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  1. Iterative Probability Kinematics.Horacio Arló-Costa & Richmond Thomason - 2001 - Journal of Philosophical Logic 30 (5):479-524.
    Following the pioneer work of Bruno De Finetti [12], conditional probability spaces (allowing for conditioning with events of measure zero) have been studied since (at least) the 1950's. Perhaps the most salient axiomatizations are Karl Popper's in [31], and Alfred Renyi's in [33]. Nonstandard probability spaces [34] are a well know alternative to this approach. Vann McGee proposed in [30] a result relating both approaches by showing that the standard values of infinitesimal probability functions are representable as Popper functions, and (...)
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  2. Semantics of Probability.John C. Bigelow - 1977 - Synthese 36 (4):459--72.
  3. Possible Worlds Foundations for Probability.John C. Bigelow - 1976 - Journal of Philosophical Logic 5 (3):299--320.
  4. Remarks on Probability.Rudolf Carnap - 1963 - Philosophical Studies 14 (5):65 - 75.
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  5. The Two Concepts of Probability: The Problem of Probability.Rudolf Carnap - 1945 - Philosophy and Phenomenological Research 5 (4):513-532.
  6. The Two Concepts of Probability.Rudolph Carnap - 1944 - Philosophy and Phenomenological Research 5:513.
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  7. 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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  8. 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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  9. 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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  10. Varieties of Conditional Probability.Kenny Easwaran - 2011 - In Prasanta Bandyopadhyay & Malcolm Forster (eds.), Handbook for Philosophy of Statistics. North Holland.
    I consider the notions of logical probability, degree of belief, and objective chance, and argue that a different formalism for conditional probability is appropriate for each.
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  11. The Philosophy of Chance.F. Y. Edgeworth - 1922 - Mind 31 (123):257-283.
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  12. The Philosophy of Chance.F. Y. Edgeworth - 1884 - Mind 9 (34):223-235.
  13. Resurrecting Logical Probability.J. Franklin - 2001 - Erkenntnis 55 (2):277-305.
    The logical interpretation of probability, or ``objective Bayesianism''''– the theory that (some) probabilitiesare strictly logical degrees of partial implication – is defended.The main argument against it is that it requires the assignment ofprior probabilities, and that any attempt to determine them by symmetryvia a ``principle of insufficient reason'''' inevitably leads to paradox.Three replies are advanced: that priors are imprecise or of little weight, sothat disagreement about them does not matter, within limits; thatit is possible to distinguish reasonable from unreasonable priorson (...)
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  14. Estimating Semantic Content: An A Priori Approach.Joseph S. Fulda - 1988 - International Journal of Intelligent Systems 3 (1):35-43.
    Gives a general method as well as some results (inspired by Asimov, 1951; since discovered to be in Bar-Hillel and Carnap [several versions; Charles Parsons referred me to /Language and Information/]) to recover meaning (eventually automatically) from logical form/logical probability, which are mirror images. (Sets are taken as extensions of predicates, and knowledge of the sizes is needed; to that extent the method is a posteriori).
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  15. The A Priori Meaningfulness Measure and Resolution Theorem Proving.Joseph S. Fulda & Kevin De Fontes - 1989 - Journal of Experimental and Theoretical Artificial Intelligence 1 (3):227-230.
    Demonstrates the validity of the measure presented in "Estimating Semantic Content" on textbook examples using (binary) resolution [a generalization of disjunctive syllogism] theorem proving; the measure is based on logical probability and is the mirror image of logical form; it dates to Popper.
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  16. Probabilistic Logics and Probabilistic Networks.Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler & Jon Williamson - 2011 - Synthese Library.
    Additionally, the text shows how to develop computationally feasible methods to mesh with this framework.
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  17. 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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  18. Degree-of-Belief and Degree-of-Support: Why Bayesians Need Both Notions.James Hawthorne - 2005 - Mind 114 (454):277-320.
    I argue that Bayesians need two distinct notions of probability. We need the usual degree-of-belief notion that is central to the Bayesian account of rational decision. But Bayesians also need a separate notion of probability that represents the degree to which evidence supports hypotheses. Although degree-of-belief is well suited to the theory of rational decision, Bayesians have tried to apply it to the realm of hypothesis confirmation as well. This double duty leads to the problem of old evidence, a problem (...)
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  19. On the Logical Form of Probability-Statements.C. G. Hempel - 1937 - Erkenntnis 7 (1):154-160.
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  20. An Analogy Principle in Inductive Logic.A. Hill & J. B. Paris - 2013 - Annals of Pure and Applied Logic 164 (12):1293-1321.
    We propose an Analogy Principle in the context of Unary Inductive Logic and characterize the probability functions which satisfy it. In particular in the case of a language with just two predicates the probability functions satisfying this principle correspond to solutions of Skyrmsʼ ‘Wheel of Fortune’.
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  21. Reasoning by Analogy in Inductive Logic.Alexandra Hill & J. B. Paris - 2011 - In Michal Peliš & Vít Punčochář (eds.), The Logica Yearbook. College Publications. pp. 63--76.
  22. Carnap's Inductive Probabilities as a Contribution to Decision Theory.Joachim Hornung - 1980 - Theoretical Medicine and Bioethics 1 (3):325-367.
    Common probability theories only allow the deduction of probabilities by using previously known or presupposed probabilities. They do not, however, allow the derivation of probabilities from observed data alone. The question thus arises as to how probabilities in the empirical sciences, especially in medicine, may be arrived at. Carnap hoped to be able to answer this question byhis theory of inductive probabilities. In the first four sections of the present paper the above mentioned problem is discussed in general. After a (...)
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  23. The Theory of Spectrum Exchangeability.E. Howarth & J. B. Paris - 2015 - Review of Symbolic Logic 8 (1):108-130.
  24. Principles of Remembering and Forgetting.E. Howarth & J. B. Paris - 2014 - Logique Et Analyse 57 (228):489-511.
    We propose two principles of inductive reasoning related to how observed information is handled by conditioning, and justify why they may be said to represent aspects of rational reasoning. A partial classification is given of the probability functions which satisfy these principles.
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  25. An Examination of the SEP Candidate Analogical Inference Rule Within Pure Inductive Logic.E. Howarth, J. B. Paris & A. Vencovská - 2016 - Journal of Applied Logic 14:22-45.
  26. Must the Logical Probability of Laws Be Zero?C. Howson - 1973 - British Journal for the Philosophy of Science 24 (2):153-163.
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  27. The Development of Logical Probability.Colin Howson - 1976 - In R. S. Cohen, P. K. Feyerabend & M. Wartofsky (eds.), Essays in Memory of Imre Lakatos. Reidel. pp. 277--298.
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  28. An Epistemic Theory of Objective Chance.Richard Johns - manuscript
    A theory of objective, single-case chances is presented and defended. The theory states that the chance of an event E is its epistemic probability, given maximal knowledge of the possible causes of E. This theory is uniquely successful in entailing all the known properties of chance, but involves heavy metaphysical commitment. It requires an objective rationality that determines proper degrees of belief in some contexts.
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  29. Methodological Problems of Logical Probability.Michael Harry Kelley - 1969 - Dissertation, The University of Wisconsin - Madison
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  30. A Treatise on Probability.John Maynard Keynes - 1921 - Dover Publications.
    With this treatise, an insightful exploration of the probabilistic connection between philosophy and the history of science, the famous economist breathed new life into studies of both disciplines. Originally published in 1921, this important mathematical work represented a significant contribution to the theory regarding the logical probability of propositions. Keynes effectively dismantled the classical theory of probability, launching what has since been termed the “logical-relationist” theory. In so doing, he explored the logical relationships between classifying a proposition as “highly probable” (...)
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  31. Probability as a Measure of Necessity.N. V. Khovanov - 1969 - Soviet Studies in Philosophy 11 (2):141--51.
    One of the characteristic features of the dynamic development of science and technology in recent decades is the constantly rising significance of probabilistic, statistical and information-theory methods in research, both theoretical and applied. Nor is the mathematical theory of probability standing still. The internal logic of its development is leading steadily to enrichment of the traditional study of probability with new axioms and constructive formal calculi.
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  32. Second Order Inductive Logic and Wilmers' Principle.M. S. Kließ & J. B. Paris - 2014 - Journal of Applied Logic 12 (4):462-476.
  33. 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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  34. Predicate Exchangeability and Language Invariance in Pure Inductive Logic.M. S. Kliess & J. B. Paris - 2014 - Logique Et Analyse 57 (228):513-540.
    In Pure Inductive Logic, the rational principle of Predicate Exchangeability states that permuting the predicates in a given language L and replacing each occurrence of a predicate in an L-sentence phi according to this permutation should not change our belief in the truth of phi. In this paper we study when a prior probability function w on a purely unary language L satisfying Predicate Exchangeability also satisfies the principle of Unary Language Invariance.
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  35. In Defense of Bertrand: The Non-Restrictiveness of Reasoning by Example.D. Klyve - 2013 - Philosophia Mathematica 21 (3):365-370.
    This note has three goals. First, we discuss a presentation of Bertrand's paradox in a recent issue of Philosophia Mathematica, which we believe to be a subtle but important misinterpretation of the problem. We compare claims made about Bertrand with his 1889 Calcul des Probabilités. Second, we use this source to understand Bertrand's true intention in describing what we now call his paradox, comparing it both to another problem he describes in the same section and to a modern treatment. Finally, (...)
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  36. A Survey of Some Recent Results on Spectrum Exchangeability in Polyadic Inductive Logic.J. Landes, J. B. Paris & A. Vencovská - 2011 - Synthese 181 (S1):19 - 47.
    We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson's Sufficientness Principle, and the corresponding de Finetti style representation theorems.
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  37. Probability Logic, Logical Probability, and Inductive Support.Isaac Levi - 2010 - Synthese 172 (1):97-118.
    This paper seeks to defend the following conclusions: The program advanced by Carnap and other necessarians for probability logic has little to recommend it except for one important point. Credal probability judgments ought to be adapted to changes in evidence or states of full belief in a principled manner in conformity with the inquirer’s confirmational commitments—except when the inquirer has good reason to modify his or her confirmational commitment. Probability logic ought to spell out the constraints on rationally coherent confirmational (...)
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  38. The Principle of Maximum Entropy and a Problem in Probability Kinematics.Stefan Lukits - 2014 - Synthese 191 (7):1-23.
    Sometimes we receive evidence in a form that standard conditioning (or Jeffrey conditioning) cannot accommodate. The principle of maximum entropy (MAXENT) provides a unique solution for the posterior probability distribution based on the intuition that the information gain consistent with assumptions and evidence should be minimal. Opponents of objective methods to determine these probabilities prominently cite van Fraassen’s Judy Benjamin case to undermine the generality of maxent. This article shows that an intuitive approach to Judy Benjamin’s case supports maxent. This (...)
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  39. A Rule of Acceptance Based on Logical Probability.Halina Mortimer - 1973 - Synthese 26 (2):259 - 263.
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  40. An Empirical Approach to Symmetry and Probability.Jill North - 2010 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (1):27-40.
    We often use symmetries to infer outcomes’ probabilities, as when we infer that each side of a fair coin is equally likely to come up on a given toss. Why are these inferences successful? I argue against answering this with an a priori indifference principle. Reasons to reject that principle are familiar, yet instructive. They point to a new, empirical explanation for the success of our probabilistic predictions. This has implications for indifference reasoning in general. I argue that a priori (...)
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  41. An Observation on Carnapʼs Continuum and Stochastic Independencies.J. B. Paris - 2013 - Journal of Applied Logic 11 (4):421-429.
  42. An Observation on Carnap's 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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  43. Combining Analogical Support in Pure Inductive Logic.J. B. Paris & A. Vencovská - 2017 - Erkenntnis 82 (2):401-419.
    We investigate the relative probabilistic support afforded by the combination of two analogies based on possibly different, structural similarity within the context of Pure Inductive Logic and under the assumption of Language Invariance. We show that whilst repeated analogies grounded on the same structural similarity only strengthen the probabilistic support this need not be the case when combining analogies based on different structural similarities. That is, two analogies may provide less support than each would individually.
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  44. 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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  45. Pure Inductive Logic.J. B. Paris & A. Vencovska - 2015 - Cambridge, UK: Cambridge University Press.
    Pure Inductive Logic is the study of rational probability treated as a branch of mathematical logic. This monograph, the first devoted to this approach, brings together the key results from the past seventy years, plus the main contributions of the authors and their collaborators over the last decade, to present a comprehensive account of the discipline within a single unified context.
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  46. Symmetry in Polyadic Inductive Logic.J. B. Paris & A. Vencovská - 2012 - Journal of Logic, Language and Information 21 (2):189-216.
    A family of symmetries of polyadic inductive logic are described which in turn give rise to the purportedly rational Permutation Invariance Principle stating that a rational assignment of probabilities should respect these symmetries. An equivalent, and more practical, version of this principle is then derived.
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  47. A Note on Irrelevance in Inductive Logic.Jeff B. Paris & Alena Vencovská - 2011 - Journal of Philosophical Logic 40 (3):357 - 370.
    We consider two formalizations of the notion of irrelevance as a rationality principle within the framework of (Carnapian) Inductive Logic: Johnson's Sufficientness Principle, JSP, which is classically important because it leads to Carnap's influential Continuum of Inductive Methods and the recently proposed Weak Irrelevance Principle, WIP. We give a complete characterization of the language invariant probability functions satisfying WIP which generalizes the Nix-Paris Continuum. We argue that the derivation of two very disparate families of inductive methods from alternative perceptions of (...)
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  48. The Principal Principle Does Not Imply the Principle of Indifference.Richard Pettigrew - manuscript
    In a recent paper in the British Journal for the Philosophy of Science, James Hawthorne, Jürgen Landes, Christian Wallmann, and Jon Williamson (henceforth HLWW) argue that the Principal Principle entails the Principle of Indifference. In this paper, I argue that it does not. Lewis’ version of the Principal Principle notoriously depends on a notion of admissibility, which Lewis uses to restrict its application. HLWW do not give a precise account either, but they do appeal to two principles concerning admissibility, which (...)
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  49. A Theory of Objective Chance.John F. Phillips - 2005 - Pacific Philosophical Quarterly 86 (2):267–283.
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  50. Bangu's Random Thoughts on Bertrand's Paradox.Darrell P. Rowbottom & Nicholas Shackel - 2010 - Analysis 70 (4):689-692.
    Bangu (2010) claims that Bertrand’s paradox rests on a hitherto unrecognized assumption, which assumption is sufficiently dubious to throw the burden of proof back onto ‘objectors to [the principle of indifference]’ (2010: 31). We show that Bangu’s objection to the assumption is ill-founded and that the assumption is provably true.
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