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...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

These axioms, apart from continuity, are often justified using the Dutch book theorems (whereas continuity is used to set aside lexicographic or infinitesimal...

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...

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...

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...

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...

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...

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...

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...