Basis-Scope Divergence Principle (BSDP)
Description
The Basis-Scope Divergence Principle (BSDP), or Basis-Scope Divergence Principle, proposes a domain-independent formal framework for analyzing situations in which a criterion is initially justified over a bounded reference domain but is subsequently applied to a progressively larger domain than the evidence or justification supports. The framework separates the basis of justification from the scope of application and defines their divergence as a measurable structural quantity.
The central distinction is expressed by
Rationality of Origin
Rationality of Extension.
Equivalently, the existence of evidence for one element does not logically entail the same property for every element:
\exists k: E_{k} \nRightarrow \forall j: E_{j}.
The proposed architecture is criterion-independent, metric-independent, medium-independent, and scalable to arbitrary finite system size, subject to explicit structural conditions. The framework is deliberately separated into three layers. Layer I develops the formal systemic mechanism. Layer II tests the architecture through computational, structural, informational, organizational, and network-style cases. Layer III interprets the same mechanism at the epistemological and philosophical level, including the human case from which the motivating paradox arises.
A central mathematical quantity is
\Delta_{BS}(t)=\mu(D_{t}\backslash R),
where R denotes the justified reference domain, D_{t} the application domain at time t, and \mu a domain measure. A normalized form is
\delta_{BS}(t)=\frac{\mu(D_{t}\backslash R)}{\mu(D_{t})},
whenever \mu(D_{t})>0. The framework does not treat a positive divergence as automatically harmful, irrational, false, or unsuccessful. Such interpretations require an additional validity test for the extended domain. Consequently, BSDP distinguishes scope expansion from scope error.
The paper derives the formal definitions, dynamic architecture, boundary conditions, null cases, counterexamples, falsification criteria, cross-domain illustrations, sensitivity relations, and limitations. All numerical simulations are synthetic demonstrations of mathematical behavior and are not presented as empirical confirmation.
Files
Basis_Scope_Divergence_Principle__BSDP_.pdf
Additional details
References
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