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  1. Ernest Adams (1998). A Primer of Probability Logic. Stanford: Csli Publications.
    This book is meant to be a primer, that is, an introduction, to probability logic, a subject that appears to be in its infancy. Probability logic is a subject envisioned by Hans Reichenbach and largely created by Adams. It treats conditionals as bearers of conditional probabilities and discusses an appropriate sense of validity for arguments such conditionals, as well as ordinary statements as premisses. This is a clear well-written text on the subject of probability logic, suitable for advanced undergraduates or (...)
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  2. Evandro Agazzi (1988). Probability in the Sciences. Monograph Collection (Matt - Pseudo).
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  3. 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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  4. 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 that this principle provides the defining role for chance; that it conflicts with his reductionist thesis of Humean supervenience, and so must be replaced by an amended version that avoids the conflict; hence that nothing _perfectly_ deserves the name 'chance', although something can come close enough by playing the role picked out (...)
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  5. 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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  6. 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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  7. Andrew Bacon (2014). Giving Your Knowledge Half a Chance. Philosophical Studies (2):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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  8. Gergei Bana, On the Formal Consistency of the Principal Principle.
    Rédei and Gyenis suggest that Lewis’s Principal Principle is meaningful only if it satisfies certain consistency conditions: starting from any assignment of subjective probabilities to some algebra of events, we should always be able to extend our algebra with events of the form “the value of the objective probability of event E is p” and assign subjective probabilities to such events in a consistent manner. We show that this extension is indeed possible in most cases. However, we also argue that (...)
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  9. Helen Beebee & David Papineau (1997). Probability as a Guide to Life. Journal of Philosophy 94 (5):217-243.
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  10. 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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  11. 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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  12. 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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  13. 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 epistomology 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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  14. Rachael Briggs (2009). The Anatomy of the Big Bad Bug. Noûs 43 (3):428-449.
  15. 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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  16. Richard N. Burnor (1984). What's the Matter with the Matter of Chance? Philosophical Studies 46 (3):349 - 365.
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  17. Michael Caie (2015). Credence in the Image of Chance. Philosophy of Science 82 (4):626-648.
    In this article, I consider what sorts of chance credence norms can be justified by appeal to the idea that ideal credences should line up with the chances. I argue that the Principal Principle cannot be so justified but that an alternative norm, the Temporal Principle—which maintains that an agent’s credence in a proposition ϕ, conditional on the temporal proposition that says that the chance of ϕ is x, should be x—can be so justified.
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  18. Salvatore Cannavo (1956). On the Epistemological Foundations of Probability. Dissertation, New York University
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  19. Fabrizio Cariani (forthcoming). Chance, Credence and Circles. Episteme.
    This is a discussion of Richard Pettigrew's book "Accuracy and the Laws of Credence". I target Pettigrew's application of the accuracy framework to derive chance-credence principles. My principal contention is that Pettigrew's preferred version of the argument might in one sense be circular and, moreover, that Pettigrew's premises have content that go beyond that of standard chance-credence principles.
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  20. 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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  21. 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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  22. Don Diespecker (1999). Quirkily Swayed by Whim. International Journal of Transpersonal Studies 18 (2):163-166.
    "Principal rivers-there are none. Principal mountains-I'm on the only one, but I don't think it's got any name. Principal towns-why, what are those creatures, making honey down there? They can't be bees-nobody ever saw bees a mile off, you know-" and for some time she stood silent, watching one of them that was bustling about among the flowers, poking its proboscis into them, "just as if it was a regular bee," thought Alice. -Lewis Carroll l.
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  23. Dylan Dodd (2013). Roger White's Argument Against Imprecise Credences. British Journal for the Philosophy of Science 64 (1):69-77.
    According to the Imprecise Credence Framework (ICF), a rational believer's doxastic state should be modelled by a set of probability functions rather than a single probability function, namely, the set of probability functions allowed by the evidence ( Joyce [2005] ). Roger White ( [2010] ) has recently given an arresting argument against the ICF, which has garnered a number of responses. In this article, I attempt to cast doubt on his argument. First, I point out that it's not an (...)
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  24. 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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  25. Cian Dorr, Jeremy Goodman & John Hawthorne (2014). Knowing Against the Odds. Philosophical Studies 170 (2):277-287.
    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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  26. A. Eagle (ed.) (2011). Philosophy of Probability: Contemporary Readings. Routledge.
    _Philosophy of Probability: Contemporary Readings_ is the first anthology to collect essential readings in this important area of philosophy. Featuring the work of leading philosophers in the field such as Carnap, Hájek, Jeffrey, Joyce, Lewis, Loewer, Popper, Ramsey, van Fraassen, von Mises, and many others, the book looks in depth at the following key topics: subjective probability and credence probability updating: conditionalization and reflection Bayesian confirmation theory classical, logical, and evidential probability frequentism physical probability: propensities and objective chances. The book (...)
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  27. Antony Eagle (2015). Probability. The Oxford Handbook of Philosophy of Science.
    Rather than entailing that a particular outcome will occur, many scientific theories only entail that an outcome will occur with a certain probability. Because scientific evidence inevitably falls short of conclusive proof, when choosing between different theories it is standard to make reference to how probable the various options are in light of the evidence. A full understanding of probability in science needs to address both the role of probabilities in theories, or chances, as well as the role of probabilistic (...)
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  28. Antony Eagle (ed.) (2011). Philosophy of Probability: Contemporary Readings. Routledge.
    _Philosophy of Probability: Contemporary Readings_ is the first anthology to collect essential readings in this important area of philosophy. Featuring the work of leading philosophers in the field such as Carnap, Hájek, Jeffrey, Joyce, Lewis, Loewer, Popper, Ramsey, van Fraassen, von Mises, and many others, the book looks in depth at the following key topics: subjective probability and credence probability updating: conditionalization and reflection Bayesian confirmation theory classical, logical, and evidential probability frequentism physical probability: propensities and objective chances. The book (...)
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  29. 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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  30. 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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  31. Peter S. Fosl (2006). Your Objective Guide to Philosophical Distinctions. The Philosophers' Magazine 35:82-82.
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  32. Simon Friederich (2015). Re-Thinking Local Causality. Synthese 192 (1):221-240.
    There is widespread belief in a tension between quantum theory and special relativity, motivated by the idea that quantum theory violates J. S. Bell’s criterion of local causality, which is meant to implement the causal structure of relativistic space-time. This paper argues that if one takes the essential intuitive idea behind local causality to be that probabilities in a locally causal theory depend only on what occurs in the backward light cone and if one regards objective probability as what imposes (...)
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  33. 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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  34. 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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  35. I. J. Good (1969). Discussion of Bruno de Finetti's Paper 'Initial Probabilities: A Prerequisite for Any Valid Induction'. Synthese 20 (1):17 - 24.
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  36. Alexei Grinbaum (2012). Which Fine-Tuning Arguments Are Fine? Foundations of Physics 42 (5):615-631.
    Fine-tuning arguments are a frequent find in the literature on quantum field theory. They are based on naturalness—an aesthetic criterion that was given a precise definition in the debates on the Higgs mechanism. We follow the history of such definitions and of their application at the scale of electroweak symmetry breaking. They give rise to a special interpretation of probability, which we call Gedankenfrequency. Finally, we show that the argument from naturalness has been extended to comparing different models of the (...)
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  37. Joshua Haddock (2011). The Principal Principle and Theories of Chance: Another Bug? Philosophy of Science 78 (5):854-863.
  38. 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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  39. 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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  40. 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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  41. Ned Hall (1994). Correcting the Guide to Objective Chance. Mind 103 (412):505-518.
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  42. 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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  43. Toby Handfield & Alastair Wilson (2014). 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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  44. 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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  45. James Hawthorne, Jürgen Landes, Christian Wallmann & Jon Williamson (forthcoming). The Principal Principle Implies the Principle of Indifference. British Journal for the Philosophy of Science:axv030.
    We argue that David Lewis’s principal principle implies a version of the principle of indifference. The same is true for similar principles that need to appeal to the concept of admissibility. Such principles are thus in accord with objective Bayesianism, but in tension with subjective Bayesianism. 1 The Argument2 Some Objections Met.
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  46. 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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  47. 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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  48. 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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  49. Carl Hoefer (1997). On Lewis's Objective Chance: "Humean Supervenience Debugged". Mind 106 (422):321-334.
  50. Colin Howson & Peter Urbach (1993). Scientific Reasoning: The Bayesian Approach. Open Court.
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