Thought: A Journal of Philosophy, ISSN 2161-2234, 03/2013, Volume 2, Issue 1, pp. 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...

Dutch book | comparative probability | probability | countable additivity | finite additivity

Dutch book | comparative probability | probability | countable additivity | finite additivity

Journal Article

Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, ISSN 0031-8116, 4/2014, Volume 168, Issue 3, pp. 619 - 628

This paper proves that certain supertasks constitute counterexamples to countable additivity even in the frame of an objective (not subjective, à la de...

Integers | Ambivalence | Conditional probabilities | Infinity | Reasoning | Sigma additivity | Lotteries | Paradoxes | Probabilities | Ethics | Philosophy of Language | Countable additivity | Epistemology | Probability | Philosophy of Mind | Metaphysics | Supertasks | Philosophy | LOTTERY | PHILOSOPHY

Integers | Ambivalence | Conditional probabilities | Infinity | Reasoning | Sigma additivity | Lotteries | Paradoxes | Probabilities | Ethics | Philosophy of Language | Countable additivity | Epistemology | Probability | Philosophy of Mind | Metaphysics | Supertasks | Philosophy | LOTTERY | PHILOSOPHY

Journal Article

Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, ISSN 0031-8116, 12/2012, Volume 161, Issue 3, pp. 381 - 390

This paper defends the claim that there is a deep tension between the principle of countable additivity and the one-third solution to the Sleeping Beauty...

Beauty | Integers | Ambivalence | Memory interference | Travelers | Information relevance | Sigma additivity | Relevant alternatives | Objective beauty | Truth | Ethics | Philosophy of Language | Countable additivity | Epistemology | Sleeping Beauty problem | Indifference principles | Brian Weatherson | Metaphysics | Philosophy of Mind | Self-locating belief | Philosophy | PHILOSOPHY | Belief & doubt

Beauty | Integers | Ambivalence | Memory interference | Travelers | Information relevance | Sigma additivity | Relevant alternatives | Objective beauty | Truth | Ethics | Philosophy of Language | Countable additivity | Epistemology | Sleeping Beauty problem | Indifference principles | Brian Weatherson | Metaphysics | Philosophy of Mind | Self-locating belief | Philosophy | PHILOSOPHY | Belief & doubt

Journal Article

Economics and Philosophy, ISSN 0266-2671, 2019, Volume 36, Issue 1, pp. 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...

Bayesian decision theory | idealization | foundations of probability | countable additivity | conceptual realism | PROBABILITY | LEBESGUE | ECONOMICS | ETHICS | Idealization | Additivity | Decision theory | Decision making | Realism | Probability | Mathematical functions | Expected utility | Decision analysis | Bayesian analysis

Bayesian decision theory | idealization | foundations of probability | countable additivity | conceptual realism | PROBABILITY | LEBESGUE | ECONOMICS | ETHICS | Idealization | Additivity | Decision theory | Decision making | Realism | Probability | Mathematical functions | Expected utility | Decision analysis | Bayesian analysis

Journal Article

Philosophical Studies, ISSN 0031-8116, 11/2017, Volume 174, Issue 11, pp. 2787 - 2794

Two reverse supertasks—one new and one invented by Pérez Laraudogoitia (Philos Stud 168:619–628, 2014)—are discussed. Contra Kerkvliet (Log Anal, 2016) and...

Countable additivity axiom | Ethics | Philosophy of Language | Epistemology | Uniform probability distributions | Philosophy, general | Philosophy of Mind | Metaphysics | Philosophy | Reverse supertasks | PARADOX | ADDITIVITY | PHILOSOPHY | Lottery industry | Distribution (Probability theory) | Lotteries

Countable additivity axiom | Ethics | Philosophy of Language | Epistemology | Uniform probability distributions | Philosophy, general | Philosophy of Mind | Metaphysics | Philosophy | Reverse supertasks | PARADOX | ADDITIVITY | PHILOSOPHY | Lottery industry | Distribution (Probability theory) | Lotteries

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 6/2015, Volume 28, Issue 2, pp. 520 - 538

De Finetti’s betting argument is used to justify finitely additive probabilities when only finitely many bets are considered. Under what circumstances can...

Finite additivity | Countable additivity | 60A05 | Coherence | Betting systems | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | STATISTICS & PROBABILITY | Mathematics - Probability

Finite additivity | Countable additivity | 60A05 | Coherence | Betting systems | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | STATISTICS & PROBABILITY | Mathematics - Probability

Journal Article

Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, ISSN 0031-8116, 3/2013, Volume 163, Issue 2, pp. 503 - 512

In two excellent recent papers, Jacob Ross has argued that the standard arguments for the 'thirder' answer to the Sleeping Beauty puzzle lead to violations of...

Sigma additivity | Equivocation | Metaphysics | Inadmissible evidence | Fregean content | Eschatology | Ethics | Philosophy of Language | Countable additivity | Epistemology | Philosophy of Mind | Sleeping beauty | Ross | Philosophy | PHILOSOPHY | Personal appearance | Probability | Generalization

Sigma additivity | Equivocation | Metaphysics | Inadmissible evidence | Fregean content | Eschatology | Ethics | Philosophy of Language | Countable additivity | Epistemology | Philosophy of Mind | Sleeping beauty | Ross | Philosophy | PHILOSOPHY | Personal appearance | Probability | Generalization

Journal Article

European Journal for Philosophy of Science, ISSN 1879-4912, 1/2018, Volume 8, Issue 1, pp. 71 - 95

An infinite lottery machine is used as a foil for testing the reach of inductive inference, since inferences concerning it require novel extensions of...

Probability | Philosophy of Science | Infinite lottery | Supertasks | Philosophy | COUNTABLE ADDITIVITY | DOME | HEADS | SEQUENCE | HISTORY & PHILOSOPHY OF SCIENCE | DETERMINISM | Foils | Probabilistic inference | Physics

Probability | Philosophy of Science | Infinite lottery | Supertasks | Philosophy | COUNTABLE ADDITIVITY | DOME | HEADS | SEQUENCE | HISTORY & PHILOSOPHY OF SCIENCE | DETERMINISM | Foils | Probabilistic inference | Physics

Journal Article

Thought: A Journal of Philosophy, ISSN 2161-2234, 12/2016, Volume 5, Issue 4, pp. 285 - 290

Vann McGee has argued that, given certain background assumptions and an ought‐implies‐can thesis about norms of rationality, Bayesianism conflicts globally...

Bayesianism | computationalism | Specker sequence | countable additivity | recursion theory | PHILOSOPHY

Bayesianism | computationalism | Specker sequence | countable additivity | recursion theory | PHILOSOPHY

Journal Article

Journal of Statistical Theory and Practice, ISSN 1559-8608, 10/2017, Volume 11, Issue 4, pp. 634 - 669

We do a thorough mathematical study of the notion of full conglomerability, that is, conglomerability with respect to all the partitions of an infinite...

continuity | imprecise probability | marginal extension | Full conglomerability | lower previsions | countable additivity | 60A05 | 28A12 | Statistical Theory and Methods | Probability Theory and Stochastic Processes | 60A10 | Statistics, general | Statistics

continuity | imprecise probability | marginal extension | Full conglomerability | lower previsions | countable additivity | 60A05 | 28A12 | Statistical Theory and Methods | Probability Theory and Stochastic Processes | 60A10 | Statistics, general | Statistics

Journal Article

Synthese, ISSN 0039-7857, 3/2018, Volume 195, Issue 3, pp. 1181 - 1210

A probability function is non-conglomerable just in case there is some proposition E and partition $$\pi $$ π of the space of possible outcomes such that the...

Philosophy of Science | Epistemology | Probability | Metaphysics | Paradoxes | Qualitative probability | Philosophy of Language | Fair infinite lotteries | Non-conglomerability | Logic | Comparative confidence | Philosophy | Monotone continuity | COUNTABLE ADDITIVITY | LOTTERIES | ALGEBRA | AXIOMS | PROBABILITY-MEASURES | HISTORY & PHILOSOPHY OF SCIENCE | INFINITESIMALS | PHILOSOPHY | FINETTI | Qualitative research | Theorems | Rationality | Confidence

Philosophy of Science | Epistemology | Probability | Metaphysics | Paradoxes | Qualitative probability | Philosophy of Language | Fair infinite lotteries | Non-conglomerability | Logic | Comparative confidence | Philosophy | Monotone continuity | COUNTABLE ADDITIVITY | LOTTERIES | ALGEBRA | AXIOMS | PROBABILITY-MEASURES | HISTORY & PHILOSOPHY OF SCIENCE | INFINITESIMALS | PHILOSOPHY | FINETTI | Qualitative research | Theorems | Rationality | Confidence

Journal Article

Synthese, ISSN 0039-7857, 1/2013, Volume 190, Issue 1, pp. 37 - 61

This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard...

Equivalence relation | Probability distributions | Axioms | Natural numbers | Nonstandard analysis | Lotteries | Free ultrafilters | Mathematical functions | Intuition | Density | Non-standard analysis | Countable additivity | Foundations of probability | Infinity | Philosophy of Science | Philosophy of Language | Epistemology | Metaphysics | Logic | Philosophy | HISTORY & PHILOSOPHY OF SCIENCE | PHILOSOPHY | Probability

Equivalence relation | Probability distributions | Axioms | Natural numbers | Nonstandard analysis | Lotteries | Free ultrafilters | Mathematical functions | Intuition | Density | Non-standard analysis | Countable additivity | Foundations of probability | Infinity | Philosophy of Science | Philosophy of Language | Epistemology | Metaphysics | Logic | Philosophy | HISTORY & PHILOSOPHY OF SCIENCE | PHILOSOPHY | Probability

Journal Article

Journal of Mathematical Economics, ISSN 0304-4068, 2010, Volume 46, Issue 5, pp. 867 - 876

This paper refines Savage’s theory of subjective probability for the case of countably additive beliefs. First, I replace his continuity axioms P6 and P7 with...

Exponential time discounting | Countable additivity | Monotone Continuity | Subjective probability | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | INTUITIVE PROBABILITY | Subjective probability Monotone Continuity Countable additivity Exponential time discounting

Exponential time discounting | Countable additivity | Monotone Continuity | Subjective probability | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | INTUITIVE PROBABILITY | Subjective probability Monotone Continuity Countable additivity Exponential time discounting

Journal Article

Journal of Philosophical Logic, ISSN 0022-3611, 12/2015, Volume 44, Issue 6, pp. 625 - 640

The foundations of probability are viewed through the lens of the subjectivist interpretation. This article surveys conditional probability, arguments for...

Bayesianism | Logical probability | Foundations of probability | Logic | Evidential probability | Conditionalisation | Philosophy | Chance | COUNTABLE ADDITIVITY | CONDITIONALIZATION | ACCURACY | CONSISTENCY | PHILOSOPHY | REPRESENTATION THEOREMS | LEXICOGRAPHIC PROBABILITIES | ARGUMENT | SLEEPING-BEAUTY | DUTCH BOOKS | language | semantics | probability | conditional sentence | Probability | Evidentiality | Bayesian analysis

Bayesianism | Logical probability | Foundations of probability | Logic | Evidential probability | Conditionalisation | Philosophy | Chance | COUNTABLE ADDITIVITY | CONDITIONALIZATION | ACCURACY | CONSISTENCY | PHILOSOPHY | REPRESENTATION THEOREMS | LEXICOGRAPHIC PROBABILITIES | ARGUMENT | SLEEPING-BEAUTY | DUTCH BOOKS | language | semantics | probability | conditional sentence | Probability | Evidentiality | Bayesian analysis

Journal Article

Economic Theory, ISSN 0938-2259, 11/2005, Volume 26, Issue 4, pp. 973 - 982

In a multiple priors model à la Gilboa and Schmeidler (1989), we provide necessary and sufficient behavioral conditions ensuring the countable additivity and...

Topological compactness | Economic models | Mathematical monotonicity | Economic theory | Axioms | Finance | Sigma additivity | Expected utility | Probabilities | Ambiguity | Economics general | Countable additivity | Non-atomicity | Analysis | Economic Theory | Multiple priors | Economics / Management Science | multiple priors | UNCERTAINTY | RISK | non-atomicity | ECONOMICS | countable additivity | Studies | Probability | Economics and Finance | Humanities and Social Sciences

Topological compactness | Economic models | Mathematical monotonicity | Economic theory | Axioms | Finance | Sigma additivity | Expected utility | Probabilities | Ambiguity | Economics general | Countable additivity | Non-atomicity | Analysis | Economic Theory | Multiple priors | Economics / Management Science | multiple priors | UNCERTAINTY | RISK | non-atomicity | ECONOMICS | countable additivity | Studies | Probability | Economics and Finance | Humanities and Social Sciences

Journal Article

Economic Theory, ISSN 0938-2259, 1/2017, Volume 63, Issue 1, pp. 131 - 157

We prove that under mild conditions individually rational Pareto optima will exist even in the presence of non-convex preferences. We consider decision-makers...

Economics | Countable set of commodities | Pareto optima | Public Finance | Economic Theory/Quantitative Economics/Mathematical Methods | Impatience | Game Theory, Economics, Social and Behav. Sciences | Optimism | Non-convex preferences | Pessimism | Microeconomics | D91 | D60 | EXPECTED-UTILITY | EQUILIBRIA | ECONOMIES | RISK | ECONOMICS | ADDITIVITY | Pareto efficiency | Analysis | Commodities | Studies | Economic theory | Pareto optimum | Risk sharing | Preferences | Economics and Finance | Humanities and Social Sciences

Economics | Countable set of commodities | Pareto optima | Public Finance | Economic Theory/Quantitative Economics/Mathematical Methods | Impatience | Game Theory, Economics, Social and Behav. Sciences | Optimism | Non-convex preferences | Pessimism | Microeconomics | D91 | D60 | EXPECTED-UTILITY | EQUILIBRIA | ECONOMIES | RISK | ECONOMICS | ADDITIVITY | Pareto efficiency | Analysis | Commodities | Studies | Economic theory | Pareto optimum | Risk sharing | Preferences | Economics and Finance | Humanities and Social Sciences

Journal Article

Mathematical Social Sciences, ISSN 0165-4896, 2010, Volume 60, Issue 2, pp. 113 - 118

I extend Machina and Schmeidler’s ( 1992) model of probabilistic sophistication to unbounded uncertain prospects (acts) and derive risk preferences over the...

Probabilistic sophistication | Countable additivity | Tail continuity | Monotone continuity | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DOMINANCE | AXIOMS | MULTIPLE PRIORS | SOCIAL SCIENCES, MATHEMATICAL METHODS | Probabilistic sophistication Countable additivity Monotone continuity Tail continuity

Probabilistic sophistication | Countable additivity | Tail continuity | Monotone continuity | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DOMINANCE | AXIOMS | MULTIPLE PRIORS | SOCIAL SCIENCES, MATHEMATICAL METHODS | Probabilistic sophistication Countable additivity Monotone continuity Tail continuity

Journal Article

Economic Theory, ISSN 0938-2259, 10/2010, Volume 45, Issue 1/2, pp. 291 - 302

An example is given in which agents agree to disagree in a countable space of equiprobable states of nature. Even in this unorthodox setting, if the sets of...

Mathematical intervals | Conditional probabilities | Abstract spaces | Economic theory | Probability theory | Sigma additivity | State of nature | Game theory | Probabilities | D84 | Economics general | Theory of probability | Countable additivity | Interactive epistemology | Economic Theory | Agreeing to disagree | Game Theory, Economics, Social and Behav. Sciences | C70 | Economics / Management Science | Bounded rationality | D82 | COMMON PRIOR ASSUMPTION | PRIORS | ECONOMICS | Geometric probabilities | Measure theory | Analysis | Combinatorial probabilities | Studies | Probability

Mathematical intervals | Conditional probabilities | Abstract spaces | Economic theory | Probability theory | Sigma additivity | State of nature | Game theory | Probabilities | D84 | Economics general | Theory of probability | Countable additivity | Interactive epistemology | Economic Theory | Agreeing to disagree | Game Theory, Economics, Social and Behav. Sciences | C70 | Economics / Management Science | Bounded rationality | D82 | COMMON PRIOR ASSUMPTION | PRIORS | ECONOMICS | Geometric probabilities | Measure theory | Analysis | Combinatorial probabilities | Studies | Probability

Journal Article

Journal of Philosophical Logic, ISSN 0022-3611, 2/2005, Volume 34, Issue 1, pp. 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...

Probabilistic modeling | Probability distributions | Conditional probabilities | Reasoning | Model theory | Semantic models | Inference | Sigma additivity | Mathematical functions | Logic | non-monotonic logic | countable additivity | belief revision | conditional probability | conditionals | Philosophy | Conditionals | Countable additivity | Conditional probability | Non-monotonic logic | Belief revision | PHILOSOPHY | LOGIC | Computer science | Economic models | Art | Epistemology | Decision theory | Semantics | Logic of language | Probability | Artificial intelligence

Probabilistic modeling | Probability distributions | Conditional probabilities | Reasoning | Model theory | Semantic models | Inference | Sigma additivity | Mathematical functions | Logic | non-monotonic logic | countable additivity | belief revision | conditional probability | conditionals | Philosophy | Conditionals | Countable additivity | Conditional probability | Non-monotonic logic | Belief revision | PHILOSOPHY | LOGIC | Computer science | Economic models | Art | Epistemology | Decision theory | Semantics | Logic of language | Probability | Artificial intelligence

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 4/1992, Volume 114, Issue 4, pp. 931 - 938

We give a counterexample of the result of Beaver and Cook concerning a generalization of the Alexandroff theorem for regular, finitely-additive states on...

Integers | Mathematical theorems | Logical theorems | Boolean data | Quantum mechanics | Inner products | Mathematical lattices | Quantum logic | Sigma additivity | Hilbert spaces | Splitting subspace | Countable additivity | Inner product space | Regular state | State | MATHEMATICS | MATHEMATICS, APPLIED

Integers | Mathematical theorems | Logical theorems | Boolean data | Quantum mechanics | Inner products | Mathematical lattices | Quantum logic | Sigma additivity | Hilbert spaces | Splitting subspace | Countable additivity | Inner product space | Regular state | State | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

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