Dominance hierarchies are ubiquitous in the societies of human and non-human animals. Evidence from comparative, developmental, and cognitive psychological investigations is presented that show how social dominance hierarchies shaped the evolution of the human mind, and hence, human social institutions. It is argued that the pressures that arise from living in hierarchical social groups laid a foundation of fundamental concepts and cognitive strategies that are crucial to surviving in social dominance hierarchies. These include recognizing and reasoning transitively about dominance relations, (...) fast-track learning of social norms (permissions, prohibitions, and obligations), detecting violations of social norms (cheating), monitoring reciprocal obligations, and reading the intentions of others. (shrink)

Epistemologists and philosophers of science have often attempted to express formally the impact of a piece of evidence on the credibility of a hypothesis. In this paper we will focus on the Bayesian approach to evidential support. We will propose a new formal treatment of the notion of degree of confirmation and we will argue that it overcomes some limitations of the currently available approaches on two grounds: (i) a theoretical analysis of the confirmation relation seen as an extension of (...) logical deduction and (ii) an empirical comparison of competing measures in an experimental inquiry concerning inductive reasoning in a probabilistic setting. (shrink)

Regularity theories of causation assert that causal or nomic notions are to be reduced into “mere” frequencies of particular, non-nomic, co-located qualities and matters of fact. In this essay, I present a critical exploration of Armstrong and Strawson’s explanatory arguments against regularity theories. The shortcomings of these older arguments for nomic realism are identified and a revamped version which is immune to such problems is outlined and defended. I argue that anti-realism suffers substantial disconfirmation due to its comparative inability to (...) unify empirical regularities in the absence of any probabilistic counterweights. I also show that realist theories are much more probable than their anti-realist competitors both individually and in aggregate. This is shown to be the case with even the most humble of observational data. This revamped argument is Bayesian in character; it is immune to the criticisms of Beebee, Everitt, Loewer, and van Fraassen ; and it is empiricist friendly to boot. (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)

Rational analysis (Anderson 1990, 1991a) is an empiricalprogram of attempting to explain why the cognitive system isadaptive, with respect to its goals and the structure of itsenvironment. We argue that rational analysis has two importantimplications for philosophical debate concerning rationality. First,rational analysis provides a model for the relationship betweenformal principles of rationality (such as probability or decisiontheory) and everyday rationality, in the sense of successfulthought and action in daily life. Second, applying the program ofrational analysis to research on human reasoning (...) leads to a radicalreinterpretation of empirical results which are typically viewed asdemonstrating human irrationality. (shrink)

Probabilistic dependence and independence are among the key concepts of Bayesian epistemology. This paper focuses on the study of one specific quantitative notion of probabilistic dependence. More specifically, section 1 introduces Keynes’s coefficient of dependence and shows how it is related to pivotal aspects of scientific reasoning such as confirmation, coherence, the explanatory and unificatory power of theories, and the diversity of evidence. The intimate connection between Keynes’s coefficient of dependence and scientific reasoning raises the question of how Keynes’s coefficient (...) of dependence is related to truth, and how it can be made fruitful for epistemological considerations. This question is answered in section 2 of the paper. Section 3 outlines the consequences the results have for epistemology and the philosophy of science from a Bayesian point of view. (shrink)

We give an analysis of the Monty Hall problem purely in terms of confirmation, without making any lottery assumptions about priors. Along the way, we show the Monty Hall problem is structurally identical to the Doomsday Argument.

This article defends the Doomsday Argument, the Halfer Position in Sleeping Beauty, the Fine-Tuning Argument, and the applicability of Bayesian confirmation theory to the Everett interpretation of quantum mechanics. It will argue that all four problems have the same structure, and it gives a unified treatment that uses simple models of the cases and no controversial assumptions about confirmation or self-locating evidence. The article will argue that the troublesome feature of all these cases is not self-location but selection effects.

Sometimes we learn what the world is like, and sometimes we learn where in the world we are. Are there any interesting differences between the two kinds of cases? The main aim of this article is to argue that learning where we are in the world brings into view the same kind of observation selection effects that operate when sampling from a population. I will first explain what observation selection effects are ( Section 1 ) and how they are relevant (...) to learning where we are in the world ( Section 2 ). I will show how measurements in the Many Worlds Interpretation of quantum mechanics can be understood as learning where you are in the world via some observation selection effect ( Section 3 ). I will apply a similar argument to the Sleeping Beauty Problem ( Section 4 ) and explain what I take the significance of the analogy to be ( Section 5 ). Finally, I will defend the Restricted Principle of Indifference on which some of my arguments depend ( Section 6 ). (shrink)

We appeal to the theory of Bayesian Networks to model different strategies for obtaining confirmation for a hypothesis from experimental test results provided by less than fully reliable instruments. In particular, we consider (i) repeated measurements of a single test consequence of the hypothesis, (ii) measurements of multiple test consequences of the hypothesis, (iii) theoretical support for the reliability of the instrument, and (iv) calibration procedures. We evaluate these strategies on their relative merits under idealized conditions and show some surprising (...) repercussions on the variety-of-evidence thesis and the Duhem-Quine thesis. (shrink)

The decision whether to have a realist or an anti-realist attitude towards scientific hypotheses is interpreted in this paper as a choice that scientists themselves have to face in their work as scientists, rather than as a ‘philosophical’ problem. Scientists’ choices between realism and instrumentalism are interpreted in this paper with the help of two different conceptual tools: a deflationary semantics grounded in the inferentialist approach to linguistic practices developed by some authors, and an epistemic utility function that tries to (...) represent the cognitive preferences of scientists. The first tool is applied to two different questions traditionally related to the problem of scientific realism: the non-miracle argument, and the continuity of reference. The second one is applied to the problem of unconceived alternatives, and to the distinction between realist and instrumentalist attitudes towards scientific hypotheses. (shrink)

The twin goals of this essay are: to investigate a family of cases in which the goal of guaranteed convergence to the truth is beyond our reach; and to argue that each of three strands prominent in contemporary epistemological thought has undesirable consequences when confronted with the existence of such problems. Approaches that follow Reichenbach in taking guaranteed convergence to the truth to be the characteristic virtue of good methods face a vicious closure problem. Approaches on which there is a (...) unique rational doxastic response to any given body of evidence can avoid incoherence only by rendering epistemology a curiously limited enterprise. Bayesian approaches rule out humility about one’s prospects of success in certain situations in which failure is typical. (shrink)

While there has been much discussion about what makes some mathematical proofs more explanatory than others, and what are mathematical coincidences, in this article I explore the distinct phenomenon of mathematical facts that call for explanation. The existence of mathematical facts that call for explanation stands in tension with virtually all existing accounts of “calling for explanation”, which imply that necessary facts cannot call for explanation. In this paper I explore what theoretical revisions are needed in order to accommodate this (...) phenomenon. One of the important upshots is that, contrary to the current consensus, low prior probability is not a necessary condition for calling for explanation. In the final section I explain how the results of this inquiry help us make progress in assessing Hartry Field’s style of reliability argument against mathematical Platonism and against robust realism in other domains of necessary facts, such as ethics. (shrink)

The notion of a severe test has played an important methodological role in the history of science. But it has not until recently been analyzed in any detail. We develop a generally Bayesian analysis of the notion, compare it with Deborah Mayo’s error-statistical approach by way of sample diagnostic tests in the medical sciences, and consider various objections to both. At the core of our analysis is a distinction between evidence and confirmation or belief. These notions must be kept separate (...) if mistakes are to be avoided; combined in the right way, they provide an adequate understanding of severity. Those who think that the weight of the evidence always enables you to choose between hypotheses “ignore one of the factors (the prior probability) altogether, and treat the other (the likelihood) as though it ...meant something other than it actually does. This is the same mistake as is made by someone who has scruples about measuring the arms of a balance (having only a tape measure at his disposal ...), but is willing to assert that the heavier load will always tilt the balance (thereby implicitly assuming, although without admitting it, that the arms are of equal length!). (Bruno de Finetti, Theory of Probability)2. (shrink)

The use of multiple means of determination to “triangulate” on the existence and character of a common phenomenon, object, or result has had a long tradition in science but has seldom been a matter of primary focus. As with many traditions, it is traceable to Aristotle, who valued having multiple explanations of a phenomenon, and it may also be involved in his distinction between special objects of sense and common sensibles. It is implicit though not emphasized in the distinction between (...) primary and secondary qualities from Galileo onward. It is arguably one of several conceptions involved in Whewell’s method of the “consilience of inductions” (Laudan 1971) and is to be found in several places in Peirce. (From M. Brewer and B. Collins, eds., (1981); Scientific Inquiry in the Social Sciences (a festschrift for Donald T. Campbell), San Francisco: Jossey-Bass, pp. 123–162.). (shrink)

Das Thema dieses Bandes ist die Frage, ob die Wissenschaftstheorie eine normative Disziplin ist. Zunächst überrascht die Frage, denn für viele Wissenschaftstheoretiker ist die Antwort ein klares „Ja“; sie halten es für einen Allgemeinplatz, dass die Wissenschaftstheorie ein normatives Unternehmen ist. Bei genauerem Hinsehen stellt sich jedoch heraus, dass die Frage unterschiedliche Interpretationen zulässt, die einzeln diskutiert werden müssen. Dies geschieht im ersten Abschnitt. Im zweiten Abschnitt suchen wir nach möglichen Erklärungen dafür, warum die Wissenschaftstheorie bisher bei dem Projekt, eine (...) allseits akzeptable Methodologie wissenschaftlichen Schließens zu formulieren und zu begründen, so wenig Erfolg hatte. Eine mögliche Erklärung für den ausbleibenden Erfolg ist der Partikularismus, wonach Methoden keine allgemeine, sondern nur eine lokale, bereichsabhängige Gültigkeit haben. Im dritten Abschnitt wollen wir an Hand des Bayesianismus zeigen, dass die Methodologie doch nicht so schlecht da steht, wie es zunächst den Anschein hat. Der Bayesianismus ist für viele Wissenschaftstheoretiker der aussichtsreichste Kandidat für eine allgemeine Theorie induktiven Räsonierens. Wir besprechen seine Vorzüge, stellen aber auch dar, welche Konzessionen er an den Partikularismus machen muss. (shrink)

The idea that there are some facts that call for explanation serves as an unexamined premise in influential arguments for the inexistence of moral or mathematical facts and for the existence of a god and of other universes. This book is the first to offer a comprehensive and critical treatment of this idea. It argues that calling for explanation is a sometimes-misleading figure of speech rather than a fundamental property of facts.

ports the thesis that there exist very many universes. The view has found favor with a number of philosophers such as Derek Parfit ~1998!, J. J. C. Smart ~1989! and Peter van Inwagen ~1993!.1 My purpose is to argue that this is a mistake. First let me set out the issue in more detail.

This article examines the effect of material evidence upon historiographic hypotheses. Through a series of successive Bayesian conditionalizations, I analyze the extended competition among several hypotheses that offered different accounts of the transition between the Bronze Age and the Iron Age in Palestine and in particular to the “emergence of Israel”. The model reconstructs, with low sensitivity to initial assumptions, the actual outcomes including a complete alteration of the scientific consensus. Several known issues of Bayesian confirmation, including the problem of (...) old evidence, the introduction and confirmation of novel theories and the sensitivity of convergence to uncertain and disputed evidence are discussed in relation to the model’s result and the actual historical process. The most important result is that convergence of probabilities and of scientific opinion is indeed possible when advocates of rival hypotheses hold similar judgment about the factual content of evidence, even if they differ sharply in their historiographic interpretation. This speaks against the contention that understanding of present remains is so irrevocably biased by theoretical and cultural presumptions as to make an objective assessment impossible. (shrink)

According to Hempel's paradox, evidence (E) that an object is a nonblack nonraven confirms the hypothesis (H) that every raven is black. According to the standard Bayesian solution, E does confirm H but only to a minute degree. This solution relies on the almost never explicitly defended assumption that the probability of H should not be affected by evidence that an object is nonblack. I argue that this assumption is implausible, and I propose a way out for Bayesians. Introduction Hempel's (...) paradox, the standard Bayesian solution, and the disputed assumption Attempts to defend the disputed assumption Attempts to refute the disputed assumption A way out for Bayesians Conclusion. (shrink)

We review the various explanations that have been offered toaccount for subjects'' behaviour in Wason ''s famous selection task. Weargue that one element that is lacking is a good understanding ofsubjects'' semantics for the key expressions involved, and anunderstanding of how this semantics is affected by the demands the taskputs upon the subject''s cognitive system. We make novel proposals inthese terms for explaining the major content effects of deonticmaterials. Throughout we illustrate with excerpts from tutorialdialogues which motivate the kinds of (...) analysis proposed. Our long termgoal is an integration of the various insights about conditionalreasoning on offer from different cognitive science methodologies. Thepurpose of this paper is to try to draw the attention of logicians andsemanticists to this area, since we believe that empirical investigationof the cognitive processes involved could benefit from semanticanalyses. (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)

Replicability is widely taken to ground the epistemic authority of science. However, in recent years, important published findings in the social, behavioral, and biomedical sciences have failed to replicate, suggesting that these fields are facing a “replicability crisis.” For philosophers, the crisis should not be taken as bad news but as an opportunity to do work on several fronts, including conceptual analysis, history and philosophy of science, research ethics, and social epistemology. This article introduces philosophers to these discussions. First, I (...) discuss precedents and evidence for the crisis. Second, I discuss methodological, statistical, and social-structural factors that have contributed to the crisis. Third, I focus on the philosophical issues raised by the crisis. Finally, I discuss proposed solutions and highlight the gaps that philosophers could focus on. (shrink)

It is widely believed that one should not become more confident that all swans are white and all lions are brave simply by observing white swans. Irrelevant conjunction or “tacking” of a theory onto another is often thought problematic for Bayesianism, especially given the ratio measure of confirmation considered here. It is recalled that the irrelevant conjunct is not confirmed at all. Using the ratio measure, the irrelevant conjunction is confirmed to the same degree as the relevant conjunct, which, it (...) is argued, is ideal: the irrelevant conjunct is irrelevant. Because the past’s really having been as it now appears to have been is an irrelevant conjunct, present evidence confirms theories about past events only insofar as irrelevant conjunctions are confirmed. Hence the ideal of not confirming irrelevant conjunctions would imply that historical claims are not confirmed. Confirmation measures partially realizing that ideal make the confirmation of historical claims by present evidence depend strongly on the (presumably subjective) degree of belief in the irrelevant conjunct. The unusually good behavior of the ratio measure has a bearing on the problem of measure sensitivity. For non-statistical hypotheses, Bayes’ theorem yields a fractional linear transformation in the prior probability, not a linear rescaling, so even the ratio measure arguably does not aptly measure confirmation in such cases. (shrink)

The Quine/Putnam indispensability approach to the confirmation of mathematical theories in recent times has been the subject of significant criticism. In this paper I explore an alternative to the Quine/Putnam indispensability approach. I begin with a van Fraassen-like distinction between accepting the adequacy of a mathematical theory and believing in the truth of a mathematical theory. Finally, I consider the problem of moving from the adequacy of a mathematical theory to its truth. I argue that the prospects for justifying this (...) move are qualitatively worse in mathematics than they are in science. (shrink)

Four experiments investigated the effects of probability manipulations on the indicative four card selection task (Wason, 1966, 1968). All looked at the effects of high and low probability antecedents (p) and consequents (q) on participants' data selections when determining the truth or falsity of a conditional rule, if p then q . Experiments 1 and 2 also manipulated believability. In Experiment 1, 128 participants performed the task using rules with varied contents pretested for probability of occurrence. Probabilistic effects were observed (...) which were partly consistent with some probabilistic accounts but not with non-probabilistic approaches to selection task performance. No effects of believability were observed, a finding replicated in Experiment 2 which used 80 participants with standardised and familiar contents. Some effects in this experiment appeared inconsistent with existing probabilistic approaches. To avoid possible effects of content, Experiments 3 (48 participants) and 4 (20 participants) used abstract material. Both experiments revealed probabilistic effects. In the Discussion we examine the compatibility of these results with the various models of selection task performance. (shrink)

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)

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)

When it is suggested that the fine‐tuning of the universe for life provides evidence for a cosmic designer, the multiple‐universe hypothesis is often presented as an alternative. Some philosophers object that the multiple‐universe hypothesis fails to explain why this universe is fine‐tuned for life. We suggest the “This Universe” objection is no better than the “This Planet” objection. We also fault proponents of the “This Universe” objection for presupposing that we could not have existed in any other universe and that (...) the values of the free parameters of the Universe could have been different. Lastly, we reflect on why fine‐tuning for life needs explaining. (shrink)

Confirmation is commonly identified with positive relevance, E being said to confirm H if and only if E increases the probability of H. Today, analyses of this general kind are usually Bayesian ones that take the relevant probabilities to be subjective. I argue that these subjective Bayesian analyses are irremediably flawed. In their place I propose a relevance analysis that makes confirmation objective and which, I show, avoids the flaws of the subjective analyses. What I am proposing is in some (...) ways a return to Carnap's conception of confirmation, though there are also important differences between my analysis and his. My analysis includes new accounts of what evidence is and of the indexicality of confirmation claims. Finally, I defend my analysis against Achinstein's criticisms of the relevance concept of confirmation. (shrink)

Bayesian confirmation theory offers an explicatum for a pretheoretic concept of confirmation. The “problem of irrelevant conjunction” for this theory is that, according to some people's intuitions, the pretheoretic concept differs from the explicatum with regard to conjunctions involving irrelevant propositions. Previous Bayesian solutions to this problem consist in showing that irrelevant conjuncts reduce the degree of confirmation; they have the drawbacks that (i) they don't hold for all ways of measuring degree of confirmation and (ii) they don't remove the (...) conflict with intuition but merely “soften the impact” (as Fitelson has written). A better solution, which avoids both these drawbacks, is to show that the intuition is wrong. (shrink)

The intuitive Variety of Evidence Thesis states that, ceteris paribus, more varied evidence for a hypothesis confirms it more strongly than less varied evidence. Recent Bayesian analyses have raised serious doubts in its validity. Claveau suggests the existence of a novel type of counter-example to this thesis: a gradual increase in source independence can lead to a decrease in hypothesis confirmation. I show that Claveau’s measure of gradual source independence suffers from two unsuspected types of inconsistencies. I hence put forward (...) a more natural measure of gradual source independence which is not plagued by inconsistencies. Claveau’s counter-examples to the variety of evidence thesis disappear with the measure I suggest. I hence argue that my measure is preferable and that this thesis does at least not seem to be troubled by Claveau’s arguments. (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)

In experimental settings, scientists often “make” new things, in which case the aim is to intervene in order to produce experimental objects and processes—characterized as ‘effects’. In this discussion, I illuminate an important performative function in measurement and experimentation in general: intervention-based experimental production (IEP). I argue that even though the goal of IEP is the production of new effects, it can be informative for causal details in scientific representations. Specifically, IEP can be informative about causal relations in: regularities under (...) study; ‘intervention systems’, which are measurement/experimental systems; and new technological systems. (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)

According to Bayesian epistemology, the epistemically rational agent updates her beliefs by conditionalization: that is, her posterior subjective probability after taking account of evidence X, pnew, is to be set equal to her prior conditional probability pold(·|X). Bayesians can be challenged to provide a justification for their claim that conditionalization is recommended by rationality—whence the normative force of the injunction to conditionalize? There are several existing justifications for conditionalization, but none directly addresses the idea that conditionalization will be epistemically rational (...) if and only if it can reasonably be expected to lead to epistemically good outcomes. We apply the approach of cognitive decision theory to provide a justification for conditionalization using precisely that idea. We assign epistemic utility functions to epistemically rational agents; an agent’s epistemic utility is to depend both upon the actual state of the world and on the agent’s credence distribution over possible states. We prove that, under independently motivated conditions, conditionalization is the unique updating rule that maximizes expected epistemic utility. (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)

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.

Formally-inclined epistemologists often theorize about ideally rational agents--agents who exemplify rational ideals, such as probabilistic coherence, that human beings could never fully realize. This approach can be defended against the well-know worry that abstracting from human cognitive imperfections deprives the approach of interest. But a different worry arises when we ask what an ideal agent should believe about her own cognitive perfection (even an agent who is in fact cognitively perfect might, it would seem, be uncertain of this fact). Consideration (...) of this question reveals an interesting feature of the structure of our epistemic ideals: for agents with limited information, our epistemic ideals turn out to conflict with one another. (shrink)

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)

The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation.

Proponents of Bayesian confirmation theory believe that they have the solution to a significant, recalcitrant problem in philosophy of science. It is the identification of the logic that governs evidence and its inductive bearing in science. That is the logic that lets us say that our catalog of planetary observations strongly confirms Copernicus’ heliocentric hypothesis; or that the fossil record is good evidence for the theory of evolution; or that the 3oK cosmic background radiation supports big bang cosmology. The definitive (...) solution to this problem would be a significant achievement. The problem is of central importance to philosophy of science, for, in the end, what distinguishes science from myth making is that we have good evidence for the content of science, or at least of mature sciences, whereas myths are evidentially ungrounded fictions. The core ideas shared by all versions of Bayesian confirmation theory are, at a good first approximation, that a scientist’s beliefs are or should conform to a probability measure; and that the incorporation of new evidence is through conditionalization using Bayes’ theorem. While the burden of this chapter will be to inventory why critics believe this theory may not be the solution after all, it is worthwhile first to summarize here the most appealing virtues of this simple account. There are three. First, the theory reduces the often nebulous notion of a logic of.. (shrink)