Related papers: What does the proof of Birnbaum's theorem prove?
Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…
In the absence of empirical confirmation, scientists may judge a theory's chances of being viable based on a wide range of arguments. The paper argues that such arguments can differ substantially with regard to their structural similarly to…
The designation ``Bernstein-von Mises theorem'' is apparently due to Lucien Le Cam. Roughly, the assertion of this theorem states that the posterior distribution of a parameter, conditioned on a large sample, is approximately normal,…
Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an…
To the frequentist who computes posteriors, not all priors are useful asymptotically: in this paper Schwartz's 1965 Kullback-Leibler condition is generalised to enable frequentist interpretation of convergence of posterior distributions…
Proof theory began in the 1920's as a part of Hilbert's program, which aimed to secure the foundations of mathematics by modeling infinitary mathematics with formal axiomatic systems and proving those systems consistent using restricted,…
Quantum decision theory is introduced here, and new basis for this theory is proposed. It is first based upon the author's general arguments for the Hilbert space formalism in quantum theory, next on arguments for the Born rule, that is,…
May's Theorem (1952), a celebrated result in social choice, provides the foundation for majority rule. May's crucial assumption of symmetry, often thought of as a procedural equity requirement, is violated by many choice procedures that…
In the theory of conditional sets, many classical theorems from areas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas such as mathematical economics or…
Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are…
Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of…
We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the…
Already in the 1970s there where attempts to present a set of ground rules, sometimes referred to as a theory of gravitation theories, which theories of gravity should satisfy in order to be considered viable in principle and, therefore,…
In this paper we formulate the problem of inference under incomplete information in very general terms. This includes modelling the process responsible for the incompleteness, which we call the incompleteness process. We allow the process…
The classical concept of bounded completeness and its relation to sufficiency and ancillarity play a fundamental role in unbiased estimation, unbiased testing, and the validity of inference in the presence of nuisance parameters. In this…
The sequential form of a statement $\forall\xi(B(\xi) \rightarrow \exists\zeta A(\xi,\zeta))$ is the statement $\forall\xi(\forall n B(\xi_n) \rightarrow \exists\zeta \forall n A(\xi_n,\zeta_n))$. There are many classically true statements…
Do completely unpredictable events exist in nature? Classical theory, being fully deterministic, completely excludes fundamental randomness. On the contrary, quantum theory allows for randomness within its axiomatic structure. Yet, the fact…
This article presents a concise proof of the famous Benford's law when the distribution has a Riemann integrable probability density function and provides a criterion to judge whether a distribution obeys the law. The proof is intuitive and…
"Bell's theorem" can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the joint assumptions of Locality and Predetermination.…
A quantum-like description of human decision process is developed, and a heuristic argument supporting the theory as sound phenomenology is given. It is shown to be capable of quantitatively explaining the conjunction fallacy in the same…