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Design+ Modern interpretations of probability

Classical (symmetric) Frequency (statistical) Axiomatic interpretation
interpretation of probability interpretation of probability of probability

Development of the
category “probability”

Development of the
category “logic”

Multi-valued Infinite-valued Probabilistic Probability Fuzzy logic
logic logic logic logic
Figure 5. The structure of the probability category and its development concerning the logic category

classical and frequentist interpretations of probability,
J. Keynes proposed to consider probability as the degree
of a reasonable belief attributed to relevant statements
(events) given exactly fixed data. “The terms credibility
and probability,” wrote J.M. Keynes, “describe the different
degrees of reasonable belief in some statement which we can
attribute to that statement under different knowledge.” 17(p.1)
In Keynes’s interpretation, probability (as some numerical
value) is established for a logical relation between two
sets of statements. It reflects the degree of belief in the
correctness (or incorrectness) of a statement, and the
numerical value of this degree of belief is not constant but
varies depending on the available knowledge (available
information) regarding the analyzed phenomena, objects,
and processes. All of the above points to the analytical
Figure 6. Portrait of Gottfried Wilhelm von Leibniz by Andreas Scheits rather than empirical nature of probability. Notably, Keynes
(1703). Image obtained from the Picryl website. 16
emphasized the objective nature of his interpretation of
Modern formal logic is often identified with probability. Although the degree of reasonable belief (the
mathematical logic. However, such a judgment cannot be value of probability) changes with changes in available
accepted in its entirety. Only a part of formal logic related to knowledge, it characterizes a relationship between objects
studying mathematical artifacts can be strictly recognized independent of human consciousness. “As an important
as mathematical. At the same time, modern logic contains category for logic,” Keynes argued, “probability is not
many sections and branches that operate with other subjective. It is not subject to human caprice. A statement
concepts, relate more to philosophy than to mathematics is probable not because we think so of it. Once the facts
(modal logic, inductive logic, multivalued logic, logic of that determine our knowledge are provided, then, under
norms and evaluations, etc.), and, consequently, apply the those circumstances, what to consider probable and what
verbal form of hypotheses and conclusions. to consider improbable is fixed objectively and does not
depend on the subject’s opinion. Probability theory is
The interpretation of probability as a degree of
reasonable belief, which was proposed by the English logical because it deals with the degree of belief that is
reasonable under given conditions, not merely with factual
scientist John Maynard Keynes in the 1920s, is considered belief, which may or may not be reasonable.” 17(p.1)
the first interpretation that largely contributed to
the foundation of structures where the concepts of Attempts to build a rigorous system (theory) of
probability and logic converge. Analyzing and criticizing probabilistic logic based on these conclusions did not succeed.

Volume 2 Issue 2 (2025) 11 doi: 10.36922/dp.6387