This Element has two main aims. The first one is an historically informed review of the philosophy of probability. It describes recent historiography, lays out the distinction between subjective and objective notions, and concludes by applying the historical lessons to the main interpretations of probability. The second aim focuses entirely on objective probability, and advances a number of novel theses regarding its role in scientific practice. A distinction is drawn between traditional attempts to interpret chance, and (...) a novel methodological study of its application. A radical form of pluralism is then introduced, advocating a tripartite distinction between propensities, probabilities and frequencies. Finally, a distinction is drawn between two different applications of chance in statistical modelling which, it is argued, vindicates the overall methodological approach. The ensuing conception of objective probability in practice is the 'complex nexus of chance'. (shrink)

Philosophy of Probability provides a comprehensive introduction to theoretical issues that occupy a central position in disciplines ranging from philosophy of ...

_Philosophy of Probability: Contemporary Readings_ is the first anthology to collect essential readings in this important area of philosophy. Featuring the work of leading philosophers in the field such as Carnap, Hájek, Jeffrey, Joyce, Lewis, Loewer, Popper, Ramsey, van Fraassen, von Mises, and many others, the book looks in depth at the following key topics: subjective probability and credence probability updating: conditionalization and reflection Bayesian confirmation theory classical, logical, and evidential probability frequentism physical probability: (...) propensities and objective chances. The book features a useful primer on the mathematics of probability, and each section includes an introduction by the editor, as well as a guide to further reading. A broad-ranging and highly accessible exploration of the subject, _Philosophy of Probability_ is ideal for any student of formal epistemology, philosophy of science, metaphysics, or philosophy of mathematics. (shrink)

This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of mathematics in general.

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)

This dissertation is a contribution to formal and computational philosophy. -/- In the first part, we show that by exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. Case 1: Infinite lotteries. We discuss how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. The solution boils down to (...) the introduction of infinitesimal probability values, which can be achieved using non-standard analysis. Our solution can be generalized to uncountable sample spaces, giving rise to a Non-Archimedean Probability (NAP) theory. Case 2: Large but finite lotteries. We propose application of the language of relative analysis (a type of non-standard analysis) to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’. -/- The second part presents a case study in social epistemology. We model a group of agents who update their opinions by averaging the opinions of other agents. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating. To that end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. The probability of ending up in an inconsistent belief state turns out to be always smaller than 2%. (shrink)

Known as an upholder of subjectivism, Bruno de finetti (1906-1985) put forward a totally original philosophy of probability. This can be qualified as a combination of empiricism and pragmatism within an entirely coherent antirealistic perspective. The paper aims at clarifying the central features of such a philosophical position, Which is not only incompatible with any perspective based on an objective notion, But cannot be assimilated to other subjective views of probability either.

Popper's writings cover a remarkably wide range of subjects. The spectrum runs from Plato's theory of politics to the foundations of quantum mechanics. Yet even amidst this variety the philosophy of probability occupies a prominent place. David Miller once pointed out to me that more than half of Popper's The Logic of Scientific Discovery is taken up with discussions of probability. I checked this claim using the 1972 6th revised impression of The Logic of Scientific Discovery , (...) and found that of the approximately 450 pages of text, approximately 250 are to do with probability. Thus Miller's claim is amply justified. It seems indeed that the philosophy of probability was one of Popper's favourite subjects, and, as we shall see, Popper certainly enriched the field with several striking innovations. In this area, as in others, Popper held very definite views, and criticized his opponents in no uncertain terms. Popper was an objectivist and anti-Bayesian, and his criticisms were directed against subjectivism and Bayesianism. (shrink)

This book explores important topics in Darwin’s theory of evolution and in the twentieth- and twenty-first-century theories that grew out of it. These topics include fitness, adaptation, altruism, intragenomic conflict, units of selection, genetic drift, the randomness of mutation, gradualism, common ancestry, taxonomy, race, phylogenetic inference, and optimality models. The book brings these and other biological topics into contact with numerous philosophical ideas − operationalism, reductionism, conventionalism, null hypotheses and default reasoning, instrumentalism versus realism, likelihoods versus probabilities, model selection, essentialism, (...) falsifiability, parsimony, the principle of the common cause, comparisons of causal power, interpretations of probaiblity, indeterminism, sensitivity to initial conditions, and the knowability of the past. (shrink)

The use of probability theory is widespread in our daily life as well as in scientific theories. In virtually all cases, calculations can be carried out within the framework of classical probability theory. A special exception is given by quantum mechanics, which gives rise to a new probability theory: quantum probability theory. This dissertation deals with the question of how this formalism can be understood from a philosophical and physical perspective. The dissertation is divided into three (...) parts. In the first part, the formalism of quantum probability theory and its relation to quantum mechanics is presented. The second part considers the possibility of reformulating quantum probability theory to embed it within classical probability. Mathematically, this possibility overlaps with the possibility of the existence of hidden variables theories of quantum mechanics: theories that attempt to solve fundamental problems in quantum mechanics by introducing additional physical properties of systems. The conclusion of this part is that, although classical reformulations of quantum probability theory are formally possible, they offer little insight into the formalism of quantum probability theory itself. The third part regards a more direct investigation of quantum probability theory. A reformulation of quantum probability theory is obtained by constructing a quantum logic on the basis of empirical non-probabilistic predictions of quantum mechanics. In this reformulation quantum probability functions are conditional probability functions on an algebra of propositions about measurements and measurement outcomes. (shrink)

Two new philosophical problems surrounding the gradation of certainty began to emerge in the 17th century and are still very much alive today. One is concerned with the evaluation of inductive reasoning, whether in science, jurisprudence, or elsewhere; the other with the interpretation of the mathematical calculus of change. This book, aimed at non-specialists, investigates both problems and the extent to which they are connected. Cohen demonstrates the diversity of logical structures that are available for judgements of probability, and (...) explores the rationale for their appropriateness in different contexts of application. Thus his study deals with the complexity of the underlying philosophical issues without simply cataloging alternative conceptions or espousing a particular "favorite" theory. (shrink)

Probability is increasingly important for our understanding of the world. What is probability? How do we model it, and how do we use it? Timothy Childers presents a lively introduction to the foundations of probability and to philosophical issues it raises. He keeps technicalities to a minimum, and assumes no prior knowledge of the subject.

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

Probability theory is a key tool of the physical, mathematical, and social sciences. It has also been playing an increasingly significant role in philosophy: in epistemology, philosophy of science, ethics, social philosophy, philosophy of religion, and elsewhere. This Handbook encapsulates and furthers the influence of philosophy on probability, and of probability on philosophy. Nearly forty articles summarise the state of play and present new insights in various areas of research at the (...) intersection of these two fields. The articles will be of special interest to practitioners of probability who seek a greater understanding of its mathematical and conceptual foundations, and to philosophers who want to get up to speed on the cutting edge of research in this area. The volume begins with a primer on those parts of probability theory that we believe are most important for philosophers to know, and the rest is divided into seven main sections: History; Formalism; Alternatives to Standard Probability Theory; Interpretations and Interpretive Issues; Probabilistic Judgment and Its Applications; Applications of Probability: Science; and Applications of Probability: Philosophy. (shrink)

In this article, I first give a short outline of the different interpretations of the concept of probability that emerged in the twentieth century. In what follows, I give an overview of the main problems and problematic concepts from the philosophy of probability and show how they relate to Bayesian inference. In this overview, I emphasise that the understanding of the main concepts related to different interpretations of probability influences the understanding and status of Bayesian inference. (...) In the conclusion, I express that, from a broad epistemological point of view, a kind of compatibilism between the two main lines of interpretations of probability is worth pursuing, as they represent different aspects of the epistemological process. (shrink)

My title is intended to recall Terence Fine's excellent survey, Theories of Probability [1973]. I shall consider some developments that have occurred in the intervening years, and try to place some of the theories he discussed in what is now a slightly longer perspective. Completeness is not something one can reasonably hope to achieve in a journal article, and any selection is bound to reflect a view of what is salient. In a subject as prone to dispute as this, (...) there will inevitably be many who will disagree with any author's views, and I take the opportunity to apologize in advance to all such people for what they will see as the narrowness and distortion of mine. (shrink)

Wesley Salmon provided three classic criteria of adequacy for satisfactory interpretations of probability. A fourth criterion is suggested here. A distinction is drawn between frequency‐driven probability models and theory‐driven probability models and it is argued that single case accounts of chance are superior to frequency accounts at least for the latter. Finally it is suggested that theories of chance should be required only to be contingently true, a position which is a natural extension of Salmon's ontic account (...) of probabilistic causality and his own later views on propensities. (shrink)

Probability theory promises to deliver an exact and unified foundation for inquiry in epistemology and philosophy of science. But philosophy of religion is also fertile ground for the application of probabilistic thinking. This volume presents original contributions from twelve contemporary researchers, both established and emerging, to offer a representative sample of the work currently being carried out in this potentially rich field of inquiry. Grouped into five parts, the chapters span a broad range of traditional issues in (...) religious epistemology. The first three parts discuss the evidential impact of various considerations that have been brought to bear on the question of the existence of God. These include witness reports of the occurrence of miraculous events, the existence of complex biological adaptations, the apparent 'fine-tuning' for life of various physical constants and the existence of seemingly unnecessary evil. The fourth part addresses a number of issues raised by Pascal's famous pragmatic argument for theistic belief. A final part offers probabilistic perspectives on the rationality of faith and the epistemic significance of religious disagreement. (shrink)

This book provides a systematic treatment of Locke's theory of probable assent. It shows how the theory applies to Locke's philosophy of science, moral epistemology, and religious epistemology. There is a powerful case to be made that the most important dimension of Locke's philosophy is his theory of rational probable assent, rather than his theory of knowledge. According to Locke, we largely live our lives in the "twilight of probability" rather than in "the sunshine of certain knowledge". (...) Locke's theory of probable assent is towering insofar as it contains a wealth of novel, independently interesting, and prescient elements that precede the modern field of formal epistemology. In this book, the author argues for the central role of probable assent in Locke's philosophy. Locke's theory of probable assent is based on an epistemic modesty that claims, roughly, that our cognitive abilities are quite limited and that we ought to carry ourselves in believing with due caution. This modesty motivates the author's discussion of other aspects of Locke's epistemology, notably his principle of proportionality, his doxastic involuntarism, his epistemological pragmatism, and his theory of testimony. The book concludes by connecting the theory of probable assent with Locke's views on the limits of science, moral epistemology, and the rationality of faith. Locke's Twilight of Probability will appeal to scholars and advanced students working on Locke and the history of early modern philosophy. (shrink)

Key Terms in Logic offers the ideal introduction to this core area in the study of philosophy, providing detailed summaries of the important concepts in the study of logic and the application of logic to the rest of philosophy. A brief introduction provides context and background, while the following chapters offer detailed definitions of key terms and concepts, introductions to the work of key thinkers and lists of key texts. Designed specifically to meet the needs of students and (...) assuming no prior knowledge of the subject, this is the ideal reference tool for those coming to Logic for the first time. (shrink)

The development of science has been a distinctive feature of human history in recent times, especially in the seventeenth and eighteenth centuries. In light of the problems that define the philosophy of science today, James Fetzer provides a foundation for inquiry into the nature of science, the history of science, and the relationship between the two. In Philosophy of Science, Fetzer investigates the aim and methods of empirical science and examines the importance of methodological commitments to the study (...) of science and the significance of interpretations of probability for understanding laws of nature and scientific explanations. This book offers a welcome framework for investigating the most recent work and the most promising solutions to the central problems that arise within this discipline. The result is a timely introduction to an increasingly important field. -- Publisher description. (shrink)

The goal of this paper is to provide an extensive account of Robert Leslie Ellisʼs largely forgotten work on philosophy of science and probability theory. On the one hand, it is suggested that both his ‘idealist’ renovation of the Baconian theory of induction and a ‘realism’ vis-à-vis natural kinds were the result of a complex dialogue with the work of William Whewell. On the other hand, it is shown to what extent the combining of these two positions contributed (...) to Ellisʼs reformulation of the metaphysical foundations of traditional probability theory. This parallel is assessed with reference to the disagreement between Ellis and Whewell on the nature of (pure) mathematics and its relation to scientific knowledge. (shrink)

In this dissertation I aim to clarify the concept of probability. There are three kinds of interpretation of probability: the objective interpretation, the logical interpretation, and the subjective interpretation. The objective interpretation understands probability as a natural property that exists independently of our minds. I will clarify and defend one version of objective probability---the propensity interpretation of probability. I reject the logical interpretation of probability that treats probability as a logical relation between evidence (...) and hypothesis, and maintain that probability is an empirical relation. The subjective interpretation of probability, which is quite influential in recent literature, understands probability as the subject's degree of confidence that is only concerned with the states of one's mind. There are two arguments to support the claim that partial beliefs satisfy the probability measure, the Dutch Book Argument and the Representation Theorem . I argue that the subjective probability derived from both arguments is in fact the subjective estimate of objective chance, rather than subjective uncertainty of the mind assumed by subjective interpretation. The clarification of the concept of probability, I think, is of crucial importance to the studies in the philosophy of science, epistemology, and statistics. (shrink)

This user-friendly text covers key issues in the philosophy of science in an accessible and philosophically serious way. It will prove valuable to students studying philosophy of science as well as science students. Prize-winning author Alex Rosenberg explores the philosophical problems that science raises by its very nature and method. He skilfully demonstrates that scientific explanation, laws, causation, theory, models, evidence, reductionism, probability, teleology, realism and instrumentalism actually pose the same questions that Plato, Aristotle, Descartes, Hume, Kant (...) and their successors have grappled with for centuries. (shrink)

It is the purpose of this paper to present a theory of probability derived from two-valued logic—the logic of which an aspect is given in Part I, Section A, of Principia Mathematica. The symbolic system of Mr. Keynes, given in his Treatise on Probability, will be shown to be a part of our system. We have, however, little if anything in common with his philosophical analysis; a definition of Keynes’ fundamental probability relation, free from psychological or material (...) reference, will be given, enabling us to offset some of the objections to his theory. (shrink)

The main objective of the paper is to propose a frequentist interpretation of probability in the context of model-based induction, anchored on the Strong Law of Large Numbers (SLLN) and justifiable on empirical grounds. It is argued that the prevailing views in philosophy of science concerning induction and the frequentist interpretation of probability are unduly influenced by enumerative induction, and the von Mises rendering, both of which are at odds with frequentist model-based induction that dominates current practice. (...) The differences between the two perspectives are brought out with a view to defend the model-based frequentist interpretation of probability against certain well-known charges, including [i] the circularity of its definition, [ii] its inability to assign ‘single event’ probabilities, and [iii] its reliance on ‘random samples’. It is argued that charges [i]–[ii] stem from misidentifying the frequentist ‘long-run’ with the von Mises collective. In contrast, the defining characteristic of the long-run metaphor associated with model-based induction is neither its temporal nor its physical dimension, but its repeatability (in principle); an attribute that renders it operational in practice. It is also argued that the notion of a statistical model can easily accommodate non-IID samples, rendering charge [iii] simply misinformed. (shrink)

The paper presents an infinite hierarchy PR m [ m = 1, 2, . . . ] of sound and complete axiomatic systems for modal logic with graded probabilistic modalities , which are to reflect what I have elsewhere called the Bolding-Ekelöf degrees of evidential strength as applied to the establishment of matters of fact in law-courts. Our present approach is seen to differ from earlier work by the author in that it treats the logic of these graded modalities not (...) only from a semantical or model-theoretic viewpoint but from a prooftheoretical and axiomatic stance as well. A paramount feature of the approach is its use of so-called systematic frame constants as labels of diverse grades of probability. Apart from this novel feature our approach can be seen to go back to pioneering work by Lou Goble in 1970. (shrink)

Do you know the Japanese equivalent for "philosophy"? That word, "tetsugaku", was coined after the Meiji Revolution. Do you know when the standard philosophy of science, in the form of the logical empiricism, was introduced into Japan? After the World War II, around 1950. Do you know whether or not the philosophy of science, especially its "hardcore", is studied seriously in Japan? Very few people are studying the philosophy of space and time, the philosophy of (...) quantum mechanics, the philosophy of evolution, the philosophy of probability, or the philosophy of social sciences. Do you know how many HPS departments exist in Japan? Only three, one is founded in 1951 and its graduate program was extended in 1970, and the other two were founded around 1993. Now, with these preparations, you are beginning to understand what I am going to talk about---Is Philosophy of Science alive in Japan? I will briefly outline the history of the philosophy of science in Japan, and discuss some of its peculiarities. And from this discussion, I wish to point out what is needed for the philosophy of science in Japan. Here is an Outline: " 1. Three Basic Facts 2. Taketani's Doctrine of the Three Stages 3. Logical Empiricism 4. Scientists and Philosophers 5. "New" Philosophy of Science 6. What is needed for Japanese Philosophy of Science? ". (shrink)

Education in statistics, the application of statistics in scientific research, and statistics itself as a scientific discipline are in crisis. Within science, the main cause of the crisis is the insufficiently clarified concept of probability. This article aims to separate the concept of probability which is scientifically based from other concepts that do not have this characteristic. The scientifically based concept of probability is Kolmogorov’s concept of probability models together with the conditions of their applicability. Bayesian (...) statistics is based on the subjective concept of probability, and as such can only have a heuristic value in searching for the truth, but it cannot and must not replace the truth. The way out of the crisis should take Kolmogorov and Bayesian analysis as elements, each of which has a well-defined and limited use. Only together with qualitative analysis and other types of quantitative analysis, and combined with experiments, they can contribute to reaching correct conclusions. (shrink)

Purpose. The research is aimed at finding out the grounds, forms and essence of the correlation between the projects of information philosophy and transhumanism from the point of view of the problematics of philosophical anthropology. Attention is focused on the status of the knowing subject and the transformations of the forms of its activity within the specified correlation. Theoretical basis. Insufficient thinking on the issue of the functioning of traditional cognitive models, in particular Kant’s transcendental questioning, which formed the (...) basis of modern rationality and classical science, in the new sociocultural reality led the authors to problematize the forms and essence of interaction and operating with knowledge and communication in the information sphere of human existence and communication. A comparative consideration of the worldviews in the information philosophy and transhumanism projects, made on the basis of a study of current scientific literature, provided an opportunity to assume the probability of implicit elimination of the problems of philosophical anthropology from the horizon of meanings of modern science through the blurring of essentially anthropological analytics. Originality. The article proves the ambivalent nature of the correlation between the projects of philosophy and transhumanism information that are externally close on the subject and problematics, and for the first time in the domestic literature, they have been compared. The content of the powerful potential of information philosophy for the development of philosophical anthropology approaches to the phenomena of the human world determined by the technological nature of civilization and the powerful sociocultural issues of modernity have been clarified. The threats of the dehumanization of the problem field in the modern science and spheres of applied digital technologies associated with transhumanism, interpreted as an ideology, are underlined. Conclusions. The analysis of theoretical positions relevant for the philosophy of information and transhumanism resulted in a number of conclusions, central among which is the statement of the "blurring" situation, the hidden elimination in the content of problematics of philosophical anthropology and its humanistic pathos within the limits of modern forms of correlation and existence in the scientific discourse of the philosophemes and ideologemes in the information philosophy and transhumanism. Epistemological phenomena of "cognitive closure" and a man as a "blind spot" in the thinking on the science and technology development, primarily communication, indicate the relevance of a full comprehensive consideration of the problems of philosophical anthropology in projects of the information philosophy and transhumanism. (shrink)

Wilfrid Sellars attempts to deflect traditional objections to the straight rule of inductive acceptance by embedding it in a complicated system of levels. This system rests on a theory of probability in which the meaning of "probable" is reconstructed in the context of Sellars' general theory of practical reason. To say a statement is probable means, according to Sellars, that there is good reason for accepting the statement as true. In this paper I examine Sellars' attempt to resuscitate the (...) straight rule and conclude that not only does he fail, but his account of "probable" is circular. (shrink)

The Philosophy of Umberto Eco stands out in the Library of Living Philosophers series as the volume on the most interdisciplinary scholar hitherto and probably the most widely translated. The Italian philosopher's name and works are well known in the humanities, both his philosophical and literary works being translated into fifteen or more languages. Eco is a founder of modern semiotics and widely known for his work in the philosophy of language and aesthetics. He is also a leading (...) figure in the emergence of postmodern literature, and is associated with cultural and mass communication studies. His writings cover topics such as advertising, television, and children's literature as well as philosophical questions bearing on truth, reality, cognition, language, and literature. The critical essays in this volume cover the full range of this output. This book has wide appeal not only because of its interdisciplinary nature but also because of Eco's famous "high and low" approach, which is deeply scholarly in conception and very accessible in outcome. The short essay "Why Philosophy?" included in the volume is exemplary in this regard: it will appeal to scholars for its wit and to high school students for its intelligibility. (shrink)