Switch to: Citations

Add references

You must login to add references.
  1. The extended mind.Andy Clark & David J. Chalmers - 1998 - Analysis 58 (1):7-19.
    Where does the mind stop and the rest of the world begin? The question invites two standard replies. Some accept the demarcations of skin and skull, and say that what is outside the body is outside the mind. Others are impressed by arguments suggesting that the meaning of our words "just ain't in the head", and hold that this externalism about meaning carries over into an externalism about mind. We propose to pursue a third position. We advocate a very different (...)
    Download  
     
    Export citation  
     
    Bookmark   1684 citations  
  • (2 other versions)Knowledge and Its Limits.Timothy Williamson - 2000 - Philosophy 76 (297):460-464.
    Download  
     
    Export citation  
     
    Bookmark   2358 citations  
  • (2 other versions)Knowledge and Its Limits.Timothy Williamson - 2003 - Philosophical Quarterly 53 (210):105-116.
    Download  
     
    Export citation  
     
    Bookmark   1497 citations  
  • Non-standard Analysis.Gert Heinz Müller - 2016 - Princeton University Press.
    Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested (...)
    Download  
     
    Export citation  
     
    Bookmark   172 citations  
  • (2 other versions)Knowledge and Its Limits.Timothy Williamson - 2005 - Philosophy and Phenomenological Research 70 (2):452-458.
    Download  
     
    Export citation  
     
    Bookmark   1265 citations  
  • A subjectivist’s guide to objective chance.David K. Lewis - 2010 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. New York: Routledge. pp. 263-293.
    Download  
     
    Export citation  
     
    Bookmark   604 citations  
  • (1 other version)On the logic of theory change: Partial meet contraction and revision functions.Carlos E. Alchourrón, Peter Gärdenfors & David Makinson - 1985 - Journal of Symbolic Logic 50 (2):510-530.
    This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...)
    Download  
     
    Export citation  
     
    Bookmark   750 citations  
  • Causal necessity: a pragmatic investigation of the necessity of laws.Brian Skyrms - 1980 - New Haven: Yale University Press.
    Download  
     
    Export citation  
     
    Bookmark   273 citations  
  • .R. G. Swinburne - 1989 - Cambridge University Press.
    Download  
     
    Export citation  
     
    Bookmark   271 citations  
  • 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">.
    Download  
     
    Export citation  
     
    Bookmark   315 citations  
  • (1 other version)Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
    Download  
     
    Export citation  
     
    Bookmark   412 citations  
  • Epistemic justification.Richard Swinburne - 2001 - New York: Oxford University Press.
    Richard Swinburne offers an original treatment of a question at the heart of epistemology: what makes a belief rational, or justified in holding? He maps the rival accounts of philosophers on epistemic justification ("internalist" and "externalist"), arguing that they are really accounts of different concepts. He distinguishes between synchronic justification (justification at a time) and diachronic justification (synchronic justification resulting from adequate investigation)--both internalist and externalist. He also argues that most kinds of justification are worth having because they are indicative (...)
    Download  
     
    Export citation  
     
    Bookmark   118 citations  
  • Subjective Probability: The Real Thing.Richard C. Jeffrey - 2002 - Cambridge and New York: Cambridge University Press.
    This book offers a concise survey of basic probability theory from a thoroughly subjective point of view whereby probability is a mode of judgment. Written by one of the greatest figures in the field of probability theory, the book is both a summation and synthesis of a lifetime of wrestling with these problems and issues. After an introduction to basic probability theory, there are chapters on scientific hypothesis-testing, on changing your mind in response to generally uncertain observations, on expectations of (...)
    Download  
     
    Export citation  
     
    Bookmark   94 citations  
  • Subjective Probabilities Should be Sharp.Adam Elga - 2010 - Philosophers' Imprint 10.
    Many have claimed that unspecific evidence sometimes demands unsharp, indeterminate, imprecise, vague, or interval-valued probabilities. Against this, a variant of the diachronic Dutch Book argument shows that perfectly rational agents always have perfectly sharp probabilities.
    Download  
     
    Export citation  
     
    Bookmark   136 citations  
  • .Brian Skyrms - 1980 - In The Role of Causal Factors in Rational Decision. Yale University Press.
    Download  
     
    Export citation  
     
    Bookmark   196 citations  
  • Probability and conditionals.Robert C. Stalnaker - 1970 - Philosophy of Science 37 (1):64-80.
    The aim of the paper is to draw a connection between a semantical theory of conditional statements and the theory of conditional probability. First, the probability calculus is interpreted as a semantics for truth functional logic. Absolute probabilities are treated as degrees of rational belief. Conditional probabilities are explicitly defined in terms of absolute probabilities in the familiar way. Second, the probability calculus is extended in order to provide an interpretation for counterfactual probabilities--conditional probabilities where the condition has zero probability. (...)
    Download  
     
    Export citation  
     
    Bookmark   164 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   91 citations  
  • (1 other version)Model Theory.C. C. Chang & H. Jerome Keisler - 1992 - Studia Logica 51 (1):154-155.
    Download  
     
    Export citation  
     
    Bookmark   117 citations  
  • (1 other version)Arguments For—Or Against—Probabilism?Alan Hájek - 2009 - In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of belief. London: Springer. pp. 229--251.
    Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned. Each argument concludes that rationality requires your credences to be probabilities. I contend that each argument is invalid as formulated. In each case there is a mirror-image theorem and (...)
    Download  
     
    Export citation  
     
    Bookmark   82 citations  
  • Fixing Frege.John P. Burgess - 2005 - Princeton University Press.
    The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previously been assumed. A variety of repaired systems have been (...)
    Download  
     
    Export citation  
     
    Bookmark   49 citations  
  • (1 other version)Coherence and the axioms of confirmation.Abner Shimony - 1955 - Journal of Symbolic Logic 20 (1):1-28.
    Download  
     
    Export citation  
     
    Bookmark   114 citations  
  • Fair bets and inductive probabilities.John G. Kemeny - 1955 - Journal of Symbolic Logic 20 (3):263-273.
    Download  
     
    Export citation  
     
    Bookmark   112 citations  
  • Desire as belief II.David K. Lewis - 1996 - Mind 105 (418):303-13.
    Download  
     
    Export citation  
     
    Bookmark   84 citations  
  • (1 other version)To Be is to be a Value of a Variable.George Boolos - 1984 - Journal of Symbolic Logic 54 (2):616-617.
    Download  
     
    Export citation  
     
    Bookmark   89 citations  
  • (1 other version)Arguments for–or against–Probabilism?Alan Hájek - 2008 - British Journal for the Philosophy of Science 59 (4):793-819.
    Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned.Each argument concludes that rationality requires your credences to be probabilities.I contend that each argument is invalid as formulated. In each case there is a mirror-image theorem and a corresponding (...)
    Download  
     
    Export citation  
     
    Bookmark   50 citations  
  • Vexing expectations.Harris Nover & Alan Hájek - 2004 - Mind 113 (450):237-249.
    We introduce a St. Petersburg-like game, which we call the ‘Pasadena game’, in which we toss a coin until it lands heads for the first time. Your pay-offs grow without bound, and alternate in sign (rewards alternate with penalties). The expectation of the game is a conditionally convergent series. As such, its terms can be rearranged to yield any sum whatsoever, including positive infinity and negative infinity. Thus, we can apparently make the game seem as desirable or undesirable as we (...)
    Download  
     
    Export citation  
     
    Bookmark   64 citations  
  • Non-Archimedean Probability.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2013 - Milan Journal of Mathematics 81 (1):121-151.
    We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and only the empty set gets assigned probability zero (in other words: the probability functions are regular). We use a non-Archimedean field as the range of the probability function. As a result, the property of countable additivity in Kolmogorov’s axiomatization of probability is replaced by (...)
    Download  
     
    Export citation  
     
    Bookmark   41 citations  
  • (1 other version)[Omnibus Review].Akihiro Kanamori - 1981 - Journal of Symbolic Logic 46 (4):864-866.
    Download  
     
    Export citation  
     
    Bookmark   71 citations  
  • Relative Expectation Theory.Mark Colyvan - 2008 - Journal of Philosophy 105 (1):37-44.
    Games such as the St. Petersburg game present serious problems for decision theory.1 The St. Petersburg game invokes an unbounded utility function to produce an infinite expectation for playing the game. The problem is usually presented as a clash between decision theory and intuition: most people are not prepared to pay a large finite sum to buy into this game, yet this is precisely what decision theory suggests we ought to do. But there is another problem associated with the St. (...)
    Download  
     
    Export citation  
     
    Bookmark   33 citations  
  • Knowledge and its Limits. [REVIEW]L. Horsten - 2000 - Tijdschrift Voor Filosofie 64 (1):200-201.
    Download  
     
    Export citation  
     
    Bookmark   2408 citations  
  • Fine-grained opinion, probability, and the logic of full belief.Bas C. van Fraassen - 1995 - Journal of Philosophical Logic 24 (4):349-377.
    Download  
     
    Export citation  
     
    Bookmark   59 citations  
  • Learning the Impossible.Vann McGee - 1994 - In Ellery Eells & Brian Skyrms (eds.), Probability and Conditionals: Belief Revision and Rational Decision. New York: Cambridge University Press. pp. 179-199.
    Download  
     
    Export citation  
     
    Bookmark   55 citations  
  • Zermelo's Axiom of Choice. Its Origins, Development, and Influence.Gregory H. Moore - 1984 - Journal of Symbolic Logic 49 (2):659-660.
    Download  
     
    Export citation  
     
    Bookmark   57 citations  
  • Countable additivity and subjective probability.Jon Williamson - 1999 - British Journal for the Philosophy of Science 50 (3):401-416.
    While there are several arguments on either side, it is far from clear as to whether or not countable additivity is an acceptable axiom of subjective probability. I focus here on de Finetti's central argument against countable additivity and provide a new Dutch book proof of the principle, To argue that if we accept the Dutch book foundations of subjective probability, countable additivity is an unavoidable constraint.
    Download  
     
    Export citation  
     
    Bookmark   52 citations  
  • (1 other version)Two autonomous axiom systems for the calculus of probabilities.Karl R. Popper - 1955 - British Journal for the Philosophy of Science 6 (21):51-57.
    Download  
     
    Export citation  
     
    Bookmark   48 citations  
  • Scotching Dutch Books?Alan Hájek - 2005 - Philosophical Perspectives 19 (1):139-151.
    The Dutch Book argument, like Route 66, is about to turn 80. It is arguably the most celebrated argument for subjective Bayesianism. Start by rejecting the Cartesian idea that doxastic attitudes are ‘all-or-nothing’; rather, they are far more nuanced degrees of belief, for short credences, susceptible to fine-grained numerical measurement. Add a coherentist assumption that the rationality of a doxastic state consists in its internal consistency. The remaining problem is to determine what consistency of credences amounts to. The Dutch Book (...)
    Download  
     
    Export citation  
     
    Bookmark   41 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   28 citations  
  • Probability Disassembled.John D. Norton - 2007 - British Journal for the Philosophy of Science 58 (2):141-171.
    While there is no universal logic of induction, the probability calculus succeeds as a logic of induction in many contexts through its use of several notions concerning inductive inference. They include Addition, through which low probabilities represent disbelief as opposed to ignorance; and Bayes property, which commits the calculus to a ‘refute and rescale’ dynamics for incorporating new evidence. These notions are independent and it is urged that they be employed selectively according to needs of the problem at hand. It (...)
    Download  
     
    Export citation  
     
    Bookmark   34 citations  
  • Preference-based arguments for probabilism.David Christensen - 2001 - Philosophy of Science 68 (3):356-376.
    Both Representation Theorem Arguments and Dutch Book Arguments support taking probabilistic coherence as an epistemic norm. Both depend on connecting beliefs to preferences, which are not clearly within the epistemic domain. Moreover, these connections are standardly grounded in questionable definitional/metaphysical claims. The paper argues that these definitional/metaphysical claims are insupportable. It offers a way of reconceiving Representation Theorem arguments which avoids the untenable premises. It then develops a parallel approach to Dutch Book Arguments, and compares the results. In each case (...)
    Download  
     
    Export citation  
     
    Bookmark   29 citations  
  • Strong and weak expectations.Kenny Easwaran - 2008 - Mind 117 (467):633-641.
    Fine has shown that assigning any value to the Pasadena game is consistent with a certain standard set of axioms for decision theory. However, I suggest that it might be reasonable to believe that the value of an individual game is constrained by the long-run payout of repeated plays of the game. Although there is no value that repeated plays of the Pasadena game converges to in the standard strong sense, I show that there is a weaker sort of convergence (...)
    Download  
     
    Export citation  
     
    Bookmark   25 citations  
  • Infinitesimal Chances.Thomas Hofweber - 2014 - Philosophers' Imprint 14.
    It is natural to think that questions in the metaphysics of chance are independent of the mathematical representation of chance in probability theory. After all, chance is a feature of events that comes in degrees and the mathematical representation of chance concerns these degrees but leaves the nature of chance open. The mathematical representation of chance could thus, un-controversially, be taken to be what it is commonly taken to be: a probability measure satisfying Kolmogorov’s axioms. The metaphysical questions about chance (...)
    Download  
     
    Export citation  
     
    Bookmark   18 citations  
  • Beyond the universal Turing machine.B. Jack Copeland & Richard Sylvan - 1999 - Australasian Journal of Philosophy 77 (1):46-66.
    Download  
     
    Export citation  
     
    Bookmark   29 citations  
  • (1 other version)The British Journal for the Philosophy of Science | Vol 73, No 3.Karl R. Popper - 1955 - British Journal for the Philosophy of Science 6 (24):351-351.
    Download  
     
    Export citation  
     
    Bookmark   29 citations  
  • (2 other versions)Causal Necessity: A Pragmatic Investigation of the Necessity of Laws.Richard C. Jeffrey - 1980 - Journal of Symbolic Logic 50 (2):557-558.
    Download  
     
    Export citation  
     
    Bookmark   29 citations  
  • Fine‐Tuning, Multiple Universes and Theism.Rodney D. Holder - 2002 - Noûs 36 (2):295–312.
    The universe appears fine-tuned for life. Bayesian confirmation theory is utilized to examine two competing explanations for this fine-tuning, namely design (theism) and the existence of many universes, in comparison with the ’null’ hypothesis that just one universe exists as a brute fact. Some authors have invoked the so-called ’inverse gambler’s fallacy’ to argue that the many-universes hypothesis does not explain the fine-tuning of ’this’ universe, but flaws in this argument are exposed. Nevertheless, the hypothesis of design, being simpler, is (...)
    Download  
     
    Export citation  
     
    Bookmark   19 citations  
  • (1 other version)Two Autonomous Axiom Systems for the Calculus of Probabilities.Karl R. Popper - 1958 - Journal of Symbolic Logic 23 (3):349-349.
    Download  
     
    Export citation  
     
    Bookmark   24 citations  
  • Beyond the universal Turing machine.Jack Copeland - 1999 - Australasian Journal of Philosophy 77 (1):46-67.
    We describe an emerging field, that of nonclassical computability and nonclassical computing machinery. According to the nonclassicist, the set of well-defined computations is not exhausted by the computations that can be carried out by a Turing machine. We provide an overview of the field and a philosophical defence of its foundations.
    Download  
     
    Export citation  
     
    Bookmark   20 citations  
  • The shooting-room paradox and conditionalizing on measurably challenged sets.Paul Bartha & Christopher Hitchcock - 1999 - Synthese 118 (3):403-437.
    We provide a solution to the well-known “Shooting-Room” paradox, developed by John Leslie in connection with his Doomsday Argument. In the “Shooting-Room” paradox, the death of an individual is contingent upon an event that has a 1/36 chance of occurring, yet the relative frequency of death in the relevant population is 0.9. There are two intuitively plausible arguments, one concluding that the appropriate subjective probability of death is 1/36, the other that this probability is 0.9. How are these two values (...)
    Download  
     
    Export citation  
     
    Bookmark   19 citations  
  • A definable nonstandard model of the reals.Vladimir Kanovei & Saharon Shelah - 2004 - Journal of Symbolic Logic 69 (1):159-164.
    We prove, in ZFC,the existence of a definable, countably saturated elementary extension of the reals.
    Download  
     
    Export citation  
     
    Bookmark   21 citations  
  • Epistemic Justification.Nicholas Everitt - 2001 - Mind 112 (447):572-575.
    Download  
     
    Export citation  
     
    Bookmark   18 citations