Related papers: What does the proof of Birnbaum's theorem prove?
We investigate infinite sets that witness the failure of certain Ramsey-theoretic statements, such as Ramsey's or (appropriately phrased) Hindman's theorem; such sets may exist if one does not assume the Axiom of Choice. We obtain very…
Null Hypothesis Statistical Testing is a dominant framework for conducting statistical analysis across the sciences. There remains considerable debate as to whether, and under what circumstances, evidence can be said to be confirmatory of a…
The famous G\"odel incompleteness theorem says that for every sufficiently rich formal theory (containing formal arithmetic in some natural sense) there exist true unprovable statements. Such statements would be natural candidates for being…
We have published several articles about generalizations and boundary-case exceptions to the Second Incompleteness Theorem during the last 25 years. The current paper will review some of our prior results and also introduce an `enriched'…
The topic of this paper is the Finiteness Conjecture for minimally unsatisfiable clause-sets (MUs), stating that for each fixed deficiency (number of clauses minus number of variables) there are only finitely many patterns, given a certain…
Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…
One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer…
Hierarchies of conditional beliefs (Battigalli and Siniscalchi 1999) play a central role for the epistemic analysis of solution concepts in sequential games. They are modelled by type structures, which allow the analyst to represent the…
Uncertainty may be taken to characterize inferences, their conclusions, their premises or all three. Under some treatments of uncertainty, the inferences itself is never characterized by uncertainty. We explore both the significance of…
In this paper, we show that the presence of the Archimedean and the mixture-continuity properties of a binary relation, both empirically non-falsifiable in principle, foreclose the possibility of consistency (transitivity) without…
Fine's theorem concerns the question of determining the conditions under which a certain set of probabilities for pairs of four bivalent quantities may be taken to be the marginals of an underlying probability distribution. The eight CHSH…
Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is…
Several years ago it was found that perturbation theory for two-dimensional O(N) models depends on boundary conditions even after the infinite volume limit has been taken termwise, provided $N>2$. There ensued a discussion whether the…
A proof procedure, in the spirit of the sequent calculus, is proposed to check the validity of entailments between Separation Logic formulas combining inductively defined predicates denoted structures of bounded tree width and theory…
Quantum theory provides an extremely accurate description of fundamental processes in physics. It thus seems likely that the theory is applicable beyond the, mostly microscopic, domain in which it has been tested experimentally. Here we…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
This paper is concerned with the causally symmetric version of the familiar de Broglie-Bohm interpretation, this version allowing the spacelike nonlocality and the configuration space ontology of the original model to be avoided via the…
An analysis is made of Deutsch's recent claim to have derived the Born rule from decision-theoretic assumptions. It is argued that Deutsch's proof must be understood in the explicit context of the Everett interpretation, and that in this…
Quantum theory provides a significant example of two intermingling hallmarks of science: the ability to consistently combine physical systems and study them compositely, and the power to extract predictions in the form of correlations. A…
We present and discuss the many results obtained concerning a famous limit theorem, the local limit theorem, which has many interfaces, with Number Theory notably, and for which, in spite of considerable efforts, the question concerning…