Related papers: Reichenbach's Transcendental Probability
We explore the different meanings of "quantum uncertainty" contained in Heisenberg's seminal paper from 1927, and also some of the precise definitions that were explored later. We recount the controversy about "Anschaulichkeit",…
In the following we revisit the frequency interpretation of probability of Richard von Mises, in order to bring the essential implicit notions in focus. Following von Mises, we argue that probability can only be defined for events that can…
The objective of this paper is not simply to present an historical overview of Einstein's cosmological considerations, but to discuss the central role they played in shaping the paradigm of relativistic cosmology. This, we'll show, was a…
Some thoughts are presented on the inter-relation between beauty and truth in science in general and theoretical physics in particular. Some conjectural procedures that can be used to create new ideas, concepts and results are illustrated…
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…
The article attempts to demonstrate the rich history of one truly remarkable problem situated at the confluence of probability theory and theory of numbers - finding the probability of co-primality of two randomly selected natural numbers.…
The intuitive reasoning of physicists in conditions of uncertainty is closer to the Bayesian approach than to the frequentist ideas taught at University and which are considered the reference framework for handling statistical problems. The…
This expository paper advocates an approach to physics in which ``typicality" is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed. Their original versions…
Heisenberg's breakthrough in his July 1925 paper that set in motion the development of Quantum Mechanics through subsequent papers by Born, Jordan, Heisenberg and also Dirac (from 1925 to 1927) is reexamined through a modern lens. In this…
Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore,…
This paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
Quantum mechanics challenges classical intuitions of space, time, and causality via the superposition principle, which allows systems to exist in multiple states simultaneously. Niels Bohr addressed these paradoxes through his…
Kantian philosophy of space, time and gravity is significantly affected in three ways by particle physics. First, particle physics deflects Schlick's General Relativity-based critique of synthetic a priori knowledge. Schlick argued that…
Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…
In his book `Physics and Philosophy', Heisenberg suggested that the quantum world is one of ``potentialities or possibilities'' and that the classical realm is one of ``things or facts''. After ascertaining that his categories most…
We suggest that not only quanta may have played a role in Einstein's ideas on relativity, but that they themselves may be related to the dynamical and relativistic behaviour of the electromagnetic field exhibited in a Poincar\'e's 1900…
According to Schopenhauer, Kant's arguments about the transcendental ideality of space and time can be extended to matter through the concept of causality and the principle of sufficient reason. In this article, I examine to what extent…
Bruno de Finetti was one of the most convinced advocates of finitely additive probabilities. The present work describes the intellectual pro- cess that led him to support that stance and provides a detailed account both of the first paper…
Quantum technology is seeing a remarkable explosion in interest due to a wave of successful commercial technology. As a wider array of engineers and scientists are needed, it is time we rethink quantum educational paradigms. Current…