Chance and Objective Probability

If a proposition is typically true, given your evidence, then you should believe that proposition; or so I argue here. In particular, in this paper, I propose and defend a principle of rationality---call it the `Typical Principle'---which links rational belief to facts about what is typical. As I show, this principle avoids several problems that other, seemingly similar principles face. And as I show, in many cases, this principle implies the verdicts of the Principal Principle: so ultimately, the Typical Principle (...) may be the more fundamental of the two. (shrink)

The propensity nature of evolutionary fitness has long been appreciated and is nowadays amply discussed. The discussion has, however, on occasion followed long standing conflations in the philosophy of probability literature between propensities, probabilities, and frequencies. In this paper, I apply a more recent conception of propensities in modelling practice to some of the key issues, regarding the mathematical representation of fitness and how it may be regarded as explanatory. The ensuing complex nexus of fitness emphasises the distinction between biological (...) propensities and the probability distributions over offspring numbers that they give rise to; and how critical it is to distinguish the possession conditions of the underlying dispositional properties from those of their probabilistic manifestations. (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)

In this work, five different interpretations of "probability" are analyzed: the classical, logical, subjective, relative frequency, and propensity interpretations. The objective is to determine which of these interpretations is most suitable for probability applications in the physical and biological sciences. The first state of this analysis involves evaluating the different interpretations with respect to the probability calculus. The objective at this point is not to reject any interpretations outright, but rather to keep in mind any difficulties in adherence to the (...) calculus when evaluating these interpretations in later chapters. The second stage involves defending the need for an "objectivity criterion" and evaluating the various interpretations of "probability" with respect to this criterion. This "objectivity criterion" states that an adequate analysis of "probability" should result in probability statements that are true or false in virtue of the way the world is, independently of anyone's state of knowledge or beliefs about the probabilities in question. Based on this criterion, the classical, logical, and subjective interpretations are rejected. The third stage involves evaluating the relative frequency interpretation in greater detail. Both the actual relative frequency interpretation and the hypothetical relative frequency interpretation are evaluated. The actual relative frequency interpretation is found to be a promising candidate for providing an adequate analysis of "probability" for the physical and biological sciences. The fourth stage involves a detailed evaluation of the propensity interpretation. The propensity interpretation is shown to be in a weaker epistemological position than the relative frequency interpretation and to stem largely from misguided motivations concerning the importance of the single case in scientific applications and the nature of scientific explanation. Ultimately, it is concluded that the traditional actual relative frequency interpretation provides the best analysis of "probability" for applications in the physical and biological sciences. (shrink)

Chapter 1 of this thesis concerns counterfactual conditionals. David Lewis has offered a natural and influential analysis of counterfactuals. But the analysis fails to take into account the asymmetry of entropy, and comes to grief precisely because of that failure. The cause of the grief is that processes involving the increase of entropy are exceedingly sensitive to small changes in their final conditions. ;Chapter 2 concerns robust dispositions. Drop an ordinary rock into hydrofluoric acid, and---almost no matter what is going (...) on far away---it will dissolve. In other words, the rock displays a disposition to dissolve that is robust with respect to small variations in its environment. Why is it that so many objects display robust dispositions to melt, cool down, explode, hatch, and so on? Because entropy increases over time. ;Chapter 3 concerns conscious experience. Take any world with fundamental dynamical laws rather like ours, but in which entropy doesn't increase. Take any system in that world that changes state by changing thermodynamically. That system has no experiences whatsoever. That's because , in order to have an experience it is necessary to display certain robust dispositions. And such systems fail to display the requisite dispositions. (shrink)

A pragmatic account of scientific understanding is used both to examine and to unify fundamental questions concerning the propensity interpretation of probability and theories of chance, causation, and explanation. One of the most important problems to be addressed is the problem of defining homogeneous reference classes in theories of chance, causation, and explanation. The consistency of the propensity interpretation is defended against traditional criticisms such as "Humphreys's paradox." It is demonstrated that the application of this interpretation to theories of chance (...) and probabilistic causation provides insights into problems common to both theories. Various approaches to causation are examined, including those based on identifying sufficient causal factors, necessary causal factors, and contrastive causes. These insights are applied to quantum mechanics and are presented in terms of a set of controlled experiments. The study of quantum mechanics focuses on the paradox of the two slit experiment and quantum logical and quantum probabilistic attempts to resolve this paradox. Finally, the analysis of chance and causation provides the basis for a version of the contrastive theory of explanation. This theory of explanation provides a unique understanding of the nature of explanation, and lessens the impact of the problems of homogeneity and of explanatory ambiguity. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps, and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may (...) freely copy and distribute this work, as no entity has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The Empire of Chance tells how quantitative ideas of chance transformed the natural and social sciences, as well as daily life over the last three centuries. A continuous narrative connects the earliest application of probability and statistics in gambling and insurance to the most recent forays into law, medicine, polling and baseball. Separate chapters explore the theoretical and methodological impact in biology, physics and psychology. Themes recur - determinism, inference, causality, free will, evidence, the shifting meaning of probability - but (...) in dramatically different disciplinary and historical contexts. In contrast to the literature on the mathematical development of probability and statistics, this book centres on how these technical innovations remade our conceptions of nature, mind and society. Written by an interdisciplinary team of historians and philosophers, this readable, lucid account keeps technical material to an absolute minimum. It is aimed not only at specialists in the history and philosophy of science, but also at the general reader and scholars in other disciplines. (shrink)

A careful presentation of the foundations of probability theory, containing many valuable innovations. Two accounts of probability are adduced: probability as a measure on the subsets of a probability set, and as a measure on the sentences of a formal language. The book stresses connections between these two accounts; of particular interest is its thesis that statistical probabilities may be regarded as estimates of inductive probabilities.—R. H. T.

Introduces probability theory largely by way of precept. Results of theory are stated, not derived, and then problems are proposed and solved by way of illustration. Although there is a commendable number of such problems, it should be noted that no exercises are concocted and left for the reader. Other topics touched upon besides discrete probability are continuous probability and probability of causes. The treatment lays bare some philosophical issues.—P. S.

In my recent article on these pages I argued that members of the Austrian School of economics have adopted and defended a faulty definition of probability. I argued that the definition of probability necessarily depends upon the nature of the world in which we live. I claimed that if the nature of the world is such that every event and phenomenon which occurs has a cause of some sort, then probability must be defined subjectively; that is, “as a measure of (...) our uncertainty about the likelihood of occurrence of some event or phenomenon, based upon evidence that need not derive solely from past frequencies of ‘collectives’ or ‘classes.’” I further claimed that the nature of the world is indeed such that all events and phenomena have prior causes, and that this fact compels us to adopt a subjective definition of probability.David Howden has recently published what he claims is a refutation of my argument in his article “Single Trial Probability Applications: Can Subjectivity Evade Frequency Limitations” . Unfortunately, Mr. Howden appears to not have understood my argument, and his purported refutation of my subjective definition consequently amounts to nothing more than a concatenation of confused and fallacious ideas that are completely irrelevant to my argument. David Howden has thus failed in his attempt to vindicate Richard von Mises’s definition of probability. (shrink)

Both Ludwig von Mises and Richard von Mises claimed that numerical probability could not be legitimately applied to singular cases. This paper challenges this aspect of the von Mises brothers’ theory of probability. It is argued that their denial that numerical probability could be applied to singular cases was based solely upon Richard von Mises’ exceptionally restrictive definition of probability. This paper challenges Richard von Mises’ definition of probability by arguing that the definition of probability necessarily depends upon whether the (...) world is governed by time-invariant causal laws. It is argued that if the world is governed by time-invariant causal laws, a subjective definition of probability must be adopted. It is further argued that both the nature of human action and the relative frequency method for calculating numerical probabilities both presuppose that the world is indeed governed by time-invariant causal laws. It is finally argued that the subjective definition of probability undercuts the von Mises claim that numerical probability cannot legitimately be applied to singular, non-replicable cases. (shrink)

Frequency probability theorists define an event’s probability distribution as the limit of a repeated set of trials belonging to a homogeneous collective. The subsets of this collective are events which we have deficient knowledge about on an individual level, although for the larger collective we have knowledge its aggregate behavior. Hence, probabilities can only be achieved through repeated trials of these subsets arriving at the established frequencies that define the probabilities. Crovelli argues that this is a mistaken approach, and that (...) a subjective assessment of individual trials should be used instead. Bifurcating between the two concepts of risk and uncertainty, Crovelli first asserts that probability is the tool used to manage uncertain situations, and then attempts to rebuild a definition of probability theory with this in mind. We show that such an attempt has little to gain, and results in an indeterminate application of entrepreneurial forecasting to uncertain decisions—a process far-removed from any application of probability theory. (shrink)

'Uncertainty and chance' is a subject with a broad span, in that there is no academic discipline or walk of life that is not beset by uncertainty and chance. In this book a range of approaches is represented by authors from varied disciplines: natural sciences, mathematics, social sciences and medical sciences. At one extreme, this volume is concerned with the foundations of probability. At the other extreme, we have scholars who acknowledge the concept of chance and uncertainty but do not (...) cope with it by means of systematic measurement or quantative analysis. (shrink)

This paper addresses the problem of the interpretation of probability in quantitative causal analysis. I argue that probability has to be interpreted according to a Bayesian framework in which degrees of belief are frequency-driven. This interpretation can account for the peculiar use and meaning of probability in generic and single-case causal inferences involved in this domain.

An approach to inference to the best explanation integrating a Popperianconception of natural laws together with a modified Hempelian account of explanation, one the one hand, and Hacking's law of likelihood, on the other, which provides a robust abductivist model of sciencethat appears to overcome the obstacles that confront its inductivist,deductivist, and hypothetico-deductivist alternatives.This philosophy of scienceclarifies and illuminates some fundamental aspects of ontology and epistemology, especially concerning the relations between frequencies and propensities. Among the most important elements of this (...) conception is thecentral role of degrees of nomic expectability in explanation, prediction,and inference, for which this investigation provides a theoretical defense. (shrink)