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  1. Horacio Arló-Costa & Richmond H. Thomason (2001). Iterative Probability Kinematics. 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. John C. Bigelow (1977). Semantics of Probability. Synthese 36 (4):459--72.
  3. John C. Bigelow (1976). Possible Worlds Foundations for Probability. Journal of Philosophical Logic 5 (3):299--320.
  4. Georg J. W. Dorn (2002). Induktion und Wahrscheinlichkeit. Ein Gedankenaustausch mit Karl Popper. 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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  5. Georg J. W. Dorn (1992/93). Popper’s Laws of the Excess of the Probability of the Conditional Over the Conditional Probability. Conceptus 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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  6. Kenny Easwaran (2011). Varieties of Conditional Probability. 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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  7. F. Y. Edgeworth (1922). The Philosophy of Chance. Mind 31 (123):257-283.
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  8. F. Y. Edgeworth (1884). The Philosophy of Chance. Mind 9 (34):223-235.
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  9. J. Franklin (2001). Resurrecting Logical Probability. 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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  10. Joseph S. Fulda (1988). Estimating Semantic Content: An A Priori Approach. 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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  11. Joseph S. Fulda & Kevin De Fontes (1989). The A Priori Meaningfulness Measure and Resolution Theorem Proving. 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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  12. Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler & Jon Williamson (2011). Probabilistic Logics and Probabilistic Networks. Synthese Library.
    Additionally, the text shows how to develop computationally feasible methods to mesh with this framework.
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  13. James Hawthorne (2005). Degree-of-Belief and Degree-of-Support: Why Bayesians Need Both Notions. 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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  14. C. Howson (1973). Must the Logical Probability of Laws Be Zero? British Journal for the Philosophy of Science 24 (2):153-163.
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  15. Richard Johns, An Epistemic Theory of Objective Chance.
    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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  16. John Maynard Keynes (1921/2004). A Treatise on Probability. 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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  17. D. Klyve (2013). In Defense of Bertrand: The Non-Restrictiveness of Reasoning by Example. 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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  18. Isaac Levi (2010). Probability Logic, Logical Probability, and Inductive Support. 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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  19. Halina Mortimer (1973). A Rule of Acceptance Based on Logical Probability. Synthese 26 (2):259 - 263.
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  20. John F. Phillips (2005). A Theory of Objective Chance. Pacific Philosophical Quarterly 86 (2):267–283.
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  21. Darrell P. Rowbottom (2013). Popper's Measure of Corroboration and P(H|B). British Journal for the Philosophy of Science 64 (4):axs029.
    This article shows that Popper’s measure of corroboration is inapplicable if, as Popper argued, the logical probability of synthetic universal statements is zero relative to any evidence that we might possess. It goes on to show that Popper’s definition of degree of testability, in terms of degree of logical content, suffers from a similar problem. 1 The Corroboration Function and P(h|b) 2 Degrees of Testability and P(h|b).
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  22. Darrell P. Rowbottom (2013). Bertrand's Paradox Revisited: Why Bertrand's 'Solutions' Are All Inapplicable. Philosophia Mathematica 21 (1):110-114.
    This paper shows that Bertrand's proposed 'solutions' to his own question, which generates his chord paradox, are inapplicable. It uses a simple analogy with cake cutting. The problem is that none of Bertrand's solutions considers all possible cuts. This is no solace for the defenders of the principle of indifference, however, because it emerges that the paradox is harder to solve than previously anticipated.
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  23. Darrell P. Rowbottom (2008). On the Proximity of the Logical and 'Objective Bayesian' Interpretations of Probability. Erkenntnis 69 (3):335-349.
    In his Bayesian Nets and Causality, Jon Williamson presents an ‘Objective Bayesian’ interpretation of probability, which he endeavours to distance from the logical interpretation yet associate with the subjective interpretation. In doing so, he suggests that the logical interpretation suffers from severe epistemological problems that do not affect his alternative. In this paper, I present a challenge to his analysis. First, I closely examine the relationship between the logical and ‘Objective Bayesian’ views, and show how, and why, they are highly (...)
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  24. Darrell P. Rowbottom & Nicholas Shackel (2010). Bangu's Random Thoughts on Bertrand's Paradox. Analysis 70 (4):689-692.
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  25. D. C. Stove (2010). Is the Theory of Logical Probability Groundless? In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge.
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  26. Hermann Vetter (1969). Logical Probability, Mathematical Statistics, and the Problem of Induction. Synthese 20 (1):56 - 71.
    In this paper I want to discuss some basic problems of inductive logic, i.e. of the attempt to solve the problem of induction by means of a calculus of logical probability. I shall try to throw some light upon these problems by contrasting inductive logic, based on logical probability, and working with undefined samples of observations, with mathematical statistics, based on statistical probability, and working with representative random samples.
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  27. John M. Vickers (1988). Chance and Structure: An Essay on the Logical Foundations of Probability. Oxford University Press.
    Discussing the relations between logic and probability, this book compares classical 17th- and 18th-century theories of probability with contemporary theories, explores recent logical theories of probability, and offers a new account of probability as a part of logic.
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