Related papers: A note on probability and Hilbert's VI problem

This study has the purpose of addressing four questions that lie at the base of the probability theory and statistics, and includes two main steps. As first, we conduct the textual analysis of the most significant works written by eminent…

One cannot justifiably presuppose the physical salience of structures derived via decoherence theory based upon an entirely uninterpreted use of the quantum formalism. Non-probabilistic accounts of the emergence of probability via…

In the modern Bayesian view classical probability theory is simply an extension of conventional logic, i.e., a quantitative tool that allows for consistent reasoning in the presence of uncertainty. Classical theory presupposes, however,…

Hay esbozos seg\'un los cuales las probabilidades se cuentan como la fundaci\'on de la teor\'i a matem\'atica de las estad\'isticas. Mas la significaci\'on f\'isica de las probabilidades matem\'aticas son oscuros, muy poco entendidos.…

This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…

Hilbert's sixth problem calls for the axiomatization of physics, particularly the derivation of macroscopic statistical laws from microscopic mechanical principles. A conceptual difficulty arises in classical probability theory: in…

In 1931 de Finetti proved what is known as his Dutch Book Theorem. This result implies that the finite additivity {\it axiom} for the probability of the disjunction of two incompatible events becomes a {\it consequence} of de Finetti's…

Introduction to the special issue of Phil. Trans. R. Soc. A 376, 2018, `Hilbert's Sixth Problem'. The essence of the Sixth Problem is discussed and the content of this issue is introduced. In 1900, David Hilbert presented 23 problems for…

This contribution derives from a rather extensive study on the foundations of probability. We start by discussing critically the two main models of the random event in Probability Theroy and cast light over a number of incongruities. We…

As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…

D. Wallace has tried to use decoherence to solve the preferred basis problem of Everettian Quantum Mechanics, and this solution lays the foundation for his proof of the Born rule. But this is a circular argument, as approximations used in…

We study the complexity of satisfiability problems in probabilistic and causal reasoning. Given random variables $X_1, X_2,\ldots$ over finite domains, the basic terms are probabilities of propositional formulas over atomic events $X_i =…

The concept of refinement from probability elicitation is considered for proper scoring rules. Taking directions from the axioms of probability, refinement is further clarified using a Hilbert space interpretation and reformulated into the…

Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on…

In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…

We formulate a property $P$ on a class of relations on the natural numbers, and formulate a general theorem on $P$, from which we get as corollaries the insolvability of Hilbert's tenth problem, G\"odel's incompleteness theorem, and…

We introduce a framework uniting algorithmic randomness with exchangeable credences to address foundational questions in philosophy of probability and philosophy of science. To demonstrate its power, we show how one might use the framework…

In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under…

This paper is motivated by the questions of how to give the concept of probability an adequate real-world meaning, and how to explain a certain type of phenomenon that can be found, for instance, in Ellsberg's paradox. It attempts to answer…

In this article we take a probabilistic look at H\"older's inequality, considering the ratio of terms in the classical H\"older inequality for random vectors in $\mathbb{R}^n$. We prove a central limit theorem for this ratio, which then…