What is Not Explicitly Prohibited is Implicitly Mandated in an infinite universe

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-20
DOI
https://doi.org/10.5281/zenodo.22026016
Primary Topic
Logic, Reasoning, and Knowledge
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

What is Not Explicitly Prohibited is Implicitly Mandated in an infinite universe

Sagar Kapadia
Zenodo (CERN European Organization for Nuclear Research)
Logic, Reasoning, and Knowledge
article

What is Not Explicitly Prohibited is Implicitly Mandated in an infinite universe

Sagar Kapadia
article en

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.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
Openalex Percentile: Top 7%
Logic, Reasoning, and Knowledge
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

What is Not Explicitly Prohibited is Implicitly Mandated in an infinite universe — Sagar Kapadia · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS