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An aspect of Peirce’s thought that may still be underappreciated is his resistance to what Levi calls _pedigree epistemology_, to the idea that a central focus in epistemology should be the justification of current beliefs. Somewhat more widely appreciated is his rejection of the subjective view of probability. We argue that Peirce’s criticisms of subjectivism, to the extent they grant such a conception of probability is viable at all, revert back to pedigree epistemology. A thoroughgoing rejection of pedigree in the (...) |
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The Stability of Belief: How Rational Belief Coheres with Probability, by LeitgebHannes. Oxford: Oxford University Press, 2017. Pp. xiv + 365. No categories |
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I want to expand the pragmatist view of probability advocated by Roberto Torretti, drawing on the propensity approach. In the first part, I will show how the concept of mathematical expectation originally formalized an Aristotelian principle of justice. In the second half, I will present the game-theoretic approach to probability developed by Shafer and Vovk, showing how it allows us to interpret the original normativity of mathematical expectations. I will finally discuss how this latter view contributes to a pragmatist understanding (...) |
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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 (...) |
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This paper argues that if propensities are displayed in objective physical chances then the appropriate representation of these chances is as indexed probability functions. Two alternative formal models, or accounts, for the relation between propensity properties and their chancy or probabilistic manifestations, in terms of conditionals and conditional probability are first reviewed. It is argued that both confront important objections, which are overcome by the account in terms of indexed probabilities. A number of further advantages of the indexed probability account (...) |
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We argue for an account of chemical reactivities as chancy propensities, in accordance with the ‘complex nexus of chance’ defended by one of us in the past. Reactivities are typically quantified as proportions, and an expression such as “A + B → C” does not entail that under the right conditions some given amounts of A and B react to give the mass of C that theoretically corresponds to the stoichiometry of the reaction. Instead, what is produced is a fraction (...) |
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_ Chance in the World: A Humean Guide to Objective Chance _, by Carl Hoefer. Oxford: Oxford University Press, 2019. Pp. xvii + 247. No categories |
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Chance in the World: A Humean Guide to Objective Chance, by HoeferCarl. Oxford: Oxford University Press, 2019. Pp. xvii + 247. No categories |
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I analyse critically what I regard as the most accomplished empiricist account of propensities, namely the long run propensity theory developed by Donald Gillies . Empiricist accounts are distinguished by their commitment to the ‘identity thesis’: the identification of propensities and objective probabilities. These theories are intended, in the tradition of Karl Popper’s influential proposal, to provide an interpretation of probability that renders probability statements directly testable by experiment. I argue that the commitment to the identity thesis leaves empiricist theories, (...) |
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Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis for Bayesian (...) |
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I argue that there are such things as nomological probabilities—probabilities that play a certain explanatory role with respect to stable, long-run relative frequencies. Indeed, I argue, we should be willing to accept nomological probabilities even if they turn out to be metaphysically weird or even wholly sui generis entities. I then give an example of one way in which this argument should shape future work on the metaphysics of chance by describing a challenge to a common group of analyses of (...) |
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David Lewis'sPrincipal Principle states that our credence in a single case follows from the general probability of all such cases. Against this stands the Challenge Argument – to show that the inference is justified. Recent law-to-chance, Bayesian, and propensity theories of probability take up the challenge – but, I argue, fall short. Rather, we should understand propensity via Aristotle's analysis of spontaneity and probabilistic reasoning via theAnti-PPand the practice ofbundling one offs, where forced bad-odds one offsilluminate how extensive a role (...) |
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One currently popular view about the nature of objective probabilities, or objective chances, is that they – or some of them, at least – are primitive features of the physical world, not reducible to anything else nor explicable in terms of frequencies, degrees of belief, or anything else. In this paper I explore the question of what the semantic content of primitive chance claims could be. Every attempt I look at to supply such content either comes up empty-handed, or begs (...) |
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I argue that the past can be objectively chancy in cases of backwards causation, and defend a view of chance that allows for this. Using a case, I argue against the popular temporal view of chance, according to which chances are defined relative to times, and all chancy events must lie in the future. I then state and defend the causal view of chance, according to which chances are defined relative to causal histories, and all chancy events must lie causally (...) |
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We review the question of whether objective chances are compatible with determinism. We first outline what we mean by chance and what we mean by determinism. We then look at the alleged incompatibility between those concepts. Finally, we look at some ways that one might attempt to overcome the incompatibility. |
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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 (...) |
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This volume focuses on various questions concerning the interpretation of probability and probabilistic reasoning in biology and physics. It is inspired by the idea that philosophers of biology and philosophers of physics who work on the foundations of their disciplines encounter similar questions and problems concerning the role and application of probability, and that interaction between the two communities will be both interesting and fruitful. In this introduction we present the background to the main questions that the volume focuses on (...) No categories |
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The paper takes up Bell's “Everett theory” and develops it further. The resulting theory is about the system of all particles in the universe, each located in ordinary, 3-dimensional space. This many-particle system as a whole performs random jumps through 3N-dimensional configuration space – hence “Tychistic Bohmian Mechanics”. The distribution of its spontaneous localisations in configuration space is given by the Born Rule probability measure for the universal wavefunction. Contra Bell, the theory is argued to satisfy the minimal desiderata for (...) |
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"Chance" crops up all over philosophy, and in many other areas. It is often assumed -- without argument -- that chances are probabilities. I explore the extent to which this assumption is really sanctioned by what we understand by the concept of chance. |
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I defend a three-fold form of pluralism about chance, involving a tripartite distinction between propensities, probabilities, and frequencies. The argument has a negative and a positive part. Negatively, I argue against the identity thesis that informs current propensity theories, which already suggests the need for a tripartite distinction. Positively, I argue that that a tripartite distinction is implicit in much statistical practice. Finally, I apply a well-known framework in the modelling literature in order to characterize these three separate concepts functionally (...) No categories |
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The prospects of a causal interpretation of probability are examined. Various accounts both from the history of scientific method and from recent developments in the tradition of the method of arbitrary functions, in particular by Strevens, Rosenthal, and Abrams, are briefly introduced and assessed. I then present a specific account of causal probability with the following features: First, the link between causal probability and a particular account of induction and causation is established, namely eliminative induction and the related difference-making account (...) |
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