arXiv:2601.00878 · v2
Heraclitean Dialectical Concept Space
摘要
We introduce Heraclitean Dialectical Concept Spaces (HDCS), a topological framework for modelling stagewise structural change in systems of concepts. A stage consists of a nonempty concept set, a feasible family generating an external topology, and a neighbourhood assignment carrying additional relational structure. Neighbourhood overlap induces adjacency and channel ideals. Candidate emergence is represented by the CCER construction: an interaction profile, finite admissible cores, and anchored witnesses determine nonempty open candidate regions in uncovered remainder structure. Selected candidates may be reified as new atomic concepts at a later stage, while partial injective carry maps separately track persistence of existing identities. The resulting history space is obtained as a quotient of the disjoint union of stage spaces with the corresponding final topology. Product concept spaces extend the construction to cross-domain interaction. We derive support characterizations, mediated-interaction components, canonical CCER envelopes, monotonicity and impossibility criteria, product-space factorization, and invariance under concept-space isomorphism. Applications to monetary transformation, zero and representation, mammalian middle-ear evolution, and AI-related labour change illustrate the framework. HDCS is intended as a structural formalism rather than a causal or predictive theory of historical change.
作者备注：124 pages, 1 figure. Major revision of the same HDCS work. The manuscript has been extensively rewritten while retaining the same framework and research question. Revisions strengthen the foundations, reformulate CCER, clarify reification, carry maps and history space, revise applications, and add new derived structural results