Tamara Kayali Browne's proposal for an Ethics Review Panel for the Diagnostic and Statistical Manual of Mental Disorders conceives of a state-sponsored panel of academic experts—philosophers, sociologists, and bioethicists—dealing in a reflective, systematic, and standardized manner with the "value judgements" that are an "integral and unavoidable part of psychiatric nosology". The panel would consider existing and new diagnostic categories, and issue authoritative vetoes and/or modifications as appropriate. Browne asserts that, "it should not be necessary to have protests and political activism, (...) such as that involved in removing homosexuality from the DSM, in... (shrink)

Chattopadhyaya (philosophy, Jadavpur U., Calcutta) examines the epistemological and methodological implications of induction and probability.

Bacon’s project suggests in theory that the obtaining of absolute certain knowledge is possible but in fact such knowledge is revealed to be impossible. Th e description of the human mind on which Bacon’s account is based seems to imply that the impossibility of obtaining absolute certainty does not depend on the contingent historical situation of a preliminary stage of the scientifi c endeavor. Consequently, a gap emerges between the proposed goal of science and the ways to reach it: Bacon (...) tried to obtain absolute certainty but he only could arrive at degrees of certainty and probability both in theories and in facts. Malgrè lui, Bacon shows himself developing in fact a kind of probabilistic science instead of surpassing the limits to knowledge posed by the skeptical arguments. Th at is the reason why many of his followers could develop a mitigated skepticism in the framework of a Baconian science. (shrink)

This book sheds light on some recent discussions of the problems in probability theory and their history, analysing their philosophical and mathematical significance, and the role pf mathematical probability theory in other sciences.

Recognizing that probability (the Greek doxa) was understood in pre-modern theories as the polar opposite of certainty (episteme), the author of this study elaborates the forms which these polar opposites have taken in some twentieth century writers and then, in greater detail, in the writings of Thomas Aquinas. Profiting from subsequent more sophisticated theories of probability, he examines how Aquinas’s judgments about everything from God to gossip depend on schematizations of the polarity between the systematic and the non-systematic: revelation/reason, science/opinion, (...) saints/philosophers, Aristotle/others. Post-medieval developments have provided the means to discern within Thomas’s thought both a logical theory and a kind of relative frequency theory of probability. The former depends on Aristotle’s theory of demonstration, the latter on his theory of an orderly cosmos; but each as used by Thomas lead to convictions that are sometimes naive, sometimes amusing or even terrifying. (shrink)

The aim of this paper is to investigate the ascription of probabilities in a causal model of an episode in the history of science. The aim of such a quantitative approach is to allow the implementation of the causal model in a computer, to run simulations. As an example, we look at the beginning of the science of magnetism, “explaining” — in a probabilistic way, in terms of a single causal model — why the field advanced in China but (...) not in Europe (the difference is due to different prior probabilities of certain cultural manifestations). Given the number of years between the occurrences of two causally connected advances X and Y, one proposes a criterion for stipulating the value pY/X of the conditional probability of an advance Y occurring, given X. Next, one must assume a specific form for the cumulative probability function pY/X(t), which we take to be the time integral of an exponential distribution function, as is done in physics of radioactive decay. Rules for calculating the cumulative functions for more than two events are mentioned, involving composition, disjunction and conjunction of causes. We also consider the problems involved in supposing that the appearance of events in time follows an exponential distribution, which are a consequence of the fact that a composition of causes does not follow an exponential distribution, but a “hypoexponential” one. We suggest that a gamma distribution function might more adequately represent the appearance of advances. (shrink)

In the framework of the histories approach to quantum mechanics developed by Griffiths and Omnès, we consider the question of the uniqueness of the probability assigned to the histories; the question was solved by Omnès only in special cases. We find conditions which ensure uniqueness of such probability in the general case.

The paper examines Wesley Salmon’s claim that the primary role of plausibility arguments in the history of science is to impose constraints on the prior probability of hypotheses. A detailed look at Copernicanism and Darwinism and, more briefly, Rutherford’s discovery of the atomic nucleus reveals a further and arguably more important role of plausibility arguments. It resides in the consideration of likelihoods, which state how likely a given hypothesis makes a given piece of evidence. In each case the likelihoods raise (...) the probability of one of the competing hypotheses and diminish the credibility of its rival, and this may happen either on the basis of ‘old’ or ‘new’ evidence.Keywords: Copernicanism; Darwinism; Atom models; Bayesianism; Likelihoods; Probability arguments. (shrink)

This volume brings together a collection of essays on the history and philosophy of probability and statistics by one of the eminent scholars in these subjects. Written over the last fifteen years, they fall into three broad categories. The first deals with the use of symmetry arguments in inductive probability, in particular, their use in deriving rules of succession. The second group deals with four outstanding individuals who made lasting contributions to probability and statistics in very different ways: Frank Ramsey, (...) R. A. Fisher, Alan Turing, and Abraham de Moivre. The last group of essays deals with the problem of 'predicting the unpredictable' - making predictions when the range of possible outcomes is unknown in advance. The essays weave together the history and philosophy of these subjects and document the fascination that they have exercised for more than three centuries. (shrink)

Probability has become one of the most characteristic con cepts of modern culture, and a 'probabilistic way of thinking' may be said to have penetrated almost every sector of our in tellectual life. However it would be difficult to determine an explicit list of 'positive' features, to be proposed as identifica tion marks of this way of thinking. One would rather say that it is characterized by certain 'negative' features, i. e. by certain at titudes which appear to be the (...) negation of well established tra ditional assumptions, conceptual frameworks, world outlooks and the like. It is because of this opposition to tradition that the probabilistic approach is perceived as expressing a 'modern' in tellectual style. As an example one could mention the widespread diffidence in philosophy with respect to self -contained systems claiming to express apodictic truths, instead of which much weaker pretensions are preferred, that express 'probable' interpretations of reality, of history, of man (the hermeneutic trend). An ana logous example is represented by the interest devoted to the study of different patterns of 'argumentation', dealing wiht reasonings which rely not so much on the truth of the premisses and stringent formal logic links, but on a display of contextual conditions (depending on the audience, and on accepted stan dards, judgements, and values), which render the premisses and the conclusions more 'probable' (the new rhetoric). (shrink)

The term probability can be used in two main senses. In the frequency interpretation it is a limiting ratio in a sequence of repeatable events. In the Bayesian view, probability is a mental construct representing uncertainty. This 2002 book is about these two types of probability and investigates how, despite being adopted by scientists and statisticians in the eighteenth and nineteenth centuries, Bayesianism was discredited as a theory of scientific inference during the 1920s and 1930s. Through the examination of a (...) dispute between two British scientists, the author argues that a choice between the two interpretations is not forced by pure logic or the mathematics of the situation, but depends on the experiences and aims of the individuals involved. The book should be of interest to students and scientists interested in statistics and probability theories and to general readers with an interest in the history, sociology and philosophy of science. (shrink)

With this treatise, an insightful exploration of the probabilistic connection between philosophy and the history of science, the famous economist breathed new life into studies of both disciplines. Originally published in 1921, this important mathematical work represented a significant contribution to the theory regarding the logical probability of propositions. Keynes effectively dismantled the classical theory of probability, launching what has since been termed the “logical-relationist” theory. In so doing, he explored the logical relationships between classifying a proposition as “highly probable” (...) and as a “justifiable induction.” Unabridged republication of the classic 1921 edition. (shrink)

John Maynard Keynes’s A Treatise on Probability is the seminal text for the logical interpretation of probability. According to his analysis, probabilities are evidential relations between a hypothesis and some evidence, just like the relations of deductive logic. While some philosophers had suggested similar ideas prior to Keynes, it was not until his Treatise that the logical interpretation of probability was advocated in a clear, systematic and rigorous way. I trace Keynes’s influence in the philosophy of probability through a (...) heterogeneous sample of thinkers who adopted his interpretation. This sample consists of Frederick C. Benenson, Roy Harrod, Donald C. Williams, Henry E. Kyburg and David Stove. The ideas of Keynes prove to be adaptable to their diverse theories of probability. My discussion indicates both the robustness of Keynes’s probability theory and the importance of its influence on the philosophers whom I describe. I also discuss the Problem of the Priors. I argue that none of those I discuss have obviously improved on Keynes’s theory with respect to this issue. (shrink)

Historical records show that there was no real concept of probability in Europe before the mid-seventeenth century, although the use of dice and other randomizing objects was commonplace. Ian Hacking presents a philosophical critique of early ideas about probability, induction, and statistical inference and the growth of this new family of ideas in the fifteenth, sixteenth, and seventeenth centuries. Hacking invokes a wide intellectual framework involving the growth of science, economics, and the theology of the period. He argues that the (...) transformations that made it possible for probability concepts to emerge have constrained all subsequent development of probability theory and determine the space within which philosophical debate on the subject is still conducted. First published in 1975, this edition includes an introduction that contextualizes his book in light of developing philosophical trends. Ian Hacking is the winner of the Holberg International Memorial Prize 2009. (shrink)

By examining in particular Augustan notions of probability and the way they provided a framework for thinking about and organising experience, Dr Patey ...

How can probabilities make sense in a deterministic many-worlds theory? We address two facets of this problem: why should rational agents assign subjective probabilities to branching events, and why should branching events happen with relative frequencies matching their objective probabilities. To address the first question, we generalise the Deutsch–Wallace theorem to a wide class of many-world theories, and show that the subjective probabilities are given by a norm that depends on the dynamics of the theory: the (...) 2-norm in the usual Many-Worlds interpretation of quantum mechanics, and the 1-norm in a classical many-worlds theory known as Kent’s universe. To address the second question, we show that if one takes the objective probability of an event to be the proportion of worlds in which this event is realised, then in most worlds the relative frequencies will approximate well the objective probabilities. This suggests that the task of determining the objective probabilities in a many-worlds theory reduces to the task of determining how to assign a measure to the worlds. (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)

Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but yields probabilities. In working out these ideas an important motif is to stay close to the standard formalism of quantum mechanics and to refrain from introducing new structure by hand. In this paper we explain how this programme can be made concrete. In particular, we show that the (...) Born probability rule, and sets of definite-valued observables to which the Born probabilities pertain, can be uniquely defined from the quantum state and Hilbert space structure. We discuss the status of probability in modal interpretations, and to this end we make a comparison with many-worlds alternatives. An overall point that we stress is that the modal ideas define a general framework and research programme rather than one definite and finished interpretation. (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)

Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but yields probabilities. In working out these ideas an important motif is to stay close to the standard formalism of quantum mechanics and to refrain from introducing new structure by hand. In this paper we explain how this programme can be made concrete. In particular, we show that the (...) Born probability rule, and sets of definite-valued observables to which the Born probabilities pertain, can be uniquely defined from the quantum state and Hilbert space structure. We discuss the status of probability in modal interpretations, and to this end we make a comparison with many-worlds alternatives. An overall point that we stress is that the modal ideas define a general framework and research programme rather than one definite and finished interpretation. (shrink)

I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but the proof is simpler and proceeds from weaker decision-theoretic assumptions. This makes it easier to discuss the conceptual ideas involved in the proof, and to show that they are defensible.

This volume explores the conceptual terrain defined by the Greek word eikos: the probable, likely, or reasonable. A term of art in Greek rhetoric, a defining feature of literary fiction, a seminal mode of historical, scientific, and philosophical inquiry, eikos was a way of thinking about the probable and improbable, the factual and counterfactual, the hypothetical and the real. These thirteen original and provocative essays examine the plausible arguments of courtroom speakers and the 'likely stories' of philosophers, verisimilitude in art (...) and literature, the likelihood of resemblance in human reproduction, the limits of human knowledge and the possibilities of ethical and political agency. The first synthetic study of probabilistic thinking in ancient Greece, the volume illuminates a fascinating chapter in the history of Western thought. (shrink)

In the Bayesian approach to quantum mechanics, probabilities—and thus quantum states—represent an agent’s degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept of certainty in quantum mechanics. Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations on the other. We first review the main arguments for the general claim that (...) probabilities always represent degrees of belief. We then argue that a quantum state prepared by some physical device always depends on an agent’s prior beliefs, implying that the probability-1 predictions derived from that state also depend on the agent’s prior beliefs. Quantum certainty is therefore always some agent’s certainty. Conversely, if facts about an experimental setup could imply agent-independent certainty for a measurement outcome, as in many Copenhagen-like interpretations, that outcome would effectively correspond to a preexisting system property. The idea that measurement outcomes occurring with certainty correspond to preexisting system properties is, however, in conflict with locality. We emphasize this by giving a version of an argument of Stairs [(1983). Quantum logic, realism, and value-definiteness. Philosophy of Science, 50, 578], which applies the Kochen–Specker theorem to an entangled bipartite system. (shrink)

Hume’s main argument against rational belief in miracles might seem to rule out rational belief in other antecedently improbable occurrences as well--for example, a certain person’s having won the lottery. Dorothy Coleman has recently defended Hume against the lottery counterexample, invoking Hume’s distinction between probability of chances and probability of causes. I argue that Coleman’s defence fails.

GRW Theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood (...) only as either single case propensities or Humean objective chances. Although single case propensities have some intuitive appeal in the context of GRW theory, on balance it seems that Humean objective chances are preferable on conceptual grounds because single case propensities suffer from various well know problems such as unlimited frequency tolerance and lack of a rationalisation of the principal principle. (shrink)

Illuminates legal reasoning -- and its justification At least since plato and Aristotle, thinkers have pondered the relationship between philosophical arguments and the "sophistical" arguments offered by the Sophists -- who were the first professional lawyers. Judges wield substantial political power, and the justifications they offer for their decisions are a vital means by which citizens can assess the legitimacy of how that power is exercised. However, to evaluate judicial justifications requires close attention to the method of reasoning behind decisions. (...) This new collection illuminates and explains the political and moral importance in justifying the exercise of judicial power. Explores enduring questions Focusing on work over the past century, the essays address important recurring questions, such as: When a judge or a lawyer reasons to a conclusion about what is legally required in a given case, must he also ask what is morally required? To what extent do a judge's personal, political, or moral biases affect his legal reasoning? What is the impact of such biases? Can all such biases be avoided? Is legal reasoning similar to reasoning in mathematics, logic, and linguistics, the physical sciences, the social sciences, or literature and history? Do formal logical modes of argument play any roles in legal reasoning? Solid coverage, well organized The articles were chosen to present some of the most influential works on the topic, as well as less familiar works that are thought provoking and informative. Each volume also offers a representative range of theoretical approaches to its topic, contains an introduction that locates the subject within the larger framework oftheories of legal reasoning and jurisprudence, and includes bibliographical notes on further readings. Many 19th century legal theorists argued that deduction is the central mode of legal reasoning, and that legal argument is like a deductive proof in mathematics or logic. They were attracted to this "deductivist" concept because it suggested that legal reasoning could be politically and morally neutral. This volume brings together some of the most thought-provoking articles on both sides of the debate. It also contains several leading articles that explain the role of probabilistic judgments and presumptions in various types of legal arguments, including the laws of evidence and criminal procedure. The collection is a solid introduction to the basic modes of logical argument in legal reasoning. (shrink)

Any attempt to introduce probabilities into quantum mechanics faces difficulties due to the mathematical structure of Hilbert space, as reflected in Birkhoff and von Neumann's proposal for a quantum logic. The (consistent or decoherent) histories solution is provided by its single framework rule, an approach that includes conventional (Copenhagen) quantum theory as a special case. Mermin's Ithaca interpretation addresses the same problem by defining probabilities which make no reference to a sample space or event algebra (“correlations without correlata”). (...) But this leads to severe conceptual difficulties, which almost inevitably couple quantum theory to unresolved problems of human consciousness. Using histories allows a sharper quantum description than is possible with a density matrix, suggesting that the latter provides an ensemble rather than an irreducible single-system description as claimed by Mermin. The histories approach satisfies the first five of Mermin's desiderata for a good interpretation of quantum mechanics, including Einstein locality, but the Ithaca interpretation seems to have difficulty with the first (independence of observers) and the third (describing individual systems). (shrink)

Objective probability in quantum mechanics is often thought to involve a stochastic process whereby an actual future is selected from a range of possibilities. Everett’s seminal idea is that all possible definite futures on the pointer basis exist as components of a macroscopic linear superposition. I demonstrate that these two conceptions of what is involved in quantum processes are linked via two alternative interpretations of the mind-body relation. This leads to a fission, rather than divergence, interpretation of Everettian theory and (...) to a novel explanation of why a principle of indifference does not apply to self-location uncertainty for a post-measurement, pre-observation subject, just as Sebens and Carroll claim. Their Epistemic Separability Principle is shown to arise out of this explanation and the derivation of the Born rule for Everettian theory is thereby put on a firmer footing. (shrink)

This paper attempts to reconstruct Hume's argument in Treatise 1.4.1, 'Of Scepticism with Regard to Reason'.

I shall argue that there is no such property of an event as its “probability.” This is why standard interpretations cannot give a sound definition in empirical terms of what “probability” is, and this is why empirical sciences like physics can manage without such a definition. “Probability” is a collective term, the meaning of which varies from context to context: it means different — dimensionless [0, 1]-valued — physical quantities characterising the different particular situations. In other words, probability is a (...) reducible concept, supervening on physical quantities characterising the state of affairs corresponding to the event in question. On the other hand, however, these “probability-like” physical quantities correspond to objective features of the physical world, and are objectively related to measurable quantities like relative frequencies of physical events based on finite samples — no matter whether the world is objectively deterministic or indeterministic. (shrink)

This paper relates both to the metaphysics of probability and to the physics of time asymmetry. Using the formalism of decoherent histories, it investigates whether intuitions about intrinsic time directedness that are often associated with probability can be justified in the context of no-collapse approaches to quantum mechanics. The standard approach to time symmetry in the decoherent histories literature is criticised, and an alternative approach is proposed, based on two decoherence conditions within the one-vector formalism. In turn, considerations of forwards (...) and backwards decoherence and of decoherence and recoherence suggest that a time-directed interpretation of probabilities, if adopted, should be both contingent and perspectival. (shrink)

We consider probability theories in general. In the first part of the paper, various constraints are imposed and classical probability and quantum theory are recovered as special cases. Quantum theory follows from a set of five reasonable axioms. The key axiom which gives us quantum theory rather than classical probability theory is the continuity axiom, which demands that there exists a continuous reversible transformation between any pair of pure states. In the second part of this paper, we consider in detail (...) how the measurement process works in both the classical and the quantum case. The key differences and similarities are elucidated. It is shown how measurement in the classical case can be given a simple ontological interpretation which is not open to us in the quantum case. On the other hand, it is shown that the measurement process can be treated mathematically in the same way in both theories even to the extent that the equations governing the state update after measurement are identical. The difference between the two cases is seen to be due not to something intrinsic to the measurement process itself but, rather, to the nature of the set of allowed states and, therefore, ultimately to the continuity axiom. (shrink)