Maxwell's deduction of the probability distribution over the velocity of gas molecules—one of the most important passages in physics (Truesdell)—presents a riddle: a physical discovery of the first importance was made in a single inferential leap without any apparent recourse to empirical evidence. -/- Tychomancy proposes that Maxwell's derivation was not made a priori; rather, he inferred his distribution from non-probabilistic facts about the dynamics of intermolecular collisions. Further, the inference is of the same sort as everyday reasoning about the (...) physical probabilities attached to such canonical chance setups as tossed coins or rolled dice. The structure of this reasoning is investigated and some simple rules for inferring physical probabilities from symmetries and other causally relevant properties of physical systems are proposed. -/- Not only physics but evolutionary biology and population ecology, the science of measurement error, and climate modeling have benefited enormously from the same kind of reasoning, the book goes on to argue. Inferences from dynamics to probability are so obvious to us, however, that their methodological importance has been largely overlooked. (shrink)

Written by one of the preeminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, economics, philosophy, cognitive science, and the health and social sciences. Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections (...) and statistical associations. Cited in more than 2,100 scientific publications, it continues to liberate scientists from the traditional molds of statistical thinking. In this revised edition, Judea Pearl elucidates thorny issues, answers readers' questions, and offers a panoramic view of recent advances in this field of research. Causality will be of interest to students and professionals in a wide variety of fields. Dr Judea Pearl has received the 2011 Rumelhart Prize for his leading research in Artificial Intelligence and systems from The Cognitive Science Society. (shrink)

The most promising accounts of ontic probability include the Spielraum conception of probabilities, which can be traced back to J. von Kries and H. Poincaré, and the best system account by D. Lewis. This paper aims at comparing both accounts and at combining them to obtain the best of both worlds. The extensions of both Spielraum and best system probabilities do not coincide because the former only apply to systems with a special dynamics. Conversely, Spielraum probabilities may not be part (...) of the best system, e.g. if a broad class of random devices is not often used. Spielraum probabilities have the potential to provide illuminating explanations of frequencies with which outcomes of trials on gambling devices arise. They ultimately fail to account for such frequencies though because they are compatible with frequencies that grossly differ from the values of the respective probabilities. I thus follow recent proposals by M. Strevens and M. Abrams and strengthen the definition of Spielraum probabilities by adding a further condition that restricts some actual frequencies. The resulting account remains limited in scope, but stands objections raised against it in the recent literature: it is neither circular nor based upon arbitrary choices of a measure or of physical variables. Nor does it lack any explanatory power. (shrink)

Metaphysicians speak of laws of nature in terms of necessity and universality; scientists, in terms of symmetry and invariance. In this book van Fraassen argues that no metaphysical account of laws can succeed. He analyzes and rejects the arguments that there are laws of nature, or that we must believe there are, and argues that we should disregard the idea of law as an adequate clue to science. After exploring what this means for general epistemology, the author develops the empiricist (...) view of science as a construction of models to represent the phenomena. (shrink)

: This paper outlines a genuinely pragmatist conception of propensity, and defends it against common objections to the propensity interpretation of probability, prominently Humphreys’ paradox. The paper reviews the paradox and identifies one of its key assumptions, the identity thesis, according to which propensities are probabilities. The identity thesis is also involved in empiricist propensity interpretations deriving from Popper’s influential original proposal, and makes such interpretations untenable. As an alternative, I urge a return to Charles Peirce’s original insights on probabilistic (...) dispositions, and offer a reconstructed version of his pragmatist conception, which rejects the identity thesis. – Correspondence to: [email protected]. (shrink)

This paper justifies the inference of probabilities from symmetries. I supply some examples of important and correct inferences of this variety. Two explanations of such inferences -- an explanation based on the Principle of Indifference and a proposal due to Poincaré and Reichenbach -- are considered and rejected. I conclude with my own account, in which the inferences in question are shown to be warranted a posteriori, provided that they are based on symmetries in the mechanisms of chance setups.

In this paper, a concept of chance is introduced that is compatible with deterministic physical laws, yet does justice to our use of chance-talk in connection with typical games of chance. We take our cue from what Poincaré called "the method of arbitrary functions," and elaborate upon a suggestion made by Savage in connection with this. Comparison is made between this notion of chance, and David Lewis' conception.

A proposal for an objective interpretation of probability is introduced and discussed: probabilities as deriving from ranges in suitably structured initial-state spaces. Roughly, the probability of an event on a chance trial is the proportion of initial states that lead to the event in question within the space of all possible initial states associated with this type of experiment, provided that the proportion is approximately the same in any not too small subregion of the space. This I would like to (...) call the “natural-range conception” of probability. Providing a substantial alternative to frequency or propensity accounts of probability in a deterministic setting, it is closely related to the so-called “method of arbitrary functions”. It is explicated, confronted with certain problems, and some ideas how these might be overcome are sketched and discussed. (shrink)

Johannes von Kries’s Spielraum-theory is regarded as one of the most important philosophical contributions of the nineteenth century to an objective interpretation of probability. This paper aims at a critical and contextual analysis of von Kries’s approach: It is contextual insofar as it reconstructs the Spielraum-theory in the historical setting that formed his scientific and philosophical outlook. It is critical insofar as it unfolds systematic tensions and inconsistencies which are rooted in this context, especially in the grave change of mechanism (...) which took place in the late nineteenth century. In this regard, the paper focuses on von Kries’s understanding of natural laws and nomological knowledge in relation to his concept of objective probability. While the formal approach of the Spielraum-theory—as far as developed by von Kries—seems sound, his epistemological claims with respect to nomological knowledge sustain classical mechanism and are hence difficult to substantiate from the point of view of modern science. (shrink)

It is argued that in deterministic contexts evidence for causal relations states whether a boundary condition makes a difference or not to a phenomenon. In order to substantiate the analysis, I show that this difference/indifference making is the basic type of evidence required for eliminative induction in the tradition of Francis Bacon and John Stuart Mill. To this purpose, an account of eliminative induction is proposed with two distinguishing features: it includes a method to establish the causal irrelevance of boundary (...) conditions by means of indifference making, which is called strict method of agreement, and it introduces the notion of a background against which causal statements are evaluated. Causal statements thus become three-place-relations postulating the relevance or irrelevance of a circumstance C to the examined phenomenon P with respect to a background B of further conditions. To underline the importance of evidence in terms of difference/indifference making, I sketch two areas, in which eliminative induction is extensively used in natural and engineering sciences. One concerns exploratory experiments, the other engineering design methods. Given that a method is discussed that has been used for centuries, I make no claims to novelty in this paper, but hope that the combined discussion of several topics that are still somewhat underrepresented in the philosophy of science literature is of some merit. (shrink)

I argue for the causal character of modeling in data-intensive science, contrary to widespread claims that big data is only concerned with the search for correlations. After discussing the concept of data-intensive science and introducing two examples as illustration, several algorithms are examined. It is shown how they are able to identify causal relevance on the basis of eliminative induction and a related difference-making account of causation. I then situate data-intensive modeling within a broader framework of an epistemology of scientific (...) knowledge. In particular, it is shown to lack a pronounced hierarchical, nested structure. The significance of the transition to such “horizontal” modeling is underlined by the concurrent emergence of novel inductive methodology in statistics such as non-parametric statistics. Data-intensive modeling is well equipped to deal with various aspects of causal complexity arising especially in the higher level and applied sciences. (shrink)

Tn this paper I explore and to an extent defend HS. The main philosophical challenges to HS come from philosophical views that say that nomic concepts-laws, chance, and causation-denote features of the world that fail to supervene on non-nomic features. Lewis rejects these views and has labored mightily to construct HS accounts of nomic concepts. His account of laws is fundamental to his program, since his accounts of the other nomic notions rely on it. Recently, a number of philosophers have (...) criticized Lewis's account, and Humean accounts of laws generally, for delivering, at best, a pale imitation ofthe genuine item. These philosophers think that the notion of law needed by science requires laws-if there are any-to be fundamental features of our world that are completely distinct from and not supervenient on the particular facts that they explain. I side with Lewis against these philosophers. Here I will argue that although Lewis-laws don't fulfill all our philosophical expectations, they do play the roles that science needs laws to play. The metaphysics and epistemology of Humean laws, and more specifically, Lewis-laws, are in much better shape than the metaphysics and epistemology of the main anti-Humean alternatives. However, I do have inisgivings about Lewis's account. Both he and his critics assume that the basic properties are so individuated so that the laws are not metaphysically necessary. If this assumption is rejected, then the question of Humean supervenience lapses. I conclude with a brief discussion of this position. (shrink)

The epistemic state of complete ignorance is not a probability distribution. In it, we assign the same, unique, ignorance degree of belief to any contingent outcome and each of its contingent, disjunctive parts. That this is the appropriate way to represent complete ignorance is established by two instruments, each individually strong enough to identify this state. They are the principle of indifference (PI) and the notion that ignorance is invariant under certain redescriptions of the outcome space, here developed into the (...) ‘principle of invariance of ignorance' (PII). Both instruments are so innocuous as almost to be platitudes. Yet the literature in probabilistic epistemology has misdiagnosed them as paradoxical or defective since they generate inconsistencies when conjoined with the assumption that an epistemic state must be a probability distribution. To underscore the need to drop this assumption, I express PII in its most defensible form as relating symmetric descriptions and show that paradoxes still arise if we assume the ignorance state to be a probability distribution. *Received February 2007; revised July 2007. †To contact the author, please write to: Department of History and Philosophy of Science, University of Pittsburgh, Pittsburgh, PA 15260; e-mail: [email protected]. (shrink)

We often use symmetries to infer outcomes’ probabilities, as when we infer that each side of a fair coin is equally likely to come up on a given toss. Why are these inferences successful? I argue against answering this with an a priori indifference principle. Reasons to reject that principle are familiar, yet instructive. They point to a new, empirical explanation for the success of our probabilistic predictions. This has implications for indifference reasoning in general. I argue that a priori (...) symmetries need never constrain our probability attributions, even when it comes to our initial credences. (shrink)

I argue that there are non-trivial objective chances (that is, objective chances other than 0 and 1) even in deterministic worlds. The argument is straightforward. I observe that there are probabilistic special scientific laws even in deterministic worlds. These laws project non-trivial probabilities for the events that they concern. And these probabilities play the chance role and so should be regarded as chances as opposed, for example, to epistemic probabilities or credences. The supposition of non-trivial deterministic chances might seem to (...) land us in contradiction. The fundamental laws of deterministic worlds project trivial probabilities for the very same events that are assigned non-trivial probabilities by the special scientific laws. I argue that any appearance of tension is dissolved by recognition of the level-relativity of chances. There is therefore no obstacle to accepting non-trivial chance-role-playing deterministic probabilities as genuine chances. (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)

" Vivid . . . immense clarity . . . the product of a brilliant and extremely forceful intellect." — Journal of the Royal Naval Scientific Service "Still a sheer joy to read." — Mathematical Gazette "Should be read by any student, teacher or researcher in mathematics." — Mathematics Teacher The originator of algebraic topology and of the theory of analytic functions of several complex variables, Henri Poincare (1854–1912) excelled at explaining the complexities of scientific and mathematical ideas to lay (...) readers. Science and Method, written in 1908, has been appreciated by a wide audience of nonprofessionals and translated into many languages. It defines the basic methodology and psychology of scientific discovery, particularly in regard to mathematics and mathematical physics. Drawing on examples from many fields, it explains how scientists analyze and choose their working facts, and it explores the nature of experimentation, theory, and the mind. 1914 edition. Translated by Francis Maitland. (shrink)

The propensity interpretation of probability was introduced by Popper ([1957]), but has subsequently been developed in different ways by quite a number of philosophers of science. This paper does not attempt a complete survey, but discusses a number of different versions of the theory, thereby giving some idea of the varieties of propensity. Propensity theories are classified into (i) long-run and (ii) single-case. The paper argues for a long-run version of the propensity theory, but this is contrasted with two single-case (...) propensity theories, one due to Miller and the later Popper, and the other to Fetzer. The three approaches are compared by examining how they deal with a key problem for the propensity approach, namely the relationship between propensity and causality and Humphreys' paradox. (shrink)

The goal of this paper is to sketch and defend a new interpretation or 'theory' of objective chance, one that lets us be sure such chances exist and shows how they can play the roles we traditionally grant them. The account is 'Humean' in claiming that objective chances supervene on the totality of actual events, but does not imply or presuppose a Humean approach to other metaphysical issues such as laws or causation. Like Lewis (1994) I take the Principal Principle (...) (PP) to be the key to understanding objective chance. After describing the main features of Humean objective chance (HOC), I deduce the validity of PP for Humean chances, and end by exploring the limitations of Humean chance. (shrink)

The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference (...) class problem. Other versions of these interpretations apparently evade the problem. But I contend that they are all “no-theory” theories of probability - accounts that leave quite obscure why probability should function as a guide to life, a suitable basis for rational inference and action. The reference class problem besets those theories that are genuinely informative and that plausibly constrain our inductive reasonings and decisions. I distinguish a “metaphysical” and an “epistemological” reference class problem. I submit that we can dissolve the former problem by recognizing that probability is fundamentally a two-place notion: conditional probability is the proper primitive of probability theory. However, I concede that the epistemological problem remains. (shrink)

In a random process, later events seem to be loosely attached to earlier ones; in other words, a substantial or tight relationship between the two is missing. This relationship is sometimes held to be the relation of cause and effect, so that random events are not caused by what preceded them. Richard Johns, however, adopts the original stance that random events are fully caused and lack only determination by their causes; according to his causal theory of chance, the physical chance (...) of an event is the degree to which the event is determined by its causes. -/- A Theory of Physical Probability addresses an important and, until now, poorly comprehended topic: chance, or physical probability. It puts forth Johns's theory of physical chance and demonstrates the implications of this theory in various areas of physics. Johns's is a novel approach to a fundamental topic in such disciplines as philosophy, philosophy of science, and physics, and it will be widely admired by scholars for its clarity and accessibility. (shrink)

The physiologist and neo-Kantian philosopher Johannes von Kries (1853-1928) wrote one of the most philosophically important works on the foundation of probability after P.S. Laplace and before the First World War, his Principien der Wohrscheinlich-keitsrechnung (1886, repr. 1927). In this book, von Kries developed a highly original interpretation of probability, which maintains it to be both logical and objectively physical. After presenting his approach I shall pursue the influence it had on Ludwig Wittgenstein and Friedrich Waismann. It seems that von (...) Kries's approach had more potential than recognized in his time and that putting Waismann's and Wittgenstein's early work in a von Kries perspective is able to shed light on the notion of an elementary proposition. (shrink)

EDITOR'S INTRODUCTION Throughout his life Bolzano's interest was divided between ethics and mathematics, between his will to reform the religion of the ...

Single-case and long-run propensity theories are among the main objective interpretations of probability. There have been various objections to these theories, e.g. that it is difficult to explain why propensities should satisfy the probability axioms and, worse, that propensities are at odds with these axioms, that the explication of propensities is circular and accordingly not informative, and that single-case propensities are metaphysical and accordingly non-scientific. We consider various propensity theories of probability and their prospects in light of these objections. We (...) argue that while propensity theories face challenges, these challenges do not undermine their validity as prospective interpretations of probability in science. (shrink)

I define a concept of causal probability and apply it to questions about the role of probability in evolutionary processes. Causal probability is defined in terms of manipulation of patterns in empirical outcomes by manipulating properties that realize objective probabilities. The concept of causal probability allows us see how probabilities characterized by different interpretations of probability can share a similar causal character, and does so in such way as to allow new inferences about relationships between probabilities realized in different chance (...) setups. I clarify relations between probabilities and properties defined in terms of them, and argue that certain widespread uses of computer simulations in evolutionary biology show that many probabilities relevant to evolutionary outcomes are causal probabilities. This supports the claim that higher-level properties such as biological fitness and processes such as natural selection are causal properties and processes, contrary to what some authors have argued. (shrink)

I describe a realist, ontologically objective interpretation of probability, "far-flung frequency (FFF) mechanistic probability". FFF mechanistic probability is defined in terms of facts about the causal structure of devices and certain sets of frequencies in the actual world. Though defined partly in terms of frequencies, FFF mechanistic probability avoids many drawbacks of well-known frequency theories and helps causally explain stable frequencies, which will usually be close to the values of mechanistic probabilities. I also argue that it's a virtue rather than (...) a failing of FFF mechanistic probability that it does not define single-case chances, and compare some aspects of my interpretation to a recent interpretation proposed by Strevens. (shrink)

The Novum Organum, (or Novum Organum Scientiarum - "New Instrument of Science"), is a philosophical work by Francis Bacon, originally published in 1620. The title is a reference to Aristotle's work Organon, which was his treatise on logic and syllogism. In Novum Organum, Bacon details a new system of logic he believes to be superior to the old ways of syllogism. This is now known as the Baconian method.

A difference-making account of causality is proposed that is based on a counterfactual definition, but differs from traditional counterfactual approaches to causation in a number of crucial respects: it introduces a notion of causal irrelevance; it evaluates the truth-value of counterfactual statements in terms of difference-making; it renders causal statements background-dependent. On the basis of the fundamental notions 'causal relevance' and 'causal irrelevance', further causal concepts are defined including causal factors, alternative causes, and importantly inus-conditions. Problems and advantages of the (...) proposed account are discussed. Finally, it is shown how the account can shed new light on three classic problems in epistemology, the problem of induction, the logic of analogy, and the framing of eliminative induction. (shrink)

The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. _Philosophical Theories of Probability_ is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.

This paper offers a metaphysics of physical probability in (or if you prefer, truth conditions for probabilistic claims about) deterministic systems based on an approach to the explanation of probabilistic patterns in deterministic systems called the method of arbitrary functions. Much of the appeal of the method is its promise to provide an account of physical probability on which probability assignments have the ability to support counterfactuals about frequencies. It is argued that the eponymous arbitrary functions are of little philosophical (...) use, but that they can be substituted for facts about frequencies without losing the ability to provide counterfactual support. The result is an account of probability in deterministic systems that has a “propensity-like” look and feel, yet which requires no supplement to the standard modern empiricist tool kit of particular matters of fact and principles of physical dynamics. (shrink)

Objective interpretations of probability are usually discussed in two varieties: frequency and propensity accounts. But there is a third, neglected possibility, namely, probabilities as deriving from ranges in suitably structured initial state spaces. Roughly, the probability of an event is the proportion of initial states that lead to this event in the space of all possible initial states, provided that this proportion is approximately the same in any not too small interval of the initial state space. This idea can also (...) be expressed by saying that in the types of situations that give rise to probabilistic phenomena we may expect to find an initial state space such that any "reasonable" density function over this space leads to the same probabilities for the possible outcomes. This "method of arbitrary functions" was introduced by Poincaré, studied and extended by Hopf and more recently by Eduardo Engel, Jan von Plato and Michael Strevens. The natural-range, or method-of-arbitrary-functions approach to probabilities is usually treated as an explanation for the occurrence of probabilistic patterns, whereas I examine its prospects for an objective interpretation of probability, in the sense of providing truth conditions for probability statements that do not depend on our state of mind or information. The main objection to such a proposal is that it is circular, i.e. presupposes the concept of probability, because a measure on the initial state has to be introduced, and density functions over the space are considered. I try to argue that this objection can be successfully met. (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)

Bayesian nets are widely used in artificial intelligence as a calculus for causal reasoning, enabling machines to make predictions, perform diagnoses, take decisions and even to discover causal relationships. This book, aimed at researchers and graduate students in computer science, mathematics and philosophy, brings together two important research topics: how to automate reasoning in artificial intelligence, and the nature of causality and probability in philosophy.

" Vivid . . . immense clarity . . . the product of a brilliant and extremely forceful intellect." — Journal of the Royal Naval Scientific Service "Still a sheer joy to read." — Mathematical Gazette "Should be read by any student, teacher or researcher in mathematics." — Mathematics Teacher The originator of algebraic topology and of the theory of analytic functions of several complex variables, Henri Poincare (1854–1912) excelled at explaining the complexities of scientific and mathematical ideas to lay (...) readers. Science and Method, written in 1908, has been appreciated by a wide audience of nonprofessionals and translated into many languages. It defines the basic methodology and psychology of scientific discovery, particularly in regard to mathematics and mathematical physics. Drawing on examples from many fields, it explains how scientists analyze and choose their working facts, and it explores the nature of experimentation, theory, and the mind. 1914 edition. Translated by Francis Maitland. (shrink)