Vorobyev, Oleg Yu
(2016)
Postulating the theory of experience and chance
as a theory of co~events (co~beings).
[Preprint]
Abstract
The aim of the paper is the axiomatic justification of the theory of experience and chance,
one of the dual halves of which is the Kolmogorov probability theory. The author’s main idea was the
natural inclusion of Kolmogorov’s axiomatics of probability theory in a number of general concepts of
the theory of experience and chance. The analogy between the measure of a set and the probability of an
event has become clear for a long time. This analogy also allows further evolution: the measure of a set is
completely analogous to the believability of an event. In order to postulate the theory of experience and
chance on the basis of this analogy, you just need to add to the Kolmogorov probability theory its dual
reflection — the believability theory, so that the theory of experience and chance could be postulated as
the certainty (believabilityprobability) theory on the Cartesian product of the probability and believability
spaces, and the central concept of the theory is the new notion of co~event as a measurable binary relation
on the Cartesian product of sets of elementary incomes and elementary outcomes. Attempts to build the
foundations of the theory of experience and chance from this general point of view are unknown to me,
and the whole range of ideas presented here has not yet acquired popularity even in a narrow circle of
specialists; in addition, there was still no complete system of the postulates of the theory of experience
and chance free from unnecessary complications. Postulating the theory of experience and chance can be
carried out in different ways, both in the choice of axioms and in the choice of basic concepts and relations.
If one tries to achieve the possible simplicity of both the system of axioms and the theory constructed
from it, then it is hardly possible to suggest anything other than axiomatization of concepts co~event and
its certainty (believabilityprobability). The main result of this work is the axiom of co~event, intended
for the sake of constructing a theory formed by dual theories of believabilities and probabilities, each of
which itself is postulated by its own Kolmogorov system of axioms. Of course, other systems of postulating
the theory of experience and chance can be imagined, however, in this work, a preference is given to
a system of postulates that is able to describe in the most simple manner the results of what I call an
experiencedrandom experiment.
Item Type: 
Preprint

Creators: 

Keywords: 
Eventology, event, co~event, experience, chance, to experience, to happen, to occur, theory
of experience and chance, theory of co~events, axiom of co~event, probability, believability, certainty
(believabilityprobability), probability theory, believability theory, certainty theory. 
Subjects: 
Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Explanation Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Methodology Specific Sciences > Mathematics > Ontology Specific Sciences > Cognitive Science Specific Sciences > Computation/Information Specific Sciences > Computation/Information > Quantum Specific Sciences > Computer Science Specific Sciences > Artificial Intelligence Specific Sciences > Economics Specific Sciences > Probability/Statistics Specific Sciences > Sociology 
Depositing User: 
Prof. Oleg Vorobyev

Date Deposited: 
23 Jul 2018 17:40 
Last Modified: 
23 Jul 2018 17:40 
Item ID: 
14894 
Official URL: 
https://www.academia.edu/34417203/Proceedings_of_t... 
Subjects: 
Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Explanation Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Methodology Specific Sciences > Mathematics > Ontology Specific Sciences > Cognitive Science Specific Sciences > Computation/Information Specific Sciences > Computation/Information > Quantum Specific Sciences > Computer Science Specific Sciences > Artificial Intelligence Specific Sciences > Economics Specific Sciences > Probability/Statistics Specific Sciences > Sociology 
Date: 
30 September 2016 
URI: 
https://philsciarchive.pitt.edu/id/eprint/14894 
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