity Conclusions CiteULike Connotea Del.icio.us What's this? (shrink)

The judgment that a given event is epistemically improbable is necessary but insufficient for us to conclude that the event is surprising. Paul Horwich has argued that surprising events are, in addition, more probable given alternative background assumptions that are not themselves extremely improbable. I argue that Horwich’s definition fails to capture important features of surprises and offer an alternative definition that accords better with intuition. An important application of Horwich’s analysis has arisen in discussions of fine-tuning arguments. In the (...) second part of the paper I consider the implications for this argument of employing my definition of surprise. I argue that advocates of fine-tuning arguments are not justified in attaching significance to the fact that we are surprised by examples of fine-tuning. (shrink)

Richard Swinburne’s argument in The Existence of God discusses many probabilities, ultimately concluding that God probably exists. Swinburne gives exact values to almost none of these probabilities. I attempted to assign values to the probabilities that met that weak condition that they could be correct. In this paper, I first present a brief outline of Swinburne’s argument in The Existence of God. I then present the problems I encountered in Swinburne’s argument, specifically problems that interfered with my attempt to arrive (...) at values for the probabilities discussed by Swinburne. Finally, I suggest that Swinburne’s argument would be more persuasive if he assigned exact values to his probabilities. (shrink)

The probabilistic corroboration of two or more hypotheses or series of observations may be performed additively or multiplicatively . For additive corroboration (e.g. by Laplace's rule of succession), stochastic independence is needed. Inferences, based on overwhelming numbers of observations without unexplained counterinstances permit hyperinduction , whereby extremely high probabilities, bordering on certainty for all practical purposes may be achieved. For multiplicative corroboration, the error probabilities (1 - Pr) of two (or more) hypotheses are multiplied. The probabilities, obtained by reconverting the (...) product, are valid for both of the hypotheses and indicate the gain by corroboration.. This method is mathematically correct, no probabilities > 1 can result (as in some conventional methods) and high probabilities with fewer observations may be obtained, however, semantical independence is a prerequisite. The combined method consists of (1) the additive computation of the error probabilities (1 - Pr) of two or more single hypotheses, whereby arbitrariness is avoided or at least reduced and (2) the multiplicative procedure . The high reliability of Empirical Counterfactual Statements is explained by the possibility of multiplicative corroboration of "all-no" statements due to their strict semantical independence. (shrink)

The paper provides a formal proof that efficient estimates of parameters, which vary as as little as possible when measurements are repeated, may be expected to provide more accurate predictions. The definition of predictive accuracy is motivated by the work of Akaike (1973). Surprisingly, the same explanation provides a novel solution for a well known problem for standard theories of scientific confirmation — the Ravens Paradox. This is significant in light of the fact that standard Bayesian analyses of the paradox (...) fail to account for the predictive utility of universal laws like All ravens are black. (shrink)

Wayne (1995) critiques the Bayesian explication of the confirmational significance of evidential diversity (CSED) offered by Horwich (1982). Presently, I argue that Wayne’s reconstruction of Horwich’s account of CSED is uncharitable. As a result, Wayne’s criticisms ultimately present no real problem for Horwich. I try to provide a more faithful and charitable rendition of Horwich’s account of CSED. Unfortunately, even when Horwich’s approach is charitably reconstructed, it is still not completely satisfying.

Hempel first introduced the paradox of confirmation in (Hempel 1937). Since then, a very extensive literature on the paradox has evolved (Vranas 2004). Much of this literature can be seen as responding to Hempel’s subsequent discussions and analyses of the paradox in (Hempel 1945). Recently, it was noted that Hempel’s intuitive (and plausible) resolution of the paradox was inconsistent with his official theory of confirmation (Fitelson & Hawthorne 2006). In this article, we will try to explain how this inconsistency affects (...) the historical dialectic about the paradox and how it illuminates the nature of confirmation. In the end, we will argue that Hempel’s intuitions about the paradox of confirmation were (basically) correct, and that it is his theory that should be rejected, in favor of a (broadly) Bayesian account of confirmation. (shrink)

In this paper, we discuss three probabilistic arguments for the existence of multiple universes. First, we provide an analysis of total evidence and use that analysis to defend Roger White's "this universe" objection to a standard fine-tuning argument for multiple universes. Second, we explain why Rodney Holder's recent cosmological argument for multiple universes is unconvincing. Third, we develop a "Cartesian argument" for multiple universes. While this argument is not open to the objections previously noted, we show that, given certain highly (...) plausible assumptions about evidence and epistemic probability, the proposition which it treats as evidence cannot coherently be regarded as evidence for anything. This raises the question of whether to reject the assumptions or accept that such a proposition cannot be evidence. (shrink)

There is good reason to believe that, if it can be decided at all, the realism debate must be decided on a posteriori grounds. But at least prima facie the prospects for an a posteriori resolution of the debate seem bleak, given that realists and antirealists disagree over two of the most fundamental questions pertaining to any kind of empirical research, to wit, what the range of accessible evidence is and what the methodological status of explanatory considerations is. The present (...) paper aims to show that, while the difficulties that face an empirical approach to the realism debate are not to be discounted, they are not insurmountable either. Specifically, it presents a broadly Bayesian strategy for resolving the debate that is capable of solving those difficulties. The strategy crucially involves answers to the aforementioned questions that diverge from both the standard realist and the standard antirealist answers, but that should appear more natural and plausible than those to realists and antirealists alike. (shrink)

External world skeptics are typically opposed to admitting as evidence anything that goes beyond the purely phenomenal, and equally typically, they disown the use of rules of inference that might enable one to move from premises about the phenomenal alone to a conclusion about the external world. This seems to bar any a posteriori resolution of the skepticism debate. This paper argues that the situation is not quite so hopeless, and that an a posteriori resolution of the debate becomes possible (...) once it is recognized that the skeptic holds overly defensive and ill-motivated positions vis-à-vis both evidence and inference, and that more reasonable ones are available. In stating these more reasonable positions, as well as in showing how they make possible an a posteriori resolution of the skepticism debate, the paper draws on the machinery of Bayesian epistemology. (shrink)

In ethical discourse, it is common practice to distinguish between normative commitments and descriptive commitments. Normative commitments reflect what a person ought to be committed to, whereas descriptive commitments reflect what a person actually is committed to. While the normative/descriptive distinction is widely accepted as a way of talking about ethical commitments, philosophers have missed this distinction in discussing ontological commitments. In this paper, I distinguish between descriptive ontological commitments and normative ontological commitments and discuss several significant benefits of recognizing (...) this distinction. I argue that just as the normative/descriptive distinction is important for fruitful ethical discourse, so too is it important for fruitful discourse concerning our ontological commitments. And, it constitutes a significant step towards resolving some prominent debates concerning our ontological commitments. (shrink)

To clarify and illuminate the place of probability in science Ellery Eells and James H. Fetzer have brought together some of the most distinguished philosophers ...

Showcasing original arguments for well-defined positions, as well as clear and concise statements of sophisticated philosophical views, this volume is an ...

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, (...) the Theorem's central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology. (shrink)

State of the art paper on the problem of induction: how to justify the conclusion that ‘all Fs are Gs’ from the premise that ‘all observed Fs are Gs’. The most prominent theories of contemporary philosophical literature are discussed and analysed, such as: inductivism, reliabilism, perspective of laws of nature, rationalism, falsificationism, the material theory of induction and probabilistic approaches, according to Carnap, Reichenbach and Bayesianism. In the end, we discuss the new problem of induction of Goodman, raised by the (...) grue predicate. (shrink)

Bayesian confirmation theory—abbreviated to in these notes—is the predominant approach to confirmation in late twentieth century philosophy of science. It has many critics, but no rival theory can claim anything like the same following. The popularity of the Bayesian approach is due to its flexibility, its apparently effortless handling of various technical problems, the existence of various a priori arguments for its validity, and its injection of subjective and contextual elements into the process of confirmation in just the places where (...) critics of earlier approaches had come to think that subjectivity and sensitivity to context were necessary. (shrink)

Many philosophers have argued that a hypothesis is better confirmed by some data if the hypothesis was not specifically designed to fit the data. ‘Prediction’, they argue, is superior to ‘accommodation’. Others deny that there is any epistemic advantage to prediction, and conclude that prediction and accommodation are epistemically on a par. This paper argues that there is a respect in which accommodation is superior to prediction. Specifically, the information that the data was accommodated rather than predicted suggests that the (...) data is less likely to have been manipulated or fabricated, which in turn increases the likelihood that the hypothesis is correct in light of the data. In some cases, this epistemic advantage of accommodation may even outweigh whatever epistemic advantage there might be to prediction, making accommodation epistemically superior to prediction all things considered. (shrink)

English abstract: This paper discusses the delicate relationship between traditional epistemology and the increasingly influential probabilistic (or ‘Bayesian’) approach to epistemology. The paper introduces some of the key ideas of probabilistic epistemology, including credences or degrees of belief, Bayes’ theorem, conditionalization, and the Dutch Book argument. The tension between traditional and probabilistic epistemology is brought out by considering the lottery and preface paradoxes as they relate to rational (binary) belief and credence respectively. It is then argued that this tension can (...) be alleviated by rejecting the requirement that rational (binary) beliefs must be consistent and closed under logical entailment. Instead, it is suggested that this logical requirement applies to a different type of binary propositional attitude, viz. acceptance. (shrink)

It is notoriously difficult to spell out the norms of inductive reasoning in a neat set of rules. I explore the idea that explanatory considerations are the key to sorting out the good inductive inferences from the bad. After defending the crucial explanatory virtue of stability, I apply this approach to a range of inductive inferences, puzzles, and principles such as the Raven and Grue problems, and the significance of varied data and random sampling.

Expanded version of a commentary on Adam Elga's "Lucky to be Rational" delivered at the 2008 Bellingham Summer Philosophy Conference.

The Paradox of the Ravens (a.k.a,, The Paradox of Confirmation) is indeed an old chestnut. A great many things have been written and said about this paradox and its implications for the logic of evidential support. The first part of this paper will provide a brief survey of the early history of the paradox. This will include the original formulation of the paradox and the early responses of Hempel, Goodman, and Quine. The second part of the paper will describe attempts (...) to resolve the paradox within a Bayesian framework, and show how to improve upon them. This part begins with a discussion of how probabilistic methods can help to clarify the statement of the paradox itself. And it describes some of the early responses to probabilistic explications. We then inspect the assumptions employed by traditional (canonical) Bayesian approaches to the paradox. These assumptions may appear to be overly strong. So, drawing on weaker assumptions, we formulate a new-and-improved Bayesian confirmation-theoretic resolution of the Paradox of the Ravens. (shrink)