What is Not Explicitly Prohibited is Implicitly Mandated in an infinite universe
Year: 2026
Type: article
Abstract: This preliminary draft presents a foundational inquiry into system dynamics, formal logic, and ontology, examining how probability and possibility behave across unbounded and infinite operational domains. Traditional analytical frameworks rely on a tripartite taxonomy that treats events as either explicitly prohibited ($p=0$), explicitly mandated ($p=1$), or implicitly sanctioned ($0 < p < 1$). In this paper, we demonstrate through a generalized measure-theoretic proof and the Borel-Cantelli Lemma that the category of the "merely allowed" is an unstable mathematical illusion over infinite domains. If a state or event possesses any non-zero intrinsic probability measure ($p > 0$) and is not structurally prohibited, the probability of its non-occurrence over an infinite sequence of realizations converges strictly to zero, while the frequency of its realization diverges to infinity. Consequently, non-prohibition in an infinite domain is logically and ontologically equivalent to an explicit mandate. Keywords and concepts: Measure theory, infinite domains, Borel-Cantelli lemma, system dynamics, ontology, formal logic, probability theory.
Author: Kapadia, Sagar
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203935644
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