The status of risk factors and disease remains a disputed question in the theory and practice of medicine and healthcare, and so does the related question of delineating disease boundaries. I present a framework based on Bernard Lonergan’s account of emergent probability for differentiating (1) generically distinct levels of systematic function within organisms and between organisms and their environments and (2) the methods of functional, genetic, and statistical investigation. I then argue on this basis that it is possible to understand (...) disease in terms of biological or higher intra-level dysfunction, risk factors—including genetic risk factors—in terms of statistical inter-level conditioning of a given stage or developmental sequence of systematic functioning, and the empirical boundaries of disease in terms of the limits of both functional categorization (from an epistemic standpoint) and upper-level integration of lower-level processes and events (from an ontological standpoint). (shrink)

We compare Karl Popper’s ideas concerning the falsifiability of a theory with similar notions from the part of statistical learning theory known as VC-theory . Popper’s notion of the dimension of a theory is contrasted with the apparently very similar VC-dimension. Having located some divergences, we discuss how best to view Popper’s work from the perspective of statistical learning theory, either as a precursor or as aiming to capture a different learning activity.

For more than 10 years, Ulrich Beck has dominated discussion of risk issues in the social sciences. We argue that Beck's criticisms of the theory and practise of risk analysis are groundless. His understanding of what risk is is badly flawed. His attempt to identify risk and risk perception fails. He misunderstands and distorts the use of probability in risk analysis. His comments about the insurance industry show that he does not understand some of the basics of that industry. And (...) his assertions about the wrongness of allowing acceptable levels of exposure to toxic chemicals do not stand up to scrutiny. Key Words: Beck • risk analysis • risk perception • probability • insurance. (shrink)

We frequently engage in activities that impose a risk of serious harm on innocent others in order to realise trivial benefits for ourselves or third parties. Many moral theories tie the evidence-relative permissibility of engaging in such activities to the size of the risk that an individual agent imposes. I argue that we should move away from such a reliance on quantified individual risks when conceptualising morally permissible risk imposition. Under most circumstances of interest, a conscientious reasoner will identify a (...) gap between the factors they deem potentially relevant to the riskiness of an agent’s behaviour, and the factors they are reasonably able to quantify. This then leads a conscientious reasoner to conclude that they cannot, in good faith, come up with a quantitative risk estimate that is genuinely tailored to the agent’s particular situation. Based on this, I argue that principles of morally permissible risk imposition fail to provide us with practical guidance if they ask us to take into account our agent-specific risks in a quantified manner. I also argue that principles of permissible risk imposition which appeal to quantified individual risks implausibly imply that it is frequently indeterminate whether engaging in some risky activity is morally permissible. For both of these reasons, I contend that principles of morally permissible risk imposition should make no reference to quantified individual risks. They should instead acknowledge that any quantitative estimates that an agent might usefully be able to consider will likely not be tailored to the agent’s idiosyncratic situation. (shrink)

This article surveys several interrelated issues in the metaphysics of chance. First, what is the relationship between the probabilities associated with types of trials (for instance, the chance that a twenty‐eight‐year old develops diabetes before age thirty) and the probabilities associated with individual token trials (for instance, the chance that I develop diabetes before age thirty)? Second, which features of the the world fix the chances: are there objective chances at all, and if so, are there non‐chancy facts on which (...) they supervene? Third, can chance be reconciled with determinism, and if so, how? (shrink)

In this paper I investigate whether the phenomenon of quantum decoherence, the vanishing of interference and detectable entanglement on quantum systems in virtue of interactions with the environment, can be understood as the manifestation of a disposition. I will highlight the advantages of this approach as a realist interpretation of the quantum formalism, and demonstrate how such an approach can benefit from advances in the metaphysics of dispositions. I will also confront some commonalities with and differences to the many worlds (...) interpretation, and address the difficulties induced by quantum non-locality. I conclude that there are ways to deal with these issues and that the proposal hence is an avenue worth pursuing. (shrink)

We argue that quantum theory does not allow for a generalization of the notion of classical conditional probability by showing that the probability defined by the Lüders rule, standardly interpreted in the literature as the quantum-mechanical conditionalization rule, cannot be interpreted as such.

Savage denied that Bayesian decision theory applies in large worlds. This paper proposes a minimal extension of Bayesian decision theory to a large-world context that evaluates an event E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E$$\end{document} by assigning it a number π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document} that reduces to an orthodox probability for a class of measurable events. The Hurwicz criterion evaluates π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document} (...) as a weighted arithmetic mean of its upper and lower probabilities, which we derive from the measurable supersets and subsets of E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E$$\end{document}. The ambiguity aversion reported in experiments on the Ellsberg paradox is then explained by assigning a larger weight to the lower probability of winning than to the upper probability. However, arguments are given here that would make anything but equal weights irrational when using the Hurwicz criterion. The paper continues by embedding the Hurwicz criterion in an extension of expected utility theory that we call expectant utility. (shrink)

As climate policy decisions are decisions under uncertainty, being based on a range of future climate change scenarios, it becomes a crucial question how to set up this scenario range. Failing to comply with the precautionary principle, the scenario methodology widely used in the Third Assessment Report of the International Panel on Climate Change (IPCC) seems to violate international environmental law, in particular a provision of the United Nations Framework Convention on Climate Change. To place climate policy advice on a (...) sound methodological basis would imply that climate simulations which are based on complex climate models had, in stark contrast to their current hegemony, hardly an epistemic role to play in climate scenario analysis at all. Their main function might actually consist in ‘foreseeing future ozone-holes’. In order to argue for these theses, I explain first of all the plurality of climate models used in climate science by the failure to avoid the problem of underdetermination. As a consequence, climate simulation results have to be interpreted as modal sentences, stating what is possibly true of our climate system. This indicates that climate policy decisions are decisions under uncertainty. Two general methodological principles which may guide the construction of the scenario range are formulated and contrasted with each other: modal inductivism and modal falsificationism. I argue that modal inductivism, being the methodology implicitly underlying the third IPCC report, is severely flawed. Modal falsificationism, representing the sound alternative, would in turn require an overhaul of the IPCC practice. (shrink)

Single-case and long-run propensity theories are among the main objective interpretations of probability. There have been various objections to these theories, e.g. that it is difficult to explain why propensities should satisfy the probability axioms and, worse, that propensities are at odds with these axioms, that the explication of propensities is circular and accordingly not informative, and that single-case propensities are metaphysical and accordingly non-scientific. We consider various propensity theories of probability and their prospects in light of these objections. We (...) argue that while propensity theories face challenges, these challenges do not undermine their validity as prospective interpretations of probability in science. (shrink)

This volume focuses on various questions concerning the interpretation of probability and probabilistic reasoning in biology and physics. It is inspired by the idea that philosophers of biology and philosophers of physics who work on the foundations of their disciplines encounter similar questions and problems concerning the role and application of probability, and that interaction between the two communities will be both interesting and fruitful. In this introduction we present the background to the main questions that the volume focuses on (...) and summarize the highlights of the individual contributions. (shrink)

De Finetti is one of the founding fathers of the subjective school of probability. He held that probabilities are subjective, coherent degrees of expectation, and he argued that none of the objective interpretations of probability make sense. While his theory has been influential in science and philosophy, it has encountered various objections. I argue that these objections overlook central aspects of de Finetti’s philosophy of probability and are largely unfounded. I propose a new interpretation of de Finetti’s theory that highlights (...) these aspects and explains how they are an integral part of de Finetti’s instrumentalist philosophy of probability. I conclude by drawing an analogy between misconceptions about de Finetti’s philosophy of probability and common misconceptions about instrumentalism. (shrink)

Cancer research is experiencing ‘paradigm instability’, since there are two rival theories of carcinogenesis which confront themselves, namely the somatic mutation theory and the tissue organization field theory. Despite this theoretical uncertainty, a huge quantity of data is available thanks to the improvement of genome sequencing techniques. Some authors think that the development of new statistical tools will be able to overcome the lack of a shared theoretical perspective on cancer by amalgamating as many data as possible. We think instead (...) that a deeper understanding of cancer can be achieved by means of more theoretical work, rather than by merely accumulating more data. To support our thesis, we introduce the analytic view of theory development, which rests on the concept of plausibility, and make clear in what sense plausibility and probability are distinct concepts. Then, the concept of plausibility is used to point out the ineliminable role played by the epistemic subject in the development of statistical tools and in the process of theory assessment. We then move to address a central issue in cancer research, namely the relevance of computational tools developed by bioinformaticists to detect driver mutations in the debate between the two main rival theories of carcinogenesis. Finally, we briefly extend our considerations on the role that plausibility plays in evidence amalgamation from cancer research to the more general issue of the divergences between frequentists and Bayesians in the philosophy of medicine and statistics. We argue that taking into account plausibility-based considerations can lead to clarify some epistemological shortcomings that afflict both these perspectives. (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)

In Baumann (American Philosophical Quarterly 42: 71–79, 2005) I argued that reflections on a variation of the Monty Hall problem throws a very general skeptical light on the idea of single-case probabilities. Levy (Synthese, forthcoming, 2007) puts forward some interesting objections which I answer here.

This paper presents a puzzle about moral responsibility. The problem is based upon the indeterminacy of relevant reference classes as applied to action. After discussing and rejecting a very tempting response I propose moral contextualism instead, that is, the idea that the truth value of judgments of the form S is morally responsible for x depends on and varies with the context of the attributor who makes that judgment. Even if this reply should not do all the expected work it (...) is a first step. (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 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)

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)

The problem of understanding how statistical inference is, and can be, applied in empirical sciences is important for the methodology of science. It is the objective of this paper to gain a better understanding of the role of statistical methods in scientific modeling. The important question of whether the applicability reduces to the representational properties of statistical models is discussed. It will be shown that while the answer to this question is positive, representation in statistical models is not purely structural. (...) In spite of the fact that representation in statistical models is based on the structural similarities between the statistical model and the empirical systems under study, these relationships are shown to be appropriate for representing relations in the target system by agent function, too. A second aspect of the paper involves the claim that agent-based components of statistical modeling are: a) interpretation of random variables, b) selection of the goal of statistical research, and c) selection of estimator properties. To justify these claims, a preliminary discussion will be presented on the role of statistics in modeling, as in regression and other structural models. This role will be explored and realized using a structural viewpoint. Also the role of statistical estimation in statistical modeling is discussed to explain the representational role of models and the inferential role of the agent in modeling. (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)

Probability theory is important because of its relevance for decision making, which also means: its relevance for the single case. The propensity theory of objective probability, which addresses the single case, is subject to two problems: Humphreys’ problem of inverse probabilities and the problem of the reference class. The paper solves both problems by restating the propensity theory using (an objectivist version of) Pearl’s approach to causality and probability, and by applying a decision-theoretic perspective. Contrary to a widely held view, (...) decision making on the basis of given propensities can proceed without a subjective-probability supplement to propensities. (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)

I define a concept of causal probability and apply it to questions about the role of probability in evolutionary processes. Causal probability is defined in terms of manipulation of patterns in empirical outcomes by manipulating properties that realize objective probabilities. The concept of causal probability allows us see how probabilities characterized by different interpretations of probability can share a similar causal character, and does so in such way as to allow new inferences about relationships between probabilities realized in different chance (...) setups. I clarify relations between probabilities and properties defined in terms of them, and argue that certain widespread uses of computer simulations in evolutionary biology show that many probabilities relevant to evolutionary outcomes are causal probabilities. This supports the claim that higher-level properties such as biological fitness and processes such as natural selection are causal properties and processes, contrary to what some authors have argued. (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)

How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences. However, standard representation theorems make strong rationality assumptions, in particular expected utility maximization. How do we ascribe subjective probability to agents which do not satisfy these strong rationality assumptions? I present a representation theorem with weak rationality assumptions which can be used to define or measure (...) subjective probability for partly irrational agents. (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)

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)

This volume seeks to further the use of formal methods in clarifying one of the central problems of philosophy: that of our free human agency and its place in our indeterministic world. It celebrates the important contributions made in this area by Nuel Belnap, American logician and philosopher. Philosophically, indeterminism and free action can seem far apart, but in Belnap’s work, they are intimately linked. This book explores their philosophical interconnectedness through a selection of original research papers that build forth (...) on Belnap’s logical and philosophical work. Some contributions take the form of critical discussions of Belnap's published work, some develop points made in his publications in new directions, and others provide additional insights on the topics of indeterminism and free action. In Nuel Belnap’s work on indeterminism and free action, three formal frameworks figure prominently: the simple branching histories framework known as "branching time;" its relativistic spatio-temporal extension, branching space-times; and the “seeing to it that” logic of agency. As those frameworks provide the formal background for the contributed papers, the volume introduction gives an overview of the current state of their development. It also introduces case-intensional first order logic, a general intensional logic offering resources for a first-order extension of the mentioned frameworks and a recent research focus of Belnap’s. The volume also contains an extended biographical interview with Nuel Belnap. (shrink)

My dissertation is about Bayesian rationality for non-ideal agents. I show how to derive subjective probabilities from preferences using much weaker rationality assumptions than other standard representation theorems. I argue that non-ideal agents might be uncertain about how they will update on new information and consider two consequences of this uncertainty: such agents should sometimes reject free information and make choices which, taken together, yield sure loss. The upshot is that Bayesian rationality for non-ideal agents makes very different normative demands (...) than ideal Bayesian rationality. (shrink)

I argue that the propensity interpretation of fitness, properly understood, not only solves the explanatory circularity problem and the mismatch problem, but can also withstand the Pandora’s box full of problems that have been thrown at it. Fitness is the propensity (i.e., probabilistic ability, based on heritable physical traits) for organisms or types of organisms to survive and reproduce in particular environments and in particular populations for a specified number of generations; if greater than one generation, “reproduction” includes descendants of (...) descendants. Fitness values can be described in terms of distributions of propensities to produce varying number of offspring and can be modeled for any number of generations using computer simulations, thus providing both predictive power and a means for comparing the fitness of different phenotypes. Fitness is a causal concept, most notably at the population level, where fitness differences are causally responsible for differences in reproductive success. Relative fitness is ultimately what matters for natural selection. (shrink)

This is a three-part exchange on the relationship between belief and credence. It begins with an opening essay by Roger Clarke that argues for the claim that the notion of credence generalizes the notion of belief. Julia Staffel argues in her reply that we need to distinguish between mental states and models representing them, and that this helps us explain what it could mean that belief is a special case of credence. Roger Clarke's final essay reflects on the compatibility of (...) the previously discussed views with dualist and monist interpretations of our mental states and our ways of modeling them. (shrink)

This volume bridges contemporary philosophical conceptions of risk and responsibility and offers an extensive examination of the topic. It shows that risk and responsibility combine in ways that give rise to new philosophical questions and problems. Philosophical interest in the relationship between risk and responsibility continues to rise, due in no small part due to environmental crises, emerging technologies, legal developments, and new medical advances. Despite such interest, scholars are just now working out how to conceive of the links between (...) risk and responsibility, the implications that risks may have to conceptions of responsibility (and vice versa), as well as how such theorizing might play out in applied cases. With contributions from leading scholars, this volume brings together new work examining the interplay between risk and responsibility, exploring its varied philosophical aspects and applications to contemporary issues in law, bioethics, technology, and environmental ethics. Risk and Responsibility in Context will be of interest to philosophers working in ethics, bioethics, philosophy of law, and philosophy of technology, as well as scholars and practitioners in law, health and science management, public policy, and environmental studies. (shrink)

Until now, antirealists have offered sketches of a theory of truth, at best. In this paper, we present a probabilist account of antirealist truth in some formal detail, and we assess its ability to deal with the problems that are standardly taken to beset antirealism.

In the methodology of scientific research programs (MSRP) there are important features on the problem of prediction, especially regarding novel facts. In his approach, Imre Lakatos proposed three different levels on prediction: aim, process, and assessment. Chapter 5 pays attention to the characterization of prediction in the methodology of research programs. Thus, it takes into account several features: (1) its pragmatic characterization, (2) the logical perspective as a proposition, (3) the epistemological component, (4) its role in the appraisal of research (...) programs, and (5) its place as a value for scientific research. -/- The notion of “novel facts” is highly relevant in his conception, where several aspects are involved: the directions of novel facts, the different kinds of novelty, and the transition from six possible options of “novel facts” to four choices. Thereafter, the prediction of novel facts as the criterion of appraisal is considered. On the one hand, this requires analyzing the theoretical, empirical, and heuristic possibilities of appraisal; and, on the other, whether there is an overemphasis on the role of prediction in methodology of scientific research programs. As a consequence, there is an analysis of Lakatos’ criterion of appraisal in MSRP and economics. (shrink)

Bertand’s paradox is a fundamental problem in probability that casts doubt on the applicability of the indifference principle by showing that it may yield contradictory results, depending on the meaning assigned to “randomness”. Jaynes claimed that symmetry requirements solve the paradox by selecting a unique solution to the problem. I show that this is not the case and that every variant obtained from the principle of indifference can also be obtained from Jaynes’ principle of transformation groups. This is because the (...) same symmetries can be mathematically implemented in different ways, depending on the procedure of random selection that one uses. I describe a simple experiment that supports a result from symmetry arguments, but the solution is different from Jaynes’. Jaynes’ method is thus best seen as a tool to obtain probability distributions when the principle of indifference is inconvenient, but it cannot resolve ambiguities inherent in the use of that principle and still depends on explicitly defining the selection procedure. (shrink)

This paper shows that Bertrand's proposed 'solutions' to his own question, which generates his chord paradox, are inapplicable. It uses a simple analogy with cake cutting. The problem is that none of Bertrand's solutions considers all possible cuts. This is no solace for the defenders of the principle of indifference, however, because it emerges that the paradox is harder to solve than previously anticipated.

Bertrand's Paradox Revisited: Why Bertrand's 'Solutions' Are All Inapplicable.

In his Bayesian Nets and Causality, Jon Williamson presents an ‘Objective Bayesian’ interpretation of probability, which he endeavours to distance from the logical interpretation yet associate with the subjective interpretation. In doing so, he suggests that the logical interpretation suffers from severe epistemological problems that do not affect his alternative. In this paper, I present a challenge to his analysis. First, I closely examine the relationship between the logical and ‘Objective Bayesian’ views, and show how, and why, they are highly (...) similar. Second, I argue that the logical interpretation is not manifestly inferior, at least for the reasons that Williamson offers. I suggest that the key difference between the logical and ‘Objective Bayesian’ views is in the domain of the philosophy of logic; and that the genuine disagreement appears to be over Platonism versus nominalism. (shrink)

Sometimes different partitions of the same space each seem to divide that space into propositions that call for equal epistemic treatment. Famously, equal treatment in the form of equal point-valued credence leads to incoherence. Some have argued that equal treatment in the form of equal interval-valued credence solves the puzzle. This paper shows that, once we rule out intervals with extreme endpoints, this proposal also leads to incoherence.

The Indifference Principle, its Paradoxes and Kolmogorov's Probability Space.

The epistemic state of complete ignorance is not a probability distribution. In it, we assign the same, unique, ignorance degree of belief to any contingent outcome and each of its contingent, disjunctive parts. That this is the appropriate way to represent complete ignorance is established by two instruments, each individually strong enough to identify this state. They are the principle of indifference (PI) and the notion that ignorance is invariant under certain redescriptions of the outcome space, here developed into the (...) ‘principle of invariance of ignorance' (PII). Both instruments are so innocuous as almost to be platitudes. Yet the literature in probabilistic epistemology has misdiagnosed them as paradoxical or defective since they generate inconsistencies when conjoined with the assumption that an epistemic state must be a probability distribution. To underscore the need to drop this assumption, I express PII in its most defensible form as relating symmetric descriptions and show that paradoxes still arise if we assume the ignorance state to be a probability distribution. *Received February 2007; revised July 2007. †To contact the author, please write to: Department of History and Philosophy of Science, University of Pittsburgh, Pittsburgh, PA 15260; e-mail: [email protected]. (shrink)

The principle of indifference (hereafter ‘Poi’) says that if one has no more reason to believe A than B (and vice versa ), then one ought not to believe A more than B (nor vice versa ). Many think it’s demonstrably false despite its intuitive plausibility, because of a particular style of thought experiment that generates counterexamples. Roger White ( 2008 ) defends Poi by arguing that its antecedent is false in these thought experiments. Like White I believe Poi, but (...) I find his defense unsatisfactory for two reasons: it appeals to false premises, and it saves Poi only at the expense of something that Poi’s believers likely find just as important. So in this essay I defend Poi by arguing that its antecedent does hold in the relevant thought experiments, and that the further propositions needed to reject Poi are false. I play only defense in this essay; I don’t argue that Poi is true (even though I think it is), but rather that one popular refutation is faulty. In showing this, I also note something that has to my knowledge gone unnoticed: given some innocuous-looking assumptions the denial of Poi is equivalent to a version of epistemic permissivism , and Poi itself is equivalent to a version of epistemic uniqueness. (shrink)

This note has three goals. First, we discuss a presentation of Bertrand's paradox in a recent issue of Philosophia Mathematica, which we believe to be a subtle but important misinterpretation of the problem. We compare claims made about Bertrand with his 1889 Calcul des Probabilités. Second, we use this source to understand Bertrand's true intention in describing what we now call his paradox, comparing it both to another problem he describes in the same section and to a modern treatment. Finally, (...) we briefly consider the importance of knowing when a specific example represents a general case. (shrink)

In this paper, I examine Plantinga’s (1993, 2000, 2011) Evolutionary Argument Against Naturalism (EAAN). While there has been much discussion about Plantinga’s use of probabilities in the argument, I contend that insufficient attention has been paid to the question of how we are to interpret those probabilities. In this paper, I argue that views Plantinga defends elsewhere limit the range of interpretations available to him here. The upshot is that the EAAN is more limited in its applicability than Plantinga alleges.