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  1. Ernest Adams (1998). A Primer of Probability Logic. Stanford: Csli Publications.
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  2. 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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  3. David Atkinson & Jeanne Peijnenburg (2008). Reichenbach's Posits Reposited. Erkenntnis 69 (1):93 - 108.
    Reichenbach’s use of ‘posits’ to defend his frequentistic theory of probability has been criticized on the grounds that it makes unfalsifiable predictions. The justice of this criticism has blinded many to Reichenbach’s second use of a posit, one that can fruitfully be applied to current debates within epistemology. We show first that Reichenbach’s alternative type of posit creates a difficulty for epistemic foundationalists, and then that its use is equivalent to a particular kind of Jeffrey conditionalization. We conclude that, under (...)
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  4. Bengt Autzen (2011). Constraining Prior Probabilities of Phylogenetic Trees. Biology and Philosophy 26 (4):567-581.
    Although Bayesian methods are widely used in phylogenetic systematics today, the foundations of this methodology are still debated among both biologists and philosophers. The Bayesian approach to phylogenetic inference requires the assignment of prior probabilities to phylogenetic trees. As in other applications of Bayesian epistemology, the question of whether there is an objective way to assign these prior probabilities is a contested issue. This paper discusses the strategy of constraining the prior probabilities of phylogenetic trees by means of the Principal (...)
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  5. Andrew Bacon (2014). Giving Your Knowledge Half a Chance. Philosophical Studies:1-25.
    One thousand fair causally isolated coins will be independently flipped tomorrow morning and you know this fact. I argue that the probability, conditional on your knowledge, that any coin will land tails is almost 1 if that coin in fact lands tails, and almost 0 if it in fact lands heads. I also show that the coin flips are not probabilistically independent given your knowledge. These results are uncomfortable for those, like Timothy Williamson, who take these probabilities to play a (...)
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  6. Helen Beebee & David Papineau (1997). Probability as a Guide to Life. Journal of Philosophy 94 (5):217-243.
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  7. Helen Beebee & David Papineau (1997). Probability as a Guide to Life. Journal of Philosophy 94 (5):217-243.
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  8. R. Black (1998). Chance, Credence, and the Principle. British Journal for the Philosophy of Science 49 (3):371-385.
    Any adequate theory of chance must accommodate some version of David Lewis's ‘Principal Principle’, and Lewis has argued forcibly that believers in primitive propensities have a problem in explaining what makes the Principle true. But Lewis can only derive (a revised version of) the Principle from his own Humean theory by putting constraints on inductive rationality which cannot be given a Humean rationale.
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  9. Robert Black (1998). Chance, Credence, and the Principal Principle. British Journal for the Philosophy of Science 49 (3):371-385.
    Any adequate theory of chance must accommodate some version of David Lewis's ‘Principal Principle’, and Lewis has argued forcibly that believers in primitive propensities have a problem in explaining what makes the Principle true. But Lewis can only derive (a revised version of) the Principle from his own Humean theory by putting constraints on inductive rationality which cannot be given a Humean rationale.
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  10. Nick Bostrom (2001). The Doomsday Argument Adam & Eve, UN++, and Quantum Joe. Synthese 127 (3):359 - 387.
    The Doomsday argument purports to show that the risk of the human species going extinct soon has been systematically underestimated. This argument has something in common with controversial forms of reasoning in other areas, including: game theoretic problems with imperfect recall, the methodology of cosmology, the epistemology of indexical belief, and the debate over so-called fine-tuning arguments for the design hypothesis. The common denominator is a certain premiss: the Self-Sampling Assumption. We present two strands of argument in favor of this (...)
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  11. Rachael Briggs (2009). The Anatomy of the Big Bad Bug. Noûs 43 (3):428-449.
  12. Rachael Briggs (2009). The Big Bad Bug Bites Anti-Realists About Chance. Synthese 167 (1):81--92.
    David Lewis’s ‘Humean Supervenience’ (henceforth ‘HS’) combines realism about laws, chances, and dispositions with a sparse ontology according to which everything supervenes on the overall spatiotemporal distribution of non-dispositional properties (Lewis 1986a, Philosophical papers: Volume II, pp. ix–xvii, New York: Oxford Univesity Press, 1994, Mind 103:473–490). HS faces a serious problem—a “big bad bug” (Lewis 1986a, p. xiv): it contradicts the Principal Principle, a seemingly obvious norm of rational credence. Two authors have tried to rescue Lewis’s ontology from the ‘big (...)
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  13. Richard N. Burnor (1984). What's the Matter with the Matter of Chance? Philosophical Studies 46 (3):349 - 365.
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  14. Milan Cirkovic (2006). Is Quantum Suicide Painless? On an Apparent Violation of the Principal Principle. Foundations of Science 11 (3):287-296.
    The experimental setup of the self-referential quantum measurement, jovially known as the ‘quantum suicide’ or the ‘quantum Russian roulette’ is analyzed from the point of view of the Principal Principle of David Lewis. It is shown that the apparent violation of this principle – relating objective probabilities and subjective chance – in this type of thought experiment is just an illusion due to the usage of some terms and concepts ill-defined in the quantum context. We conclude that even in the (...)
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  15. Milan M. Ćirković (2006). Is Quantum Suicide Painless? On an Apparent Violation of the Principal Principle. Foundations of Science 11 (3):287-296.
    The experimental setup of the self-referential quantum measurement, jovially known as the ‘quantum suicide’ or the ‘quantum Russian roulette’ is analyzed from the point of view of the Principal Principle of David Lewis. It is shown that the apparent violation of this principle – relating objective probabilities and subjective chance – in this type of thought experiment is just an illusion due to the usage of some terms and concepts ill-defined in the quantum context. We conclude that even in the (...)
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  16. 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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  17. Cian Dorr, Jeremy Goodman & John Hawthorne (2013). Knowing Against the Odds. Philosophical Studies:1-11.
    We present and discuss a counterexample to the following plausible principle: if you know that a coin is fair, and for all you know it is going to be flipped, then for all you know it will land tails.
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  18. Antony Eagle (2004). A Causal Theory of Chance? [REVIEW] Studies in History and Philosophy of Science Part A 35 (4):883-890.
    An essay review of Richard Johns "A Theory of Physical Probability" (University of Toronto Press, 2002). Forthcoming in Studies in History and Philosophy of Science.
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  19. Justin C. Fisher (2006). On Higher-Order and Free-Floating Chances. British Journal for the Philosophy of Science 57 (4):691-707.
    considers what I call free-floating chances—objective chances that obtain at a given time despite the fact that their values are not determined by the laws of nature together with the full history of non-chancy facts up to that time. I offer an intuitive example of this phenomenon, and use it to argue that free-floating chances are indeed possible. Their possibility violates three quite widely held principles about chances: the lawful magnitude principle, the principle that chances evolve by conditionalization and a (...)
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  20. Roman Frigg & Carl Hoefer (2007). Probability in GRW Theory. Studies in History and Philosophy of Science Part B 38 (2):371-389.
    GRW Theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as either single (...)
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  21. Luke Glynn (2011). D. H. MELLOR The Matter of Chance. British Journal for the Philosophy of Science 62 (4):899-906.
    Though almost forty years have elapsed since its first publication, it is a testament to the philosophical acumen of its author that 'The Matter of Chance' contains much that is of continued interest to the philosopher of science. Mellor advances a sophisticated propensity theory of chance, arguing that this theory makes better sense than its rivals (in particular subjectivist, frequentist, logical and classical theories) of ‘what professional usage shows to be thought true of chance’ (p. xi) – in particular ‘that (...)
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  22. Joshua Haddock (2011). The Principal Principle and Theories of Chance: Another Bug? Philosophy of Science 78 (5):854-863.
  23. 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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  24. Ned Hall (2004). Two Mistakes About Credence and Chance. Australasian Journal of Philosophy 82 (1):93 – 111.
    David Lewis's influential work on the epistemology and metaphysics of objective chance has convinced many philosophers of the central importance of the following two claims: First, it is a serious cost of reductionist positions about chance (such as that occupied by Lewis) that they are, apparently, forced to modify the Principal Principle--the central principle relating objective chance to rational subjective probability--in order to avoid contradiction. Second, it is a perhaps more serious cost of the rival non-reductionist position that, unlike reductionism, (...)
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  25. Ned Hall (2004). Two Mistakes About Credence and Chance. Australasian Journal of Philosophy 82 (1):93 – 111.
    David Lewis's influential work on the epistemology and metaphysics of objective chance has convinced many philosophers of the central importance of the following two claims: First, it is a serious cost of reductionist positions about chance (such as that occupied by Lewis) that they are, apparently, forced to modify the Principal Principle--the central principle relating objective chance to rational subjective probability--in order to avoid contradiction. Second, it is a perhaps more serious cost of the rival non-reductionist position that, unlike reductionism, (...)
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  26. Ned Hall (1994). Correcting the Guide to Objective Chance. Mind 103 (412):505-518.
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  27. John F. Halpin (1998). Lewis, Thau, and Hall on Chance and the Best-System Account of Law. Philosophy of Science 65 (2):349-360.
    August 16, 1997 David Lewis2 has long defended an account of scientific law acceptable even to an empiricist with significant metaphysical scruples. On this account, the laws are defined to be the consequences of the best system for axiomitizing all occurrent fact. Here "best system" means the set of sentences which yields the best combination of strength of descriptive content 3 with simplicity of exposition. And occurrent facts, the facts to be systematized, are roughly the particular facts about a localized (...)
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  28. Toby Handfield & Alastair Wilson (forthcoming). Chance and Context. In Alastair Wilson (ed.), Chance and Temporal Asymmetry. Oxford University Press.
    The most familiar philosophical conception of objective chance renders determinism incompatible with non-trivial chances. This conception – associated in particular with the work of David Lewis – is not a good fit with our use of the word ‘chance’ and its cognates in ordinary discourse. In this paper we show how a generalized framework for chance can reconcile determinism with non-trivial chances, and provide for a more charitable interpretation of ordinary chance-talk. According to our proposal, variation in an admissible ‘evidence (...)
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  29. William Harper, Sheldon J. Chow & Gemma Murray (2012). Bayesian Chance. Synthese 186 (2):447-474.
    This paper explores how the Bayesian program benefits from allowing for objective chance as well as subjective degree of belief. It applies David Lewis’s Principal Principle and David Christensen’s principle of informed preference to defend Howard Raiffa’s appeal to preferences between reference lotteries and scaling lotteries to represent degrees of belief. It goes on to outline the role of objective lotteries in an application of rationality axioms equivalent to the existence of a utility assignment to represent preferences in Savage’s famous (...)
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  30. John Hawthorne & Maria Lasonen-Aarnio (2009). Knowledge and Objective Chance. In Patrick Greenough & Duncan Pritchard (eds.), Williamson on Knowledge. Oxford University Press. 92--108.
    We think we have lots of substantial knowledge about the future. But contemporary wisdom has it that indeterminism prevails in such a way that just about any proposition about the future has a non-zero objective chance of being false.2, 3 What should one do about this? One, pessimistic, reaction is scepticism about knowledge of the future. We think this should be something of a last resort, especially since this scepticism is likely to infect alleged knowledge of the present and past. (...)
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  31. Carl Hoefer (2007). The Third Way on Objective Probability: A Sceptic's Guide to Objective Chance. Mind 116 (463):549-596.
    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 (...)
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  32. Carl Hoefer (2007). The Third Way on Objective Probability: A Sceptic's Guide to Objective Chance. Mind 116 (463):549-596.
    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 subtitle obviously emulates the title of Lewis seminal 1980 paper A Subjectivist s Guide to Objective Chance while indicating an important difference in perspective. The view developed below shares two major tenets with Lewis last (1994) account of objective chance: (1) (...)
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  33. Carl Hoefer (1997). On Lewis's Objective Chance: "Humean Supervenience Debugged". Mind 106 (422):321-334.
  34. Colin Howson & Peter Urbach (1993). Scientific Reasoning: The Bayesian Approach. Open Court.
  35. Jenann Ismael, Raid! The Big, Bad Bug Dissolved.
    There’s a long history of discussion of probability in philosophy, but objective chance separated itself off and came into its own as a topic with the advent of a physical theory - quantum mechanics - in which chances play a central, and apparently ineliminable, role. In 1980 David Lewis wrote a paper pointing out that a very broad class of accounts of the nature of chance apparently lead to a contradiction when combined with a principle that expresses the role of (...)
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  36. James M. Joyce (2007). Epistemic Deference: The Case of Chance. Proceedings of the Aristotelian Society 107 (2):187 - 206.
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  37. Isaac Levi (1977). Direct Inference. Journal of Philosophy 74 (1):5-29.
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  38. David Lewis (1994). Humean Supervenience Debugged. Mind 103 (412):473-490.
    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 (...)
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  39. David Lewis (1994). Humean Supervenience Debugged. Mind 103 (412):473--490.
    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 (...)
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  40. David Lewis (1980). A Subjectivist's Guide to Objective Chance. In Richard C. Jeffrey (ed.), Studies in Inductive Logic and Probability. University of California Press. 83--132.
  41. Christian List & Marcus Pivato, Emergent Chance.
    We offer a new argument for the claim that there can be non-degenerate objective chance (“true randomness”) in a deterministic world. Using a formal model of the relationship between different levels of description of a system, we show how objective chance at a higher level can coexist with its absence at a lower level. Unlike previous arguments for the level-specificity of chance, our argument shows, in a precise sense, that higher-level chance does not collapse into epistemic probability, despite higher-level properties (...)
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  42. Barry Loewer (2004). David Lewis's Humean Theory of Objective Chance. Philosophy of Science 71 (5):1115--25.
    The most important theories in fundamental physics, quantum mechanics and statistical mechanics, posit objective probabilities or chances. As important as chance is there is little agreement about what it is. The usual “interpretations of probability” give very different accounts of chance and there is disagreement concerning which, if any, is capable of accounting for its role in physics. David Lewis has contributed enormously to improving this situation. In his classic paper “A Subjectivist's Guide to Objective Chance” he described a framework (...)
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  43. Christopher J. G. Meacham (forthcoming). Autonomous Chances and the Conflicts Problem. In Toby Handfield & Alastair Wilson (eds.), Asymmetries in Chance and Time. Oxford University Press.
    In recent work, Callender and Cohen (2009) and Hoefer (2007) have proposed variants of the account of chance proposed by Lewis (1994). One of the ways in which these accounts diverge from Lewis’s is that they allow special sciences and the macroscopic realm to have chances that are autonomous from those of physics and the microscopic realm. A worry for these proposals is that autonomous chances may place incompatible constraints on rational belief. I examine this worry, and attempt to determine (...)
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  44. Christopher J. G. Meacham (2010). Two Mistakes Regarding the Principal Principle. British Journal for the Philosophy of Science 61 (2):407-431.
    This paper examines two mistakes regarding David Lewis’ Principal Principle that have appeared in the recent literature. These particular mistakes are worth looking at for several reasons: The thoughts that lead to these mistakes are natural ones, the principles that result from these mistakes are untenable, and these mistakes have led to significant misconceptions regarding the role of admissibility and time. After correcting these mistakes, the paper discusses the correct roles of time and admissibility. With these results in hand, the (...)
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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. Christopher J. G. Meacham (2005). Three Proposals Regarding a Theory of Chance. Philosophical Perspectives 19 (1):281–307.
    I argue that the theory of chance proposed by David Lewis has three problems: (i) it is time asymmetric in a manner incompatible with some of the chance theories of physics, (ii) it is incompatible with statistical mechanical chances, and (iii) the content of Lewis's Principal Principle depends on how admissibility is cashed out, but there is no agreement as to what admissible evidence should be. I proposes two modifications of Lewis's theory which resolve these difficulties. I conclude by tentatively (...)
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  47. D. H. Mellor (2004). The Matter of Chance. Cambridge University Press.
    This book deals not so much with statistical methods as with the central concept of chance, or statistical probability, which statistical theories apply to nature.
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  48. David Miller (1966). A Paradox of Information. British Journal for the Philosophy of Science 17 (1):59-61.
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  49. Roberta L. Millstein (2000). Chance and Macroevolution. Philosophy of Science 67 (4):603-624.
    When philosophers of physics explore the nature of chance, they usually look to quantum mechanics. When philosophers of biology explore the nature of chance, they usually look to microevolutionary phenomena, such as mutation or random drift. What has been largely overlooked is the role of chance in macroevolution. The stochastic models of paleobiology employ conceptions of chance that are similar to those at the microevolutionary level, yet different from the conceptions of chance often associated with quantum mechanics and Laplacean determinism.
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  50. Kevin Nelson (2009). On Background: Using Two-Argument Chance. Synthese 166 (1):165 - 186.
    I follow Hájek (Synthese 137:273–323, 2003c) by taking objective probability to be a function of two propositional arguments—that is, I take conditional probability as primitive. Writing the objective probability of q given r as P(q, r), I argue that r may be chosen to provide less than a complete and exact description of the world’s history or of its state at any time. It follows that nontrivial objective probabilities are possible in deterministic worlds and about the past. A very simple (...)
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