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A Treatise on Probability
TLDR
In this article, the authors present a constructive theory of probability in the theory of groups, with special reference to logical consistence, inference, and logical priority, and the fundamental theorems of probable inference and probability.Abstract:
Part 1 Fundamental ideas: the meaning of probability - probability in relation to the theory of knowledge - the measurement of probabilities - the principle of indifference - other methods of determining probabilities - the weight of arguments - historical retrospect - the frequency theory of probability - the constructive theory of part 1 summarized. Part 2 Fundamental theorems: introductory - the theory of groups, with special reference to logical consistence, inference, and logical priority - the definitions and axioms of inference and probability - the fundamental theorems of probable inference - numerical measurement and approximation of probabilities - observations on the theorems of chapter 14 and their developments, including testimony - some problems in inverse probability, including averages. Part 3 Induction and analogy: introduction - the nature of argument by analogy - the value of multiplication of instances, or pure induction - the nature of inductive argument continued - the justification of these methods - some historical notes on induction - notes on part 3. Part 4 Some philosophical applications of probability: the meanings of objective chance, and of randomness - some problems arising out of the discussion of change - the application of probability to conduct. Part 5 The foundations of statistical inference: the nature of statistical inference - the law of great numbers - the use of a priori probabilities for the prediction of statistical frequency - the mathematical use of statistical frequencies for the determination of probability a posteriori - the inversion of Bernoulli's theorem - the inductive use of statistical frequencies for the determination of probability a posteriori - outline of a constructive theory.read more
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Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
TL;DR: Probabilistic Reasoning in Intelligent Systems as mentioned in this paper is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty, and provides a coherent explication of probability as a language for reasoning with partial belief.
Book ChapterDOI
Falsification and the Methodology of Scientific Research Programmes
TL;DR: For centuries knowledge meant proven knowledge, proven either by the power of the intellect or by the evidence of the senses as discussed by the authors. But the notion of proven knowledge was questioned by the sceptics more than two thousand years ago; but they were browbeaten into confusion by the glory of Newtonian physics.
Book
Heuristics and Biases: The Psychology of Intuitive Judgment
TL;DR: In this article, a review is presented of the book "Heuristics and Biases: The Psychology of Intuitive Judgment, edited by Thomas Gilovich, Dale Griffin, and Daniel Kahneman".
Journal ArticleDOI
On the Mathematical Foundations of Theoretical Statistics
TL;DR: In this paper, the authors define the center of location as the abscissa of a frequency curve for which the sampling errors of optimum location are uncorrelated with those of optimum scaling.
Journal ArticleDOI
Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment.
Amos Tversky,Daniel Kahneman +1 more
TL;DR: The conjunction rule as mentioned in this paper states that the probability of a conjunction cannot exceed the probabilities of its constituents, P (A) and P (B), because the extension (or the possibility set) of the conjunction is included in the extension of their constituents.
References
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An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities
TL;DR: In this paper, the authors use the symbolic language of mathematics to establish a method to examine the nature of the human mind using logic and the theory of probabilities, and they consider language not just as a mode of expression, but as a system one can use to understand human mind.
Journal ArticleDOI
Zur theorie der stabilität statistischer Reihen
TL;DR: In this paper, auffallende Gesetzmassigkeit der auf Massenbeobachtungen beruhenden statistischen Zahlen zu erklaren is discussed.
Cournot et la renaissance du probabilisme au XIXe siècle
TL;DR: In this article, Cournot et al. situate the philosophy of Cournot dans l'histoire de l'esprit humain, degager ses antecedents and ses prolongements, and exposer ses idees fondamentales, celles who servent de cles a l'œuvre.