There is widespread excitement in the literature about the method of arbitrary functions: many take it to show that it is from the dynamics of systems that the objectivity of probabilities emerge. In this paper, I differentiate three ways in which a probability function might be objective, and I argue that the method of arbitrary functions cannot help us show that dynamics objectivise probabilities in any of these senses.

We survey a variety of possible explications of the term “Individual Risk.” These in turn are based on a variety of interpretations of “Probability,” including classical, enumerative, frequency, formal, metaphysical, personal, propensity, chance and logical conceptions of probability, which we review and compare. We distinguish between “groupist” and “individualist” understandings of probability, and explore both “group to individual” and “individual to group” approaches to characterising individual risk. Although in the end that concept remains subtle and elusive, some pragmatic suggestions for (...) progress are made. (shrink)

The Bad-Difference View of disability says, roughly, that disability makes one worse off. The Mere-Difference View of disability says, roughly, that it doesn’t. In recent work, Barnes – a MDV proponent – offers a detailed exposition of the MDV. No BDV proponent has done the same. While many thinkers make it clear that they endorse a BDV, they don’t carefully articulate their view. In this paper, I clarify the nature of the BDV. I argue that its best interpretation is probabilistic (...) and comparative: it is the view that a person is likely to be, all things considered, worse off with a disability than without. As such, Barnes – who criticises the version of the BDV that disability by itself, intrinsically or automatically makes a person worse off – misses an opportunity to attack the most plausible and relevant version of the BDV, and the best version remains unchallenged. (shrink)

ABSTRACT Issues concerning the putative perception/cognition divide are not only age-old, but also resurface in contemporary discussions in various forms. In this paper, I connect a relatively new debate concerning perceptual confidence to the perception/cognition divide. The term ‘perceptual confidence’ is quite common in the empirical literature, but there is an unsettled question about it, namely: are confidence assignments perceptual or post-perceptual? John Morrison in two recent papers puts forward the claim that confidence arises already at the level of perception. (...) In this paper, I first argue that Morrison’s case is unconvincing, and then develop one picture on perceptual precision with the notion of ‘matching profile’ and ‘supervaluation’ : 481–495.), highlighting the fact that this is a vagueness account, which is similar to but importantly different from indeterminacy accounts : 156–184.). With this model in hand, there can be rich resources with which to draw a theoretical line between perception and cognition. (shrink)

Remarkable progress in the mathematics and computer science of probability has led to a revolution in the scope of probabilistic models. In particular, ‘sophisticated’ probabilistic methods apply to structured relational systems such as graphs and grammars, of immediate relevance to the cognitive sciences. This Special Issue outlines progress in this rapidly developing field, which provides a potentially unifying perspective across a wide range of domains and levels of explanation. Here, we introduce the historical and conceptual foundations of the approach, explore (...) how the approach relates to studies of explicit probabilistic reasoning, and give a brief overview of the field as it stands today. (shrink)

In this article, I analyze Quine’s conception of science, which is a radical defence of extensionalism on the grounds that first‐order logic is the most adequate logic for science. I examine some criticisms addressed to it, which show the role of modalities and probabilities in science and argue that Quine’s treatment of probability minimizes the intensional character of scientific language and methods by considering that probability is extensionalizable. But this extensionalizing leads to untenable results in some cases and is not (...) consistent with the fact that Quine himself admits confirmation which includes probability. Quine’s extensionalism does not account for this fact and then seems unrealistic, even if science ought to be extensional in so far as it is descriptive and mathematically expressible. (shrink)

This paper presents and defends a model of religious faith as an epistemic disposition. According to the model, religious faith is a disposition to take certain doxastic attitudes toward propositions of religious significance upon entertaining certain mental states. Three distinct advantages of the model are advanced. First, the model allows for religious faith to explain the presence and epistemic appropriateness of religious belief. Second, the model accommodates a variety of historically significant perspectives concerning the relationships between faith and evidence, faith (...) and volition, and faith and doubt. And, finally, the model offers an appealing account of what unifies religious faith with other kinds of faith. (shrink)

How should an agent revise her epistemic state in the light of doxastic disagreement? The problems associated with answering this question arise under the assumption that an agent’s epistemic state is best represented by her degree of belief function alone. We argue that for modeling cases of doxastic disagreement an agent’s epistemic state is best represented by her confirmation commitments and the evidence available to her. Finally, we argue that given this position it is possible to provide an adequate answer (...) to the question of how to rationally revise one’s epistemic state in the light of disagreement. (shrink)

Any theory of confirmation must answer the following question: what is the purpose of its conception of confirmation for scientific inquiry? In this article, we argue that no Bayesian conception of confirmation can be used for its primary intended purpose, which we take to be making a claim about how worthy of belief various hypotheses are. Then we consider a different use to which Bayesian confirmation might be put, namely, determining the epistemic value of experimental outcomes, and thus to decide (...) which experiments to carry out. Interestingly, Bayesian confirmation theorists rule out that confirmation be used for this purpose. We conclude that Bayesian confirmation is a means with no end. 1 Introduction2 Bayesian Confirmation Theory3 Bayesian Confirmation and Belief4 Confirmation and the Value of Experiments5 Conclusion. (shrink)

In this paper I argue against the claim, recently put forward by some philosophers of biology and evolutionary biologists, that there can be two or more ontologically distinct levels of selection. I show by comparing the fitness of individuals with that of collectives of individuals in the same environment and over the same period of time – as required to decide if one or more levels of selection is acting in a population – that the selection of collectives is a (...) by-product of selection at the individual level; thus, talking about two or more levels of selection represents merely a different perspective on one and the same process. (shrink)

ABSTRACTIn Darwinian Population and Natural Selection, Peter Godfrey-Smith brought the topic of natural selection back to the forefront of philosophy of biology, highlighting different issues surro...

Drift is often characterized in statistical terms. Yet such a purely statistical characterization is ambiguous for it can accept multiple physical interpretations. Because of this ambiguity it is important to distinguish what sorts of processes can lead to this statistical phenomenon. After presenting a physical interpretation of drift originating from the most popular interpretation of fitness, namely the propensity interpretation, I propose a different one starting from an analysis of the concept of drift made by Godfrey-Smith. Further on, I show (...) how my interpretation relates to previous attempts to make sense of the notion of expected value in deterministic setups. The upshot of my analysis is a physical conception of drift that is compatible with both a deterministic and indeterministic world. (shrink)

In recent works, Kind has argued that imagination is a skill, since it possesses the two hallmarks of skill: improvability by practice, and control. I agree with Kind that and are indeed hallmarks of skill, and I also endorse her claim that imagination is a skill in virtue of possessing these two features. However, in this paper, I argue that Kind’s case for imagination’s being a skill is unsatisfactory, since it lacks robust empirical evidence. Here, I will provide evidence for (...) by considering data from mental rotation experiments and for by considering data from developmental experiments. I conclude that imagination is a skill, but there is a further pressing question of how the cognitive architecture of imagination has to be structured to make this possible. I begin by considering how can be implemented sub-personally. I argue that this can be accounted for by positing a selection mechanism which selects content from memory representations to be recombined into imaginings, using Bayesian generation. I then show that such an account can also explain. On this basis, I hold that not only is imagination a skill, but that it is also plausibly implemented sub-personally by a Bayesian selection mechanism. (shrink)

Over the last 40 years or so, there has been an explosion of cultural evolution research in anthropology and archaeology. In each discipline, cultural evolutionists investigate how interactions between individuals translate into group level patterns, with the aim of explaining the diachronic dynamics and diversity of cultural traits. However, while much attention has been given to deterministic processes, we contend that current evolutionary accounts of cultural change are limited because they do not adopt a systematic stochastic approach. First, we show (...) that, in contrast with the intense debates in ecology and population genetics, the importance of stochasticity in evolutionary processes has generated little discussion in the sciences of cultural evolution to date. Second, we speculate on the reasons, both ideological and methodological, why that should be so. Third, we highlight the inadequacy of genetically-inspired stochastic models in the context of cultural evolution modelling, and ask which fundamental stochastic processes might be more relevant to take up. We conclude that the field of cultural evolution would benefit from a stochastic revolution. For that to occur, stochastic models ought to be developed specifically for cultural data and not through a copy-pasting of neutral models from population genetics or ecology. (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)

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)

Promotion is the relation between an act and a desire that obtains when the act advances or serves the desire. Under what conditions does an act promote a desire? Probabilistic accounts of promotion, the most prominent accounts, analyze promotion in terms of an increase in the probability of the desire’s satisfaction. In this paper, we clarify the promotion relation and explain why probabilistic accounts are attractive. Then we identify two questions probabilistic accounts must answer: the Baseline Question and the Interpretation (...) Question. We discuss and reject the three answers to the Baseline Question found in the literature, and explain the challenge future attempts at answering this question will face. Proponents of probabilistic accounts have not adequately addressed the Interpretation Question. We survey three answers to this question, finding each unsatisfactory. We conclude that no satisfactory probabilistic account has yet been offered, and that there are significant hurdles to providing one in the future. (shrink)

The aim of the article is to propose a way to determine to what extent a hypothesis H is confirmed if it has successfully passed a classical significance test. Bayesians have already raised many serious objections against significance testing, but in doing so they have always had to rely on epistemic probabilities and a further Bayesian analysis, which are rejected by classical statisticians. Therefore, I will suggest a purely frequentist evaluation procedure for significance tests that should also be accepted by (...) a classical statistician. This procedure likewise indicates some additional problems of significance tests. In some situations, such tests offer only a weak incremental support of a hypothesis, although an absolute confirmation is necessary, and they overestimate positive results for small effects, since the confirmation of H is often rather marginal in these cases. In specific cases, for example, in cases of ESP-hypotheses, such as precognition, this phenomenon leads too easily to a significant confirmation and can be regarded as a form of the probabilistic falsification fallacy. (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)

When it comes to disagreements about religious, moral or political questions, many people consider a tolerant ‘live-and-let-live’ attitude to be the best reaction toward conflicting opinions. However, many epistemologists are rather skeptical about the epistemic acceptability of such a tolerant attitude. More specifically, the worry is that a tolerant reaction toward recognized disagreement is necessarily epistemically irrational. After setting out this worry in a little more detail, I will present and discuss three different arguments for the epistemic irrationality of a (...) tolerant attitude toward disagreement. I will argue that while all these arguments ultimately fail, they still reveal some substantial limitations to the epistemic adequacy of intellectual tolerance. (shrink)

We propose a new model for forming and revising beliefs about unknown probabilities. To go beyond what is known with certainty and represent the agent’s beliefs about probability, we consider a plausibility map, associating to each possible distribution a plausibility ranking. Beliefs are defined as in Belief Revision Theory, in terms of truth in the most plausible worlds. We consider two forms of conditioning or belief update, corresponding to the acquisition of two types of information: learning observable evidence obtained by (...) repeated sampling from the unknown distribution; and learning higher-order information about the distribution. The first changes only the plausibility map, but leaves the given set of possible distributions essentially unchanged; the second rules out some distributions, thus shrinking the set of possibilities, without changing their plausibility ordering.. We look at stability of beliefs under either of these types of learning, defining two related notions, as well as a measure of the verisimilitude of a given plausibility model. We prove a number of convergence results, showing how our agent’s beliefs track the true probability after repeated sampling, and how she eventually gains in a sense knowledge of that true probability. Finally, we sketch the contours of a dynamic doxastic logic for statistical learning. (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)

One finds intertwined with ideas at the core of evolutionary theory claims about frequencies in counterfactual and infinitely large populations of organisms, as well as in sets of populations of organisms. One also finds claims about frequencies in counterfactual and infinitely large populations—of events—at the core of an answer to a question concerning the foundations of evolutionary theory. The question is this: To what do the numerical probabilities found throughout evolutionary theory correspond? The answer in question says that evolutionary probabilities (...) are “hypothetical frequencies” (including what are sometimes called “long-run frequencies” and “long-run propensities”). In this paper, I review two arguments against hypothetical frequencies. The arguments have implications for the interpretation of evolutionary probabilities, but more importantly, they seem to raise problems for biologists’ claims about frequencies in counterfactual or infinite populations of organisms and sets of populations of organisms. I argue that when properly understood, claims about frequencies in large and infinite populations of organisms and sets of populations are not threatened by the arguments. Seeing why gives us a clearer understanding of the nature of counterfactual and infinite population claims and probability in evolutionary theory. (shrink)

Credences are similar to levels of confidence, represented as a value on the [0,1] interval. This chapter sheds light on questions about credence, including its relationship to full belief, with an eye toward the empirical relevance of credence. First, I’ll provide a brief epistemological history of credence and lay out some of the main theories of the nature of credence. Then, I’ll provide an overview of the main views on how credences relate to full beliefs. Finally, I’ll turn to the (...) empirical, and suggest some ways that cognitive science does and could answer questions about credence, such as what credences one has, how credences relate to beliefs, and the extent to which we can control our credences. (shrink)

Hájek (Erkenntnis 70(2):211–235, 2009) argues that probabilities cannot be the limits of relative frequencies in counterfactual infinite sequences. I argue for a different understanding of these limits, drawing on Norton’s (Philos Sci 79(2):207–232, 2012) distinction between approximations (inexact descriptions of a target) and idealizations (separate models that bear analogies to the target). Then, I adapt Hájek’s arguments to this new context. These arguments provide excellent reasons not to use hypothetical frequencies as idealizations, but no reason not to use them as (...) approximations. (shrink)

Self-locating attitudes and assertions provide a challenge to the received view of mental and linguistic intentionality. In this paper I try to show that the best way to meet this challenge is to adopt relativistic, centred possible worlds accounts for both belief and communication. First, I argue that self-locating beliefs support a centred account of belief. Second, I argue that self-locating utterances support a complementary centred account of communication. Together, these two claims motivate a unified centred conception of belief and (...) communication. (shrink)

The article is a plea for ethicists to regard probability as one of their most important concerns. It outlines a series of topics of central importance in ethical theory in which probability is implicated, often in a surprisingly deep way, and lists a number of open problems. Topics covered include: interpretations of probability in ethical contexts; the evaluative and normative significance of risk or uncertainty; uses and abuses of expected utility theory; veils of ignorance; Harsanyi’s aggregation theorem; population size problems; (...) equality; fairness; giving priority to the worse off; continuity; incommensurability; nonexpected utility theory; evaluative measurement; aggregation; causal and evidential decision theory; act consequentialism; rule consequentialism; and deontology. (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)

Swear words are highly colloquial expressions that have the capacity to signal the speaker's affective states, i.e., to display the speaker's feelings with respect to a certain stimulus. For this reason, swear words are often called 'expressives'. Which linguistic mechanisms allow swear words display affective states, and, more importantly, how can such 'affective content' be characterized in a theory of meaning? Even though research on expressive meaning has produced models that integrate the affective aspects of swear words in a compositional (...) framework, there is extensive evidence that swear words cannot be assigned a single or stable affective interpretation across contexts. For example, even though expletive adjectives (e.g., 'damn'), particularistic insults (e.g., 'bastard') and slurs (e.g., 'wop') typically express (and elicit) negatively valenced affective states, they can also be interpreted positively in some contexts. Thus, inspired in recent developments in formal sociolinguistics, I propose an 'indexical' approach to affective meaning. Under this approach, an affective expression is associated with a set of affective qualities, anyone of which may emerge at a given context depending on the interpreter's prior assumptions about the speaker's affective states and/or relation with the target of the swear word. To define this set, also called 'indexical field', I will use the dimensions pleasure, arousal and dominance, standardly employed in cognitive psychology to characterize and measure affective episodes. In this dissertation, thus, the affective meaning of an expression is given by the set of affective states it typically conveys within a linguistic community, but its interpretation at a given context is established by taking into account the interpreter's prior assumptions about the speaker's affective states and/or attitudes with respect to the target of the affective expression. (shrink)

In this short survey article, I discuss Bell’s theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2) superdeterminism. The issues they raised not only apply to a wide class of no-go theorems about quantum mechanics but are also of general philosophical interest.

Quantum mechanics portrays the universe as involving non-local influences that are difficult to reconcile with relativity theory. By postulating backward causation, retro-causal interpretations of quantum mechanics could circumvent these influences and accordingly reconcile quantum mechanics with relativity. The postulation of backward causation poses various challenges for the retro-causal interpretations of quantum mechanics and for the existing conceptual frameworks for analyzing counterfactual dependence, causation and causal explanation. In this chapter, we analyze the nature of time, causation and explanation in a local, (...) deterministic retro-causal interpretation of quantum mechanics that is inspired by Bohmian mechanics. This interpretation of quantum mechanics offers a deterministic, local ‘hidden-variables’ model of the Einstein-Podolsky-Rosen experiment that poses a new challenge for Reichenbach’s principle of the common cause. In this model, the common cause – the state of particles at the emission from the source – screens off the correlation between its effects – the distant measurement outcomes – but nevertheless fails to explain the correlation between the effects. (shrink)

In this paper, I defend an empiricist account of modality that keeps a substantive account of modal commitment, but throws out the metaphysics. I suggest that if we pair a deflationary attitude toward representation with a substantive account of how scientific models are constructed and put to use, the result is an account that deflates the metaphysics of modal commitment without deflating the content of modal claims.

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

The classical interpretation of probability together with the principle of indifference is formulated in terms of probability measure spaces in which the probability is given by the Haar measure. A notion called labelling invariance is defined in the category of Haar probability spaces; it is shown that labelling invariance is violated, and Bertrand’s paradox is interpreted as the proof of violation of labelling invariance. It is shown that Bangu’s attempt to block the emergence of Bertrand’s paradox by requiring the re-labelling (...) of random events to preserve randomness cannot succeed non-trivially. A non-trivial strategy to preserve labelling invariance is identified, and it is argued that, under the interpretation of Bertrand’s paradox suggested in the paper, the paradox does not undermine either the principle of indifference or the classical interpretation and is in complete harmony with how mathematical probability theory is used in the sciences to model phenomena. It is shown in particular that violation of labelling invariance does not entail that labelling of random events affects the probabilities of random events. It also is argued, however, that the content of the principle of indifference cannot be specified in such a way that it can establish the classical interpretation of probability as descriptively accurate or predictively successful. 1 The Main Claims2 The Elementary Classical Interpretation of Probability3 The General Classical Interpretation of Probability in Terms of Haar Measures4 Labelling Invariance and Labelling Irrelevance5 General Bertrand’s Paradox6 Attempts to Save Labelling Invariance7 Comments on the Classical Interpretation of Probability. (shrink)

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

This paper introduces a new infinite paradox. The main novelty is that it poses problems of causality in a very different form from to the one in use until now. By means of a probabilistic generalization, the paradox shows that the disposition to act according to a specific plan is not always necessary to derive causal effects in Benardete-type contexts involving infinity. It also suggests that, in such cases, the explanation for those causal effects requires a propensity interpretation of probability.

How ought you to evaluate your options if you're uncertain about what's fundamentally valuable? A prominent response is Expected Value Maximisation (EVM)—the view that under axiological uncertainty, an option is better than another if and only if it has the greater expected value across axiologies. But the expected value of an option depends on quantitative probability and value facts, and in particular on value comparisons across axiologies. We need to explain what it is for such facts to hold. Also, EVM (...) is by no means self-evident. We need an argument to defend that it’s true. This book introduces an axiomatic approach to answer these worries. It provides an explication of what EVM means by use of representation theorems: intertheoretic comparisons can be understood in terms of facts about which options are better than which, and mutatis mutandis for intratheoretic comparisons and axiological probabilities. And it provides a systematic argument to the effect that EVM is true: the theory can be vindicated through simple axioms. The result is a formally cogent and philosophically compelling extension of standard decision theory, and original take on the problem of axiological or normative uncertainty. (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.

The principle of indifference has fallen from grace in contemporary philosophy, yet some papers have recently sought to vindicate its plausibility. This paper follows suit. In it, I articulate a version of the principle and provide what appears to be a novel argument in favour of it. The argument relies on a thought experiment where, intuitively, an agent’s confidence in any particular outcome being true should decrease with the addition of outcomes to the relevant space of possible outcomes. Put simply: (...) the greater the number of outcomes, the weaker your confidence should be in any one of those outcomes. The argument holds that this intuition favours the principle of indifference. I point out that, in contrast, the intuition is also incompatible with a major alternative to the principle which prescribes imprecise credences: the so-called wide interval view. Consequently, the argument may also be seen as an argument against the wide interval view. (shrink)

Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random phenomena are interpreted as classical probabilities, and this interpretation of equally likely chance outcomes is applied to statistical inference using urn models. These are used to address Bayesian criticisms of frequentist methods. Recent descriptions of p-values, confidence intervals, and power are viewed through the lens of classical probability (...) based on a single random sample from the population. (shrink)

This paper critically assesses existing accounts of the nature of difficulty, finds them wanting, and proposes a new account. The concept of difficulty is routinely invoked in debates regarding degrees of moral responsibility, and the value of achievement. Until recently, however, there has not been any sustained attempt to provide an account of the nature of difficulty itself. This has changed with Gwen Bradford’s Achievement, which argues that difficulty is a matter of how much intense effort is expended. But while (...) this account captures something important about the relationship between difficulty and achievement, it fails to account for the fact that part of what makes achievements great is that they are difficult in a moderately agent-neutral kind of way. Nor is this thought captured by any other extant account. I argue that to fill this gap we should think of difficulty in terms of low probability of success. (shrink)

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

The view that chances are relative frequencies of occurrence within actual, finite reference classes has long been written off. I argue that it ought to be reconsidered. Focusing on non-deterministic chance, I defend a version of finite frequentism in which reference classmates are required to have qualitatively identical pasts. While my analysis can evade or resist several standard objections, it has a counterintuitive consequence: non-trivial chances entail the existence of past light cones that are perfect intrinsic duplicates. In mitigation, I (...) argue that our scientific knowledge is consistent with the hypothesis that there are many such duplicates in the actual world. Moreover, my analysis has some striking advantages: it is simple, it is metaphysically undemanding, and it makes possible a satisfying explanation of the chance–credence connection. 1 Introduction2 Target3 Sketch and Skirmish4 Articulation5 Standard Worries5.1 Frequency tolerance5.2 Leibniz’s dictum5.3 Single case chance5.4 Missing values5.5 Explanation5.6 Counterfactual chances6 Chance and Credence6.1 An indefeasible indifference intuition6.2 Articulating the credence principle6.3 Appraising the credence principle7 Confirmation8 Laws9 Summing Up. (shrink)

Explaining the emergence of stochastic irreversible macroscopic dynamics from time-reversible deterministic microscopic dynamics is one of the key problems in philosophy of physics. The Mori-Zwanzig projection operator formalism, which is one of the most important methods of modern nonequilibrium statistical mechanics, allows for a systematic derivation of irreversible transport equations from reversible microdynamics and thus provides a useful framework for understanding this issue. However, discussions of the MZ formalism in philosophy of physics tend to focus on simple variants rather than (...) on the more sophisticated ones used in modern physical research. In this work, I will close this gap by studying the problems of probability and irreversibility using the example of Grabert’s time-dependent projection operator formalism. This allows to better understand how general proposals for understanding probability in statistical mechanics, namely quantum approaches and almost-objective probabilities, can be accomodated in the MZ formalism. Moreover, I will provide a detailed physical analysis, based on the MZ formalism, of various proposals from the philosophical literature, such as Robertson’s theory of justifying coarse-graining via autonomous macrodynamics, Myrvold’s problem of explaining autonomous macrodynamics, and Wallace’s simple dynamical conjecture. (shrink)