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  1. A Comprehensive Theory of Induction and Abstraction, Part II.Cael Hasse - manuscript
    This is part II in a series of papers outlining Abstraction Theory, a theory that I propose provides a solution to the characterisation or epistemological problem of induction. Logic is built from first principles severed from language such that there is one universal logic independent of specific logical languages. A theory of (non-linguistic) meaning is developed which provides the basis for the dissolution of the `grue' problem and problems of the non-uniqueness of probabilities in inductive logics. The problem of counterfactual (...)
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  2. A Comprehensive Theory of Induction and Abstraction, Part I.Cael L. Hasse - manuscript
    I present a solution to the epistemological or characterisation problem of induction. In part I, Bayesian Confirmation Theory (BCT) is discussed as a good contender for such a solution but with a fundamental explanatory gap (along with other well discussed problems); useful assigned probabilities like priors require substantive degrees of belief about the world. I assert that one does not have such substantive information about the world. Consequently, an explanation is needed for how one can be licensed to act as (...)
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  3. Sure-Wins Under Coherence: A Geometrical Perspective.Stefano Bonzio, Tommaso Flaminio & Paolo Galeazzi - 2019 - In Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science.
    In this contribution we will present a generalization of de Finetti's betting game in which a gambler is allowed to buy and sell unknown events' betting odds from more than one bookmaker. In such a framework, the sole coherence of the books the gambler can play with is not sucient, as in the original de Finetti's frame, to bar the gambler from a sure-win opportunity. The notion of joint coherence which we will introduce in this paper characterizes those coherent books (...)
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  4. Imprecise Probability and the Measurement of Keynes's "Weight of Arguments".William Peden - 2018 - IfCoLog Journal of Logics and Their Applications 5 (4):677-708.
    Many philosophers argue that Keynes’s concept of the “weight of arguments” is an important aspect of argument appraisal. The weight of an argument is the quantity of relevant evidence cited in the premises. However, this dimension of argumentation does not have a received method for formalisation. Kyburg has suggested a measure of weight that uses the degree of imprecision in his system of “Evidential Probability” to quantify weight. I develop and defend this approach to measuring weight. I illustrate the usefulness (...)
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  5. Ancient Indian Logic and Analogy.J. B. Paris & A. Vencovska - 2017 - In S. Ghosh & S. Prasad (eds.), Logic and its Applications, Lecture Notes in Computer Science 10119. Springer. pp. 198-210.
    B.K.Matilal, and earlier J.F.Staal, have suggested a reading of the `Nyaya five limb schema' (also sometimes referred to as the Indian Schema or Hindu Syllogism) from Gotama's Nyaya-Sutra in terms of a binary occurrence relation. In this paper we provide a rational justification of a version of this reading as Analogical Reasoning within the framework of Polyadic Pure Inductive Logic.
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  6. Second Order Inductive Logic and Wilmers' Principle.M. S. Kliess & J. B. Paris - 2014 - Journal of Applied Logic 12 (4):462-476.
    We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship to the first order principles of Regularity and Super Regularity.
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  7. Non-Deductive Logic in Mathematics: The Probability of Conjectures.James Franklin - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Springer. pp. 11--29.
    Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...)
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  8. An Observation on Carnapʼs Continuum and Stochastic Independencies.J. B. Paris - 2013 - Journal of Applied Logic 11 (4):421-429.
    We characterize those identities and independencies which hold for all probability functions on a unary language satisfying the Principle of Atom Exchangeability. We then show that if this is strengthen to the requirement that Johnson's Sufficientness Principle holds, thus giving Carnap's Continuum of inductive methods for languages with at least two predicates, then new and somewhat inexplicable identities and independencies emerge, the latter even in the case of Carnap's Continuum for the language with just a single predicate.
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  9. The Objective Bayesian Conceptualisation of Proof and Reference Class Problems.James Franklin - 2011 - Sydney Law Review 33 (3):545-561.
    The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning by the (...)
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  10. Wittgenstein on Prior Probabilities.Michael E. Cuffaro - 2010 - Proceedings of the Canadian Society for History and Philosophy of Mathematics 23:85-98.
    Wittgenstein did not write very much on the topic of probability. The little we have comes from a few short pages of the Tractatus, some 'remarks' from the 1930s, and the informal conversations which went on during that decade with the Vienna Circle. Nevertheless, Wittgenstein's views were highly influential in the later development of the logical theory of probability. This paper will attempt to clarify and defend Wittgenstein's conception of probability against some oft-cited criticisms that stem from a misunderstanding of (...)
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  11. John Maynard Keynes and Ludwig von Mises on Probability.Ludwig van den Hauwe - 2010 - Journal of Libertarian Studies 22 (1):471-507.
    The economic paradigms of Ludwig von Mises on the one hand and of John Maynard Keynes on the other have been correctly recognized as antithetical at the theoretical level, and as antagonistic with respect to their practical and public policy implications. Characteristically they have also been vindicated by opposing sides of the political spectrum. Nevertheless the respective views of these authors with respect to the meaning and interpretation of probability exhibit a closer conceptual affinity than has been acknowledged in the (...)
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  12. Induktion und Wahrscheinlichkeit. Ein Gedankenaustausch mit Karl Popper.Georg J. W. Dorn - 2002 - In Edgar Morscher (ed.), Was wir Karl R. Popper und seiner Philosophie verdanken. Zu seinem 100. Geburtstag. Academia Verlag.
    Zwischen 1987 und 1994 sandte ich 20 Briefe an Karl Popper. Die meisten betrafen Fragen bezüglich seiner Antiinduktionsbeweise und seiner Wahrscheinlichkeitstheorie, einige die organisatorische und inhaltliche Vorbereitung eines Fachgesprächs mit ihm in Kenly am 22. März 1989 (worauf hier nicht eingegangen werden soll), einige schließlich ganz oder in Teilen nicht-fachliche Angelegenheiten (die im vorliegenden Bericht ebenfalls unberücksichtigt bleiben). Von Karl Popper erhielt ich in diesem Zeitraum 10 Briefe. Der bedeutendste ist sein siebter, bestehend aus drei Teilen, geschrieben am 21., 22. (...)
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  13. Popper’s Laws of the Excess of the Probability of the Conditional Over the Conditional Probability.Georg J. W. Dorn - 1992/93 - Conceptus: Zeitschrift Fur Philosophie 26:3–61.
    Karl Popper discovered in 1938 that the unconditional probability of a conditional of the form ‘If A, then B’ normally exceeds the conditional probability of B given A, provided that ‘If A, then B’ is taken to mean the same as ‘Not (A and not B)’. So it was clear (but presumably only to him at that time) that the conditional probability of B given A cannot be reduced to the unconditional probability of the material conditional ‘If A, then B’. (...)
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