Bayesian confirmation theory is our best formal framework for describing inductive reasoning. The problem of old evidence is a particularly difficult one for confirmation theory, because it suggests that this framework fails to account for central and important cases of inductive reasoning and scientific inference. I show that we can appeal to the fragmentation of doxastic states to solve this problem for confirmation theory. This fragmentation solution is independently well-motivated because of the success of fragmentation in solving other problems. I (...) also argue that the fragmentation solution is preferable to other solutions to the problem of old evidence. These other solutions are already committed to something like fragmentation, but suffer from difficulties due to their additional commitments. If these arguments are successful, Bayesian confirmation theory is saved from the problem of old evidence, and the argument for fragmentation is bolstered by its ability to solve yet another problem. (shrink)

I present a cumulative case for the thesis that we only know propositions that are certain for us. I argue that this thesis can easily explain the truth of eight plausible claims about knowledge: -/- (1) There is a qualitative difference between knowledge and non-knowledge. (2) Knowledge is valuable in a way that non-knowledge is not. (3) Subjects in Gettier cases do not have knowledge. (4) If S knows that P, P is part of S’s evidence. (5) If S knows (...) that P, ~P is epistemically impossible for S. (6) If S knows that P, S can rationally act as if P. (7) If S knows that P, S can rationally stop inquiring whether P. (8) If S knows each of {P1, P2, … Pn}, and competently deduces Q from these propositions, S knows that Q. -/- I then argue that the skeptical costs of this thesis are outweighed by its explanatory power. (shrink)

The principle of epistemic closure is the claim that what is known to follow from knowledge is known to be true. This intuitively plausible idea is endorsed by a vast majority of knowledge theorists. There are significant problems, however, that have to be addressed if epistemic closure – closed knowledge – is endorsed. The present essay locates the problem for closed knowledge in the separation it imposes between knowledge and evidence. Although it might appear that all that stands between knowing (...) the truth of the premises of a valid inference and knowledge of its conclusion is inferring it from the premises, the evidence for each of the premises may jointly count against the conclusion. The intuitive view regarding inferred knowledge says one thing, the evidence says another. One epistemological framework that seems to have the resources to resolve this tension endorses the view that knowledge always requires conclusive evidence. A second framework resolves the tension by limiting the scope of the closure principle. Only inferences drawn directly from propositions contained in the scope of a single knowledge operator are considered closed. The aim of the present essay is to revive the unpopular third option, the idea that knowledge is open. The essay proceeds by arguing that in different ways the two former frameworks only succeed in relocating the problem, not in resolving it. The first framework, the infallibilist view, relocates the problem to a sharp separation between knowledge of the occurrences of events from knowledge of their chance of occurring, a separation leading to several significant additional problems. The fallibilist view, the second framework, in endorsing closure neglects to take into full account the ways in which evidence fails to be transitive. For instance, evidence can count in favor of a conjunction while counting against each of its conjuncts. This fact, which is argued for in the essay on probabilistic as well as non-probabilistic grounds, is used as the foundation of an argument against closed knowledge that can be used as a way to understand several of the most fundamental challenges of epistemology. Not only can an open knowledge view that is based on open evidence resolve all these problems in a simple and natural way, it can also respond to formidable challenges that significantly hinder other open knowledge views. There are good reasons, then, to view both knowledge and evidence as open. (shrink)

The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability.

How should we reason in science? Jan Sprenger and Stephan Hartmann offer a refreshing take on classical topics in philosophy of science, using a single key concept to explain and to elucidate manifold aspects of scientific reasoning. They present good arguments and good inferences as being characterized by their effect on our rational degrees of belief. Refuting the view that there is no place for subjective attitudes in 'objective science', Sprenger and Hartmann explain the value of convincing evidence in terms (...) of a cycle of variations on the theme of representing rational degrees of belief by means of subjective probabilities (and changing them by Bayesian conditionalization). In doing so, they integrate Bayesian inference—the leading theory of rationality in social science—with the practice of 21st century science. Bayesian Philosophy of Science thereby shows how modeling such attitudes improves our understanding of causes, explanations, confirming evidence, and scientific models in general. It combines a scientifically minded and mathematically sophisticated approach with conceptual analysis and attention to methodological problems of modern science, especially in statistical inference, and is therefore a valuable resource for philosophers and scientific practitioners. (shrink)

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

According to a captivating picture, epistemic justification is essentially a matter of epistemic or evidential likelihood. While certain problems for this view are well known, it is motivated by a very natural thought—if justification can fall short of epistemic certainty, then what else could it possibly be? In this paper I shall develop an alternative way of thinking about epistemic justification. On this conception, the difference between justification and likelihood turns out to be akin to the more widely recognised difference (...) between ceteris paribus laws and brute statistical generalisations. I go on to discuss, in light of this suggestion, issues such as classical and lottery-driven scepticism as well as the lottery and preface paradoxes. (shrink)

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)

The likelihood principle (LP) is a core issue in disagreements between Bayesian and frequentist statistical theories. Yet statements of the LP are often ambiguous, while arguments for why a Bayesian must accept it rely upon unexamined implicit premises. I distinguish two propositions associated with the LP, which I label LP1 and LP2. I maintain that there is a compelling Bayesian argument for LP1, based upon strict conditionalization, standard Bayesian decision theory, and a proposition I call the practical relevance principle. In (...) contrast, I argue that there is no similarly compelling argument for or against LP2. I suggest that these conclusions lead to a restrictedly pluralistic view of Bayesian confirmation measures. (shrink)

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

One of the most troubling and persistent challenges for Bayesian Confirmation Theory is the Problem of Old Evidence. The problem arises for anyone who models scientific reasoning by means of Bayesian Conditionalization. This article addresses the problem as follows: First, I clarify the nature and varieties of the POE and analyze various solution proposals in the literature. Second, I present a novel solution that combines previous attempts while making weaker and more plausible assumptions. Third and last, I summarize my findings (...) and put them into the context of the general debate about POE and Bayesian reasoning. (shrink)

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

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. In this paper, we present a model of a new type of intertheoretic relation, called 'Montague Reduction', which is assumed in Montague's framework for the analysis and interpretation of natural language syntax. To motivate the adoption of our new model, we show that this model extends (...) the scope of application of the Nagelian (or related) models, and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework. (shrink)

We argue that concerns about double-counting—using the same evidence both to calibrate or tune climate models and also to confirm or verify that the models are adequate—deserve more careful scrutiny in climate modelling circles. It is widely held that double-counting is bad and that separate data must be used for calibration and confirmation. We show that this is far from obviously true, and that climate scientists may be confusing their targets. Our analysis turns on a Bayesian/relative-likelihood approach to incremental confirmation. (...) According to this approach, double-counting is entirely proper. We go on to discuss plausible difficulties with calibrating climate models, and we distinguish more and less ambitious notions of confirmation. Strong claims of confirmation may not, in many cases, be warranted, but it would be a mistake to regard double-counting as the culprit. 1 Introduction2 Remarks about Models and Adequacy-for-Purpose3 Evidence for Calibration Can Also Yield Comparative Confirmation3.1 Double-counting I3.2 Double-counting II4 Climate Science Examples: Comparative Confirmation in Practice4.1 Confirmation due to better and worse best fits4.2 Confirmation due to more and less plausible forcings values5 Old Evidence6 Doubts about the Relevance of Past Data7 Non-comparative Confirmation and Catch-Alls8 Climate Science Example: Non-comparative Confirmation and Catch-Alls in Practice9 Concluding Remarks. (shrink)

In this paper, we identify a new and mathematically well-defined sense in which the coherence of a set of hypotheses can be truth-conducive. Our focus is not, as usual, on the probability but on the confirmation of a coherent set and its members. We show that, if evidence confirms a hypothesis, confirmation is “transmitted” to any hypotheses that are sufficiently coherent with the former hypothesis, according to some appropriate probabilistic coherence measure such as Olsson’s or Fitelson’s measure. Our findings have (...) implications for scientific methodology, as they provide a formal rationale for the method of indirect confirmation and the method of confirming theories by confirming their parts. (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)

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)

This paper aims to contribute to our understanding of the notion of coherence by explicating in probabilistic terms, step by step, what seem to be our most basic intuitions about that notion, to wit, that coherence is a matter of hanging or fitting together, and that coherence is a matter of degree. A qualitative theory of coherence will serve as a stepping stone to formulate a set of quantitative measures of coherence, each of which seems to capture well the aforementioned (...) intuitions. Subsequently it will be argued that one of those measures does better than the others in light of some more specific intuitions about coherence. This measure will be defended against two seemingly obvious objections. (shrink)

How do multiple reasons combine to support a conclusion about what to do or believe? This question raises two challenges: How can we represent the strength of a reason? How do the strengths of multiple reasons combine? Analogous challenges about confirmation have been answered using probabilistic tools. Can reductive and nonreductive theories of reasons use these tools to answer their challenges? Yes, or more exactly: reductive theories can answer both challenges. Nonreductive theories, with the help of a result in confirmation (...) theory, can answer one, and there are grounds for optimism that they can answer the other. (shrink)

Logical Probability (LP) is strictly distinguished from Statistical Probability (SP). To measure semantic information or confirm hypotheses, we need to use sampling distribution (conditional SP function) to test or confirm fuzzy truth function (conditional LP function). The Semantic Information Measure (SIM) proposed is compatible with Shannon’s information theory and Fisher’s likelihood method. It can ensure that the less the LP of a predicate is and the larger the true value of the proposition is, the more information there is. So the (...) SIM can be used as Popper's information criterion for falsification or test. The SIM also allows us to optimize the true-value of counterexamples or degrees of disbelief in a hypothesis to get the optimized degree of belief, i. e. Degree of Confirmation (DOC). To explain confirmation, this paper 1) provides the calculation method of the DOC of universal hypotheses; 2) discusses how to resolve Raven Paradox with new DOC and its increment; 3) derives the DOC of rapid HIV tests: DOC of “+” =1-(1-specificity)/sensitivity, which is similar to Likelihood Ratio (=sensitivity/(1-specificity)) but has the upper limit 1; 4) discusses negative DOC for excessive affirmations, wrong hypotheses, or lies; and 5) discusses the DOC of general hypotheses with GPS as example. (shrink)

Conditionalization is a widely endorsed rule for updating one’s beliefs. But a sea of complaints have been raised about it, including worries regarding how the rule handles error correction, changing desiderata of theory choice, evidence loss, self-locating beliefs, learning about new theories, and confirmation. In light of such worries, a number of authors have suggested replacing Conditionalization with a different rule — one that appeals to what I’ll call “ur-priors”. But different authors have understood the rule in different ways, and (...) these different understandings solve different problems. In this paper, I aim to map out the terrain regarding these issues. I survey the different problems that might motivate the adoption of such a rule, flesh out the different understandings of the rule that have been proposed, and assess their pros and cons. I conclude by suggesting that one particular batch of proposals, proposals that appeal to what I’ll call “loaded evidential standards”, are especially promising. (shrink)

Hierarchies of evidence are an important and influential tool for appraising evidence in medicine. In recent years, hierarchies have been formally adopted by organizations including the Cochrane Collaboration [1], NICE [2,3], the WHO [4], the US Preventive Services Task Force [5], and the Australian NHMRC [6,7]. The development of such hierarchies has been regarded as a central part of Evidence-Based Medicine, a movement within healthcare which prioritises the use of epidemiological evidence such as that provided by Randomised Controlled Trials. Philosophical (...) work on the methodology of medicine has so far mostly focused on claims about the superiority of RCTs, and hence has largely neglected the questions of what hierarchies are, what assumptions they require, and how they affect clinical practice. This thesis shows that there is great variation in the hierarchies defended and in the interpretations they are, and can be, given. The interpretative assumptions made in using hierarchies are crucial to the content and defensibility of the underlying philosophical commitments concerning evidence and medical practice. Once this variation is been identified, it becomes clear that the little philosophical work that has been done so far affects only some hierarchies, under some interpretations. Modest interpretations offered by La Caze [11], conditional hierarchies like GRADE [12-14], and heuristic approaches such as that defended by Howick et al. [15,16] all survive previous philosophical criticism. This thesis extends previous criticisms by arguing that modest interpretations are so weak as to be unhelpful for clinical practice; that GRADE and similar conditional models omit clinically relevant information, such as information about variation in treatments’ effects and the causes of different responses to therapy; and that heuristic approaches lack the necessary empirical support. The conclusion is that hierarchies in general embed untenable philosophical assumptions: principally that information about average treatment effects backed by high-quality evidence can justify strong recommendations, and that the impact of evidence from individual studies can and should be appraised in isolation. Hierarchies are a poor basis for the application of evidence in clinical practice. The Evidence-Based Medicine movement should move beyond them and explore alternative tools for appraising the overall evidence for therapeutic claims. (shrink)

I argue that so-called 'background knowledge' in confirmation theory has little, if anything, to do with 'knowledge' in the sense of mainstream epistemology. I argue that it is better construed as 'background information', which need not be believed in, justified, or true.

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)

Science depends on judgments of the bearing of evidence on theory. Scientists must judge whether an observation or the result of an experiment supports, disconfirms, or is simply irrelevant to a given hypothesis. Similarly, scientists may judge that, given all the available evidence, a hypothesis ought to be accepted as correct or nearly so, rejected as false, or neither. Occasionally, these evidential judgments can be made on deductive grounds. If an experimental result strictly contradicts a hypothesis, then the truth of (...) the data deductively entails the falsity of the hypothesis. In the great majority of cases, however, the connection between evidence and hypothesis is non-demonstrative, or inductive. In particular, this is so whenever a general hypothesis is inferred to be correct on the basis of the available data, since the truth of the data will not deductively entail the truth of the hypothesis. It always remains possible that the hypothesis is false even though the data are correct. (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)

Several forms of symmetry in degrees of evidential support areconsidered. Some of these symmetries are shown not to hold in general. This has implications for the adequacy of many measures of degree ofevidential support that have been proposed and defended in the philosophical literature.

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

Naive deductive accounts of confirmation have the undesirable consequence that if E confirms H, then E also confirms the conjunction H & X, for any X—even if X is utterly irrelevant to H (and E). Bayesian accounts of confirmation also have this property (in the case of deductive evidence). Several Bayesians have attempted to soften the impact of this fact by arguing that—according to Bayesian accounts of confirmation— E will confirm the conjunction H & X less strongly than E confirms (...) H (again, in the case of deductive evidence). I argue that existing Bayesian “resolutions” of this problem are inadequate in several important respects. In the end, I suggest a new‐and‐improved Bayesian account (and understanding) of the problem of irrelevant conjunction. (shrink)

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

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)

This paper argues that a successful philosophical analysis of models and simulations must accommodate an account of mathematically rigorous results. Such rigorous results may be thought of as genuinely model-specific contributions, which can neither be deduced from fundamental theory nor inferred from empirical data. Rigorous results provide new indirect ways of assessing the success of models and simulations and are crucial to understanding the connections between different models. This is most obvious in cases where rigorous results map different models on (...) to one another. Not only does this put constraints on the extent to which performance in specific empirical contexts may be regarded as the main touchstone of success in scientific modelling, it also allows for the transfer of warrant across different models. Mathematically rigorous results can thus come to be seen as not only strengthening the cohesion between scientific strategies of modelling and simulation, but also as offering new ways of indirect confirmation. (shrink)

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)

Proposals for rigorously explicating the concept of confirmation in probabilistic terms abound. To foster discussions on the formal properties of the proposed measures, recent years have seen the upshot of a number of representation theorems that uniquely determine a confirmation measure based on a number of desiderata. However, the results that have been presented so far focus exclusively on the concept of incremental confirmation. This leaves open the question whether similar results can be obtained for the concept of absolute confirmation. (...) This article closes the gap by providing a representation theorem for absolute confirmation measures. (shrink)

It is known that evidential support, on the Bayesian definition of this notion, is intransitive. According to some, however, the Bayesian definition is too weak to be materially adequate. This paper investigates whether evidential support is transitive on some plausible probabilistic strengthening of that definition. It is shown that the answer is negative. In fact, it will appear that even under conditions under which the Bayesian notion of evidential support is transitive, the most plausible candidate strengthenings are not.

A simple rule of probability revision ensures that the final result ofa sequence of probability revisions is undisturbed by an alterationin the temporal order of the learning prompting those revisions.This Uniformity Rule dictates that identical learning be reflectedin identical ratios of certain new-to-old odds, and is grounded in the oldBayesian idea that such ratios represent what is learned from new experiencealone, with prior probabilities factored out. The main theorem of this paperincludes as special cases (i) Field's theorem on commuting probability-kinematical (...) revisions and (ii) the equivalence of two strategiesfor generalizing Jeffrey's solution to the old evidence problem tothe case of uncertain old evidence and probabilistic new explanation. (shrink)

Ideal agents are role models whose perfection in some normative domain we try to approximate. But which form should this striving take? It is well known that following ideal rules of practical reasoning can have disastrous results for non-ideal agents. Yet, this issue has not been explored with respect to rules of theoretical reasoning. I show how we can extend Bayesian models of ideally rational agents in order to pose and answer the question of whether non-ideal agents should form new (...) degrees of belief in the same way as their ideal counterparts. I demonstrate that the epistemic and the practical case are parallel: following ideal rules does not always lead to optimal outcomes for non-ideal agents. (shrink)

This paper studies the Lockean thesis from the perspective of contemporary epistemic logic. The Lockean thesis states that belief can be defined as ‘sufficiently high degree of belief’. Its main problem is that it gives rise to a notion of belief which is not closed under conjunction. This problem is typical for classical epistemic logic: it is single-agent and static. I argue that from the perspective of contemporary epistemic logic, the Lockean thesis fares much better. I briefly mention that it (...) can successfully be extended from single-agent to multi-agent settings. More importantly, I show that accepting the Lockean thesis (and a more sophisticated version for conditional beliefs) leads to a significant and unexpected unification in the dynamic behavior of (conditional) belief and high (conditional) probability with respect to public announcements. This constitutes a methodological argument in favor of the Lockean thesis. Furthermore, if one accepts Baltag’s Erlangen program for epistemology, this technical observation has even stronger philosophical implications: because belief and high probability display the same dynamic behavior, it is plausible that they are indeed one and the same epistemic notion. (shrink)

Probability ratio and likelihood ratio measures of inductive support and related notions have appeared as theoretical tools for probabilistic approaches in the philosophy of science, the psychology of reasoning, and artificial intelligence. In an effort of conceptual clarification, several authors have pursued axiomatic foundations for these two families of measures. Such results have been criticized, however, as relying on unduly demanding or poorly motivated mathematical assumptions. We provide two novel theorems showing that probability ratio and likelihood ratio measures can be (...) axiomatized in a way that overcomes these difficulties. (shrink)

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. This paper presents a case study of a new type of intertheoretic relation that is inspired by Montague’s analysis of the linguistic syntax-semantics relation. The paper develops a simple model of this relation. To motivate the adoption of our new model, we show that this model (...) extends the scope of application of the Nagelian models and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework. (shrink)

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

Glymour’s theory of bootstrap confirmation is a purely qualitative account of confirmation; it allows us to say that the evidence confirms a given theory, but not that it confirms the theory to a certain degree. The present paper extends Glymour’s theory to a quantitative account and investigates the resulting theory in some detail. It also considers the question how bootstrap confirmation relates to justification.