In decision theory, economics, and probability theory, the Dutch book arguments are a set of results showing that agents must satisfy the axioms of rational...
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Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...
92 KB (12,132 words) - 22:29, 5 July 2024
These axioms, apart from continuity, are often justified using the Dutch book theorems (whereas continuity is used to set aside lexicographic or infinitesimal...
20 KB (3,294 words) - 02:14, 30 August 2024
Bayesian epistemology (section Dutch books)
method in contrast to traditional epistemology is that its concepts and theorems can be defined with a high degree of precision. It is based on the idea...
34 KB (4,364 words) - 00:12, 3 January 2024
cases of this behaviour can be considered rational. However, the Dutch book theorems show that this comes at a major cost of internal coherence, such...
58 KB (7,293 words) - 19:00, 28 August 2024
Bayesian probability (section Dutch book approach)
pose; the constraints are justified by the Dutch book argument or by decision theory and de Finetti's theorem. The objective and subjective variants of...
33 KB (3,415 words) - 23:59, 6 August 2024
ring with a Hecke algebra (now referred to as an R=T theorem) to prove modularity lifting theorems has been an influential development in algebraic number...
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increases without bound. These theorems require stronger hypotheses than the forms of the central limit theorem given above. Theorems of this type are often called...
65 KB (8,861 words) - 09:16, 20 August 2024
Bayesians will often motivate the Kolmogorov axioms by invoking Cox's theorem or the Dutch book arguments instead. The assumptions as to setting up the axioms...
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axiomatic basis, writing in a 1973 book that Bayes' theorem "is to the theory of probability what the Pythagorean theorem is to geometry". Stephen Stigler...
52 KB (7,460 words) - 14:35, 30 August 2024