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Design+ Modern interpretations of probability

This means that in the mathematical function categories, as well as the essence of the mutual penetration
“probability,” the argument “time” should be taken into (certain fusion) of the concepts of logic and probability,
account as well, for after some time, in the future, as and the consequences of this process, can be understood
the amount of knowledge increases, some stochastic exclusively within the framework of the corresponding
phenomena will pass for a future person into the category historical discourse.
of deterministic ones. However, when analyzing complex Logic is believed to have originated in the fourth century
phenomena, such as social processes, which influence not BC in ancient Greece and was associated with oratory. At
just the actions of an individual but the behavior of millions that time, logic and rhetoric reflected mastering the basics
of people over decades or even centuries, it is certainly of argumentation, logical rules of proof, and forming forms
impossible to describe these processes analytically, neither of thinking. It took a long time before the works of Francis
now nor even in the future. Thus, the distance between the Bacon, René Descartes, and Gottfried Leibniz directed
probable and the obligatory deterministic is represented logic (already as a science) to form conclusions based on
by the phenomenon’s cognition level. Hence, the corollary judgments. The English scientist F. Bacon, the founder of
follows: the more comprehensive our knowledge, the scientific induction and inductive logic, was one of the
less likely phenomena appear to us. However, a person first to turn to experiments in his research. He proclaimed
remains such that achieving goals causes the emergence of induction, the movement of thoughts from individual facts
new, more complex goals, demonstrating the restless and
boundless curiosity of humans. (hypotheses) to generalizing conclusions, as a universal
research method. French philosopher R. Descartes
Of course, the world is cognizable. But at any moment, supported deductive logic, which aimed at establishing the
the ratio between the cognizable and the cognizable truth of specific facts based on general conclusions. German
will, unfortunately (or, fortunately), favor the latter. This philosopher G. Leibniz was the first to suggest the necessity
means that the ratio between deterministic and random of creating symbolic or mathematical logic. The portrait of
phenomena will always be outweighed in favor of the latter, Gottfried Wilhelm von Leibniz is shown in Figure 6. 16
which, in turn, will yield to hyper-random phenomena,
processes, and events. Thus, mathematicians, physicists, Moreover, G. Leibniz believed that in the future, it was
sociologists, and scientists will always have a job in this symbolic logic that has all chances to turn into the “art of
world, regardless of its perfection. calculations,” according to which the results of appropriate
calculations can solve all contradictions between people:
6. The interpenetration of the concepts of “The only way to improve our judgments is to make them
probability and logic visual, so that errors can be found with the eyes, and if
there is a dispute among people, it is necessary to say, “Let’s
The interpretation of probability as the degree of possibility calculate!,” then without much formality, it will be possible
of realization of a corresponding event, or the degree of to see who is right and who is wrong. However, Leibniz’s
confirmation or non-confirmation of this or that conclusion, idea about the possibility, necessity, and productivity
has gained relevance not only among mathematicians and of reducing judgments to appropriate calculations for
specialists who regularly face the need to predict events or many years did not find a response among philosophers
process large arrays of data but also in a variety of other or mathematicians. Further development of science
fields. Probability as a category of the cognitive process was showed that not all processes of human cognition of the
(and still is) of considerable interest to the philosophical surrounding world or judgments can be written down in
community. This was especially evident at the turn of the symbolic language. However, Leibniz’s idea of introducing
19 and 20 centuries against the background of advances appropriate symbolism in logic turned out to be, as reality
th
th
in physics, as well as against the background of the search shows, both effective and productive. Symbolic logic began
for new non-binary logical structures. Interpretations to be created only in the middle of the 19 century by
th
of probability as a certain category, and philosophical George Boole, Augustus De Morgan, Charles Peirce, and
studies of this category, taking into account multivalued others. Applying symbolic logic methods to solve problems
(non-binary) logical structures, led to the emergence of arising in formal logic allowed not only the solving of these
integrated logical-probabilistic structures widely applied problems but also the formulation and, to a large extent,
in various fields today (Figure 5). The structure of the the solving of problems that could not even be posed
“probability” category and its development concerning the within the framework of formal logic. This, of course,
“logic” category is shown in Figure 5. caused revolutionary shifts in the early 20 century, both
th
The formation of the foundations of mathematical in formal logic and in all scientific directions, in one way
logic as a development of the corresponding philosophical or another, related to it.

Volume 2 Issue 2 (2025) 10 doi: 10.36922/dp.6387