Many have claimed that epistemic rationality sometimes requires us to have imprecise credal states (i.e. credal states representable only by sets of credence functions) rather than precise ones (i.e. credal states representable by single credence functions). Some writers have recently argued that this claim conflicts with accuracy-centered epistemology, i.e., the project of justifying epistemic norms by appealing solely to the overall accuracy of the doxastic states they recommend. But these arguments are far from decisive. In this essay, we prove some (...) new results, which show that there is little hope for reconciling the rationality of credal imprecision with accuracy-centered epistemology. (shrink)

Bayesians often assume, suppose, or conjecture that for any reasonable explication of the notion of simplicity a prior can be designed that will enforce a preference for hypotheses simpler in just that sense. But it is shown here that there are simplicity-driven approaches to curve-fitting problems that cannot be captured within the orthodox Bayesian framework.

A piece of folklore enjoys some currency among philosophical Bayesians, according to which Bayesian agents that, intuitively speaking, spread their credence over the entire space of available hypotheses are certain to converge to the truth. The goals of the present discussion are to show that kernel of truth in this folklore is in some ways fairly small and to argue that Bayesian convergence-to-the-truth results are a liability for Bayesianism as an account of rationality, since they render a certain sort of (...) arrogance rationally mandatory. (shrink)

The most promising accounts of ontic probability include the Spielraum conception of probabilities, which can be traced back to J. von Kries and H. Poincaré, and the best system account by D. Lewis. This paper aims at comparing both accounts and at combining them to obtain the best of both worlds. The extensions of both Spielraum and best system probabilities do not coincide because the former only apply to systems with a special dynamics. Conversely, Spielraum probabilities may not be part (...) of the best system, e.g. if a broad class of random devices is not often used. Spielraum probabilities have the potential to provide illuminating explanations of frequencies with which outcomes of trials on gambling devices arise. They ultimately fail to account for such frequencies though because they are compatible with frequencies that grossly differ from the values of the respective probabilities. I thus follow recent proposals by M. Strevens and M. Abrams and strengthen the definition of Spielraum probabilities by adding a further condition that restricts some actual frequencies. The resulting account remains limited in scope, but stands objections raised against it in the recent literature: it is neither circular nor based upon arbitrary choices of a measure or of physical variables. Nor does it lack any explanatory power. (shrink)

What Do the Data Tell Us? Justification of scientific theories is a three-place relation between data, theories, and background knowledge. Though this should be a commonplace, many methodologies in science neglect it. The article will elucidate the significance and function of our background knowledge in epistemic justification and their consequences for different scientific methodologies. It is argued that there is no simple and at the same time acceptable statistical algorithm that justifies a given theory merely on the basis of certain (...) data. And even if we think to know the probability of a theory, that does not decide whether we should accept it or not. (shrink)

The quantitative problem of old evidence is the problem of how to measure the degree to which e confirms h for agent A at time t when A regards e as justified at t. Existing attempts to solve this problem have applied the e-difference approach, which compares A's probability for h at t with what probability A would assign h if A did not regard e as justified at t. The quantitative problem has been widely regarded as unsolvable primarily on (...) the grounds that the e-difference approach suffers from intractable problems. Various philosophers have proposed that 'Bayesianism' should be rejected as a research strategy in confirmation theory in part because of the unsolvability of this problem. I develop a version of the e-difference approach which overcomes these problems and possesses various advantages (but also certain limitations). I develop an alternative 'theistic' approach which handles many cases that my development of the e-difference approach does not handle. I conclude with an assessment of the significance of the quantitative problem for Bayesianism and argue that this problem is misunderstood in so far as it is regarded as unsolvable, and in so far as it is regarded as a problem only for Bayesians. (shrink)

The Principle of Indifference, which dictates that we ought to assign two outcomes equal probability in the absence of known reasons to do otherwise, is vulnerable to well-known objections. Nevertheless, the appeal of the principle, and of symmetry-based assignments of equal probability, persists. We show that, relative to a given class of symmetries satisfying certain properties, we are justified in calling certain outcomes equally probable, and more generally, in defining what we call relative probabilities. Relative probabilities are useful in providing (...) a generalized approach to conditionalization. The technique is illustrated by application to simple examples. (shrink)

De Finetti would claim that we can make sense of a draw in which each positive integer has equal probability of winning. This requires a uniform probability distribution over the natural numbers, violating countable additivity. Countable additivity thus appears not to be a fundamental constraint on subjective probability. It does, however, seem mandated by Dutch Book arguments similar to those that support the other axioms of the probability calculus as compulsory for subjective interpretations. These two lines of reasoning can be (...) reconciled through a slight generalization of the Dutch Book framework. Countable additivity may indeed be abandoned for de Finetti's lottery, but this poses no serious threat to its adoption in most applications of subjective probability. Introduction The de Finetti lottery Two objections to equiprobability 3.1 The ‘No random mechanism’ argument 3.2 The Dutch Book argument Equiprobability and relative betting quotients The re-labelling paradox 5.1 The paradox 5.2 Resolution: from symmetry to relative probability Beyond the de Finetti lottery. (shrink)

We introduce a distinction, unnoticed in the literature, between four varieties of objective Bayesianism. What we call ' strong objective Bayesianism' is characterized by two claims, that all scientific inference is 'logical' and that, given the same background information two agents will ascribe a unique probability to their priors. We think that neither of these claims can be sustained; in this sense, they are 'dogmatic'. The first fails to recognize that some scientific inference, in particular that concerning evidential relations, is (...) not (in the appropriate sense) logical, the second fails to provide a non-question-begging account of 'same background information'. We urge that a suitably objective Bayesian account of scientific inference does not require either of the claims. Finally, we argue that Bayesianism needs to be fine-grained in the same way that Bayesians fine-grain their beliefs. (shrink)

The Principle of Indifference is a central element of the ‘classical’ conception of probability, but, for all its strong intuitive appeal, it is widely believed that it faces a devastating objection: the so-called (by Poincare´) ‘Bertrand paradoxes’ (in essence, cases in which the same probability question receives different answers). The puzzle has fascinated many since its discovery, and a series of clever solutions (followed promptly by equally clever rebuttals) have been proposed. However, despite the long-standing interest in this problem, an (...) important assumption, necessary for its generation, has been overlooked. My aim in this paper is to identify this assumption. Since what it claims turns out to be prima facie problematic, I will urge that the burden of proof now shifts to the objectors to PI; they have to provide reasons why this assumption holds. (shrink)

There is a debate in Bayesian confirmation theory between subjective and non-subjective accounts of evidence. Colin Howson has provided a counterexample to our non-subjective account of evidence: the counterexample refers to a case in which there is strong evidence for a hypothesis, but the hypothesis is highly implausible. In this article, we contend that, by supposing that strong evidence for a hypothesis makes the hypothesis more believable, Howson conflates the distinction between confirmation and evidence. We demonstrate that Howson’s counterexample fails (...) for a different pair of hypotheses. (shrink)

The underdetermination thesis poses a threat to rational choice of scientific theories. We discuss two arguments for the thesis. One draws its strength from deductivism together with the existence thesis, and the other is defended on the basis of the failure of a reliable inductive method. We adopt a partially subjective/objective pragmatic Bayesian epistemology of science framework, and reject both arguments for the thesis. Thus, in science we are able to reinstate rational choice called into question by the underdetermination thesis.

Elliott Sober is both an empiricist and an instrumentalist. His empiricism rests on a principle called actualism, whereas his instrumentalism violates this. This violation generates a tension in his work. We argue that Sober is committed to a conflicting methodological imperative because of this tension. Our argument illuminates the contemporary debate between realism and empiricism which is increasingly focused on the application of scientific inference to testing scientific theories. Sober’s position illustrates how the principle of actualism drives a wedge between (...) two conceptions of scientific inference and at the same time brings to the surface a deep conflict between empiricism and instrumentalism. (shrink)

Knowledge of residual perturbations in the orbit of Uranus in the early 1840s did not lead to the refutation of Newton's law of gravitation but instead to the discovery of Neptune in 1846. Karl Popper asserts that this case is atypical of science and that the law of gravitation was at least prima facie falsified by these perturbations. I argue that these assertions are the product of a false, a priori methodological position I call, 'Weak Popperian Falsificationism'. Further, on the (...) evidence the law was not prima facie false and was not generally considered so by astronomers at the time. Many of Popper's commentators presuppose WPF and their views on this case and its implications for scientific rationality and method suffer from this same defect. (shrink)

Despite the consensus promoted by the evidence-based medicine framework, many authors continue to express doubts about the superiority of randomized controlled trials. This paper evaluates four objections targeting the legitimacy, feasibility, and extrapolation problems linked to the experimental practice of random allocation. I argue that random allocation is a methodologically sound and feasible practice contributing to the internal validity of controlled experiments dealing with heterogeneous populations. I emphasize, however, that random allocation is solely designed to ensure the validity of causal (...) inferences at the level of groups. By itself, random allocation cannot enhance test precision, doesn’t contribute to external validity, and limits the applicability of causal claims to individuals. (shrink)

Current debates surrounding the virtues and shortcomings of randomization are symptomatic of a lack of appreciation of the fact that causation can be inferred by two distinct inference methods, each requiring its own, specific experimental design. There is a non-statistical type of inference associated with controlled experiments in basic biomedical research; and a statistical variety associated with randomized controlled trials in clinical research. I argue that the main difference between the two hinges on the satisfaction of the comparability requirement, which (...) is in turn dictated by the nature of the objects of study, namely homogeneous or heterogeneous populations of biological systems. Among other things, this entails that the objection according to which randomized experiments fail to provide better evidence for causation because randomization cannot guarantee comparability is mistaken. (shrink)

Although Bayesian methods are widely used in phylogenetic systematics today, the foundations of this methodology are still debated among both biologists and philosophers. The Bayesian approach to phylogenetic inference requires the assignment of prior probabilities to phylogenetic trees. As in other applications of Bayesian epistemology, the question of whether there is an objective way to assign these prior probabilities is a contested issue. This paper discusses the strategy of constraining the prior probabilities of phylogenetic trees by means of the Principal (...) Principle. In particular, I discuss a proposal due to Velasco (Biol Philos 23:455–473, 2008) of assigning prior probabilities to tree topologies based on the Yule process. By invoking the Principal Principle I argue that prior probabilities of tree topologies should rather be assigned a weighted mixture of probability distributions based on Pinelis’ (P Roy Soc Lond B Bio 270:1425–1431, 2003) multi-rate branching process including both the Yule distribution and the uniform distribution. However, I argue that this solves the problem of the priors of phylogenetic trees only in a weak form. (shrink)

Reichenbach’s use of ‘posits’ to defend his frequentistic theory of probability has been criticized on the grounds that it makes unfalsifiable predictions. The justice of this criticism has blinded many to Reichenbach’s second use of a posit, one that can fruitfully be applied to current debates within epistemology. We show first that Reichenbach’s alternative type of posit creates a difficulty for epistemic foundationalists, and then that its use is equivalent to a particular kind of Jeffrey conditionalization. We conclude that, under (...) particular circumstances, Reichenbach’s approach and that of the Bayesians amount to the same thing, thereby presenting us with a new instance in which chance and credence coincide. (shrink)

We use the method of fixed points to describe a form of probabilistic truth approximation which we illustrate by means of three examples. We then contrast this form of probabilistic truth approximation with another, more familiar kind, where no fixed points are used. In probabilistic truth approximation with fixed points the events are dependent on one another, but in the second kind they are independent. The first form exhibits a phenomenon that we call ‘fading origins’, the second one is subject (...) to a phenomenon known as ‘the washing out of the prior’. We explain that the two phenomena may seem very similar, but are in fact quite different. (shrink)

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian (...) conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality. (shrink)

The Dutch Book argument, like Route 66, is about to turn 80. It is arguably the most celebrated argument for subjective Bayesianism. Start by rejecting the Cartesian idea that doxastic attitudes are ‘all-or-nothing’; rather, they are far more nuanced degrees of belief, for short credences, susceptible to fine-grained numerical measurement. Add a coherentist assumption that the rationality of a doxastic state consists in its internal consistency. The remaining problem is to determine what consistency of credences amounts to. The Dutch Book (...) argument, in a nutshell, says that if your credences do not obey the probability calculus, you are ‘incoherent’—susceptible to sure losses at the hands of a ‘Dutch Bookie’—and thus irrational. Conclusion: rationality requires your credences to obey the probability calculus. And like Route 66, the fortunes of the Dutch Book argument have been mixed. Opinions on the argument are sharply divided. The list of its proponents is quite a ‘who’s who’ of philosophers of probability; they include de Finetti (1937, 1980), Carnap (1950, 1962, and more fully, 1955), Kemeny (1955), Lehman (1955), Shimony (1955), Adams (1962), Mellor (1971), Rosenkrantz (1981), van Fraassen (1989), Jeffrey (1983, 1992). (shrink)

The Humean argument concerning miracles says that one should always think it more likely that anyone who testifies to a miracle is lying or deluded than that the alleged miracle actually occurred, and so should always reject any single report of it. A longstanding and widely accepted objection is that even if this is right, the concurring and non-collusive testimony of many witnesses should make it rational to believe in whatever miracle they all report. I argue that on the contrary, (...) even multiple reports from non-collusive witnesses lack the sort of independence that could make trouble for Hume. (shrink)

According to an infinite frequency principle, it is rational, under certain conditions, to set your credence in an outcome to the limiting frequency of that outcome if the experiment were repeated indefinitely. I argue that most infinite frequency principles are undesirable in at least one of the following ways: accepting the principle would lead you to accept bets with sure losses, the principle gives no guidance in the case of deterministic experiments like coin tosses and the principle relies on a (...) metaphysical property, ‘chanciness’, whose necessary and sufficient conditions are unknown. I show that a frequency principle that is based on the principal principle suffers from problems related to the definition of ‘chance’ or ‘chanciness’, which could lead to all three of the above problems. I introduce a version of the infinite frequency principle that does not rely on a notion of chance or chanciness and does not suffer from any of these problems. (shrink)

I describe a realist, ontologically objective interpretation of probability, "far-flung frequency (FFF) mechanistic probability". FFF mechanistic probability is defined in terms of facts about the causal structure of devices and certain sets of frequencies in the actual world. Though defined partly in terms of frequencies, FFF mechanistic probability avoids many drawbacks of well-known frequency theories and helps causally explain stable frequencies, which will usually be close to the values of mechanistic probabilities. I also argue that it's a virtue rather than (...) a failing of FFF mechanistic probability that it does not define single-case chances, and compare some aspects of my interpretation to a recent interpretation proposed by Strevens. (shrink)

Epistemic theories of objective chance hold that chances are idealised epistemic probabilities of some sort. After giving a brief history of this approach to objective chance, I argue for a particular version of this view, that the chance of an event E is its epistemic probability, given maximal knowledge of the possible causes of E. The main argument for this view is the demonstration that it entails all of the commonly-accepted properties of chance. For example, this analysis entails that chances (...) supervene on the physical facts, that the chance function is an expert probability, that the existence of stable frequencies results from invariant chances in repeated experiments, and that chances are probably close to long-run relative frequencies in repeated experiments. Despite these virtues, epistemic approaches to chance have been neglected in recent decades, on account of their conflict with accepted views about closely related topics such as causation, laws of nature, and epistemic probability. However, existing views on these topics are also very problematic, and I believe that the epistemic view of chance is a key piece of this puzzle that, once in place, allows all the other pieces to fit together into a new and coherent way. I also respond to some criticisms of the epistemic theory that I favour. (shrink)

Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned. Each argument concludes that rationality requires your credences to be probabilities. I contend that each argument is invalid as formulated. In each case there is a mirror-image theorem and (...) a corresponding argument of exactly equal strength that concludes that rationality requires your credences not to be probabilities. Some further consideration is needed to break this symmetry in favour of probabilism. (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)

Some of the most interesting recent work in formal epistemology has focused on developing accuracy-based approaches to justifying Bayesian norms. These approaches are interesting not only because they offer new ways to justify these norms, but because they potentially offer a way to justify all of these norms by appeal to a single, attractive epistemic goal: having accurate beliefs. Recently, Easwaran & Fitelson (2012) have raised worries regarding whether such “all-accuracy” or “purely alethic” approaches can accommodate and justify evidential Bayesian (...) norms. In response, proponents of purely alethic approaches, such as Pettigrew (2013b) and Joyce (2016), have argued that scoring rule arguments provide us with compatible and purely alethic justifications for the traditional Bayesian norms, including evidential norms. In this paper I raise several challenges to this claim. First, I argue that many of the justifications these scoring rule arguments provide are not compatible. Second, I raise worries for the claim that these scoring rule arguments provide purely alethic justifications. Third, I turn to assess the more general question of whether purely alethic justifications for evidential norms are even possible, and argue that, without making some contentious assumptions, they are not. Fourth, I raise some further worries for the possibility of providing purely alethic justifications for content-sensitive evidential norms, like the Principal Principle. (shrink)

One popular approach to statistical mechanics understands statistical mechanical probabilities as measures of rational indifference. Naive formulations of this ``indifference approach'' face reversibility worries - while they yield the right prescriptions regarding future events, they yield the wrong prescriptions regarding past events. This paper begins by showing how the indifference approach can overcome the standard reversibility worries by appealing to the Past Hypothesis. But, the paper argues, positing a Past Hypothesis doesn't free the indifference approach from all reversibility worries. For (...) while appealing to the Past Hypothesis allows it to escape one kind of reversibility worry, it makes it susceptible to another - the Meta-Reversibility Objection. And there is no easy way for the indifference approach to escape the Meta-Reversibility Objection. As a result, reversibility worries pose a steep challenge to the viability of the indifference approach. (shrink)

Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand’s chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum sized state spaces. Articulating the nature of such spaces involves some deep mathematics and that is perhaps why the recent literature on Bertrand’s Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication. At the same time, the (...) philosophy of probability has been left out. In particular, left out entirely are the philosophical ground of the principle of indifference, the nature of the principle itself, the stringent constraint this places on the mathematical representation of the principle needed for its application to continuum sized event spaces, and what these entail for rigour in developing the paradox itself. This book puts the philosophy and its entailments back in and in so doing casts a new light on the paradox, giving original analyses of the paradox, its possible solutions, the source of the paradox, the philosophical errors we make in attempting to solve it and what the paradox proves for the philosophy of probability. The book finishes with the author’s proposed solution—a solution in the spirit of Bertrand’s, indeed—in which an epistemic principle more general than the principle of indifference offers a principled restriction of the domain of the principle of indifference. (shrink)

These are the introduction chapters to the forthcoming collection of essays published by Springer (Synthese Library) and entitled Probabilities, Causes and Propensities in Physics.

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)

Policymakers who seek to make scientifically informed decisions are constantly confronted by scientific uncertainty and expert disagreement. This thesis asks: how can policymakers rationally respond to expert disagreement and scientific uncertainty? This is a work of non-ideal theory, which applies formal philosophical tools developed by ideal theorists to more realistic cases of policymaking under scientific uncertainty. I start with Bayesian approaches to expert testimony and the problem of expert disagreement, arguing that two popular approaches— supra-Bayesianism and the standard model of (...) expert deference—are insufficient. I develop a novel model of expert deference and show how it can deal with many of these problems raised for them. I then turn to opinion pooling, a popular method for dealing with disagreement. I show that various theoretical motivations for pooling functions are irrelevant to realistic policymaking cases. This leads to a cautious recommendation of linear pooling. However, I then show that any pooling method relies on value judgements, that are hidden in the selection of the scoring rule. My focus then narrows to a more specific case of scientific uncertainty: multiple models of the same system. I introduce a particular case study involving hurricane models developed to support insurance decision-making. I recapitulate my analysis of opinion pooling in the context of model ensembles, confirming that my hesitations apply. This motivates a shift of perspective, to viewing the problem as a decision theoretic one. I rework a recently developed ambiguity theory, called the confidence approach, to take input from model ensembles. I show how it facilitates the resolution of the policymaker’s problem in a way that avoids the issues encountered in previous chapters. This concludes my main study of the problem of expert disagreement. In the final chapter, I turn to methodological reflection. I argue that philosophers who employ the mathematical methods of the prior chapters are modelling. Employing results from the philosophy of scientific models, I develop the theory of normative modelling. I argue that it has important methodological conclusions for the practice of formal epistemology, ruling out popular moves such as searching for counterexamples. (shrink)

Scientific realism is a doctrine that was both in and out of fashion several times during the twentieth century. I begin by noting three presuppositions of a succinct characterization of scientific realism offered initially by the foremost critic in the latter part of the century, Bas van Fraassen. The first presupposition is that there is a fundamental distinction to be made between what is “empirical” and what is “theoretical”. The second presupposition is that a genuine scientific realism is committed to (...) their being “a literally true story of what the world is like”. The third presupposition is that there are methods for justifying a belief in the empirical adequacy of a theory which do not also suffice to justify beliefs in its literal truth. Each of these presuppositions raises a number of problems, some of which are quite old and others rather newer. In each case, I briefly review some of the old problems and then elaborate the newer problems. (shrink)

The ?Dimensioned? view analyzes (multiple) realization in terms of compositional relation, and the ?Flat? view analyzes (multiple) realization in terms of causal-functional mechanism. The two different analyses of realization lead to the disagreement about whether realization is transitive. The two views, perhaps not surprisingly, have different consequences on testing for multiple realization, and prescribe different ?reconstructions? for the evidential significance of observation for multiple realization. I examine the differences between the two views on testing for multiple realization within a model-selection (...) theoretical framework. I claim that the model-selection theoretical framework provides a ground to discuss and assess evidence for multiple realization. (shrink)

Tight correlations between mental states and brain states have been observed time and again within the ethology of biologically ingrained animal behaviors, the comparative psychology of animal minds, the evolutionary psychology of mental adaptations, the behavioral genetics of inherited mental traits, the developmental psychology of the maturing mind, the psychopharmacology of mind-altering substances, and cognitive neuroscience more generally. They imply that our mental lives are only made possible because of brain activity—that having a functioning brain is a necessary condition for (...) having conscious experiences. This mind-brain dependence thesis yields predictions that have been spectacularly confirmed by the evidence, whereas its antithesis has been massively disconfirmed—at least so long as it is not formulated so vaguely as to yield no specific empirical consequences at all. Dualists are thus forced to make a difficult choice: either retain a belief in personal survival at the expense of ignoring or dismissing the implications of our best evidence, or accept those implications at the expense of acknowledging that the prospects for personal survival are extremely dim. -/- 1. Introduction: A Probabilistic Argument -- 2. Scientific Reasoning I: Mill’s Methods and Modern Epidemiological Principles - 2.1 When Correlation Indicates Causation -- 3. Scientific Reasoning II: Inference to the Best Explanation, Testability, and Predictive Success - 3.1 Parsimony: Tempering Explanations to Minimize False Beliefs - 3.2 Plausibility: Harmonizing Explanations with Background Knowledge - 3.3 Testability and Confirmation: Checking Hypotheses Against the Data - 3.3.1 Confirmation of the Dependence Thesis from Failed Attempts to Falsify It - 3.3.2 Confirmation of the Dependence Thesis from the Falsification of its Rival - 3.4 Scope: Bringing Disparate Facts Together - 3.5 Fertility: Generating New Lines of Research - 3.6 Overview -- 4. Scientific Reasoning III: Bayesian and Information-Theoretic Approaches - 4.1 Bayesian Probability - 4.2 Bayesian Confirmation Theory - 4.3 A Bayesian Approach to the Dependence and Independence Theses - 4.4 The Probabilistic Price of Ad Hoc Accommodation: Simplicity vs. Goodness of Fit - 4.4.1 Simplicity Reflected in the Likelihood - 4.4.2 Simplicity Reflected in the Prior Probability - 4.5 Prediction vs. Accommodation - 4.6 Bayesian Analysis of the Dependence and Independence Theses -- 5. The Dualist’s Dilemma: Reject Science, or Reject Personal Survival? - 5.1 What’s Left for a Soul to Do? -- 6. Conclusion. (shrink)

A number of cases involving self-locating beliefs have been discussed in the Bayesian literature. I suggest that many of these cases, such as the sleeping beauty case, are entangled with issues that are independent of self-locating beliefs per se. In light of this, I propose a division of labor: we should address each of these issues separately before we try to provide a comprehensive account of belief updating. By way of example, I sketch some ways of extending Bayesianism in order (...) to accommodate these issues. Then, putting these other issues aside, I sketch some ways of extending Bayesianism in order to accommodate self-locating beliefs. Finally, I propose a constraint on updating rules, the "Learning Principle", which rules out certain kinds of troubling belief changes, and I use this principle to assess some of the available options. (shrink)

This book examines the philosophical conception of abductive reasoning as developed by Charles S. Peirce, the founder of American pragmatism. It explores the historical and systematic connections of Peirce's original ideas and debates about their interpretations. Abduction is understood in a broad sense which covers the discovery and pursuit of hypotheses and inference to the best explanation. The analysis presents fresh insights into this notion of reasoning, which derives from effects to causes or from surprising observations to explanatory theories. The (...) author outlines some logical and AI approaches to abduction as well as studies various kinds of inverse problems in astronomy, physics, medicine, biology, and human sciences to provide examples of retroductions and abductions. The discussion covers also everyday examples with the implication of this notion in detective stories, one of Peirce’s own favorite themes. The author uses Bayesian probabilities to argue that explanatory abduction is a method of confirmation. He uses his own account of truth approximation to reformulate abduction as inference which leads to the truthlikeness of its conclusion. This allows a powerful abductive defense of scientific realism. This up-to-date survey and defense of the Peircean view of abduction may very well help researchers, students, and philosophers better understand the logic of truth-seeking. (shrink)

Peter Achinstein has argued at length and on many occasions that the view according to which evidential support is defined in terms of probability-raising faces serious counterexamples and, hence, should be abandoned. Proponents of the positive probabilistic relevance view have remained unconvinced. The debate seems to be in a deadlock. This paper is an attempt to move the debate forward and revisit some of the central claims within this debate. My conclusion here will be that while Achinstein may be right (...) that his counterexamples undermine probabilistic relevance views of what it is for e to be evidence that h, there is still room for a defence of a related probabilistic view about an increase in being supported, according to which, if p > p, then h is more supported given e than it is without e. My argument relies crucially on an insight from recent work on the linguistics of gradable adjectives. (shrink)

Scientific theories are used for a variety of purposes. For example, physical theories such as classical mechanics and electrodynamics have important applications in engineering and technology, and we trust that this results in useful machines, stable bridges, and the like. Similarly, theories such as quantum mechanics and relativity theory have many applications as well. Beyond that, these theories provide us with an understanding of the world and address fundamental questions about space, time, and matter. Here we trust that the answers (...) scientific theories give are reliable and that we have good reason to believe that the features of the world are similar to what the theories say about them. But why do we trust scientific theories, and what counts as evidence in favor of them? (shrink)

It is often loosely said that Ramsey The foundations of mathematics and other logical essays, Routledge and Kegan Paul, Abingdon, pp 156–198, 1931) and de Finetti Studies in subjective probability, Kreiger Publishing, Huntington, 1937) proved that if your credences are inconsistent, then you will be willing to accept a Dutch Book, a wager portfolio that is sure to result in a loss. Of course, their theorems are true, but the claim about acceptance of Dutch Books assumes a particular method of (...) calculating expected utilities given the inconsistent credences. I will argue that there are better ways of calculating expected utilities given a potentially inconsistent credence assignment, and that for a large class of credences—a class that includes many inconsistent examples—these ways are immune to Dutch Books and single-shot domination failures. The crucial move is to replace Finite Additivity with Monotonicity, then \\le P\)) and then calculate expected utilities for positive U via the formula \\, dy\). This shows that Dutch Book arguments for probabilism, the thesis that one’s credences should be consistent, do not establish their conclusion. Finally, I will consider a modified argument based on multi-step domination failure that does better, but nonetheless is not as compelling as the Dutch Book arguments appeared to be. (shrink)