Randomness and Foundations of Probability: Von Mises' Axiomatization of Random Sequences

@inproceedings{Lambalgen1996RandomnessAF,
  title={Randomness and Foundations of Probability: Von Mises' Axiomatization of Random Sequences},
  author={Michiel van Lambalgen},
  year={1996}
}
Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be… Expand
Randomness? What Randomness?
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability,Expand
Causation, randomness, and pseudo-randomness in John Venn's logic of chance
In 1866, the young John Venn published The Logic of Chance, motivated largely by the desire to correct what he saw as deep fallacies in the reasoning of historical determinists such as Henry BuckleExpand
3 0 N ov 2 01 9 Randomness ? What randomness ?
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability,Expand
Elementary Proof of a Theorem of Jean Ville
TLDR
It is shown that some sequences admitted by Von Mises as "random" in fact manifest a certain kind of systematicity, and an expanded version of the latter, alternative argument is provided. Expand
3 0 Ju l 2 01 9 Randomness ? What randomness ?
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability,Expand
Probabilistic issues in statistical mechanics
Abstract Beyond the syntax of statistical mechanics, the focus here is on those of its semantic aspects that depend on the foundations of probability theory. The first problem is to confront theExpand
Randomness: Old and New Ideas
TLDR
The survey of classical theories of randomness is provided, and an alternative model is proposed that is based on the lattice theory, has the strong mathematical basis and easily used in practice. Expand
Von Mises' Frequentist Approach to Probability
Richard Von Mises (1883-1953), the originator of the birthday problem, viewed statistics and probability theory as a science that deals with and is based on real objects rather than as a branch ofExpand
Equidistribution, uniform distribution: a probabilist's perspective
The theory of equidistribution is about hundred years old, and has been developed primarily by number theorists and theoretical computer scientists. A motivated uninitiated peer could encounterExpand
Cryptographic protocol design
TLDR
This work investigates the security of interactive computations and discusses how to formalise various security goals, such as inputprivacy, output-consistency and complete security, and how to choose a security goal that is appropriate for a specific setting. Expand
...
1
2
3
...

References

SHOWING 1-10 OF 57 REFERENCES
Von Mises' Definition of Random Sequences Reconsidered
We review briefly the attempts to define random sequences (?0). These attempts suggest two theorems: one concerning the number of subsequence selection procedures that transform a random sequenceExpand
Independence, Randomness and the Axiom of Choice
TLDR
The results show that these axioms, when added to ZF, imply the failure of AC, but the axiom of extensionality plays an essential role in the derivation, and a deeper analysis may ultimately show that randomness is incompatible with extensionality. Expand
On the concept of a random sequence
ly the Kollektiv may be represented by an infinite sequence of points of an appropriate space, the Merkmalraum. Or if the number of possible outcomes of a trial is finite (and it may well be arguedExpand
The Axiomatization of Randomness
TLDR
A byproduct is a quantifier elimination theorem for Friedman's “almost all” quantifier in terms of this independence relation, using an abstract independence relation of von Mises' notion of a random sequence. Expand
Independence structures in set theory
The axioms for "independent choices" presented in van Lambalgen [1992] are strengthened here, so that they can be seen as introducing a new type of indiscernibles in set theory. The resulting systemExpand
On the Foundations of Probability and Statistics
It's not surprisingly when entering this site to get the book. One of the popular books now is the foundations of probability and statistics. You may be confused because you can't find the book inExpand
An Introduction to Kolmogorov Complexity and Its Applications
  • Ming Li, P. Vitányi
  • Computer Science, Psychology
  • Texts and Monographs in Computer Science
  • 1993
TLDR
The book presents a thorough treatment of the central ideas and their applications of Kolmogorov complexity with a wide range of illustrative applications, and will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics. Expand
An Introduction To Probability Theory And Its Applications
TLDR
A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics. Expand
Realism and the aim of science
TLDR
The author explains the development of the Objective and Subjective Probabilities Index and its application to the Theory of Probability. Expand
...
1
2
3
4
5
...