Results for 'finitely additive probability'

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  1.  9
    On linear aggregation of infinitely many finitely additive probability measures.Michael Nielsen - 2019 - Theory and Decision 86 (3-4):421-436.
    We discuss Herzberg’s :319–337, 2015) treatment of linear aggregation for profiles of infinitely many finitely additive probabilities and suggest a natural alternative to his definition of linear continuous aggregation functions. We then prove generalizations of well-known characterization results due to :410–414, 1981). We also characterize linear aggregation of probabilities in terms of a Pareto condition, de Finetti’s notion of coherence, and convexity.
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  2.  15
    Probability logic of finitely additive beliefs.Chunlai Zhou - 2010 - Journal of Logic, Language and Information 19 (3):247-282.
    Probability logics have been an active topic of investigation of beliefs in type spaces in game theoretical economics. Beliefs are expressed as subjective probability measures. Savage’s postulates in decision theory imply that subjective probability measures are not necessarily countably additive but finitely additive. In this paper, we formulate a probability logic Σ + that is strongly complete with respect to this class of type spaces with finitely additive probability measures, i.e. (...)
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  3.  17
    Finite Additivity, Complete Additivity, and the Comparative Principle.Teddy Seidenfeld, Joseph B. Kadane, Mark J. Schervish & Rafael B. Stern - forthcoming - Erkenntnis:1-24.
    In the longstanding foundational debate whether to require that probability is countably additive, in addition to being finitely additive, those who resist the added condition raise two concerns that we take up in this paper. (1) _Existence_: Settings where no countably additive probability exists though finitely additive probabilities do. (2) _Complete Additivity_: Where reasons for countable additivity don’t stop there. Those reasons entail complete additivity—the (measurable) union of probability 0 sets has (...)
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  4.  31
    A conflict between finite additivity and avoiding dutch book.Teddy Seidenfeld & Mark J. Schervish - 1983 - Philosophy of Science 50 (3):398-412.
    For Savage (1954) as for de Finetti (1974), the existence of subjective (personal) probability is a consequence of the normative theory of preference. (De Finetti achieves the reduction of belief to desire with his generalized Dutch-Book argument for Previsions.) Both Savage and de Finetti rebel against legislating countable additivity for subjective probability. They require merely that probability be finitely additive. Simultaneously, they insist that their theories of preference are weak, accommodating all but self-defeating desires. In (...)
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  5.  15
    Extension of relatively |sigma-additive probabilities on Boolean algebras of logic.Mohamed A. Amer - 1985 - Journal of Symbolic Logic 50 (3):589 - 596.
    Contrary to what is stated in Lemma 7.1 of [8], it is shown that some Boolean algebras of finitary logic admit finitely additive probabilities that are not σ-additive. Consequences of Lemma 7.1 are reconsidered. The concept of a C-σ-additive probability on B (where B and C are Boolean algebras, and $\mathscr{B} \subseteq \mathscr{C}$ ) is introduced, and a generalization of Hahn's extension theorem is proved. This and other results are employed to show that every S̄(L)-σ- (...) probability on s̄(L) can be extended (uniquely, under some conditions) to a σ-additive probability on S̄(L), where L belongs to a quite extensive family of first order languages, and S̄(L) and s̄(L) are, respectively, the Boolean algebras of sentences and quantifier free sentences of L. (shrink)
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  6.  5
    Remarks on the theory of conditional probability: Some issues of finite versus countable additivity.Teddy Seidenfeld - unknown
    This paper (based on joint work with M.J.Schervish and J.B.Kadane) discusses some differences between the received theory of regular conditional distributions, which is the countably additive theory of conditional probability, and a rival theory of conditional probability using the theory of finitely additive probability. The focus of the paper is maximally "improper" conditional probability distributions, where the received theory requires, in effect, that P{a: P(a|a) = 0} = 1. This work builds upon the (...)
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  7.  11
    Remarks on the theory of conditional probability: Some issues of finite versus countable additivity.Teddy Seidenfeld - 2001 - In Vincent F. Hendricks, Stig Andur Pedersen & Klaus Frovin Jørgensen (eds.), Probability Theory: Philosophy, Recent History and Relations to Science. Synthese Library, Kluwer.
    This paper discusses some differences between the received theory of regular conditional distributions, which is the countably additive theory of conditional probability, and a rival theory of conditional probability using the theory of finitely additive probability. The focus of the paper is maximally "improper" conditional probability distributions, where the received theory requires, in effect, that P{a: P = 0} = 1. This work builds upon the results of Blackwell and Dubins.
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  8.  25
    Axioms for Type-Free Subjective Probability.Cezary Cieśliński, Leon Horsten & Hannes Leitgeb - 2024 - Review of Symbolic Logic 17 (2):493-508.
    We formulate and explore two basic axiomatic systems of type-free subjective probability. One of them explicates a notion of finitely additive probability. The other explicates a concept of infinitely additive probability. It is argued that the first of these systems is a suitable background theory for formally investigating controversial principles about type-free subjective probability.
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  9.  9
    Countable Additivity and the Foundations of Bayesian Statistics.John V. Howard - 2006 - Theory and Decision 60 (2-3):127-135.
    At a very fundamental level an individual (or a computer) can process only a finite amount of information in a finite time. We can therefore model the possibilities facing such an observer by a tree with only finitely many arcs leaving each node. There is a natural field of events associated with this tree, and we show that any finitely additive probability measure on this field will also be countably additive. Hence when considering the foundations (...)
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  10.  98
    Obligation, Permission, and Bayesian Orgulity.Michael Nielsen & Rush T. Stewart - 2019 - Ergo: An Open Access Journal of Philosophy 6.
    This essay has two aims. The first is to correct an increasingly popular way of misunderstanding Belot's Orgulity Argument. The Orgulity Argument charges Bayesianism with defect as a normative epistemology. For concreteness, our argument focuses on Cisewski et al.'s recent rejoinder to Belot. The conditions that underwrite their version of the argument are too strong and Belot does not endorse them on our reading. A more compelling version of the Orgulity Argument than Cisewski et al. present is available, however---a point (...)
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  11.  24
    Why Countable Additivity?Kenny Easwaran - 2013 - Thought: A Journal of Philosophy 2 (1):53-61.
    It is sometimes alleged that arguments that probability functions should be countably additive show too much, and that they motivate uncountable additivity as well. I show this is false by giving two naturally motivated arguments for countable additivity that do not motivate uncountable additivity.
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  12.  11
    Convergence to the Truth Without Countable Additivity.Michael Nielsen - 2020 - Journal of Philosophical Logic 50 (2):395-414.
    Must probabilities be countably additive? On the one hand, arguably, requiring countable additivity is too restrictive. As de Finetti pointed out, there are situations in which it is reasonable to use merely finitely additive probabilities. On the other hand, countable additivity is fruitful. It can be used to prove deep mathematical theorems that do not follow from finite additivity alone. One of the most philosophically important examples of such a result is the Bayesian convergence to the truth (...)
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  13.  8
    Conditional Probability and Defeasible Inference.Rohit Parikh - 2005 - Journal of Philosophical Logic 34 (1):97 - 119.
    We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey-Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of nonmonotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).'Expectation' is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form (...)
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  14.  30
    Internal laws of probability, generalized likelihoods and Lewis' infinitesimal chances–a response to Adam Elga.Frederik Herzberg - 2007 - British Journal for the Philosophy of Science 58 (1):25-43.
    The rejection of an infinitesimal solution to the zero-fit problem by A. Elga ([2004]) does not seem to appreciate the opportunities provided by the use of internal finitely-additive probability measures. Indeed, internal laws of probability can be used to find a satisfactory infinitesimal answer to many zero-fit problems, not only to the one suggested by Elga, but also to the Markov chain (that is, discrete and memory-less) models of reality. Moreover, the generalization of likelihoods that Elga (...)
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  15.  5
    Computability of validity and satisfiability in probability logics over finite and countable models.Greg Yang - 2015 - Journal of Applied Non-Classical Logics 25 (4):324-372.
    The -logic of Terwijn is a variant of first-order logic with the same syntax in which the models are equipped with probability measures and the quantifier is interpreted as ‘there exists a set A of a measure such that for each,...’. Previously, Kuyper and Terwijn proved that the general satisfiability and validity problems for this logic are, i) for rational, respectively -complete and -hard, and ii) for, respectively decidable and -complete. The adjective ‘general’ here means ‘uniformly over all languages’. (...)
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  16.  5
    Aggregating infinitely many probability measures.Frederik Herzberg - 2015 - Theory and Decision 78 (2):319-337.
    The problem of how to rationally aggregate probability measures occurs in particular when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and when an individual whose belief system is compatible with several probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory. We investigate this problem by first recalling some negative results from preference (...)
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  17.  2
    Adaptive Finite-Time Fault-Tolerant Control for Half-Vehicle Active Suspension Systems with Output Constraints and Random Actuator Failures.Jie Lan & Tongyu Xu - 2021 - Complexity 2021:1-16.
    The problem of adaptive finite-time fault-tolerant control and output constraints for a class of uncertain nonlinear half-vehicle active suspension systems are investigated in this work. Markovian variables are used to denote in terms of different random actuators failures. In adaptive backstepping design procedure, barrier Lyapunov functions are adopted to constrain vertical motion and pitch motion to suppress the vibrations. Unknown functions and coefficients are approximated by the neural network. Assisted by the stochastic practical finite-time theory and FTC theory, the proposed (...)
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  18.  3
    Four and a Half Axioms for Finite-Dimensional Quantum Probability.Alexander Wilce - 2012 - In Yemima Ben-Menahem & Meir Hemmo (eds.), Probability in Physics. Springer. pp. 281--298.
    It is an old idea, lately out of fashion but now experiencing a revival, that quantum mechanics may best be understood, not as a physical theory with a problematic probabilistic interpretation, but as something closer to a probability calculus per se. However, from this angle, the rather special C *-algebraic apparatus of quantum probability theory stands in need of further motivation. One would like to find additional principles, having clear physical and/or probabilistic content, on the basis of which (...)
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  19. Countable Additivity, Idealization, and Conceptual Realism.Yang Liu - 2020 - Economics and Philosophy 36 (1):127-147.
    This paper addresses the issue of finite versus countable additivity in Bayesian probability and decision theory -- in particular, Savage's theory of subjective expected utility and personal probability. I show that Savage's reason for not requiring countable additivity in his theory is inconclusive. The assessment leads to an analysis of various highly idealised assumptions commonly adopted in Bayesian theory, where I argue that a healthy dose of, what I call, conceptual realism is often helpful in understanding the interpretational (...)
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  20.  13
    Non-conglomerability for countably additive measures that are not κ-additive.Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane - 2014 - Review of Symbolic Logic 10 (2):284-300.
    Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti and Dubins, subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-­additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than κ. This generalizes our result, where we established that each finite but not countably (...)
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  21. A Simpler and More Realistic Subjective Decision Theory.Haim Gaifman & Yang Liu - 2018 - Synthese 195 (10):4205--4241.
    In his classic book “the Foundations of Statistics” Savage developed a formal system of rational decision making. The system is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation that (...)
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  22.  13
    Counting finite models.Alan R. Woods - 1997 - Journal of Symbolic Logic 62 (3):925-949.
    Let φ be a monadic second order sentence about a finite structure from a class K which is closed under disjoint unions and has components. Compton has conjectured that if the number of n element structures has appropriate asymptotics, then unlabelled (labelled) asymptotic probabilities ν(φ) (μ(φ) respectively) for φ always exist. By applying generating series methods to count finite models, and a tailor made Tauberian lemma, this conjecture is proved under a mild additional condition on the asymptotics of the number (...)
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  23.  27
    Measure Semantics and Qualitative Semantics for Epistemic Modals.Wesley H. Holliday & Thomas F. Icard - 2013 - Proceedings of SALT 23:514-534.
    In this paper, we explore semantics for comparative epistemic modals that avoid the entailment problems shown to result from Kratzer’s (1991) semantics by Yalcin (2006, 2009, 2010). In contrast to the alternative semantics presented by Yalcin and Lassiter (2010, 2011), based on finitely additive probability measures, we introduce semantics based on qualitatively additive measures, as well as semantics based on purely qualitative orderings, including orderings on propositions derived from orderings on worlds in the tradition of Kratzer (...)
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  24.  4
    Completeness theorem for propositional probabilistic models whose measures have only finite ranges.Radosav Dordević, Miodrag Rašković & Zoran Ognjanović - 2004 - Archive for Mathematical Logic 43 (4):557-563.
    A propositional logic is defined which in addition to propositional language contains a list of probabilistic operators of the form P ≥s (with the intended meaning ‘‘the probability is at least s’’). The axioms and rules syntactically determine that ranges of probabilities in the corresponding models are always finite. The completeness theorem is proved. It is shown that completeness cannot be generalized to arbitrary theories.
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  25.  9
    Quantum geometry, logic and probability.Shahn Majid - 2020 - Philosophical Problems in Science 69:191-236.
    Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these ‘lattice spacing’ weights do not have to be independent of the direction of the arrow. We use this greater freedom to give a quantum geometric interpretation of discrete Markov processes with transition probabilities as arrow weights, namely taking the diffusion form ∂+f = f for the graph Laplacian Δθ, potential functions q, p built from the probabilities, and (...)
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  26.  24
    Logic, probability, and coherence.John M. Vickers - 2001 - Philosophy of Science 68 (1):95-110.
    How does deductive logic constrain probability? This question is difficult for subjectivistic approaches, according to which probability is just strength of (prudent) partial belief, for this presumes logical omniscience. This paper proposes that the way in which probability lies always between possibility and necessity can be made precise by exploiting a minor theorem of de Finetti: In any finite set of propositions the expected number of truths is the sum of the probabilities over the set. This is (...)
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  27.  3
    Automorphism invariant measures and weakly generic automorphisms.Gábor Sági - 2022 - Mathematical Logic Quarterly 68 (4):458-478.
    Let be a countable ℵ0‐homogeneous structure. The primary motivation of this work is to study different amenability properties of (subgroups of) the automorphism group of ; the secondary motivation is to study the existence of weakly generic automorphisms of. Among others, we present sufficient conditions implying the existence of automorphism invariant probability measures on certain subsets of A and of ; we also present sufficient conditions implying that the theory of is amenable. More concretely, we show that if the (...)
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  28.  12
    Strong convergence in finite model theory.Wafik Boulos Lotfallah - 2002 - Journal of Symbolic Logic 67 (3):1083-1092.
    In [9] we introduced a new framework for asymptotic probabilities, in which a $\sigma-additive$ measure is defined on the sample space of all sequences $A = $ of finite models, where the universe of An is {1, 2, .., n}. In this framework we investigated the strong 0-1 law for sentences, which states that each sentence either holds in An eventually almost surely or fails in An eventually almost surely. In this paper we define the strong convergence law for (...)
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  29.  11
    States on pseudo MV-Algebras.Anatolij Dvurečenskij - 2001 - Studia Logica 68 (3):301-327.
    Pseudo MV-algebras are a non-commutative extension of MV-algebras introduced recently by Georgescu and Iorgulescu. We introduce states (finitely additive probability measures) on pseudo MV-algebras. We show that extremal states correspond to normal maximal ideals. We give an example in that, in contrast to classical MV-algebras introduced by Chang, states can fail on pseudo MV-algebras. We prove that representable and normal-valued pseudo MV-algebras admit at least one state.
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  30. Conglomerability, disintegrability and the comparative principle.Rush T. Stewart & Michael Nielsen - 2021 - Analysis 81 (3):479-488.
    Our aim here is to present a result that connects some approaches to justifying countable additivity. This result allows us to better understand the force of a recent argument for countable additivity due to Easwaran. We have two main points. First, Easwaran’s argument in favour of countable additivity should have little persuasive force on those permissive probabilists who have already made their peace with violations of conglomerability. As our result shows, Easwaran’s main premiss – the comparative principle – is strictly (...)
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  31.  6
    Possibility and probability.Isaac Levi - 1989 - Erkenntnis 31 (2-3):365--86.
    De Finetti was a strong proponent of allowing 0 credal probabilities to be assigned to serious possibilities. I have sought to show that (pace Shimony) strict coherence can be obeyed provided that its scope of applicability is restricted to partitions into states generated by finitely many ultimate payoffs. When countable additivity is obeyed, a restricted version of ISC can be applied to partitions generated by countably many ultimate payoffs. Once this is appreciated, perhaps the compelling character of the Shimony (...)
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  32.  31
    Products of non-additive measures: a Fubini-like theorem.Christian Bauer - 2012 - Theory and Decision 73 (4):621-647.
    For non-additive set functions, the independent product, in general, is not unique and the Fubini theorem is restricted to slice-comonotonic functions. In this paper, we use the representation theorem of Gilboa and Schmeidler (Math Oper Res 20:197–212, 1995) to extend the Möbius product for non-additive set functions to non-finite spaces. We extend the uniqueness result of Ghirardato (J Econ Theory 73:261–291, 1997) for products of two belief functions and weaken the requirements on the marginals necessary to obtain the (...)
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  33.  15
    Perspectives on a Pair of Envelopes.Piers Rawling - 1997 - Theory and Decision 43 (3):253-277.
    The two envelopes problem has generated a significant number of publications (I have benefitted from reading many of them, only some of which I cite; see the epilogue for a historical note). Part of my purpose here is to provide a review of previous results (with somewhat simpler demonstrations). In addition, I hope to clear up what I see as some misconceptions concerning the problem. Within a countably additive probability framework, the problem illustrates a breakdown of dominance with (...)
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  34.  10
    Automorphism–invariant measures on ℵ0-categorical structures without the independence property.Douglas E. Ensley - 1996 - Journal of Symbolic Logic 61 (2):640 - 652.
    We address the classification of the possible finitely-additive probability measures on the Boolean algebra of definable subsets of M which are invariant under the natural action of $\operatorname{Aut}(M)$ . This pursuit requires a generalization of Shelah's forking formulas [8] to "essentially measure zero" sets and an application of Myer's "rank diagram" [5] of the Boolean algebra under consideration. The classification is completed for a large class of ℵ 0 -categorical structures without the independence property including those which (...)
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  35.  8
    Decision Making in `Random in a Broad Sense' Environments.V. I. Ivanenko & B. Munier - 2000 - Theory and Decision 49 (2):127-150.
    It is shown that the uncertainty connected with a `random in a broad sense' (not necessarily stochastic) event always has some `statistical regularity' (SR) in the form of a family of finite-additive probability distributions. The specific principle of guaranteed result in decision making is introduced. It is shown that observing this principle of guaranteed result leads to determine the one optimality criterion corresponding to a decision system with a given `statistical regularity'.
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  36.  2
    Experiment in the General Decision Problem.V. Ivanenko & V. Labkovskii - 2004 - Theory and Decision 57 (4):309-330.
    We consider an experiment that conducts observations on an uncertain parameter. Experiments observing a parameter with a stochastic uncertainty have been studied exhaustively and their characteristics have been described by many authors [see, e.g., De Groot, M. (1974), Optimal Statistical Decisions (Russian translation)]. In this article, we assume that uncertainty is generated by a mechanism which is “random in the broad sense” [a term introduced by Kolmogorov, A.N. (1986), in Probability Theory and Mathematical Statistics (in Russia), pp. 467–471]. Ivanenko, (...)
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  37. And.T. Seidenfeld - unknown
    SUMMARY. We consider how an unconditional, finite-valued, finitely additive probability P on a countable set may localize its non-conglomerability (non-disintegrability). Nonconglomerability, a characteristic of merely finitely additive probability, occurs when the unconditional probability of an event P(E) lies outside the closed interval of conditional probability..
     
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  38.  7
    The limits of probability modelling: A serendipitous tale of goldfish, transfinite numbers, and pieces of string. [REVIEW]Ranald R. Macdonald - 2000 - Mind and Society 1 (2):17-38.
    This paper is about the differences between probabilities and beliefs and why reasoning should not always conform to probability laws. Probability is defined in terms of urn models from which probability laws can be derived. This means that probabilities are expressed in rational numbers, they suppose the existence of veridical representations and, when viewed as parts of a probability model, they are determined by a restricted set of variables. Moreover, probabilities are subjective, in that they apply (...)
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  39.  15
    Strong 0-1 laws in finite model theory.Wafik Boulos Lotfallah - 2000 - Journal of Symbolic Logic 65 (4):1686-1704.
    We introduce a new framework for asymptotic probabilities of sentences, in which we have a σ-additive measure on the sample space of all sequences A = {A n } of finite models, where the universe of A n is {1,2... n}, and use this framework to strengthen 0-1 laws for logics.
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  40.  18
    Bayesian humility.Adam Elga - 2016 - Philosophy of Science 83 (3):305-323.
    Say that an agent is "epistemically humble" if she is less than certain that her opinions will converge to the truth, given an appropriate stream of evidence. Is such humility rationally permissible? According to the orgulity argument : the answer is "yes" but long-run convergence-to-the-truth theorems force Bayesians to answer "no." That argument has no force against Bayesians who reject countable additivity as a requirement of rationality. Such Bayesians are free to count even extreme humility as rationally permissible.
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  41.  15
    Comparative infinite lottery logic.Matthew W. Parker - 2020 - Studies in History and Philosophy of Science Part A 84:28-36.
    As an application of his Material Theory of Induction, Norton (2018; manuscript) argues that the correct inductive logic for a fair infinite lottery, and also for evaluating eternal inflation multiverse models, is radically different from standard probability theory. This is due to a requirement of label independence. It follows, Norton argues, that finite additivity fails, and any two sets of outcomes with the same cardinality and co-cardinality have the same chance. This makes the logic useless for evaluating multiverse models (...)
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  42.  4
    Strong 0-1 laws in finite model theory.Wafik Boulos Lotfallah - 2000 - Journal of Symbolic Logic 65 (4):1686-1704.
    We introduce a new framework for asymptotic probabilities of sentences, in which we have a σ-additive measure on the sample space of all sequencesA= {} of finite models, where the universe ofis {1,2, …, n}. and use this framework to strengthen 0-1 laws for logics.
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  43.  6
    De Finetti Coherence and Logical Consistency.James M. Dickey, Morris L. Eaton & William D. Sudderth - 2009 - Notre Dame Journal of Formal Logic 50 (2):133-139.
    The logical consistency of a collection of assertions about events can be viewed as a special case of coherent probability assessments in the sense of de Finetti.
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  44. Empirical evidence for moral Bayesianism.Haim Cohen, Ittay Nissan-Rozen & Anat Maril - 2024 - Philosophical Psychology 37 (4):801-830.
    Many philosophers in the field of meta-ethics believe that rational degrees of confidence in moral judgments should have a probabilistic structure, in the same way as do rational degrees of belief. The current paper examines this position, termed “moral Bayesianism,” from an empirical point of view. To this end, we assessed the extent to which degrees of moral judgments obey the third axiom of the probability calculus, ifP(A∩B)=0thenP(A∪B)=P(A)+P(B), known as finite additivity, as compared to degrees of beliefs on the (...)
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  45.  9
    Repelling a Prussian charge with a solution to a paradox of Dubins.Colin Howson - 2018 - Synthese 195 (1).
    Pruss uses an example of Lester Dubins to argue against the claim that appealing to hyperreal-valued probabilities saves probabilistic regularity from the objection that in continuum outcome-spaces and with standard probability functions all save countably many possibilities must be assigned probability 0. Dubins’s example seems to show that merely finitely additive standard probability functions allow reasoning to a foregone conclusion, and Pruss argues that hyperreal-valued probability functions are vulnerable to the same charge. However, Pruss’s (...)
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  46.  7
    Avoiding Dutch Books despite inconsistent credences.Alexander R. Pruss - 2020 - Synthese 198 (12):11265-11289.
    It is often loosely said that Ramsey The foundations of mathematics and other logical essays, Routledge and Kegan Paul, Abingdon, pp 156–198, 1931) and de Finetti Studies in subjective probability, Kreiger Publishing, Huntington, 1937) proved that if your credences are inconsistent, then you will be willing to accept a Dutch Book, a wager portfolio that is sure to result in a loss. Of course, their theorems are true, but the claim about acceptance of Dutch Books assumes a particular method (...)
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  47.  18
    Accuracy, probabilism and Bayesian update in infinite domains.Alexander R. Pruss - 2022 - Synthese 200 (6):1-29.
    Scoring rules measure the accuracy or epistemic utility of a credence assignment. A significant literature uses plausible conditions on scoring rules on finite sample spaces to argue for both probabilism—the doctrine that credences ought to satisfy the axioms of probabilism—and for the optimality of Bayesian update as a response to evidence. I prove a number of formal results regarding scoring rules on infinite sample spaces that impact the extension of these arguments to infinite sample spaces. A common condition in the (...)
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    Finite additivity, another lottery paradox and conditionalisation.Colin Howson - 2014 - Synthese 191 (5):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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    Maximal beable subalgebras of quantum-mechanical observables.Hans Halvorson & Rob Clifton - 1999 - International Journal of Theoretical Physics 38:2441-2484.
    The centerpiece of Jeffrey Bub's book Interpreting the Quantum World is a theorem (Bub and Clifton 1996) which correlates each member of a large class of no-collapse interpretations with some 'privileged observable'. In particular, the Bub-Clifton theorem determines the unique maximal sublattice L(R,e) of propositions such that (a) elements of L(R,e) can be simultaneously determinate in state e, (b) L(R,e) contains the spectral projections of the privileged observable R, and (c) L(R,e) is picked out by R and e alone. In (...)
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  50.  39
    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 (...)
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