A frequentist confidence interval can be constructed by inverting a hypothesis test, such that the interval contains only parameter values that would not have been rejected by the test. We show how a similar definition can be employed to construct a Bayesian support interval. Consistent with Carnap’s theory of corroboration, the support interval contains only parameter values that receive at least some minimum amount of support from the data. The support interval is not subject to Lindley’s paradox and provides an (...) evidence-based perspective on inference that differs from the belief-based perspective that forms the basis of the standard Bayesian credible interval. (shrink)

Many papers have been devoted to the semantic turn Carnap took in the late 1930s after Tarski had explained to him his method for defining truth and his work on the establishment of scientific semantics. Commentators have often argued that the major turn in Carnap’s approach to languages had already been taken in the Logical Syntax of Language, but they have usually assumed that Carnap was happy to subsequently follow Tarski and adopt Tarskian semantics. In this paper, it is argued (...) that this assumption needs to be qualified and that Carnap was actually far from following Tarski when he decided to complement his syntactic method with a semantic one. Carnap and Tarski had different goals, divergent programs, and dissenting views on truth and semantics. After exploring several possible methods for the explication of logical concepts such as L-truth and L-implication, Carnap opted for definitions based on concepts he had found in Wittgenstein’s Tractatus and Waismann’s work on a logical interpretation of probability. Carnap’s reasons for taking a semantic turn are to be understood in the context of his principle of tolerance. He first hoped he could use Tarski’s technique to recover in the semantic setting the completeness result he had tried to establish in the Logical Syntax. His eventual adoption of non-Tarskian semantics can be accounted for by his program of a logical analysis of science—including empirical science—and his ambition to elaborate a unified logical framework for deductive, inductive, and modal logic, and for explicating analyticity. (shrink)

The project of integrated HPS has occupied philosophers of science in one form or another since at least the 1960s. Yet, despite this substantial interest in bringing together philosophical and historical reflections on the nature of science, history of science and formal philosophy of science remain as divided as ever. In this paper, I will argue that the continuing separation between historical and formal philosophy of science is ill-founded. I will argue for this in both abstract and concrete terms. At (...) the abstract level, I reconstruct two possible arguments for the incompatibility of historical and formal philosophy of science and argue that they are both wanting. At the concrete level, I discuss how historical and formal philosophy of science have been brought together in practice, namely: in the form of a largely forgotten research tradition that I will refer to here as the study of formalized macro-units. After a brief exposition, I argue that this research tradition has been unduly overlooked by historically minded philosophers of science. Bringing together these observations, I argue that the divide between historical and formal philosophy of science is not grounded in any substantive arguments, but can be primarily attributed to disciplinary happenstance. (shrink)

Conceptual analysis has been typically recognized as a traditional methodology within analytic philosophy, but many philosophers have heavily criticized it. In contrast, the methodology of Carnapian explication has been undergoing a revival as a methodological alternative due to its revisionary aim. I will make explicit the shared structural properties and goals of Carnapian explication and the kind of conceptual analysis advanced by the advocates of the Canberra Plan. Also, I will argue that although their goal to make philosophy more scientific (...) is desirable, they cannot achieve their goal of clearly distinguishing philosophy from science. Moreover, since traditional conceptual analysis is an element of both revisionary methodologies, it is also unable to mark a clear distinction between them. The comparison throws some light on the relationship between traditional conceptual analysis and the two revisionary methodologies, their implicit theoretical commitments and deficiencies. (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)

Stanley Stevens draws a useful distinction among ordinal scales, interval scales, and ratio scales. Most recent discussions of confirmation measures have proceeded on the ordinal level of analysis. In this article, I give a more quantitative analysis. In particular, I show that the requirement that our desired confirmation measure be at least an interval measure naturally yields necessary conditions that jointly entail the log-likelihood measure. Thus, I conclude that the log-likelihood measure is the only good candidate interval measure.

Christopher Boorse’s Health care ethics: an introduction, Temple University Press, Philadelphia, pp 359–393, 1987; in Humber, Almeder, Totowa What is disease?, Humana Press, New York City, pp 1–134, 1997; J Med Philos, 39:683–724, 2014) Bio-Statistical Theory comprehends diseases in terms of departures from natural norms, which involve an objectively describable deviation from the proper physiological or psychological functioning of parts of the human organism. I argue that while recent revisions and additional considerations shield the BST from a number of issues (...) raised by critics, they give rise to significant new challenges. These are related to the attribution of epistemic authority, the possibility of multiple concepts in the authoritative literature, and the framing of BST as “philosophical explication.” The conclusion is that, in its current form, the BST is unable to provide a robust framework for a naturalist classification. (shrink)

Recently, natural language pragmatics started to make use of decision-, game-, and information theoretical tools to determine the usefulness of questions and assertions in a quantitative way. In the first part of this paper several of these notions are related with each other. It is shown that under particular natural assumptions the utility of questions and answers reduces to their informativity, and that the ordering relation induced by utility sometimes even reduces to the logical relation of entailment. The second part (...) of the paper shows how different proposals (using either protocols or likelihood functions) to measure the relevance/utility of non-partitional questions come down to the same thing. (shrink)

In debates about the nature of scientific explanation, one theme repeatedly arises: that explanation is about providing understanding. However, the concept of understanding has only recently been explored in any depth, and this paper attempts to introduce a useful concept of understanding to that literature and explore it. Understanding is a higher level cognition, the recognition of connections between various pieces of knowledge. This conception can be brought to bear on the conceptual issues that have thus far been unclear in (...) the literature. Though this notion of understanding is broad, explaining various concepts of explanation, it is robust enough to underwrite an objective and useful notion of explanation. (shrink)

I show how scoring rules, interpreted as measuring the inaccuracy of a set of degrees of belief, may be exploited to construct confirmation measures as used in Bayesian confirmation theory. I construct two confirmation measures from two particular standard scoring rules. One of these measures is genuinely new, the second is trivially ordinally equivalent to the difference measure. These two measures are tested against three well-known measures of confirmation in a simple but illuminating case that contains in a natural way (...) the problem of irrelevant conjunction. The genuinely new measure emerges, arguably, as the best. (shrink)

In this paper we discuss the new Tweety puzzle. The original Tweety puzzle was addressed by approaches in non-monotonic logic, which aim to adequately represent the Tweety case, namely that Tweety is a penguin and, thus, an exceptional bird, which cannot fly, although in general birds can fly. The new Tweety puzzle is intended as a challenge for probabilistic theories of epistemic states. In the first part of the paper we argue against monistic Bayesians, who assume that epistemic states can (...) at any given time be adequately described by a single subjective probability function. We show that monistic Bayesians cannot provide an adequate solution to the new Tweety puzzle, because this requires one to refer to a frequency-based probability function. We conclude that monistic Bayesianism cannot be a fully adequate theory of epistemic states. In the second part we describe an empirical study, which provides support for the thesis that monistic Bayesianism is also inadequate as a descriptive theory of cognitive states. In the final part of the paper we criticize Bayesian approaches in cognitive science, insofar as their monistic tendency cannot adequately address the new Tweety puzzle. We, further, argue against monistic Bayesianism in cognitive science by means of a case study. In this case study we show that Oaksford and Chater’s (2007, 2008) model of conditional inference—contrary to the authors’ theoretical position—has to refer also to a frequency-based probability function. (shrink)

This paper concerns the issue of whether the so-called left wing of the Vienna Circle (Carnap, Neurath, Frank) can be understood as having provided the blueprint for a bipartite metatheory with a formal-logical part (the “logic of science”) supporting and being supported by a naturalistic-empirical part (the “behavioristics of science”). A claim to this effect was recently met by a counterclaim that there was indeed an attempt made to broaden Carnap’s formalist conception of philosophy by the pragmatist Morris, but that (...) this initiative failed and that Carnap showed no interest in it. To defend the original claim this paper provides an analysis of Carnap and Morris on the subject matter of pragmatics in order to show that and how Carnap adopted Morris’s proposals in so far as they agreed with bipartite metatheory conception. (shrink)

This paper offers a refutation of J. C. Pinto de Oliveira's recent critique of revisionist Carnap scholarship as giving undue weight to two brief letters to Kuhn expressing his interest in the latter's work. First an argument is provided to show that Carnap and Kuhn are by no means divided by a radical mismatch of their conceptions of the rationality of science as supposedly evidenced by their stance towards the distinction of the contexts of discovery and justification. This is followed (...) by an argument to the effect that the fact that Carnap's own work concentrated on formal aspects of scientific theories does not licence the conclusion that he thought historical investigations and concerns irrelevant for what we nowadays would rightly call "philosophy of science". (shrink)

It is well known that a degree-of-belief function P is coherent if and only if it satisfies the probability calculus. In this paper, we show that the notion of coherence can be extended to higher order probabilities such as P(P(h)=p)=q, and that a higher order degree-of-belief function P is coherent if and only if it satisfies the probability calculus plus the following axiom: P(h)=p iff P(P(h)=p)=1. Also, a number of lemmata which extend an incomplete probability function to a complete one (...) are established. (shrink)

In attempting to form rational personal probabilities by direct inference, it is usually assumed that one should prefer frequency information concerning more specific reference classes. While the preceding assumption is intuitively plausible, little energy has been expended in explaining why it should be accepted. In the present article, I address this omission by showing that, among the principled policies that may be used in setting one’s personal probabilities, the policy of making direct inferences with a preference for frequency information for (...) more specific reference classes yields personal probabilities whose accuracy is optimal, according to all proper scoring rules, in situations where all of the relevant frequency information is point-valued. Assuming that frequency information for narrower reference classes is preferred, when the relevant frequency statements are point-valued, a dilemma arises when choosing whether to make a direct inference based upon relatively precise-valued frequency information for a broad reference class, R, or upon relatively imprecise-valued frequency information for a more specific reference class, R*. I address such cases, by showing that it is often possible to make a precise-valued frequency judgment regarding R* based on precise-valued frequency information for R, using standard principles of direct inference. Having made such a frequency judgment, the dilemma of choosing between and is removed, and one may proceed by using the precise-valued frequency estimate for the more specific reference class as a premise for direct inference. (shrink)

This target article presents a new computational theory of explanatory coherence that applies to the acceptance and rejection of scientific hypotheses as well as to reasoning in everyday life, The theory consists of seven principles that establish relations of local coherence between a hypothesis and other propositions. A hypothesis coheres with propositions that it explains, or that explain it, or that participate with it in explaining other propositions, or that offer analogous explanations. Propositions are incoherent with each other if they (...) are contradictory, Propositions that describe the results of observation have a degree of acceptability on their own. An explanatory hypothesis is acccpted if it coheres better overall than its competitors. The power of the seven principles is shown by their implementation in a connectionist program called ECHO, which treats hypothesis evaluation as a constraint satisfaction problem. Inputs about the explanatory relations are used to create a network of units representing propositions, while coherende and incoherence relations are encoded by excitatory and inbihitory links. ECHO provides an algorithm for smoothly integrating theory evaluation based on considerations of explanatory breadth, simplicity, and analogy. It has been applied to such important scientific cases as Lovoisier's argument for oxygen against the phlogiston theory and Darwin's argument for evolution against creationism, and also to cases of legal reasoning. The theory of explanatory coherence has implications for artificial intelligence, psychology, and philosophy. (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)

Philosophical debates about emergence are often marred by equivocation and lack of common ground, and dialogue about emergence between scientists and philosophers can be equally difficult. In this paper I offer a unified explication of emergence and argue that this explication can cut through much of the confusion evident in discussions of emergence. I defend an explication of the concept of emergence as the unavailability of a certain kind of scientific explanation for an observer or observers.

How should we account for self-knowledge of our inner lives? Some have argued that just as we have various senses that allow us to perceive the environment, we have an inner sense that allows us to perceive our inner lives. But others find such a view implausible and think that there are other ways to account for self-knowledge. With respect to all-or-nothing beliefs, some have held that we may account for self-knowledge by appealing to the claim that such beliefs are (...) transparent--that we may answer the question 'Do you believe p?' by answering the question 'Is it the case that p?' But surprisingly, little or no attention has been paid to the question of whether partial beliefs are transparent. In this paper, I clarify the question of whether partial beliefs are transparent. I also consider various attempts to answer the question in the affirmative. To anticipate, my verdict is pessimistic: I argue that such attempts fail. (shrink)

According to a popular interpretation, Carnap’s interpretation of probability had evolved from a logical towards a subjective conception. However Carnap himself insisted that his basic philosophical view of probability was always the same. I address this apparent clash between Carnap's self-identification and the subsequent interpretations of his work. Following its original intentions, I reconstruct inductive logic as an explication. The emerging picture is of a versatile linguistic framework, whose main function is not the discovery of objective logical relations in the (...) object language, but the stipulation of conceptual possibilities. Within this representation, I map out the changes that the project went through. Seen from such an explication-based perspective, inductive logic becomes quite hard to categorize using the standard labels. (shrink)

Attribute spaces are a type of conceptual spaces which Carnap introduced in his late basic system of inductive logic. This article shows how to extend Carnap's use of them into a full model of inductive reasoning with geometrically represented concepts, extending my earlier work. The proposed model draws on Bayesian non-parametric techniques in order to define a probability distribution over the attribute space and a way of updating it with data. The model is another example of conceptual and formal continuity (...) of Carnapian inductive logic with subsequent developments in statistics. (shrink)

Criteria of empirical significance are supposed to state conditions under which reference to an unobservable object or property is “empirically meaningful”. The intended kind of empirical meaningfulness should be necessary for admissibility into the selective contexts of scientific inquiry. I defend Justus’s recent argument that the reasons generally given for rejecting the project of defining a significance criterion are unpersuasive. However, as I show, this project remains wedded to an overly narrow conception of its subject matter. Even the most cutting (...) edge significance criteria identify empirical significance with predictive power, and thereby rule out vocabulary with legitimate scientific functions. In a nutshell, the problem is that there are terms that reduce the computational burden of extracting predictions from theory, and that may therefore be scientifically useful, but that do not produce any additional predictions, and so are ruled scientifically inadmissibility by existing significance criteria. I spell out this objection by specifying terms of this kind that are ruled inadmissible by Creath’s and Schurz’s criteria. Having objected in this way to extant criteria, and to the equation of empirical significance with predictive power in general, I discuss an approach to defining empirical significance that is capable of avoiding my objection and, more ambitiously, that may break the cycle of “punctures and patches” that has plagued the project from the beginning: I gloss Goldfarb and Ricketts’s idea of “case-by-case” delineations of empirically significant terms as the provision of special rather than general explications of the informal concept of empirical significance. (shrink)

I analyse critically what I regard as the most accomplished empiricist account of propensities, namely the long run propensity theory developed by Donald Gillies . Empiricist accounts are distinguished by their commitment to the ‘identity thesis’: the identification of propensities and objective probabilities. These theories are intended, in the tradition of Karl Popper’s influential proposal, to provide an interpretation of probability that renders probability statements directly testable by experiment. I argue that the commitment to the identity thesis leaves empiricist theories, (...) including Gillies’ version, vulnerable to a variant of what is known as Humphreys’ paradox. I suggest that the tension may be resolved only by abandoning the identity thesis, and by adopting instead an understanding of propensities as explanatory properties of chancy objects. (shrink)

The thesis of this article is that the nature of probability is centered on its formal properties, not on any of its standard interpretations. Section 2 is a survey of Bayesian applications. Section 3 focuses on two examples from physics that seem as completely objective as other physical concepts. Section 4 compares the conflict between subjective Bayesians and objectivists about probability to the earlier strident conflict in physics about the nature of force. Section 5 outlines a pragmatic approach to the (...) various interpretations of probability. Finally, Sect. 6 argues that the essential formal nature of probability is expressed in the standard axioms, but more explicit attention should be given to the concept of randomness. (shrink)

The paper suggests a modal predicate logic that deals with classical quantification and modalities as well as intermediate operators, like “most” and “mostly”. Following up the theory of generalized quantifiers, we will understand them as two-placed operators and call them determiners. Quantifiers as well as modal operators will be constructed from them. Besides the classical deduction, we discuss a weaker probabilistic inference “therefore, probably” defined by symmetrical probability measures in Carnap’s style. The given probabilistic inference relates intermediate quantification to singular (...) statements: “Most S are P” does not logically entail that a particular individual S is also P, but it follows that this is probably the case, where the probability is not ascribed to the propositions but to the inference. We show how this system deals with single case expectations while predictions of statistical statements remain generally problematic. (shrink)

In recent decades, the logical study of rational belief dynamics has played an increasingly important role in philosophy. However, the dynamics of concepts such as conceptual learning received comparatively little attention within this debate. This is problematic insofar as the occurrence of conceptual change (especially in the sciences) has been an influential argument against a merely logical analysis of beliefs. Especially Kuhn’s ideas about the incommensurability, i.e., untranslatability, of succeeding theories seem to stand in the way of logical reconstruction. This (...) paper investigates conceptual change as model-changing operations similar to belief revision and relates it to the notion of incommensurability. I consider several versions of conceptual change and discuss their influences on the expressive power, translatability and the potential arising of incommensurability. The paper concludes with a discussion of animal taxonomy in Aristotle’s and Linnaeus’s work. (shrink)

Does the Bayesian theory of confirmation put real constraints on our inductive behavior? Or is it just a framework for systematizing whatever kind of inductive behavior we prefer? Colin Howson (Hume's Problem) has recently championed the second view. I argue that he is wrong, in that the Bayesian apparatus as it is usually deployed does constrain our judgments of inductive import, but also that he is right, in that the source of Bayesianism's inductive prescriptions is not the Bayesian machinery itself, (...) but rather what David Lewis calls the ``Principal Principle''. (shrink)

The no-free-lunch theorems promote a skeptical conclusion that all possible machine learning algorithms equally lack justification. But how could this leave room for a learning theory, that shows that some algorithms are better than others? Drawing parallels to the philosophy of induction, we point out that the no-free-lunch results presuppose a conception of learning algorithms as purely data-driven. On this conception, every algorithm must have an inherent inductive bias, that wants justification. We argue that many standard learning algorithms should rather (...) be understood as model-dependent: in each application they also require for input a model, representing a bias. Generic algorithms themselves, they can be given a model-relative justification. (shrink)

Why is common priors are implicit or explicit in the vast majority of the differential information literature in economics and game theory? Why has the economic community been unwilling, in practice, to accept and actually use the idea of truly personal probabilities in much the same way that it did accept the idea of personal utility functions? After all, in, both the utilities and probabilities are derived separately for each decision maker. Why were the utilities accepted as personal, and the (...) probabilities not? (shrink)

Algorithmic information theory gives an idealized notion of compressibility that is often presented as an objective measure of simplicity. It is suggested at times that Solomonoff prediction, or algorithmic information theory in a predictive setting, can deliver an argument to justify Occam’s razor. This article explicates the relevant argument and, by converting it into a Bayesian framework, reveals why it has no such justificatory force. The supposed simplicity concept is better perceived as a specific inductive assumption, the assumption of effectiveness. (...) It is this assumption that is the characterizing element of Solomonoff prediction and wherein its philosophical interest lies. (shrink)

Robustness is a common platitude: hypotheses are better supported with evidence generated by multiple techniques that rely on different background assumptions. Robustness has been put to numerous epistemic tasks, including the demarcation of artifacts from real entities, countering the “experimenter’s regress,” and resolving evidential discordance. Despite the frequency of appeals to robustness, the notion itself has received scant critique. Arguments based on robustness can give incorrect conclusions. More worrying is that although robustness may be valuable in ideal evidential circumstances (i.e., (...) when evidence is concordant), often when a variety of evidence is available from multiple techniques, the evidence is discordant. †To contact the author, please write to: Jacob Stegenga, Department of Philosophy, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093; e‐mail: [email protected]. (shrink)

Putnam construed the aim of Carnap’s program of inductive logic as the specification of a “universal learning machine,” and presented a diagonal proof against the very possibility of such a thing. Yet the ideas of Solomonoff and Levin lead to a mathematical foundation of precisely those aspects of Carnap’s program that Putnam took issue with, and in particular, resurrect the notion of a universal mechanical rule for induction. In this paper, I take up the question whether the Solomonoff–Levin proposal is (...) successful in this respect. I expose the general strategy to evade Putnam’s argument, leading to a broader discussion of the outer limits of mechanized induction. I argue that this strategy ultimately still succumbs to diagonalization, reinforcing Putnam’s impossibility claim. (shrink)

In this paper I examine a neglected question concerning the centerpiece of Carnap's philosophy: the principle of tolerance. The principle of tolerance states that we are free to devise and adopt any well-defined form of language or linguistic framework we please. A linguistic framework defines framework-internal standards of correct reasoning that guide us in our first-order scientific pursuits. The choice of a linguistic framework, on the other hand, is an ‘external’ question to be settled on pragmatic grounds and so not (...) itself constrained by these standards. However, even if choosing a framework is a practical matter, we would nevertheless expect the process of framework selection to be subject to rational norms. But which norms might those be? And where do they come from? I begin by showing that these questions are crucial to the success of Carnap's entire philosophical project. I then offer a response on behalf of the Carnapian which guarantees the rationality of the process of framework selection, while remaining true to Carnap's firm commitment to tolerance. (shrink)

In this paper I examine the question of logic’s normative status in the light of Carnap’s Principle of Tolerance. I begin by contrasting Carnap’s conception of the normativity of logic with that of his teacher, Frege. I identify two core features of Frege’s position: first, the normative force of the logical laws is grounded in their descriptive adequacy; second, norms implied by logic are constitutive for thinking as such. While Carnap breaks with Frege’s absolutism about logic and hence with the (...) notion that any system of logic should have a privileged claim to correctness, I argue that there is a sense in which Carnap’s framework-relative conception of logical norms has a constitutive role to play: though they are not constitutive for the conceptual activity for thinking, they do nevertheless set the ground rules that make certain forms of scientific inquiry possible in the first place. I conclude that Carnap’s principle of tolerance is tamer than one might have thought and that, despite remaining differences, Frege’s and Carnap’s conceptions of logic have more in common than one might have thought. (shrink)

To consider metaphysical claims a priori and devoid of empirical content, is a rather commonplace received opinion. This paper attempts an exploration of a contemporary philosophical heresy: it is possible to test metaphysical claims if they play an indispensable role in producing empirical success, i.e. novel predictions. To do so one, firstly, needs to express the metaphysical claims employed in the logico-mathematical language of a scientific theory, i.e. to explicate them. Secondly, one should have an understanding of what it is (...) to test and to verify or to falsify a metaphysical claim. Finally, one also need to consider the philosophical practice of testing a metaphysical claim. These three aspects are introduced in this paper and they are illustrated by means of the metaphysical concept of common cause and the principle of the common cause. (shrink)

Disputes between advocates of Bayesians and more orthodox approaches to statistical inference presuppose that Bayesians must regard must regard stopping rules, which play an important role in orthodox statistical methods, as evidentially irrelevant.In this essay, I show that this is not the case and that the stopping rule is evidentially relevant given some Bayesian confirmation measures that have been seriously proposed. However, I show that accepting a confirmation measure of this sort comes at the cost of rejecting two useful ancillaryBayesian (...) principles. (shrink)