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  1. Frank Arntzenius & Ned Hall (2003). On What We Know About Chance. British Journal for the Philosophy of Science 54 (2):171-179.
    The ‘Principal Principle’ states, roughly, that one's subjective probability for a proposition should conform to one's beliefs about that proposition's objective chance of coming true. David Lewis has argued (i) that this principle provides the defining role for chance; (ii) that it conflicts with his reductionist thesis of Humean supervenience, and so must be replaced by an amended version that avoids the conflict; hence (iii) that nothing perfectly deserves the name ‘chance’, although something can come close enough by playing the (...)
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  2. S. B. (1997). Henri Poincare and Bruno de Finetti: Conventions and Scientific Reasoning. Studies in History and Philosophy of Science Part A 28 (4):657-679.
    In his account of probable reasoning, Poincare used the concept, or at least the language, of conventions. In particular, he claimed that the prior probabilities essential for inverse probable reasoning are determined conventionally. This paper investigates, in the light of Poincare's well known claim about the conventionality of metric geometry, what this could mean, and how it is related to other views about the determination of prior probabilities. Particular attention is paid to the similarities and differences between Poincare's conventionalism as (...)
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  3. Prasanta S. Bandyopadhyay & Robert J. Boik (1999). The Curve Fitting Problem: A Bayesian Rejoinder. Philosophy of Science 66 (3):402.
    In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit pull in opposite directions. To solve this problem, two proposals, the first one based on Bayes's theorem criterion (BTC) and the second one advocated by Forster and Sober based on Akaike's Information Criterion (AIC) are discussed. We show that AIC, which is frequentist in spirit, is logically equivalent to BTC, provided that a suitable choice of priors is made. We evaluate the charges against Bayesianism and contend that AIC approach (...)
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  4. Rudolf Carnap (1952). The Continuum of Inductive Methods. [Chicago]University of Chicago Press.
  5. 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. -/- Suitable for researchers, lecturers and students in statistics and the history of science this book is aimed at those who have had some exposure to statistical theory. It is also useful to logicians and philosophers (...)
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  6. Bruno de Finetti (1970). Theory of Probability. New York: John Wiley.
  7. Bruno de Finetti (1937). La Prévision: Ses Lois Logiques, Ses Sources Subjectives. Annales de l'Institut Henri Poincaré 17:1-68.
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  8. Franz Dietrich & Christian List (2013). Reasons for (Prior) Belief in Bayesian Epistemology. Synthese 190 (5):781-786.
    Bayesian epistemology tells us with great precision how we should move from prior to posterior beliefs in light of new evidence or information, but says little about where our prior beliefs come from. It offers few resources to describe some prior beliefs as rational or well-justified, and others as irrational or unreasonable. A different strand of epistemology takes the central epistemological question to be not how to change one’s beliefs in light of new evidence, but what reasons justify a given (...)
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  9. David L. Dowe, Steve Gardner & and Graham Oppy (2007). Bayes Not Bust! Why Simplicity Is No Problem for Bayesians. British Journal for the Philosophy of Science 58 (4):709 - 754.
    The advent of formal definitions of the simplicity of a theory has important implications for model selection. But what is the best way to define simplicity? Forster and Sober ([1994]) advocate the use of Akaike's Information Criterion (AIC), a non-Bayesian formalisation of the notion of simplicity. This forms an important part of their wider attack on Bayesianism in the philosophy of science. We defend a Bayesian alternative: the simplicity of a theory is to be characterised in terms of Wallace's Minimum (...)
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  10. John Earman (1992). Bayes or Bust? Bradford.
    There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes's original paper to contemporary formal learning theory. (...)
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  11. John Earman (1992). Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory. Mit Press.
  12. Kenny Easwaran (2011). Bayesianism II: Applications and Criticisms. Philosophy Compass 6 (5):321-332.
    In the first paper, I discussed the basic claims of Bayesianism (that degrees of belief are important, that they obey the axioms of probability theory, and that they are rationally updated by either standard or Jeffrey conditionalization) and the arguments that are often used to support them. In this paper, I will discuss some applications these ideas have had in confirmation theory, epistemol- ogy, and statistics, and criticisms of these applications.
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  13. Festa, Roberto, Optimum Inductive Methods. A Study in Inductive Probability, Bayesian Statistics, and Verisimilitude.
    According to the Bayesian view, scientific hypotheses must be appraised in terms of their posterior probabilities relative to the available experimental data. Such posterior probabilities are derived from the prior probabilities of the hypotheses by applying Bayes'theorem. One of the most important problems arising within the Bayesian approach to scientific methodology is the choice of prior probabilities. Here this problem is considered in detail w.r.t. two applications of the Bayesian approach: (1) the theory of inductive probabilities (TIP) developed by Rudolf (...)
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  14. 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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  15. Haim Gaifman & Marc Snir (1982). Probabilities Over Rich Languages, Testing and Randomness. Journal of Symbolic Logic 47 (3):495-548.
  16. David H. Glass (2005). Problems with Priors in Probabilistic Measures of Coherence. Erkenntnis 63 (3):375 - 385.
    Two of the probabilistic measures of coherence discussed in this paper take probabilistic dependence into account and so depend on prior probabilities in a fundamental way. An example is given which suggests that this prior-dependence can lead to potential problems. Another coherence measure is shown to be independent of prior probabilities in a clearly defined sense and consequently is able to avoid such problems. The issue of prior-dependence is linked to the fact that the first two measures can be understood (...)
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  17. Ian Hacking (1971). Equipossibility Theories of Probability. British Journal for the Philosophy of Science 22 (4):339-355.
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  18. Ned Hall (1994). Correcting the Guide to Objective Chance. Mind 103 (412):505-518.
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  19. James Hawthorne (1989). Giving Up Judgment Empiricism: The Bayesian Epistemology of Bertrand Russell and Grover Maxwell. In C. Wade Savage & C. Anthony Anderson (eds.), ReReading Russell: Bertrand Russell's Metaphysics and Epistemology; Minnesota Studies in the Philosophy of Science, Volume 12. University of Minnesota Press.
    This essay is an attempt to gain better insight into Russell's positive account of inductive inference. I contend that Russell's postulates play only a supporting role in his overall account. At the center of Russell's positive view is a probabilistic, Bayesian model of inductive inference. Indeed, Russell and Maxwell actually held very similar Bayesian views. But the Bayesian component of Russell's view in Human Knowledge is sparse and easily overlooked. Maxwell was not aware of it when he developed his own (...)
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  20. Jr: Henry E. Kyburg (1990). Probabilistic Inference and Probabilistic Reasoning. Philosophical Topics 18 (2):107-116.
  21. 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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  22. Kenneth Einar Himma (2002). Prior Probabilities and Confirmation Theory: A Problem with the Fine-Tuning Argument. [REVIEW] International Journal for Philosophy of Religion 51 (3):175-194.
    Fine-tuning arguments attempt to infer God’s existence from the empirical fact that life would not be possible if any of approximately two-dozen fundamental laws and properties of the universe had been even slightly different. In this essay, I consider a version that relies on the following principle: if an observation O is more likely to occur under hypothesis H1 than under hypothesis H2, then O supports accepting H1 over H2. I argue that this particular application of this principle is vulnerable (...)
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  23. Colin Howson (1996). Bayesian Rules of Updating. Erkenntnis 45 (2-3):195 - 208.
    This paper discusses the Bayesian updating rules of ordinary and Jeffrey conditionalisation. Their justification has been a topic of interest for the last quarter century, and several strategies proposed. None has been accepted as conclusive, and it is argued here that this is for a good reason; for by extending the domain of the probability function to include propositions describing the agent's present and future degrees of belief one can systematically generate a class of counterexamples to the rules. Dynamic Dutch (...)
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  24. Colin Howson (1987). Popper, Prior Probabilities, and Inductive Inference. British Journal for the Philosophy of Science 38 (2):207-224.
  25. Colin Howson & Peter Urbach (2010). Bayesian Versus Non-Bayesian Approaches to Confirmation. In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge.
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  26. Colin Howson & Peter Urbach (1993). Scientific Reasoning: The Bayesian Approach. Open Court.
  27. 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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  28. Valeriano Iranzo (2009). Probabilidad Inicial y Éxito Probabilístico. Análisis Filosófico 29 (1):39-71.
    Una cuestión controvertida en la teoría bayesiana de la confirmación es el estatus de las probabilidades iniciales. Aunque la tendencia dominante entre los bayesianos es considerar que la única constricción legítima sobre los valores de dichas probabilidades es la consistencia formal con los teoremas de la teoría matemática de la probabilidad, otros autores -partidarios de lo que se ha dado en llamar "bayesianismo objetivo"- defienden la conveniencia de restricciones adicionales. Mi propuesta, en el marco del bayesianismo objetivo, recoge una sugerencia (...)
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  29. Valeriano Iranzo (2008). Bayesianism and Inference to the Best Explanation. Theoria 23 (1):89-106.
    Bayesianism and Inference to the best explanation (IBE) are two different models of inference. Recently there has been some debate about the possibility of “bayesianizing” IBE. Firstly I explore several alternatives to include explanatory considerations in Bayes’s Theorem. Then I distinguish two different interpretationsof prior probabilities: “IBE-Bayesianism” (IBE-Bay) and “frequentist-Bayesianism” (Freq-Bay). After detailing the content of the latter, I propose a rule for assessing the priors. I also argue that Freq-Bay: (i) endorses a role for explanatory value in the assessment (...)
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  30. 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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  31. 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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  32. James Joyce, Bayes' Theorem. Stanford Encyclopedia of Philosophy.
    Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, (...)
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  33. James M. Joyce (1998). A Nonpragmatic Vindication of Probabilism. Philosophy of Science 65 (4):575-603.
    The pragmatic character of the Dutch book argument makes it unsuitable as an "epistemic" justification for the fundamental probabilist dogma that rational partial beliefs must conform to the axioms of probability. To secure an appropriately epistemic justification for this conclusion, one must explain what it means for a system of partial beliefs to accurately represent the state of the world, and then show that partial beliefs that violate the laws of probability are invariably less accurate than they could be otherwise. (...)
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  34. Cory Juhl (1993). Bayesianism and Reliable Scientific Inquiry. Philosophy of Science 60 (2):302-319.
    The inductive reliability of Bayesian methods is explored. The first result presented shows that for any solvable inductive problem of a general type, there exists a subjective prior which yields a Bayesian inductive method that solves the problem, although not all subjective priors give rise to a successful inductive method for the problem. The second result shows that the same does not hold for computationally bounded agents, so that Bayesianism is "inductively incomplete" for such agents. Finally a consistency proof shows (...)
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  35. Cory F. Juhl (1996). Objectively Reliable Subjective Probabilities. Synthese 109 (3):293 - 309.
    Subjective Bayesians typically find the following objection difficult to answer: some joint probability measures lead to intuitively irrational inductive behavior, even in the long run. Yet well-motivated ways to restrict the set of reasonable prior joint measures have not been forthcoming. In this paper I propose a way to restrict the set of prior joint probability measures in particular inductive settings. My proposal is the following: where there exists some successful inductive method for getting to the truth in some situation, (...)
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  36. Herbert Keuth (1973). On Prior Probabilities of Rejecting Statistical Hypotheses. Philosophy of Science 40 (4):538-546.
    Meehl's statement "in most psychological research, Improved power of a statistical design leads to a prior probability approaching 1/2 of finding a significant difference in the theoretically predicted direction" (philosophy of science, Volume 34, Pages 103-115), Is without foundation. The computation of prior probabilities of accepting or rejecting a hypothesis presupposes knowledge of the prior probabilities that this hypothesis or any of its conceivable alternatives are true. As we do not have such knowledge, We cannot give any numerical values of (...)
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  37. 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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  38. I. A. Kieseppä (2003). AICand Large Samples. Philosophy of Science 70 (5):1265-1276.
    I discuss the behavior of the Akaike Information Criterion in the limit when the sample size grows. I show the falsity of the claim made recently by Stanley Mulaik in Philosophy of Science that AIC would not distinguish between saturated and other correct factor analytic models in this limit. I explain the meaning and demonstrate the validity of the familiar, more moderate criticism that AIC is not a consistent estimator of the number of parameters of the smallest correct model. I (...)
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  39. Keith Lehrer (1982). Skepticism and Prior Probabilities. Philosophia 11 (1-2):89-93.
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  40. 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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  41. Patrick Maher (1996). Subjective and Objective Confirmation. Philosophy of Science 63 (2):149-174.
    Confirmation is commonly identified with positive relevance, E being said to confirm H if and only if E increases the probability of H. Today, analyses of this general kind are usually Bayesian ones that take the relevant probabilities to be subjective. I argue that these subjective Bayesian analyses are irremediably flawed. In their place I propose a relevance analysis that makes confirmation objective and which, I show, avoids the flaws of the subjective analyses. What I am proposing is in some (...)
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  42. 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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  43. Vann McGee (1994). Learning the Impossible. In Ellery Eells & Brian Skyrms (eds.), Probability and Conditionals: Belief Revision and Rational Decision. Cambridge University Press. 179-199.
  44. Christopher J. G. Meacham (2013). Impermissive Bayesianism. Erkenntnis:1-33.
    This paper examines the debate between permissive and impermissive forms of Bayesianism. It briefly discusses some considerations that might be offered by both sides of the debate, and then replies to some new arguments in favor of impermissivism offered by Roger White. First, it argues that White’s (Oxford studies in epistemology, vol 3. Oxford University Press, Oxford, pp 161–186, 2010) defense of Indifference Principles is unsuccessful. Second, it contends that White’s (Philos Perspect 19:445–459, 2005) arguments against permissive views do not (...)
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  45. Christopher J. G. Meacham (2008). Sleeping Beauty and the Dynamics of de Se Beliefs. Philosophical Studies 138 (2):245-269.
    This paper examines three accounts of the sleeping beauty case: an account proposed by Adam Elga, an account proposed by David Lewis, and a third account defended in this paper. It provides two reasons for preferring the third account. First, this account does a good job of capturing the temporal continuity of our beliefs, while the accounts favored by Elga and Lewis do not. Second, Elga’s and Lewis’ treatments of the sleeping beauty case lead to highly counterintuitive consequences. The proposed (...)
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  46. Amos Nathan (1984). The Fallacy of Intrinsic Distributions. Philosophy of Science 51 (4):677-684.
    Jaynes contends that in many statistical problems a seemingly indeterminate probability distribution is made unique by the transformation group of necessarily implied invariance properties, thereby justifying the principle of indifference. To illustrate and substantiate his claims he considers Bertrand's Paradox. These assertions are here refuted and the traditional attitude is vindicated.
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  47. Samir Okasha (2000). Bayes, Levi, and the Taxicabs. Behavioral and Brain Sciences 23 (5):693-693.
    Stanovich & West (S&W) are wrong to think that all “reject-the-norm” theorists simply wish to reduce the normative/descriptive gap. They have misunderstood Issac Levi's reasons for rejecting Tversky and Kahneman's normative assumptions in the “base-rate” experiments. In their discussion of the taxicab experiment, (S&W) erroneously claim that subjects' responses indicate whether they have reasoned in accordance with Bayesian principles or not.
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  48. Daniel Osherson, Edward E. Smith, Eldar Shafir, Antoine Gualtierotti & Kevin Biolsi (1995). A Source of Bayesian Priors. Cognitive Science 19 (3):377-405.
  49. David Owen (1987). Hume Versus Price on Miracles and Prior Probabilities: Testimony and the Bayesian Calculation. Philosophical Quarterly 37 (147):187-202.
    Hume’s celebrated argument concerning miracles, and an 18th century criticism of it put forward by Richard Price, is here interpreted in terms of the modern controversy over the base-rate fallacy. When considering to what degree we should trust a witness, should we or should we not take into account the prior probability of the event reported? The reliability of the witness (’Pr’(says e/e)) is distinguished from the credibility of the testimony (’Pr’(e/says e)), and it is argued that Hume, as a (...)
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  50. Matthew W. Parker, More Trouble for Regular Probabilitites.
    In standard probability theory, probability zero is not the same as impossibility. But many have suggested that only impossible events should have probability zero. This can be arranged if we allow infinitesimal probabilities, but infinitesimals do not solve all of the problems. We will see that regular probabilities are not invariant over rigid transformations, even for simple, bounded, countable, constructive, and disjoint sets. Hence, regular chances cannot be determined by space-time invariant physical laws, and regular credences cannot satisfy seemingly reasonable (...)
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