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  1. Pareto Principles in Infinite Ethics.Amanda Askell - 2018 - Dissertation, New York University
    It is possible that the world contains infinitely many agents that have positive and negative levels of well-being. Theories have been developed to ethically rank such worlds based on the well-being levels of the agents in those worlds or other qualitative properties of the worlds in question, such as the distribution of agents across spacetime. In this thesis I argue that such ethical rankings ought to be consistent with the Pareto principle, which says that if two worlds contain the same (...)
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  • How probable is an infinite sequence of heads? A reply to Williamson.Ruth Weintraub - 2008 - Analysis 68 (299):247-250.
    It is possible that a fair coin tossed infinitely many times will always land heads. So the probability of such a sequence of outcomes should, intuitively, be positive, albeit miniscule: 0 probability ought to be reserved for impossible events. And, furthermore, since the tosses are independent and the probability of heads (and tails) on a single toss is half, all sequences are equiprobable. But Williamson has adduced an argument that purports to show that our intuitions notwithstanding, the probability of an (...)
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  • Symmetry arguments against regular probability: A reply to recent objections.Matthew W. Parker - 2019 - European Journal for Philosophy of Science 9 (1):1-21.
    A probability distribution is regular if it does not assign probability zero to any possible event. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson and Benci et al. have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s “isomorphic” events are not in fact isomorphic, but Howson is speaking (...)
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  • Symmetry arguments against regular probability: A reply to recent objections.Matthew W. Parker - 2018 - European Journal for Philosophy of Science 9 (1):8.
    A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson is speaking (...)
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  • The Foundations of Statistics.Leonard J. Savage - 1956 - Philosophy of Science 23 (2):166-166.
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  • Logic and Theism: Arguments for and Against Beliefs in God.Jordan Howard Sobel - 2003 - New York: Cambridge University Press. Edited by Jordan Howard Sobel.
    This is a wide-ranging 2004 book about arguments for and against beliefs in God. The arguments for the belief are analysed in the first six chapters and include ontological arguments from Anselm to Gödel, the cosmological arguments of Aquinas and Leibniz, and arguments from evidence for design and miracles. The next two chapters consider arguments against belief. The last chapter examines Pascalian arguments for and against belief in God. There are discussions of Cantorian problems for omniscience, of challenges to divine (...)
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  • How probable is an infinite sequence of heads?Timothy Williamson - 2007 - Analysis 67 (3):173-180.
    Isn't probability 1 certainty? If the probability is objective, so is the certainty: whatever has chance 1 of occurring is certain to occur. Equivalently, whatever has chance 0 of occurring is certain not to occur. If the probability is subjective, so is the certainty: if you give credence 1 to an event, you are certain that it will occur. Equivalently, if you give credence 0 to an event, you are certain that it will not occur. And so on for other (...)
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  • Infinite Lotteries, Perfectly Thin Darts and Infinitesimals.Alexander R. Pruss - 2012 - Thought: A Journal of Philosophy 1 (2):81-89.
    One of the problems that Bayesian regularity, the thesis that all contingent propositions should be given probabilities strictly between zero and one, faces is the possibility of random processes that randomly and uniformly choose a number between zero and one. According to classical probability theory, the probability that such a process picks a particular number in the range is zero, but of course any number in the range can indeed be picked. There is a solution to this particular problem on (...)
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  • Regularity and Hyperreal Credences.Kenny Easwaran - 2014 - Philosophical Review 123 (1):1-41.
    Many philosophers have become worried about the use of standard real numbers for the probability function that represents an agent's credences. They point out that real numbers can't capture the distinction between certain extremely unlikely events and genuinely impossible ones—they are both represented by credence 0, which violates a principle known as “regularity.” Following Skyrms 1980 and Lewis 1980, they recommend that we should instead use a much richer set of numbers, called the “hyperreals.” This essay argues that this popular (...)
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  • The Foundations of Statistics.Leonard J. Savage - 1954 - Wiley Publications in Statistics.
    Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.
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  • God, freedom, and evil.Alvin Plantinga - 1978 - Grand Rapids: Eerdmans.
    This book discusses and exemplifies the philosophy of religion, or philosophical reflection on central themes of religion.
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  • The Nature of Necessity.Alvin Plantinga - 1974 - Oxford, England: Clarendon Press.
    This book, one of the first full-length studies of the modalities to emerge from the debate to which Saul Kripke, David Lewis, Ruth Marcus, and others are contributing, is an exploration and defense of the notion of modality de re, the idea that objects have both essential and accidental properties. Plantinga develops his argument by means of the notion of possible worlds and ranges over such key problems as the nature of essence, transworld identity, negative existential propositions, and the existence (...)
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  • Infinite utilitarianism: More is always better.Luc Lauwers & Peter Vallentyne - 2004 - Economics and Philosophy 20 (2):307-330.
    We address the question of how finitely additive moral value theories (such as utilitarianism) should rank worlds when there are an infinite number of locations of value (people, times, etc.). In the finite case, finitely additive theories satisfy both Weak Pareto and a strong anonymity condition. In the infinite case, however, these two conditions are incompatible, and thus a question arises as to which of these two conditions should be rejected. In a recent contribution, Hamkins and Montero (2000) have argued (...)
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  • What conditional probability could not be.Alan Hájek - 2003 - Synthese 137 (3):273--323.
    Kolmogorov''s axiomatization of probability includes the familiarratio formula for conditional probability: 0).$$ " align="middle" border="0">.
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  • Should utilitarians be cautious about an infinite future?Luc Van Liedekerke - 1995 - Australasian Journal of Philosophy 73 (3):405-407.
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  • Infinite value and finitely additive value theory.Peter Vallentyne & Shelly Kagan - 1997 - Journal of Philosophy 94 (1):5-26.
    000000001. Introduction Call a theory of the good—be it moral or prudential—aggregative just in case (1) it recognizes local (or location-relative) goodness, and (2) the goodness of states of affairs is based on some aggregation of local goodness. The locations for local goodness might be points or regions in time, space, or space-time; or they might be people, or states of nature.1 Any method of aggregation is allowed: totaling, averaging, measuring the equality of the distribution, measuring the minimum, etc.. Call (...)
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  • With infinite utility, more needn't be better.Joel David Hamkins & Barbara Montero - 2000 - Australasian Journal of Philosophy 78 (2):231 – 240.
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  • Probability: Theory and Examples.Rick Durrett - 2005 - Thomson.
    This book is an introduction to probability theory covering laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems.
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  • Utilitarianism, decision theory and eternity.Frank Arntzenius - 2014 - Philosophical Perspectives 28 (1):31-58.
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  • Infinite Ethics.Nick Bostrom - 2011 - Analysis and Metaphysics 10:9–59.
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  • The logic of preference reconsidered.G. H. Von Wright - 1972 - Theory and Decision 3 (2):140-169.
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  • The Conception of Intrinsic Value.G. E. Moore - 1998 - In James Rachels (ed.), Ethical theory. New York: Oxford University Press.
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  • The Foundations of Statistics.Leonard J. Savage - 1954 - Synthese 11 (1):86-89.
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  • How probable is an infinite sequence of heads?Timothy Williamson - 2007 - Analysis 67 (3):173-180.
    Isn't probability 1 certainty? If the probability is objective, so is the certainty: whatever has chance 1 of occurring is certain to occur. Equivalently, whatever has chance 0 of occurring is certain not to occur. If the probability is subjective, so is the certainty: if you give credence 1 to an event, you are certain that it will occur. Equivalently, if you give credence 0 to an event, you are certain that it will not occur. And so on for other (...)
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  • To My Critics with Appreciation: Responses to Taliaferro, Swinburne, and Koons.Jordan Howard Sobel - 2006 - Philosophia Christi 8 (2):249 - 292.
    This response to critics includes elaboration of ideas and arguments in ’Logic and Theism’ regarding cumulative arguments for theism, probabilities, ’fine-tuning’ and many worlds, and Gödel’s ontological proof probabilities subjective and objective, and Mackiean doubts concerning the latter, are explained. There is discussion of ’dividing the evidence’ in Bayesian confirmation exercises, with some of it allowed to target ’priors’ of hypotheses, and there is a note on my problems with old evidence. Tentatively explored are Gödel’s considered modal opinions, which may (...)
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  • A neglected family of aggregation problems in ethics.Krister Segerberg - 1976 - Noûs 10 (2):221-244.
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  • The Problem of Endless Joy: Is Infinite Utility Too Much for Utilitarianism?M. T. Nelson & J. L. A. Garcia - 1994 - Utilitas 6 (2):183-192.
    What if human joy went on endlessly? Suppose, for example, that each human generation were followed by another, or that the Western religions are right when they teach that each human being lives eternally after death. If any such possibility is true in the actual world, then an agent might sometimes be so situated that more than one course of action would produce an infinite amount of utility. Deciding whether to have a child born this year rather than next is (...)
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