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Design+ Modern interpretations of probability

(and rightfully so) the most adequate and effective tool for judgments and conclusions across the diverse contexts in
solving many practical problems in various fields of human which they are applied.
activity. If we consider probability as a philosophical category

2. Interpretations of the concept of that characterizes the reality surrounding a person, then
probability we should state its bifurcation, the separation of objective
probability and subjective probability.
Among the considered concepts (probability, logic, and Objective probability is a concept that characterizes a
fuzziness), the concept of probability has undergone quantitative measure of the possibility of the occurrence
the most significant variation of definitions and (realization) of an event under certain conditions. This
interpretations throughout its existence. Within this type of probability characterizes the objective properties
context, each proposed interpretation of probability always of mass events of a random nature and is studied by
corresponded to certain conditions and goals regarding the mathematical theory of probability. Mathematical
the practical application of probabilistic tools or their probability is an objective quantitative characteristic of the
theoretical justification. Nevertheless, scientific discourses degree (measure) of the possibility of the realization of a
around the concept of probability are ongoing, which may certain event, which can be repeated an unlimited number
indicate the possibility (or rather, the necessity) of the of times under specific predetermined conditions.
emergence of new interpretations of this concept and new
areas of usage of this field of knowledge. Subjective probability allows us to analyze the
peculiarities of a person’s subjective cognitive activity
In the 20 century, the concept of probability and under conditions of uncertainty (incomplete certainty).
th
the tools based on this concept became the focus of In this case, probability acts as a measure of subjective
attention not only for specialists in technical fields, where confidence in realizing a certain event. This confidence
the randomness of the realization of events began to is determined, firstly, by the information available (or
gain more and more weight but (as a consequence) also absent) in a given person regarding the event under
for the philosophical community. After all, immersion study, and secondly, by the psychological features of this
into the content and essence of probability inevitably person. This psychological aspect plays an important role
leads to philosophical reflections and conclusions. The in how individuals assess the likelihood of a given event’s
spread of the application of probabilistic tools as the occurrence. The studies of subjective probability, as shown
basis of many algorithms for constructing new systems below, played a significant role in developing scientific
in telecommunication, energy, military, and space directions, where probabilistic and logical characteristics
technology, as well as in comprehensive studies of human of observable events are combined, as well as in the origin
society, has led to the need to comprehend the very concept and development of the theory of fuzzy sets.
of probability. This has prompted scholars in the field of
logic and philosophy, which are traditionally associated 3. Classical (symmetric) interpretation of
with the study of the essence of scientific theories, to probability
examine the internal content and foundational meaning The classical interpretation of probability was historically
of probability.
the first attempt to estimate the results of the realization
Probability theory has become an independent branch of events. The initial probabilistic representations,
1,2
of mathematics in the last century and is finding new concepts, and methods emerged from analyzing situations
application areas. However, as the application of this that manifest themselves in gambling. It is important to
theory becomes wider and more diverse, the interpretation note that gambling is usually organized in a manner that
of probability and the content of probabilistic conclusions makes different realizations of the corresponding event
become more difficult. Consequently, it becomes more equally probable. In the example of throwing a dice (which
difficult to find an (better would be a universal, unified, has become classical), the events connected with the
generalized) interpretation of probability, one that not only falling of any face of this dice are equally possible. From
satisfies the logical and methodological demands of relevant this condition, it is easy to calculate the probability of
research but also aligns naturally with everyday intuitions events concerning falling out of one of the faces, without
and commonly accepted understandings of probability the necessity to address the experiment. If the die is made
based on its established applications. The existence of a carefully (and it is the obligatory condition of identicalness
mathematical theory of probability, unfortunately, does of events), the probability of falling out of any face will
not (as will be demonstrated later) provide grounds for be 1/6. The definition of probability using this approach
forming a unified view of the content of probabilistic is detailed by Jacob Bernoulli in his work The Art of

Volume 2 Issue 2 (2025) 3 doi: 10.36922/dp.6387