Related papers: What does the proof of Birnbaum's theorem prove?
The paper by Mayo claims to provide a new clarification and critique of Birnbaum's argument for showing that sufficiency and conditionality principles imply the likelihood principle. However, much of the arguments go back to arguments made…
Deborah Mayo claims to have refuted Birnbaum's argument that the Likelihood Principle is a logical consequence of the Sufficiency and Conditionality Principles. However, this claim fails because her interpretation of the Conditionality…
This is an invited contribution to the discussion on Professor Deborah Mayo's paper, "On the Birnbaum argument for the strong likelihood principle," to appear in Statistical Science. Mayo clearly demonstrates that statistical methods…
The likelihood principle makes strong claims about the nature of statistical evidence but is controversial. Its claims are undermined by the existence of several examples that are assumed to show that it allows, with unity probability,…
We discuss Birnbaum's result, its relevance to statistical reasoning, Mayo's objections and the result in [Electron. J. Statist. 7 (2013) 2645-2655] that the proof of this result doesn't establish what is commonly believed.…
In this note, we provide critical commentary on two articles that cast doubt on the validity and implications of Birnbaum's theorem: Evans (2013) and Mayo (2014). In our view, the proof is correct and the consequences of the theorem are…
We defend a new theory of statistical evidence, which we call Robust Bayesianism (RB). We prove that, under widely accepted assumptions, RB entails the law of likelihood [Royall, 1997], the likelihood principle [Berger and Wolpert, 1988],…
While it is widely agreed that Bell's theorem is an important result in the foundations of quantum physics, there is much disagreement about what exactly Bell's theorem shows. It is agreed that Bell derived a contradiction with experimental…
There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…
We investigate relationships between versions of derivability conditions for provability predicates. We show several implications and non-implications between the conditions, and we discuss unprovability of consistency statements induced by…
We consider Brouwer's fixed point theorem and Sperner's lemma in one dimension. We present a proof of the Brouwer theorem using the Sperner lemma, and vice versa. However, we also show that they are not equivalent, because the Sperner lemma…
This paper continues the author's previous study \cite{Kura20}, showing that several weak principles inspired by non-normal modal logic suffice to derive various refined forms of the second incompleteness theorem. Among the main results of…
Every experiment or observational study is made in a context. This context is being explicitly considered in this book. To do so, a conceptual variable is defined as any variable which can be defined by (a group of) researchers in a given…
Bell's theorem shows that the reasonable relativistic causal principle known as "local causality" is not compatible with the predictions of quantum mechanics. It is not possible maintain a satisfying causal principle of this type while…
The consistency formula for set theory can be stated in terms of the free-variables theory of primitive recursive maps. Free-variable p. r. predicates are decidable by set theory, main result here, built on recursive evaluation of p. r. map…
The independence of the continuum hypothesis is a result of broad impact: it settles a basic question regarding the nature of N and R, two of the most familiar mathematical structures; it introduces the method of forcing that has become the…
An essential component of inference based on familiar frequentist notions, such as $p$-values, significance and confidence levels, is the relevant sampling distribution. This feature results in violations of a principle known as the strong…
Bell's 1964 theorem causes a severe problem for the notion that correlations require explanation, encapsulated in Reichenbach's Principle of Common Cause. Despite being a hallmark of scientific thought, dropping the principle has been…
Feferman proved in 1962 that any arithmetical theorem is a consequence of a suitable transfinite iteration of full uniform reflection of $\mathsf{PA}$. This result is commonly known as Feferman's completeness theorem. The purpose of this…
The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a…