Related papers: Applying Popper's Probability
Corroboration or confirmation is a prominent philosophical debate of the 20th century. Many philosophers have been involved in this debate most notably the proponents of confirmation led by Hempel and its most powerful criticism by the…
A history and drama of the development of quantum probability theory is outlined starting from the discovery of the Plank's constant exactly a 100 years ago. It is shown that before the rise of quantum mechanics 75 years ago, the quantum…
We will show that Carl Stumpf's interpretation of the concept of probability is best understood as that of an objective Bayesian. First we analyse Stumpf's work in relation to that of his contemporary Johannes von Kries, and after that we…
Feyerabend frequently discussed physics. He also referred to the history of the subject when motivating his philosophy of science. Alas, as some examples show, his understanding of physics remained superficial. In this respect, Feyerabend…
Commonly observed patterns typically follow a few distinct families of probability distributions. Over one hundred years ago, Karl Pearson provided a systematic derivation and classification of the common continuous distributions. His…
The crucial but very confidential fact is brought into evidence that, as Kolmogorov himself repeatedly claimed, the mathematical theory of probabilities cannot be applied to physical, factual probabilistic situations because the factual…
This article was written for the Logic in Computer Science column in the February 2015 issue of the Bulletin of the European Association for Theoretical Computer Science. The intended audience is general computer science audience. The…
The aim of this article is twofold. First, we shall review and analyse the Neo-Kantian justification for the application of probabilistic concepts in physics that was defended by Hans Reichenbach early in his career, notably in his…
The sciences of complexity present some recurrent themes: the emergence of qualitatively new behaviors in dissipative systems out of equilibrium, the aparent tendency of complex system to lie at the border of phase transitions and…
There are important problems in physics related to the concept of probability. One of these problems is related to negative probabilities used in physics from 1930s. In spite of many demonstrations of usefulness of negative probabilities,…
In an effort to challenge the Copenhagen interpretation of quantum mechanics, Karl Popper proposed an experiment involving spatially separated entangled particles. In this experiment, one of the particles passes through a very narrow slit,…
Physicists have, hitherto, mostly adopted a frequentist conception of probability, according to which probability statements apply only to ensembles. It is argued that we should, instead, adopt an epistemic, or Bayesian conception, in which…
Standard probability theory has been extremely successful but there are some conceptually possible scenarios, such as fair infinite lotteries, that it does not model well. For this reason alternative probability theories have been…
The last century saw dramatic challenges to the Laplacian predictability which had underpinned scientific research for around 300 years. Basic to this was Alan Turing's 1936 discovery (along with Alonzo Church) of the existence of…
Alan Turing is considered as a founder of current computer science together with Kurt Godel, Alonzo Church and John von Neumann. In this paper multiple new research results are presented. It is demonstrated that there would not be Alan…
Hypotheses are central to information acquisition, decision-making, and discovery. However, many real-world hypotheses are abstract, high-level statements that are difficult to validate directly. This challenge is further intensified by 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…
An experiment proposed by Karl Popper to test the standard interpretation of quantum mechanics was realized by Kim and Shih. We use a quantum mechanical calculation to analyze Popper's proposal, and find a surprising result for the location…
We correct a common (but mistaken) attribution of the evaluation of the probability integral, usually attributed to Poisson, Gauss, or Laplace.
The paper is devoted to the contribution in the Probability Theory of the well-known Soviet mathematician Alexander Yakovlevich Khintchine (1894-1959). Several of his results are described, in particular those fundamental results on the…