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  1. Colin Howson (forthcoming). A Continuum-Valued Logic of Degrees of Probability. Erkenntnis:1-13.
    Leibniz seems to have been the first to suggest a logical interpretation of probability, but there have always seemed formidable mathematical and interpretational barriers to implementing the idea. De Finetti revived it only, it seemed, to reject it in favour of a purely decision-theoretic approach. In this paper I argue that not only is it possible to view (Bayesian) probability as a continuum-valued logic, but that it has a very close formal kinship with classical propositional logic.
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  2. Colin Howson (2013). Finite Additivity, Another Lottery Paradox and Conditionalisation. Synthese:1-24.
    In this paper I argue that de Finetti provided compelling reasons for rejecting countable additivity. It is ironical therefore that the main argument advanced by Bayesians against following his recommendation is based on the consistency criterion, coherence, he himself developed. I will show that this argument is mistaken. Nevertheless, there remain some counter-intuitive consequences of rejecting countable additivity, and one in particular has all the appearances of a full-blown paradox. I will end by arguing that in fact it is no (...)
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  3. Colin Howson (2013). Hume's Theorem. Studies in History and Philosophy of Science Part A 44 (3):339-346.
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  4. Colin Howson (2012). Modelling Uncertain Inference. Synthese 186 (2):475-492.
    Kyburg’s opposition to the subjective Bayesian theory, and in particular to its advocates’ indiscriminate and often questionable use of Dutch Book arguments, is documented and much of it strongly endorsed. However, it is argued that an alternative version, proposed by both de Finetti at various times during his long career, and by Ramsey, is less vulnerable to Kyburg’s misgivings. This is a logical interpretation of the formalism, one which, it is argued, is both more natural and also avoids other, widely-made (...)
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  5. Colin Howson (2011). No Answer to Hume. International Studies in the Philosophy of Science 25 (3):279 - 284.
    In a recent article in this journal, Daniel Steel charges me with committing a fallacy in my discussion of inductive rules. I show that the charge is false, and that Steel's own attempt to validate enumerative induction in terms of formal learning theory is itself fallacious. I go on to argue that, contra Steel, formal learning theory is in principle incapable of answering Hume's famous claim that any attempt to justify induction will beg the question.
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  6. Colin Howson (2011). Objecting to God. Cambridge University Press.
    Machine generated contents note: Preface; 1. The trouble with God; 2. God unlimited; 3. How to reason if you must; 4. The well-tempered universe; 5. What does it all mean?; 6. Moral equilibrium; 7. What is life without thee?; 8. It necessarily ain't so.
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  7. Colin Howson, Truth and the Liar.
    Frege famously claimed that logic is the science of truth: “To discover truths is the task of all science; it falls to logic to discern the laws of truth” (Frege, 1956, p. 289). But just like the other foundational concept of set, truth at that time was intimately associated with paradox; in the case of truth, the Liar paradox. The set-theoretical paradoxes had their teeth drawn by being recognised as reductio proofs of assumptions that had seemed too obvious to warrant (...)
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  8. Colin Howson & Peter Urbach (2010). Bayesian Versus Non-Bayesian Approaches to Confirmation. In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge.
  9. Colin Howson (2009). Epistemic Probability and Coherent Degrees of Belief. In. In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of Belief. Springer. 97--119.
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  10. Colin Howson (2009). Sorites is No Threat to Modus Ponens: A Reply to Kochan. International Studies in the Philosophy of Science 23 (2):209-212.
    A recent article by Jeff Kochan contains a discussion of modus ponens that among other thing alleges that the paradox of the heap is a counterexample to it. In this note I show that it is the conditional major premise of a modus ponens inference, rather than the rule itself, that is impugned. This premise is the contrapositive of the inductive step in the principle of mathematical induction, confirming the widely accepted view that it is the vagueness of natural language (...)
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  11. Colin Howson (2008). De Finetti, Countable Additivity, Consistency and Coherence. British Journal for the Philosophy of Science 59 (1):1-23.
    Many people believe that there is a Dutch Book argument establishing that the principle of countable additivity is a condition of coherence. De Finetti himself did not, but for reasons that are at first sight perplexing. I show that he rejected countable additivity, and hence the Dutch Book argument for it, because countable additivity conflicted with intuitive principles about the scope of authentic consistency constraints. These he often claimed were logical in nature, but he never attempted to relate this idea (...)
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  12. Colin Howson (2007). An Interview with Colin Howson. The Reasoner 1 (6):1-3.
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  13. Colin Howson (2007). Logic with Numbers. Synthese 156 (3):491-512.
    Many people regard utility theory as the only rigorous foundation for subjective probability, and even de Finetti thought the betting approach supplemented by Dutch Book arguments only good as an approximation to a utility-theoretic account. I think that there are good reasons to doubt this judgment, and I propose an alternative, in which the probability axioms are consistency constraints on distributions of fair betting quotients. The idea itself is hardly new: it is in de Finetti and also Ramsey. What is (...)
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  14. Colin Howson (2007). Reply to Hudson:" Howson on Novel Confirmation". Logic and Philosophy of Science 5 (1):33-41.
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  15. Colin Howson, Bayesian Evidence.
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  16. Colin Howson (2003). Review of David Howie, Interpreting Probability: Controversies and Developments in the Early Twentieth Century. [REVIEW] Notre Dame Philosophical Reviews 2003 (2).
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  17. Colin Howson (2001). The Logical Basis of Uncertainty. In David Corfield & Jon Williamson (eds.), Foundations of Bayesianism. Kluwer Academic Publishers. 137--159.
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  18. Colin Howson (2000). Hume's Problem: Induction and the Justification of Belief. Oxford University Press.
    In the mid-eighteenth century David Hume argued that successful prediction tells us nothing about the truth of the predicting theory. But physical theory routinely predicts the values of observable magnitudes within very small ranges of error. The chance of this sort of predictive success without a true theory suggests that Hume's argument is flawed. However, Colin Howson argues that there is no flaw and examines the implications of this disturbing conclusion; he also offers a solution to one of the central (...)
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  19. Colin Howson (2000). Induction and the Justification of Belief. Oxford University Press, Inc..
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  20. Allan Franklin & Colin Howson (1998). Comment on "the Structure of a Scientific Paper" by Frederick Suppe. Philosophy of Science 65 (3):411-416.
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  21. Colin Howson (1998). A Logical Journey. From Gödel to Philosophy by Hao Wang. MIT Press, Cambridge, Mass., 1996, Pp. XI+391. Philosophy 73 (3):495-523.
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  22. Frederick Suppe, Allan Franklin & Colin Howson (1998). Comment on The Structure of a Scientific Paper. Philosophy of Science 65 (3):411-416.
     
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  23. Colin Howson (1997). A Logic of Induction. Philosophy of Science 64 (2):268-290.
    In this paper, I present a simple and straightforward logic of induction: a consequence relation characterized by a proof theory and a semantics. This system will be called LI. The premises will be restricted to, on the one hand, a set of empirical data and, on the other hand, a set of background generalizations. Among the consequences will be generalizations as well as singular statements, some of which may serve as predictions and explanations.
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  24. Colin Howson (1997). Error Probabilities in Error. Philosophy of Science 64 (4):194.
    The Bayesian theory is outlined and its status as a logic defended. In this it is contrasted with the development and extension of Neyman-Pearson methodology by Mayo in her recently published book (1996). It is shown by means of a simple counterexample that the rule of inference advocated by Mayo is actually unsound. An explanation of why error-probablities lead us to believe that they supply a sound rule is offered, followed by a discussion of two apparently powerful objections to the (...)
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  25. Colin Howson (1997). Logic and Probability. British Journal for the Philosophy of Science 48 (4):517-531.
    This paper argues that Ramsey's view of the calculus of subjective probabilities as, in effect, logical axioms is the correct view, with powerful heuristic value. This heuristic value is seen particularly in the analysis of the role of conditionalization in the Bayesian theory, where a semantic criterion of synchronic coherence is employed as the test of soundness, which the traditional formulation of conditionalization fails. On the other hand, there is a generally sound rule which supports conditionalization in appropriate contexts, though (...)
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  26. Colin Howson (1997). Logic with Trees: An Introduction to Symbolic Logic. Routledge.
    Logic With Trees is a new and original introduction to modern formal logic. It contains discussions on philosophical issues such as truth, conditionals and modal logic, presenting the formal material with clarity, and preferring informal explanations and arguments to intimidatingly rigorous development. Worked examples and exercises guide beginners through the book, with answers to selected exercises enabling readers to check their progress. Logic With Trees equips students with: a complete and clear account of the truth-tree system for first order logic; (...)
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  27. Colin Howson (1997). On Chihara's 'the Howson-Urbach Proofs of Bayesian Principles'. British Journal for the Philosophy of Science 48 (1):83-90.
    This paper discusses and rejects some objections raised by Chihara to the book Scientific Reasoning: the Bayesian Approach, by Howson and Urbach. Some of Chihara's objections are of independent interest because they reflect widespread misconceptions. One in particular, that the Bayesian theory presupposes logical omniscience, is widely regarded as being fatal to the entire Bayesian enterprise, It is argued here that this is no more true than the parallel charge that the theory of deductive logic is fatally (...)
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  28. 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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  29. Colin Howson (1996). Bayesian Updating. Aristotelian Society Supplementary Volume 70:63-77.
     
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  30. Colin Howson & Paul Castell (1996). Epistemic Probability. Aristotelian Society Supplementary Volume 70:63 - 94.
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  31. Colin Howson (1995). Theories of Probability. British Journal for the Philosophy of Science 46 (1):1-32.
    My title is intended to recall Terence Fine's excellent survey, Theories of Probability [1973]. I shall consider some developments that have occurred in the intervening years, and try to place some of the theories he discussed in what is now a slightly longer perspective. Completeness is not something one can reasonably hope to achieve in a journal article, and any selection is bound to reflect a view of what is salient. In a subject as prone to dispute as this, there (...)
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  32. Colin Howson (1994). Betting on Theories, Patrick Maher. Cambridge: Cambridge University Press, 1993, Xii + 309 Pages. [REVIEW] Economics and Philosophy 10 (02):343-.
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  33. Colin Howson & Allan Franklin (1994). Bayesian Conditionalization and Probability Kinematics. British Journal for the Philosophy of Science 45 (2):451-466.
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  34. Colin Howson (1993). Personalistic Bayesianism. In. In J. Dubucs (ed.), Philosophy of Probability. Kluwer, Dordrecht. 1--12.
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  35. Colin Howson & Peter Urbach (1993). Scientific Reasoning: The Bayesian Approach. Open Court.
    Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...
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  36. Peter Urbach & Colin Howson (1993). Scientific Reasoning: The Bayesian Approach. Open Court.
  37. Colin Howson (1992). Dutch Book Arguments and Consistency. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:161 - 168.
    I consider Dutch Book arguments for three principles of classical Bayesianism: (i) agents' belief-probabilities are consistent only if they obey the probability axioms. (ii) beliefs are updated by Bayesian conditionalisation. (iii) that the so-called Principal Principle connects statistical and belief probabilities. I argue that while there is a sound Dutch Book argument for (i), the standard ones for (ii) based on the Lewis-Teller strategy are unsound, for reasons pointed out by Christensen. I consider a type of Dutch Book argument for (...)
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  38. Colin Howson (1992). Mathematics in Philosophy. In Javier Echeverria, Andoni Ibarra & Thomas Mormann (eds.), The Space of Mathematics. De Gruyter. 192.
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  39. Colin Howson (1991). The Last Word on Induction? Erkenntnis 34 (1):73 - 82.
    Recent arguments of Watkins, one purporting to show the impossibility of probabilistic induction, and the other to be a solution of the practical problem of induction, are examined and two are shown to generate inconsistencies in his system. The paper ends with some reflections on the Bayesian theory of inductive inference.
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  40. Colin Howson (1991). The 'Old Evidence' Problem. British Journal for the Philosophy of Science 42 (4):547-555.
    This paper offers an answer to Glymour's ‘old evidence’ problem for Bayesian confirmation theory, and assesses some of the objections, in particular those recently aired by Chihara, that have been brought against that answer. The paper argues that these objections are easily dissolved, and goes on to show how the answer it proposes yields an intuitively satisfactory analysis of a problem recently discussed by Maher. Garber's, Niiniluoto's and others’ quite different answer to Glymour's problem is considered and rejected, and the (...)
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  41. Colin Howson & Allan Franklin (1991). Maher, Mendeleev and Bayesianism. Philosophy of Science 58 (4):574-585.
    Maher (1988, 1990) has recently argued that the way a hypothesis is generated can affect its confirmation by the available evidence, and that Bayesian confirmation theory can explain this. In particular, he argues that evidence known at the time a theory was proposed does not confirm the theory as much as it would had that evidence been discovered after the theory was proposed. We examine Maher's arguments for this "predictivist" position and conclude that they do not, in fact, support his (...)
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  42. Ned Block, Richard Boyd, Robert Butts, Ronald Giere, Clark Glymour, Adolf Grunbaum, Erwin Hiebert, Colin Howson, David Hull & Paul Humphreys (1990). Consensus Institute Staff. In C. Wade Savage (ed.), Scientific Theories. University of Minnesota Press. 417.
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  43. Colin Howson (1990). Fitting Your Theory to the Facts: Probably Not Such a Bad Thing After All. Minnesota Studies in the Philosophy of Science 14:224-44.
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  44. Colin Howson (1990). Some Further Reflections on the Popper-Miller 'Disproof' of Probabilistic Induction. Australasian Journal of Philosophy 68 (2):221 – 228.
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  45. Colin Howson (1990). The Poverty of Historicism. Studies in History and Philosophy of Science Part A 21 (1):173-179.
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  46. Colin Howson (1989). On a Recent Objection to Popper and Miller's "Disproof" of Probabilistic Induction. Philosophy of Science 56 (4):675-680.
    Dunn and Hellman's objection to Popper and Miller's alleged disproof of inductive probability is considered and rejected. Dunn and Hellman base their objection on a decomposition of the incremental support P(h/e)-P(h) of h by e dual to that of Popper and Miller, and argue, dually to Popper and Miller, to a conclusion contrary to the latters' that all support is deductive in character. I contend that Dunn and Hellman's dualizing argument fails because the elements of their decomposition are not supports (...)
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  47. Colin Howson (1989). Subjective Probabilities and Betting Quotients. Synthese 81 (1):1 - 8.
    This paper addresses the problem of why the conditions under which standard proofs of the Dutch Book argument proceed should ever be met. In particular, the condition that there should be odds at which you would be willing to bet indifferently for or against are hardly plausible in practice, and relaxing it and applying Dutch book considerations gives only the theory of upper and lower probabilities. It is argued that there are nevertheless admittedly rather idealised circumstances in which the classic (...)
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  48. Allan Franklin & Colin Howson (1988). It Probably is a Valid Experimental Result: A Bayesian Approach to the Epistemology of Experiment. Studies in History and Philosophy of Science Part A 19 (4):419-427.
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  49. Colin Howson (1988). Accommodation, Prediction and Bayesian Confirmation Theory. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:381 - 392.
    This paper examines the famous doctrine that independent prediction garners more support than accommodation. The standard arguments for the doctrine are found to be invalid, and a more realistic position is put forward, that whether evidence supports or not a hypothesis depends on the prior probability of the hypothesis, and is independent of whether it was proposed before or after the evidence. This position is implicit in the subjective Bayesian theory of confirmation, and the paper ends with a brief account (...)
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  50. Colin Howson (1988). On a Recent Argument for the Impossibility of a Statistical Explanation of Single Events, and a Defence of a Modified Form of Hempel's Theory of Statistical Explanation. Erkenntnis 29 (1):113 - 124.
    An argument has been recently proposed by Watkins, whose objective is to show the impossibility of a statistical explanation of single events. This present paper is an attempt to show that Watkins's argument is unsuccessful, and goes on to argue for an account of statistical explanation which has much in common with Hempel's classic treatment.
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