The paper’s target is the historically influential betting interpretation of subjective probabilities due to Ramsey and de Finetti. While there are several classical and well-known objections to this interpretation, the paper focuses on just one fundamental problem: There is a sense in which degrees of belief cannot be interpreted as betting rates. The reasons differ in different cases, but there’s one crucial feature that all these cases have in common: The agent’s degree of belief in a proposition A does not (...) coincide with her degree of belief in a conditional that A would be the case if she were to bet on A, where the belief in this conditional itself is conditioned on the supposition that the agent will have an opportunity to make such a bet. Even though the two degrees of belief sometimes can coincide (they will coincide in those cases when the bet has no expected causal bearings on the proposition A and the opportunity to bet have no evidential bearings on that proposition), it is the latter belief rather than the former that guides the agent’s rational betting behaviour. The reason is that this latter belief takes into consideration potential interferences that bet opportunities and betting itself might create with regard to the proposition to be betted on. It is because of this interference problem that the agent’s degree of belief in A cannot be interpreted as her betting rate for A. (shrink)

Enjoying great popularity in decision theory, epistemology, and philosophy of science, Bayesianism as understood here is fundamentally concerned with epistemically ideal rationality. It assumes a tight connection between evidential probability and ideally rational credence, and usually interprets evidential probability in terms of such credence. Timothy Williamson challenges Bayesianism by arguing that evidential probabilities cannot be adequately interpreted as the credences of an ideal agent. From this and his assumption that evidential probabilities cannot be interpreted as the actual credences of human (...) agents either, he concludes that no interpretation of evidential probabilities in terms of credence is adequate. I argue to the contrary. My overarching aim is to show on behalf of Bayesians how one can still interpret evidential probabilities in terms of ideally rational credence and how one can maintain a tight connection between evidential probabilities and ideally rational credence even if the former cannot be interpreted in terms of the latter. By achieving this aim I illuminate the limits and prospects of Bayesianism. (shrink)

To answer the question of whether mathematics needs new axioms, it seems necessary to say what role axioms actually play in mathematics. A first guess is that they are inherently obvious statements that are used to guarantee the truth of theorems proved from them. However, this may neither be possible nor necessary, and it doesn’t seem to fit the historical facts. Instead, I argue that the role of axioms is to systematize uncontroversial facts that mathematicians can accept from a wide (...) variety of philosophical positions. Once the axioms are generally accepted, mathematicians can expend their energies on proving theorems instead of arguing philosophy. Given this account of the role of axioms, I give four criteria that axioms must meet in order to be accepted. Penelope Maddy has proposed a similar view in Naturalism in Mathematics, but she suggests that the philosophical questions bracketed by adopting the axioms can in fact be ignored forever. I contend that these philosophical arguments are in fact important, and should ideally be resolved at some point, but I concede that their resolution is unlikely to affect the ordinary practice of mathematics. However, they may have effects in the margins of mathematics, including with regards to the controversial “large cardinal axioms” Maddy would like to support. (shrink)

Probability and logic are two branches of mathematics that have important philosophical applications. This article discusses several areas of intersection between them. Several involve the role for probability in giving semantics for logic or the role of logic in governing assignments of probability. Some involve probability over non-classical logic or self-referential sentences.

Both I and Belnap, motivated the "Belnap-Dunn 4-valued Logic" by talk of the reasoner being simply "told true" (T) and simply "told false" (F), which leaves the options of being neither "told true" nor "told false" (N), and being both "told true" and "told false" (B). Belnap motivated these notions by consideration of unstructured databases that allow for negative information as well as positive information (even when they conflict). We now experience this on a daily basis with the Web. But (...) the 4-valued logic is deductive in nature, and its matrix is discrete: there are just four values. In this paper I investigate embedding the 4-valued logic into a context of probability. Jøsang's Subjective Logic introduced uncertainty to allow for degrees of belief, disbelief, and uncertainty. We extend this so as to allow for two kinds of uncertainty— that in which the reasoner has too little information (ignorance) and that in which the reasoner has too much information (conflicted). Jøsang's "Opinion Triangle" becomes an "Opinion Tetrahedron" and the 4-values can be seen as its vertices. I make/prove various observations concerning the relation of non-classical "probability" to non-classical logic. (shrink)

I argue that a pragmatic scepticism about metaphysical modality is a perfectly reasonable position to maintain. I then illustrate the difficulties and limitations associated with some strategies for defeating such scepticism. These strategies appeal to associations between metaphysical modality and the following: objective probability, counterfactuals and distinctive explanatory value.

The anti-causal prophecies of last century have been disproved. Causality is neither a ‘relic of a bygone’ nor ‘another fetish of modern science’; it still occupies a large part of the current debate in philosophy and the sciences. This investigation into causal modelling presents the rationale of causality, i.e. the notion that guides causal reasoning in causal modelling. It is argued that causal models are regimented by a rationale of variation, nor of regularity neither invariance, thus breaking down the dominant (...) Human paradigm. The notion of variation is shown to be embedded in the scheme of reasoning behind various causal models: e.g. Rubin’s model, contingency tables, and multilevel analysis. It is also shown to be latent – yet fundamental – in many philosophical accounts. Moreover, it has significant consequences for methodological issues: the warranty of the causal interpretation of causal models, the levels of causation, the characterisation of mechanisms, and the interpretation of probability. This book offers a novel philosophical and methodological approach to causal reasoning in causal modelling and provides the reader with the tools to be up to date about various issues causality rises in social science. (shrink)

In this contribution, I comment on Raffaella Campaner’s defense of explanatory pluralism in psychiatry (in this volume). In her paper, Campaner focuses primarily on explanatory pluralism in contrast to explanatory reductionism. Furthermore, she distinguishes between pluralists who consider pluralism to be a temporary state on the one hand and pluralists who consider it to be a persisting state on the other hand. I suggest that it would be helpful to distinguish more than those two versions of pluralism – different understandings (...) of explanatory pluralism both within philosophy of science and psychiatry – namely moderate/temporary pluralism, anything goes pluralism, isolationist pluralism, integrative pluralism and interactive pluralism. Next, I discuss the pros and cons of these different understandings of explanatory pluralism. Finally, I raise the question of how to implement or operationalize explanatory pluralism in scientific practice; how to structure the “genuine dialogue” or shape “the pluralistic attitude” Campaner is referring to. As tentative answers, I explore a question-based framework for explanatory pluralism as well as social-epistemological procedures for interaction among competing approaches and explanations. (shrink)

My goal, in this paper, is to critically assess the categorization of “interpretations of probability” as it appears in the literature. In some sources only Carnap’s treatment of probability is understood to be the best example of “logical” probability. This is surprisingly narrow and I will here suggest otherwise. In fact, I believe that certain forms of Baysianism should also be included in the logical camp.

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...) of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

There are two central questions concerning probability. First, what are its formal features? That is a mathematical question, to which there is a standard, widely (though not universally) agreed upon answer. This answer is reviewed in the next section. Second, what sorts of things are probabilities---what, that is, is the subject matter of probability theory? This is a philosophical question, and while the mathematical theory of probability certainly bears on it, the answer must come from elsewhere. To see why, observe (...) that there are many things in the world that have the mathematical structure of probabilities---the set of measurable regions on the surface of a table, for example---but that one would never mistake for being probabilities. So probability is distinguished by more than just its formal characteristics. The bulk of this essay will be taken up with the central question of what this “more” might be. (shrink)

When members of a group doxastically disagree with each other, decisions in the group are often hard to make. The members are supposed to find an epistemic compromise. How do members of a group reach a rational epistemic compromise on a proposition when they have different (rational) credences in the proposition? I answer the question by suggesting the Fine-Grained Method of Aggregation, which is introduced in Brössel and Eder 2014 and is further developed here. I show how this method faces (...) challenges of the standard method of aggregation, Weighted Straight Averaging, in a successful way. One of the challenges concerns the fact that Weighted Straight Averaging does not respect the evidential states of agents. Another challenge arises because Weighted Straight Averaging does not account for synergetic effects. (shrink)

This thesis has two goals. Firstly, we consider the problem of model selection for the purposes of prediction. In modern science predictive mathematical models are ubiquitous and can be found in such diverse fields as weather forecasting, economics, ecology, mathematical psychology, sociology, etc. It is often the case that for a given domain of inquiry there are several plausible models, and the issue then is how to discriminate between them – this is the problem of model selection. We consider approaches (...) to model selection that are used in classical [also known as frequentist] statistics, and fashionable in recent years methods of Akaike Information Criterion [AIC] and Bayes Information Criterion [BIC], the latter being a part of a broader Bayesian approach. We show the connection between AIC and BIC, and provide comparison of performance of these methods. Secondly, we consider some philosophical arguments that arise within the setting of the model selection approaches investigated in the first part. These arguments aim to provide counterexamples to the epistemic thesis of scientific realism, viz., that predictively successful scientific theories are approximately true, and to the idea that truth and predictive accuracy go together. We argue for the following claims: 1) that none of the criticisms brought forward in the philosophical literature against the AIC methodology are devastating, and AIC remains a viable method of model selection; 2) that the BIC methodology likewise survives the numerous criticisms; 3) that the counterexamples to scientific realism that ostensibly arise within the framework of model selection are flawed; 4) that in general the model selection methods discussed in this thesis are neutral with regards to the issue of scientific realism; 5) that a plurality of methodologies should be applied to the problem of model selection with full awareness of the foundational issues that each of these methodologies has. (shrink)

The objective of this thesis is to present a naturalised metaphysics of information, or to naturalise information, by way of deploying a scientific metaphysics according to which contingency is privileged and a-priori conceptual analysis is excluded (or at least greatly diminished) in favour of contingent and defeasible metaphysics. The ontology of information is established according to the premises and mandate of the scientific metaphysics by inference to the best explanation, and in accordance with the idea that the primacy of physics (...) constraint accommodates defeasibility of theorising in physics. This metametaphysical approach is used to establish a field ontology as a basis for an informational structural realism. This is in turn, in combination with information theory and specifically mathematical and algorithmic theories of information, becomes the foundation of what will be called a source ontology, according to which the world is the totality of information sources. Information sources are to be understood as causally induced configurations of structure that are, or else reduce to and/or supervene upon, bounded (including distributed and non-contiguous) regions of the heterogeneous quantum field (all quantum fields combined) and fluctuating vacuum, all in accordance with the above-mentioned quantum field-ontic informational structural realism (FOSIR.) Arguments are presented for realism, physicalism, and reductionism about information on the basis of the stated contingent scientific metaphysics. In terms of philosophical argumentation, realism about information is argued for primarily by way of an indispensability argument that defers to the practice of scientists and regards concepts of information as just as indispensable in their theories as contingent representations of structure. Physicalism and reductionism about information are adduced by way of the identity thesis that identifies the substance of the structure of ontic structural realism as identical to selections of structure existing in re to combined heterogeneous quantum fields, and to the total heterogeneous quantum field comprised of all such fields. Adjunctly, an informational statement of physicalism is arrived at, and a theory of semantic information is proposed, according to which information is intrinsically semantic and alethically neutral. (shrink)

In this paper I address the question of whether the probabilities that appear in models of stochastic gene expression are objective or subjective. I argue that while our best models of the phenomena in question are stochastic models, this fact should not lead us to automatically assume that the processes are inherently stochastic. After distinguishing between models and reality, I give a brief introduction to the philosophical problem of the interpretation of probability statements. I argue that the objective vs. subjective (...) distinction is a false dichotomy and is an unhelpful distinction in this case. Instead, the probabilities in our models of gene expression exhibit standard features of both objectivity and subjectivity. (shrink)

My dissertation explores the ways in which Rudolf Carnap sought to make philosophy scientific by further developing recent interpretive efforts to explain Carnap’s mature philosophical work as a form of engineering. It does this by looking in detail at his philosophical practice in his most sustained mature project, his work on pure and applied inductive logic. I, first, specify the sort of engineering Carnap is engaged in as involving an engineering design problem and then draw out the complications of design (...) problems from current work in history of engineering and technology studies. I then model Carnap’s practice based on those lessons and uncover ways in which Carnap’s technical work in inductive logic takes some of these lessons on board. This shows ways in which Carnap’s philosophical project subtly changes right through his late work on induction, providing an important corrective to interpretations that ignore the work on inductive logic. Specifically, I show that paying attention to the historical details of Carnap’s attempt to apply his work in inductive logic to decision theory and theoretical statistics in the 1950s and 1960s helps us understand how Carnap develops and rearticulates the philosophical point of the practical/theoretical distinction in his late work, offering thus a new interpretation of Carnap’s technical work within the broader context of philosophy of science and analytical philosophy in general. (shrink)

In October 2009 I decided to stop doing philosophy. This meant, in particular, stopping work on the book that I was writing on the nature of probability. At that time, I had no intention of making my unfinished draft available to others. However, I recently noticed how many people are reading the lecture notes and articles on my web site. Since this draft book contains some important improvements on those materials, I decided to make it available to anyone who wants (...) to read it. That is what you have in front of you. The account of Laplace’s theory of probability in Chapter 4 is very different to what I said in my seminar lectures, and also very different to any other account I have seen; it is based on a reading of important texts by Laplace that appear not to have been read by other commentators. The discussion of von Mises’ theory in Chapter 7 is also new, though perhaps less revolutionary. And the final chapter is a new attempt to come to grips with the popular, but amorphous, subjective theory of probability. The material in the other chapters has mostly appeared in previous articles of mine but things are sometimes expressed differently here. I would like to say again that this is an incomplete draft of a book, not the book I would have written if I had decided to finish it. It no doubt contains poor expressions, it may contain some errors or inconsistencies, and it doesn’t cover all the theories that I originally intended to discuss. Apart from this preface, I have done no work on the book since October 2009. (shrink)

You and I lead different lives. While we share a society and a world, our existence is separate from one another. You and I matter individually, by ourselves. My dissertation is about this simple thought. I argue that this simple insight, the separateness of persons, tells us something fundamental about morality. My dissertation seeks to answer how the separateness of persons matters. I develop a precise view of the demands of the separateness of persons. The separateness of persons imposes both (...) a requirement on the justification of first-order moral principles as well as a requirement on the content of first-order moral principles. In specifying these demands, I argue that respecting the separateness of persons requires taking into consideration each person’s point of view separately. This requires taking into account the moral relations in which individuals stand to one another. I make use of this relational understanding of the separateness of persons to advance various debates in moral and political philosophy. I argue for a framework to assess to which extent the veil of ignorance can be reconciled with the separateness of persons. I also argue for a new view on the ethics of risk which is a form of contractualism that discounts risks only by their objective risk. Furthermore, I argue for a new solution to the problem of aggregation that is skeptical of aggregation and can set plausible limits to aggregation. Lastly, I provide a new relational agent-based justification for deontological constraints. In addition to answering how the separateness of persons matters, I defend the separateness of persons against challenges. Most importantly, I argue that the importance of the separateness of persons is not undermined even if we believe that our personal identity, i.e. whether we persist as the same person, is unimportant. (shrink)

The aim of this thesis dissertation is to propose a novel position in the debate on scientific realism, modal empiricism, and to show its fruitfulness when it comes to interpreting the cognitive content of scientific theories. Modal empiricism is an empiricist position, according to which the aim of science is to produce empirically adequate theories rather than true theories. However, it suggests adopting a broader comprehension of experience than traditional versions of empiricism, through a commitment to natural modalities. Following modal (...) empiricism, there are possibilities in nature, and constraints on what is possible, and a theory is empirically adequate if it correctly delimits the range of possible experiences. The position rests on a situated and pragmatic conception of natural modalities and of empirical confrontation. We claim that it can do justice to the empirical success of science, while not falling prey to the problem of theory change that undermines scientific realism. We explain how constraints of necessity on phenomena can be known by induction, and how this modal epistemology fits with scientific practice. Finally, we claim that a commitment to natural modalities allows for a rich interpretation of the cognitive content of theories. Modal empiricism could renew some metaphysical debates within a pragmatist framework, by tying them to experience and not being constrained by realist prejudices. -/- L'objet de cette thèse est de proposer une position originale dans le débat sur le réalisme scientifique, l'empirisme modal, et d'en démontrer la fructuosité quand il s'agit de tirer des enseignements du contenu cognitif des théories scientifiques. L'empirisme modal est une position empiriste, suivant laquelle le but de la science n'est pas de produire des théories vraies, mais des théories empiriquement adéquate. Cependant, il propose d'adopter un cadre plus large que les versions traditionnelles d'empirisme pour penser l'expérience, en incorporant un engagement envers les modalités naturelles, ou l'idée qu'il y a du possible dans la nature, et des contraintes sur les possibles. Nos théories sont empiriquement adéquates si elles délimitent correctement l'étendue des expériences possibles. Cette position s'appuie sur une conception située et pragmatique des modalités naturelles et de la confrontation empirique. Nous prétendons qu'elle est à même de rendre justice au succès empirique des sciences, sans pour autant faire face au problème du changement théorique qui mine le réalisme scientifique. Nous expliquons comment les contraintes de nécessité sur les phénomènes peuvent être connues à l'issue d'une induction, et en quoi cette façon de voir s'accorde avec la pratique scientifique. Enfin, nous affirmons qu'un engagement envers les modalités naturelles offre une richesse interprétative à même de renouveler, dans un cadre pragmatiste, plus ouvert que le réalisme, certaines questions métaphysiques tout en les ramenant à l'expérience . (shrink)

What kind of thing do you believe when you believe that you are in a certain place, that it is a certain time, and that you are a certain individual? What happens if you get lost, or lose track of the time? Can you ever be unsure of your own identity? These are the kind of questions considered in my thesis. Beliefs about where, when and who you are are what are called in the literature de se, or self-locating beliefs. (...) This thesis examines how we can represent de se beliefs, and how we can reason about de se uncertainty. In the first part of the thesis, I present and motivate a specific account of the content of de se belief, based on the one given by David Lewis. On this account, the content of de se beliefs are centred propositions. I defend this view against a rival account, put forward by Robert Stalnaker, according to whom the content of de se beliefs are ordinary propositions. In the second part of the thesis, I explore how we can reason probabilistically about de se uncertainty. I start by defining probabilities over centred propositions, and investigate what probabilities mean in this context. As it turns out, all the main interpretations of probability can be extended to centred propositions. The only trouble seems to arise for the Bayesian principle of updating via conditionalization. After giving a diagnosis of the problem, I offer a solution by formulating a natural extension of conditionalization, which I argue preserves the essential features of Bayesian reasoning. In the final chapter, I apply my view and show that it leads to a natural resolution of a puzzle that is generally taken to be a test case for any account of centred updating. (shrink)

Concrete Causation centers about theories of causation, their interpretation, and their embedding in metaphysical-ontological questions, as well as the application of such theories in the context of science and decision theory. The dissertation is divided into four chapters, that firstly undertake the historical-systematic localization of central problems (chapter 1) to then give a rendition of the concepts and the formalisms underlying David Lewis' and Judea Pearl's theories (chapter 2). After philosophically motivated conceptual deliberations Pearl's mathematical-technical framework is drawn on for (...) an epistemic interpretation and for emphasizing the knowledge-organizing aspect of causality in an extension of the interventionist Bayes net account of causation (chapter 3). Integrating causal and non-causal knowledge in unified structures ultimately leads to an approach towards solving problems of (causal) decision theory and at the same time facilitates the representation of logical-mathematical, synonymical, as well as reductive relationships in efficiently structured, operational nets of belief propagation (chapter 4). (shrink)

When do probability distribution functions (PDFs) about future climate misrepresent uncertainty? How can we recognise when such misrepresentation occurs and thus avoid it in reasoning about or communicating our uncertainty? And when we should not use a PDF, what should we do instead? In this paper we address these three questions. We start by providing a classification of types of uncertainty and using this classification to illustrate when PDFs misrepresent our uncertainty in a way that may adversely affect decisions. We (...) then discuss when it is reasonable and appropriate to use a PDF to reason about or communicate uncertainty about climate. We consider two perspectives on this issue. On one, which we argue is preferable, available theory and evidence in climate science basically excludes using PDFs to represent our uncertainty. On the other, PDFs can legitimately be provided when resting on appropriate expert judgement and recognition of associated risks. Once we have specified the border between appropriate and inappropriate uses of PDFs, we explore alternatives to their use. We briefly describe two formal alternatives, namely imprecise probabilities and possibilistic distribution functions, as well as informal possibilistic alternatives. We suggest that the possibilistic alternatives are preferable. -/- . (shrink)

The thesis consists of an introduction and five papers. The introduction gives a brief historical survey of empirical investigations into the effectiveness of medicinal interventions, as well as surveys of the concept of evidence and of the history and philosophy of experiments. The main ideas of the EBM movement are also presented. Paper I: Concerns have been raised that clinical trials do not offer reliable evidence for some types of treatment, in particular for highly individualised treatments, for example traditional homeopathy. (...) With respect to individualised treatments, it is argued that such concerns are unfounded. There are two minimal conditions related to the nature of the treatments that must be fulfilled for evaluability in a clinical trial, namely the proper distinction of treatment groups and the elimination of confounding variables or variations. These conditions do not preclude the testing of individualised medicine. Paper II: Traditionally, mechanistic reasoning has been assigned a negligible role in the EBM literature. When discussed, mechanistic reasoning has almost exclusively been positive – both in an epistemic sense of claiming that there is a mechanistic chain and in a health-related sense of there being claimed benefits for the patient. Negative mechanistic reasoning has been neglected. I distinguish three main types of negative mechanistic reasoning and subsume them under a new definition. One of the three distinguished types, which is negative only in the health-related sense, has a corresponding positive counterpart, whereas the other two, which are epistemically negative, do not have such counterparts, at least not that are particularly interesting as evidence. Accounting for negative mechanistic reasoning in EBM is therefore partly different from accounting for positive mechanistic reasoning. Paper III: Evidence hierarchies are lists of investigative strategies ordered with regard to the claimed strength of evidence. They have been used for a couple of decades within EBM, particularly for the assessment of evidence for treatment recommendations, but they remain controversial. An under-investigated question is what the order in the hierarchy means. Four interpretations of the order are distinguished and discussed. The two most credible ones are, in rough terms, “typically stronger” and “ideally stronger”. The GRADE framework seems to be based on the “typically stronger” reading. Even if the interpretation of an evidence hierarchy were established, hierarchies appear to be rather unhelpful for the task of evidence aggregation. However, specifying the intended order relation may help sort out disagreements. Paper IV: There are three main arguments for randomisation that connect inseparably to theoretical concepts: Randomisation is useful for performing null hypothesis testing. Randomisation is needed for plausible causal inferences from treatment to effect. Randomisation is acceptable and computationally convenient in a Bayesian setting. A critical scrutiny of these arguments shows that is acceptable in the context of clinical trials. As for, it is argued that randomisation only provides weak reasons for drawing causal inferences in the context of real clinical trials. Argument is weak because it is controversial among Bayesians, and because formally Bayesian analyses of trial results are rarely asked for. Paper V: Practical arguments for randomisation are arguments with no necessary connections to theoretical frameworks like null hypothesis testing or causal inferences. Four common practical arguments in the context of clinical trials are distinguished and assessed: Randomisation contributes to allocation concealment. Randomisation contributes to the baseline balance of treatment groups. Randomisation decreases self-selection bias. Randomisation removes allocation bias. Argument is rejected. Arguments and are approved. Argument is rejected if it is formulated so as to be independent from and, but it is true that randomisation contributes to balance through the mechanisms mentioned in and. It is judged that may be the strongest single argument. (shrink)

Abstract : A measurement result is never absolutely accurate: it is affected by an unknown “measurement error” which characterizes the discrepancy between the obtained value and the “true value” of the quantity intended to be measured. As a consequence, to be acceptable a measurement result cannot take the form of a unique numerical value, but has to be accompanied by an indication of its “measurement uncertainty”, which enunciates a state of doubt. What, though, is the value of measurement uncertainty? What (...) is its numerical value: how does one calculate it? What is its epistemic value: how one should interpret a measurement result? Firstly, we describe the statistical models that scientists make use of in contemporary metrology to perform an uncertainty analysis, and we show that the issue of the interpretation of probabilities is vigorously debated. This debate brings out epistemological issues about the nature and function of physical measurements, metrologists insisting in particular on the subjective aspect of measurement. Secondly, we examine the philosophical elaboration of metrologists in their technical works, where they criticize the use of the notion of “true value” of a physical quantity. We then challenge this elaboration and defend such a notion. The third part turns to a specific use of measurement uncertainty in order to address our thematic from the perspective of precision physics, considering the activity of the adjustments of physical constants. In the course of this activity, physicists have developed a dynamic conception of the accuracy of their measurement results, oriented towards a future progress of knowledge, and underlining the epistemic virtues of a never-ending process of identification and correction of measurement errors. (shrink)

In probability textbooks, it is widely claimed that zero probability does not mean impossibility. But what stands behind this claim? In this paper I offer an explanation to this claim based on Kolmogorov's formalism. As such, this explanation is relevant to all interpretations of Kolmogorov's probability theory. I start by clarifying that this claim refers only to nonempty events, since empty events are always considered as impossible. Then, I offer the following three reasons for the claim that nonempty events with (...) zero probability are considered as possible: The main reason is simply because they are nonempty. Hence, they are considered as possible despite their zero probability. The second reason is that sometimes the zero probability is taken to be an approximation of some infinitesimal probability value. Such a value is strictly positive and as such does not imply impossibility in a strict sense. Finally, the third reason is that there are interpretations according to which the same event can have different probabilities. Specifically, it is assumed that an event with exactly zero probability can have strictly positive probabilities. This means that such an event can be possible which implies that its zero probability does not mean impossibility. (shrink)

In robustness analysis, hypotheses are supported to the extent that a result proves robust, and a result is robust to the extent that we detect it in diverse ways. But what precise sense of diversity is at work here? In this paper, I show that the formal explications of evidential diversity most often appealed to in work on robustness – which all draw in one way or another on probabilistic independence – fail to shed light on the notion of diversity (...) relevant to robustness analysis. I close by briefly outlining a promising alternative approach inspired by Horwich’s (1982) eliminative account of evidential diversity. (shrink)

Many degree programs in science and engineering aim at enabling their students to perform interdisciplinary problem solving. In this paper we present three types of expertise that are involved in different ways in interdisciplinary problem solving. In doing so we shall first characterise two important epistemological challenges commonly faced in interdisciplinary problem solving, namely the communication challenge that arises from the use of different concepts within different scientific domains, and the integration challenge that arises from the differences between domain-specific epistemological (...) standards. Next, drawing on recent work on expertise developed within science studies, we characterize the interactional expertise that is a precondition for scientists to communicate across scientific domains, and the integrational expertise that is a precondition for scientists to be able to integrate cognitive resources originating in different domains. Finally, we shall analyse how different types of interdisciplinary problem solving sets different requirements for interactional and integrational expertise and discuss the implications for science and engineering programs in higher education. (shrink)

There is a growing interest in the foundations as well as the application of imprecise probability in contemporary epistemology. This dissertation is concerned with the application. In particular, the research presented concerns ways in which imprecise probability, i.e. sets of probability measures, may helpfully address certain philosophical problems pertaining to rational belief. The issues I consider are disagreement among epistemic peers, complete ignorance, and inductive reasoning with imprecise priors. For each of these topics, it is assumed that belief can be (...) modeled with imprecise probability, and thus there is a non-classical solution to be given to each problem. I argue that this is the case for peer disagreement and complete ignorance. However, I discovered that the approach has its shortcomings, too, specifically in regard to inductive reasoning with imprecise priors. Nevertheless, the dissertation ultimately illustrates that imprecise probability as a model of rational belief has a lot of promise, but one should be aware of its limitations also. (shrink)

In this thesis I will examine the philosophy of the physicist Max Born. As well as his scientific work, Born wrote on a number of philosophical topics: causation, realism, determinism, and probability. They appear as an interest throughout his career, but he particularly concentrates on them from the 1940s onwards. Born is a significant figure in the development of quantum mechanics whose philosophical work has been left largely unexamined. It is the aim of this thesis to elucidate and to critically (...) examine that work. I will give a defence of presentist historiography in the history and philosophy of science and a brief biography of Born. With regards to causation, the thesis will argue that he holds that there exist principles regarding causal relations that have guided the development of physics and have, in the modern formulation of the subject, been confirmed as having an empirical status. I will argue that he is a selective realist, initially with regards to invariant properties and, later on, a structural realist. With regards to determinism, I will argue that Born has produced an argument, compatible with modern philosophical definitions of determinism, that we were never entitled to conclude from the success of classical mechanics that the world was deterministic. Finally, I will argue that Born holds an objective interpretation of probabilities in quantum mechanics which, due to his strong belief in the physical reality of quantum-mechanical probabilities and his apparent disbelief in the superposition of the wave-function, is most likely a long-run propensity theory. (shrink)

How should an agent decide what to do when she is uncertain not just about morally relevant empirical matters, like the consequences of some course of action, but about the basic principles of morality itself? This question has only recently been taken up in a systematic way by philosophers. Advocates of moral hedging claim that an agent should weigh the reasons put forward by each moral theory in which she has positive credence, considering both the likelihood that that theory is (...) true and the strength of the reasons it posits. The view that it is sometimes rational to hedge for one's moral uncertainties, however, has recently come under attack both from those who believe that an agent should always be guided by the dictates of the single moral theory she deems most probable and from those who believe that an agent's moral beliefs are simply irrelevant to what she ought to do. Among the many objections to hedging that have been pressed in the recent literature is the worry that there is no non-arbitrary way of making the intertheoretic comparisons of moral value necessary to aggregate the value assignments of rival moral theories into a single ranking of an agent's options. -/- This dissertation has two principal objectives: First, I argue that, contra these recent objections, an agent's moral beliefs and uncertainties are relevant to what she rationally ought to do, and more particularly, that agents are at least sometimes rationally required to hedge for their moral uncertainties. My principal argument for these claims appeals to the enkratic conception of rationality, according to which the requirements of practical rationality derive from an agent's beliefs about the objective, desire-independent value or choiceworthiness of her options. Second, I outline a new general theory of rational choice under moral uncertainty. Central to this theory is the idea of content-based aggregation, that the principles according to which an agent should compare and aggregate rival moral theories are grounded in the content of those theories themselves, including not only their value assignments but also the metaethical and other non-surface-level propositions that underlie, justify, or explain those value assignments. (shrink)

We critically examine the role and status probabilities, as they enter via the Quantum Equilibrium Hypothesis, play in the standard, deterministic interpretation of deBroglie’s and Bohm’s Pilot Wave Theory (dBBT), by considering interpretations of probabilities in terms of ignorance, typicality and Humean Best Systems, respectively. We argue that there is an inherent conflict between dBBT and probabilities, thus construed. The conflict originates in dBBT’s deterministic nature, rooted in the Guidance Equation. Inquiring into the latter’s role within dBBT, we find it (...) explanatorily redundant (in particular for dBBT’s solution of the Measurement Problem, which only requires that the corpuscles possess definite positions), and subject to a number of difficulties. Following a suggestion from Bell, we propose to abandon the Guidance Equation, whilst retaining dBBT’s point particle-based Primitive Ontology, with positions as local beables. The resultant theory, which we identify as a stochastic, minimally deBroglie-Bohmian theory, describes a random walk through configuration space. Its probabilities, we propose, are best understood as dispositions of possible corpuscle configurations to manifest themselves. We subsequently evaluate the merits of sdBBT vis-à-vis dBBT, such as the justification of the Symmetrisation Postulate and the violation of the Action-Reaction Principle. Not only is sdBBT an attractive Bohmian theory that, whilst retaining dBBT's virtues, overcomes many of its shortcomings; it also sparks off a number of exciting follow-up questions, such as a comparison between sdBBT and other stochastic hidden-variable theories, e.g. Nelson Stochastics, or between sdBBT and the Everett interpretation. (shrink)

This paper is an explication and critique of a new theory of causation found in part II of Gregg Rosenberg's _A Place for Consciousness._ According to Rosenberg's Theory of Causal significance, causation constrains indeterminate possibilities, and according to his Carrier Theory, physical properties are dispositions which have phenomenal properties as their causal bases. This author finds Rosenberg's metaphysics excessively speculative, with disappointing implications for the place of consciousness in the natural world.

If chances are propensities, what reason do we have to expect them to be probabilities? I will offer a new answer to this question. It comes in two parts. First, I will defend an accuracy-centred account of what it is for a causal system to have precise propensities in the first place. Second, I will prove that, given some pretty weak assumptions about the nature of comparative causal dispositions, and some fairly standard assumptions about reasonable measures of inaccuracy, propensities must (...) be probabilities. (shrink)

In order to tackle the question posed by the title – notoriously answered in the positive, among others, by Heisenberg, Margenau, Popper and Redhead – I first discuss some attempts at distinguishing dispositional from non-dispositional properties, and then relate the distinction to the formalism of quantum mechanics. Since any answer to the question titling the paper must be interpretation-dependent, I review some of the main interpretations of quantum mechanics in order to argue that the ontology of theories regarding “wave collapse” (...) as a genuine physical process could be interpreted as being irreducibly dispositional. In non-collapse interpretations, on the contrary, the appeal to dispositions is simply a way to reformulate the predictive content of the algorithm of the theory in a fancier metaphysical language. (shrink)

Una cuestión controvertida en la teoría bayesiana de la confirmación es el estatus de las probabilidades iniciales. Aunque la tendencia dominante entre los bayesianos es considerar que la única constricción legítima sobre los valores de dichas probabilidades es la consistencia formal con los teoremas de la teoría matemática de la probabilidad, otros autores -partidarios de lo que se ha dado en llamar "bayesianismo objetivo"- defienden la conveniencia de restricciones adicionales. Mi propuesta, en el marco del bayesianismo objetivo, recoge una sugerencia (...) de Wesley Salmon. No obstante, mientras que para Salmon las probabilidades iniciales se justifican en tanto incorporan la frecuencia de éxito de las hipótesis del pasado, el factor decisivo en mi opinión es el éxito probabilístico de las hipótesis del pasado. Así, la asignación de una probabilidad inicial a una hipótesis h será correcta si refleja el éxito probabilístico de hipótesis del pasado semejantes a h. En esta línea, propongo una regla para fijar las probabilidades iniciales de las hipótesis, y acabo discutiendo algunas objeciones generales en contra de mi planteamiento. One of the most controversial issues for Bayesian theory of confirmation concerns the status of prior probabilities. Orthodox Bayesianism claims that logical consistency with the theorems of mathematical theory of probability is the only constraint on prior probabilities, while some authors claim for further requirements. I agree with the latter standpoint. My proposal is inspired by Wesley Salmon's frequentist justification of prior probabilities. According to him, prior probabilities are the best assessments of past scientific hypotheses' success. I think that historical information is relevant here, but I propose to focus on a particular sort of success -i.e., "probabilistic success". I claim that a particular prior for h is correct insofar as it reflects the probabilistic success of past scientific hypotheses similar to h. I also suggest a rule to set the priors for contemporary hypotheses. The closing paragraphs are devoted to some general objections against this proposal. (shrink)

Bruno de Finetti is one of the founding fathers of the subjectivist school of probability, where probabilities are interpreted as rational degrees of belief. His work on the relation between the theorems of probability and rationality is among the corner stones of modern subjective probability theory. De Finetti maintained that rationality requires that degrees of belief be coherent, and he argued that the whole of probability theory could be derived from these coherence conditions. De Finetti’s interpretation of probability has been (...) highly influential in science. This paper focuses on the application of this interpretation to quantum mechanics. We argue that de Finetti held that the coherence conditions of degrees of belief in events depend on their verifiability. Accordingly, the standard coherence conditions of degrees of belief that are familiar from the literature on subjective probability only apply to degrees of belief in events which could be jointly verified; and the coherence conditions of degrees of belief in events that cannot be jointly verified are weaker. While the most obvious explanation of de Finetti’s verificationism is the influence of positivism, we argue that it could be motivated by the radical subjectivist and instrumental nature of probability in his interpretation; for as it turns out, in this interpretation it is difficult to make sense of the idea of coherent degrees of belief in, and accordingly probabilities of unverifiable events. We then consider the application of this interpretation to quantum mechanics, concentrating on the Einstein-Podolsky-Rosen experiment and Bell’s theorem. (shrink)

This paper offers some reflections on the concepts of objective and subjective probability and Lewis' Principal Principle.

This essay assesses Paul Draper's argument from evolution to atheism.

This chapter is a philosophical survey of some leading approaches in formal epistemology in the so-called ‘Bayesian’ tradition. According to them, a rational agent’s degrees of belief—credences—at a time are representable with probability functions. We also canvas various further putative ‘synchronic’ rationality norms on credences. We then consider ‘diachronic’ norms that are thought to constrain how credences should respond to evidence. We discuss some of the main lines of recent debate, and conclude with some prospects for future research.

Leibniz’s account of probability has come into better focus over the past decades. However, less attention has been paid to a certain domain of application of that account, that is, the application of it to the moral or ethical domain—the sphere of action, choice and practice. This is significant, as Leibniz had some things to say about applying probability theory to the moral domain, and thought the matter quite relevant. Leibniz’s work in this area is conducted at a high level (...) of abstraction. It establishes a proof of concept, rather than concrete guidelines for how to apply calculations to specific cases. Still, this highly abstract material does allow us to begin to construct a framework for thinking about Leibniz’s approach to the ethical side of probability. (shrink)