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  1. Mr István A. Aranyosi, The Doomsday Simulation Argument. Or Why Isn't the End Nigh, and You're Not Living in a Simulation.
    According to the Carter-Leslie Doomsday Argument, we should assign a high probability to the hypothesis that the human species will go extinct very soon. The argument is based on the application of Bayes’s theo-rem and a certain indifference principle with respect to the temporal location of our observed birth rank within the totality of birth ranks of all humans who will ever have lived. According to Bostrom’s Simulation Argument, which appeals to a weaker indifference principle than the Doomsday Argument, at (...)
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  2. Sorin Bangu (2010). On Bertrand's Paradox. Analysis 70 (1):30-35.
    The Principle of Indifference is a central element of the ‘classical’ conception of probability, but, for all its strong intuitive appeal, it is widely believed that it faces a devastating objection: the so-called (by Poincare´) ‘Bertrand paradoxes’ (in essence, cases in which the same probability question receives different answers). The puzzle has fascinated many since its discovery, and a series of clever solutions (followed promptly by equally clever rebuttals) have been proposed. However, despite the long-standing interest in this problem, an (...)
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  3. Paul Bartha (2004). Countable Additivity and the de Finetti Lottery. British Journal for the Philosophy of Science 55 (2):301-321.
    De Finetti would claim that we can make sense of a draw in which each positive integer has equal probability of winning. This requires a uniform probability distribution over the natural numbers, violating countable additivity. Countable additivity thus appears not to be a fundamental constraint on subjective probability. It does, however, seem mandated by Dutch Book arguments similar to those that support the other axioms of the probability calculus as compulsory for subjective interpretations. These two lines of reasoning can be (...)
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  4. Paul Bartha & Richard Johns (2001). Probability and Symmetry. Proceedings of the Philosophy of Science Association 2001 (3):S109-.
    The Principle of Indifference, which dictates that we ought to assign two outcomes equal probability in the absence of known reasons to do otherwise, is vulnerable to well-known objections. Nevertheless, the appeal of the principle, and of symmetry-based assignments of equal probability, persists. We show that, relative to a given class of symmetries satisfying certain properties, we are justified in calling certain outcomes equally probable, and more generally, in defining what we call relative probabilities. Relative probabilities are useful in providing (...)
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  5. Yann Benétreau-Dupin (forthcoming). Blurring Out Cosmic Puzzles. Philosophy of Science.
    The Doomsday argument and anthropic reasoning are two puzzling examples of probabilistic confirmation. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, they constitute a challenge to Bayesianism. Several attempts, some successful, have been made to avoid these conclusions, but some versions of these arguments cannot be dissolved within the framework of orthodox Bayesianism. I show that adopting an imprecise framework of probabilistic reasoning allows for a more adequate representation of (...)
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  6. Yann Benétreau-Dupin (2015). The Bayesian Who Knew Too Much. Synthese 192 (5):1527-1542.
    In several papers, John Norton has argued that Bayesianism cannot handle ignorance adequately due to its inability to distinguish between neutral and disconfirming evidence. He argued that this inability sows confusion in, e.g., anthropic reasoning in cosmology or the Doomsday argument, by allowing one to draw unwarranted conclusions from a lack of knowledge. Norton has suggested criteria for a candidate for representation of neutral support. Imprecise credences (families of credal probability functions) constitute a Bayesian-friendly framework that allows us to avoid (...)
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  7. Nick Bostrom (2008). The Doomsday Argument. Think 6 (17-18):23-28.
    A recent paper by Korb and Oliver in this journal attempts to refute the Carter-Leslie Doomsday argument. I organize their remarks into five objections and show that they all fail. Further efforts are thus called upon to find out what, if anything, is wrong with Carter and Leslie’s disturbing reasoning. While ultimately unsuccessful, Korb and Oliver’s objections do however in some instances force us to become clearer about what the Doomsday argument does and doesn’t imply.
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  8. Darren Bradley (2011). Confirmation in a Branching World: The Everett Interpretation and Sleeping Beauty. British Journal for the Philosophy of Science 62 (2):323-342.
    Sometimes we learn what the world is like, and sometimes we learn where in the world we are. Are there any interesting differences between the two kinds of cases? The main aim of this article is to argue that learning where we are in the world brings into view the same kind of observation selection effects that operate when sampling from a population. I will first explain what observation selection effects are ( Section 1 ) and how they are relevant (...)
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  9. Marc Burock, Indifference, Sample Space, and the Wine/Water Paradox.
    Von Mises’ wine/water paradox has served as a foundation for detractors of the Principle of Indifference and logical probability. Mikkelson recently proposed a first solution, and here several additional solutions to the paradox are explained. Learning from the wine/water paradox, I will argue that it is meaningless to consider a particular probability apart from the sample space containing the probabilistic event in question.
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  10. Marc Burock, An Outcome of the de Finetti Infinite Lottery is Not Finite.
    A randomly selected number from the infinite set of positive integers—the so-called de Finetti lottery—will not be a finite number. I argue that it is still possible to conceive of an infinite lottery, but that an individual lottery outcome is knowledge about set-membership and not element identification. Unexpectedly, it appears that a uniform distribution over a countably infinite set has much in common with a continuous probability density over an uncountably infinite set.
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  11. René Carmona (ed.) (2008). Indifference Pricing: Theory and Applications. Princeton University Press.
    This is the first book about the emerging field of utility indifference pricing for valuing derivatives in incomplete markets.
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  12. Rudolf Carnap (1952). The Continuum of Inductive Methods. [Chicago]University of Chicago Press.
  13. Paul Castell (1998). A Consistent Restriction of the Principle of Indifference. British Journal for the Philosophy of Science 49 (3):387-395.
    I argue that a particular restricted version of the Principle of Indiference is a consistent, indispensible tool for guiding our probabilistic judgements.
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  14. Ariel Caticha (2000). Insufficient Reason and Entropy in Quantum Theory. Foundations of Physics 30 (2):227-251.
    The objective of the consistent-amplitude approach to quantum theory has been to justify the mathematical formalism on the basis of three main assumptions: the first defines the subject matter, the second introduces amplitudes as the tools for quantitative reasoning, and the third is an interpretative rule that provides the link to the prediction of experimental outcomes. In this work we introduce a natural and compelling fourth assumption: if there is no reason to prefer one region of the configuration space over (...)
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  15. Shoutir Kishore Chatterjee (2003). Statistical Thought: A Perspective and History. OUP Oxford.
    In this unique monograph, based on years of extensive work, Chatterjee presents the historical evolution of statistical thought from the perspective of various approaches to statistical induction. Developments in statistical concepts and theories are discussed alongside philosophical ideas on the ways we learn from experience.
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  16. Rodolfo De Cristofaro (2008). A New Formulation of the Principle of Indifference. Synthese 163 (3):329 - 339.
    The idea of a probabilistic logic of inductive inference based on some form of the principle of indifference has always retained a powerful appeal. However, up to now all modifications of the principle failed. In this paper, a new formulation of such a principle is provided that avoids generating paradoxes and inconsistencies. Because of these results, the thesis that probabilities cannot be logical quantities, determined in an objective way through some form of the principle of indifference, is no longer supportable. (...)
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  17. John F. Cyranski (1978). Analysis of the Maximum Entropy Principle “Debate”. Foundations of Physics 8 (5-6):493-506.
    Jaynes's maximum entropy principle (MEP) is analyzed by considering in detail a recent controversy. Emphasis is placed on the inductive logical interpretation of “probability” and the concept of “total knowledge.” The relation of the MEP to relative frequencies is discussed, and a possible realm of its fruitful application is noted.
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  18. Rodolfo de Cristofaro (2008). A New Formulation of the Principle of Indifference. Synthese 163 (3):329-339.
    The idea of a probabilistic logic of inductive inference based on some form of the principle of indifference has always retained a powerful appeal. However, up to now all modifications of the principle failed. In this paper, a new formulation of such a principle is provided that avoids generating paradoxes and inconsistencies. Because of these results, the thesis that probabilities cannot be logical quantities, determined in an objective way through some form of the principle of indifference, is no longer supportable. (...)
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  19. Cian Dorr (2010). The Eternal Coin: A Puzzle About Self-Locating Conditional Credence. Philosophical Perspectives 24 (1):189-205.
    The Eternal Coin is a fair coin has existed forever, and will exist forever, in a region causally isolated from you. It is tossed every day. How confident should you be that the Coin lands heads today, conditional on (i) the hypothesis that it has landed Heads on every past day, or (ii) the hypothesis that it will land Heads on every future day? I argue for the extremely counterintuitive claim that the correct answer to both questions is 1.
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  20. Alon Drory (2015). Failure and Uses of Jaynes’ Principle of Transformation Groups. Foundations of Physics 45 (4):439-460.
    Bertand’s paradox is a fundamental problem in probability that casts doubt on the applicability of the indifference principle by showing that it may yield contradictory results, depending on the meaning assigned to “randomness”. Jaynes claimed that symmetry requirements solve the paradox by selecting a unique solution to the problem. I show that this is not the case and that every variant obtained from the principle of indifference can also be obtained from Jaynes’ principle of transformation groups. This is because the (...)
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  21. Adam Elga (2004). Defeating Dr. Evil with Self-Locating Belief. Philosophy and Phenomenological Research 69 (2):383–396.
    Dr. Evil learns that a duplicate of Dr. Evil has been created. Upon learning this, how seriously should he take the hypothesis that he himself is that duplicate? I answer: very seriously. I defend a principle of indifference for self-locating belief which entails that after Dr. Evil learns that a duplicate has been created, he ought to have exactly the same degree of belief that he is Dr. Evil as that he is the duplicate. More generally, the principle shows that (...)
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  22. Marc Finthammer & Christoph Beierle (2012). How to Exploit Parametric Uniformity for Maximum Entropy Reasoning in a Relational Probabilistic Logic. In Luis Farinas del Cerro, Andreas Herzig & Jerome Mengin (eds.), Logics in Artificial Intelligence. Springer 189--201.
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  23. Branden Fitelson (2006). Logical Foundations of Evidential Support. Philosophy of Science 73 (5):500-512.
    Carnap’s inductive logic (or confirmation) project is revisited from an “increase in firmness” (or probabilistic relevance) point of view. It is argued that Carnap’s main desiderata can be satisfied in this setting, without the need for a theory of “logical probability”. The emphasis here will be on explaining how Carnap’s epistemological desiderata for inductive logic will need to be modified in this new setting. The key move is to abandon Carnap’s goal of bridging confirmation and credence, in favor of bridging (...)
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  24. J. Franklin (2001). Resurrecting Logical Probability. Erkenntnis 55 (2):277-305.
    The logical interpretation of probability, or ``objective Bayesianism''''– the theory that (some) probabilitiesare strictly logical degrees of partial implication – is defended.The main argument against it is that it requires the assignment ofprior probabilities, and that any attempt to determine them by symmetryvia a ``principle of insufficient reason'''' inevitably leads to paradox.Three replies are advanced: that priors are imprecise or of little weight, sothat disagreement about them does not matter, within limits; thatit is possible to distinguish reasonable from unreasonable priorson (...)
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  25. Philippe Gagnon (2015). Review Article on Amir D. Aczel, Why Science Does Not Disprove God (New York: W. Morrow, 2014). [REVIEW] ESSSAT News and Reviews 25 (2):22-27.
    Review of the book by mathematician and science writer Amir Aczel, Why Science does not Disprove God, recently reissued in paperback, with a focus on the chapters on mathematics and God, and criticisms from the standpoint of the epistemology of the science and religion dialogue.
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  26. Austin Gerig, The Doomsday Argument in Many Worlds.
    You and I are highly unlikely to exist in a civilization that has produced only 70 billion people, yet we find ourselves in just such a civilization. Our circumstance, which seems difficult to explain, is easily accounted for if (1) many other civilizations exist and if (2) nearly all of these civilizations (including our own) die out sooner than usually thought, i.e., before trillions of people are produced. Because the combination of (1) and (2) make our situation likely and alternatives (...)
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  27. James C. Guszcza (2000). Topics in the Foundations of Statistical Inference and Statistical Mechanics. Dissertation, The University of Chicago
    This essay explores the philosophical issues concerning the interpretation of probabilities in the context of equilibrium classical statistical mechanics. One reason why investigators have never settled on a single interpretation of probability is that different theories seem to demand different concepts of probability. For example, quantum physics seems to demand an ontic "propensity" concept of probability, while decision theory demands an epistemic "personalist" concept of probability. Statistical mechanics is a branch of physics which uses probabilities to enable experimenters to make (...)
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  28. B. J. H. (1962). Entropy and the Unity of Knowledge. Review of Metaphysics 15 (4):676-677.
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  29. Ian Hacking (1971). Equipossibility Theories of Probability. British Journal for the Philosophy of Science 22 (4):339-355.
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  30. Alan Hájek & Michael Smithson (2012). Rationality and Indeterminate Probabilities. Synthese 187 (1):33-48.
    We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required . Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our second argument begins with our (...)
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  31. H. Haken (1993). Application of the Maximum Entropy Principle to Nonlinear Systems Far From Equilibrium. In E. T. Jaynes, Walter T. Grandy & Peter W. Milonni (eds.), Physics and Probability: Essays in Honor of Edwin T. Jaynes. Cambridge University Press 239.
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  32. M. J. Hill, J. B. Paris & G. M. Wilmers (2002). Some Observations on Induction in Predicate Probabilistic Reasoning. Journal of Philosophical Logic 31 (1):43-75.
    We consider the desirability, or otherwise, of various forms of induction in the light of certain principles and inductive methods within predicate uncertain reasoning. Our general conclusion is that there remain conflicts within the area whose resolution will require a deeper understanding of the fundamental relationship between individuals and properties.
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  33. Douglas N. Hoover (1980). A Note on Regularity. In Richard C. Jeffrey (ed.), Studies in Inductive Logic and Probability. Berkeley: University of California Press
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  34. Colin Howson & Peter Urbach (1993). Scientific Reasoning: The Bayesian Approach. Open Court.
  35. Michael Huemer (2009). Explanationist Aid for the Theory of Inductive Logic. British Journal for the Philosophy of Science 60 (2):345-375.
    A central problem facing a probabilistic approach to the problem of induction is the difficulty of sufficiently constraining prior probabilities so as to yield the conclusion that induction is cogent. The Principle of Indifference, according to which alternatives are equiprobable when one has no grounds for preferring one over another, represents one way of addressing this problem; however, the Principle faces the well-known problem that multiple interpretations of it are possible, leading to incompatible conclusions. I propose a partial solution to (...)
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  36. Edwin T. Jaynes (1973). The Well-Posed Problem. Foundations of Physics 3 (4):477-493.
    Many statistical problems, including some of the most important for physical applications, have long been regarded as underdetermined from the standpoint of a strict frequency definition of probability; yet they may appear wellposed or even overdetermined by the principles of maximum entropy and transformation groups. Furthermore, the distributions found by these methods turn out to have a definite frequency correspondence; the distribution obtained by invariance under a transformation group is by far the most likely to be observed experimentally, in the (...)
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  37. Harold Jeffreys (1973). Scientific Inference. Cambridge [Eng.]Cambridge University Press.
    Thats logic. LEWIS CARROLL, Through the Looking Glass 1-1. The fundamental problem of this work is the question of the nature of scientific inference.
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  38. Richard Johns (2001). Probability and Symmetry. Philosophy of Science 68 (3):S109 - S122.
    The Principle of Indifference, which dictates that we ought to assign two outcomes equal probability in the absence of known reasons to do otherwise, is vulnerable to well-known objections. Nevertheless, the appeal of the principle, and of symmetry-based assignments of equal probability, persists. We show that, relative to a given class of symmetries satisfying certain properties, we are justified in calling certain outcomes equally probable, and more generally, in defining what we call relative probabilities. Relative probabilities are useful in providing (...)
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  39. John Maynard Keynes (1921/2004). A Treatise on Probability. Dover Publications.
    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” (...)
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  40. D. Klyve (2013). In Defense of Bertrand: The Non-Restrictiveness of Reasoning by Example. Philosophia Mathematica 21 (3):365-370.
    This note has three goals. First, we discuss a presentation of Bertrand's paradox in a recent issue of Philosophia Mathematica, which we believe to be a subtle but important misinterpretation of the problem. We compare claims made about Bertrand with his 1889 Calcul des Probabilités. Second, we use this source to understand Bertrand's true intention in describing what we now call his paradox, comparing it both to another problem he describes in the same section and to a modern treatment. Finally, (...)
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  41. Theo A. F. Kuipers (1984). Inductive Analogy in Carnapian Spirit. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984:157 - 167.
    In this paper it is shown that there is a natural way of dealing with analogy by similarity in inductive systems by extending intuitive ways of introduction of systems without analogy. This procedure leads to Carnap-like systems, with zero probability for contingent generalizations, satisfying a general principle of so-called virtual analogy. This new principle is different from, but compatible with, Carnap's principle. It will be shown that the latter principle is satisfied, and should only be satisfied, if the underlying distance (...)
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  42. Jürgen Landes & Jon Williamson, Justifying Objective Bayesianism on Predicate Languages.
    Objective Bayesianism says that the strengths of one’s beliefs ought to be probabilities, calibrated to physical probabilities insofar as one has evidence of them, and otherwise sufficiently equivocal. These norms of belief are often explicated using the maximum entropy principle. In this paper we investigate the extent to which one can provide a unified justification of the objective Bayesian norms in the case in which the background language is a first-order predicate language, with a view to applying the resulting formalism (...)
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  43. Jürgen Landes & Jon Williamson, Objective Bayesianism and the Maximum Entropy Principle.
    Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities, they should be calibrated to our evidence of physical probabilities, and they should otherwise equivocate sufficiently between the basic propositions that we can express. The three norms are sometimes explicated by appealing to the maximum entropy principle, which says that a belief function should be a probability function, from all those that are calibrated to evidence, that has maximum entropy. However, the three norms of objective Bayesianism (...)
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  44. Isaac Levi (2010). Probability Logic, Logical Probability, and Inductive Support. Synthese 172 (1):97 - 118.
    This paper seeks to defend the following conclusions: The program advanced by Carnap and other necessarians for probability logic has little to recommend it except for one important point. Credal probability judgments ought to be adapted to changes in evidence or states of full belief in a principled manner in conformity with the inquirer’s confirmational commitments—except when the inquirer has good reason to modify his or her confirmational commitment. Probability logic ought to spell out the constraints on rationally coherent confirmational (...)
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  45. Hallvard Lillehammer (2014). Who is My Neighbour? Understanding Indifference as a Vice. Philosophy 89 (350).
    Indifference is often described as a vice. Yet who is indifferent; to what; and in what way is poorly understood, and frequently subject to controversy and confusion. This paper proposes a framework for the interpretation and analysis of ethically problematic forms of indifference in terms of how different states of indifference can be either more or less dynamic, or more or less sensitive to the nature and state of their object.
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  46. Patrick Maher (2006). The Concept of Inductive Probability. Erkenntnis 65 (2):185 - 206.
    The word ‘probability’ in ordinary language has two different senses, here called inductive and physical probability. This paper examines the concept of inductive probability. Attempts to express this concept in other words are shown to be either incorrect or else trivial. In particular, inductive probability is not the same as degree of belief. It is argued that inductive probabilities exist; subjectivist arguments to the contrary are rebutted. Finally, it is argued that inductive probability is an important concept and that it (...)
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  47. Louis Marinoff (1994). A Resolution of Bertrand's Paradox. Philosophy of Science 61 (1):1-24.
    Bertrand's random-chord paradox purports to illustrate the inconsistency of the principle of indifference when applied to problems in which the number of possible cases is infinite. This paper shows that Bertrand's original problem is vaguely posed, but demonstrates that clearly stated variations lead to different, but theoretically and empirically self-consistent solutions. The resolution of the paradox lies in appreciating how different geometric entities, represented by uniformly distributed random variables, give rise to respectively different nonuniform distributions of random chords, and hence (...)
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  48. Elinor Mason (2004). Consequentialism and the Principle of Indifference. Utilitas 16 (3):316-321.
    James Lenman argues that consequentialism fails as a moral theory because it is impossible to predict the long-term consequences of our actions. I agree that it is impossible to predict the long-term consequences of actions, but argue that this does not count as a strike against consequentialism. I focus on the principle of indifference, which tells us to treat unforeseeable consequences as cancelling each other out, and hence value-neutral. I argue that though we cannot defend this principle independently, we cannot (...)
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  49. Ernan McMullin (1993). Indifference Principle and Anthropic Principle in Cosmology. Studies in History and Philosophy of Science Part A 24 (3):359-389.
    The successes scored by the big bang model of cosmic evolution in the 1960’s led to an intensive application of quantum theory to the problem of how the expansion might have begun and what its likely first stages were. It seemed as though an incredibly precise setting of the initial conditions would have been needed in order that a long-lived galactic universe containing heavy elements might develop. One response was to suppose that the fine-tuning could somehow be explained by the (...)
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  50. Christopher J. G. Meacham (forthcoming). The Meta-Reversibility Objection. In Barry Loewer, Brad Weslake & Eric Winsberg (eds.), Time's Arrow and the Probability Structure of the World.
    One popular approach to statistical mechanics understands statistical mechanical probabilities as measures of rational indifference. Naive formulations of this ``indifference approach'' face reversibility worries - while they yield the right prescriptions regarding future events, they yield the wrong prescriptions regarding past events. This paper begins by showing how the indifference approach can overcome the standard reversibility worries by appealing to the Past Hypothesis. But, the paper argues, positing a Past Hypothesis doesn't free the indifference approach from all reversibility worries. For (...)
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