An Axiomatic Framework for a Coherent Abstract System of Holistic Logic
The book “Metaholistics” provides an extensive and detailed formalization of a novel abstract system of holistic logic developed to complement and integrate with the dominant Western atomistic logic. It elaborates complex modal-temporal logics and their semantics, axioms, operators, canonical models, and dynamic polarity and harmony processes.
Below is a comprehensive summary and explanation addressing the key insights and core components of this abstract system of holistic logic as presented in the document
1. Overview of Metaholistics
Metaholistics formalizes a complementary holistic logic to Western atomistic logic, aiming to reconcile persistent crises arising from Western Modernity’s fragmented, reductionist epistemic framework. It is built on an abstract axiomatic system that integrates the dual polarities of persistence (continuity, stability) and novelty (change, innovation), embedding these within a modal-temporal semantic framework which accounts for both cosmic directionality and local conditionality.
2. Fundamental Concepts
Nothingness as Ontological Ground: All differentiated states emerge from an undifferentiated horizon of “nothingness,” conceived as a generative plenum of potentiality.
Polarity Fields: The dynamic interplay of persistence vs. novelty fields animates emergence and transformation.
Assemblies & Arbitrage: Local assemblies filter and arbitrate possible transitions between states, enforcing harmony and governing local evolution and stability.
Harmony as Modal Constraint: Only transitions preserving or restoring systemic harmony are possible; disharmony leads to collapse or regression.
Hierarchy of Emergence: Layers of reality emerge in strict partial order: nothingness → physical → biological → societal → synthetic.
Eternal Cosmic Directionality with Local Reversibility: The overall cosmic evolution is unidirectional and irreversible, but local systems may revert or collapse conditionally.
3. Formal Axioms and Logical Structure
The system is axiomatically formalized with explicit modal-temporal logic using Kripke semantics and strong mathematical rigor:
4. Modal-Temporal Logic and Semantics
States and Worlds (W): Represent configurations embedding layered poles of persistence and novelty, context, and assemblies.
Accessibility Relations (R): Govern possible transitions filtered for harmony, context, and assemblies, encoding emergence, collapse, or local reversibility.
Temporal Operators such as Next (X), Always (G), Eventually (F) model time evolution of states.
Polarity Modalities (□p, ◇v): Express necessary persistence and possible novelty, with their cyclic oscillation fundamental to systemic evolution and stability.
Multi-Modal Extension: Distinguish cosmic (universal) and local (contingent) modalities to reflect layered realities.
Canonical Kripke Models: Built from maximally consistent sets of formulas, serving as semantic universes validating the logical system and providing completeness.
5. Dynamic Modeling of Polarity and Harmony
Polarity oscillations cycle between persistence and novelty, driving the evolutionary dynamics in physical, biological, societal, and synthetic domains.
Assemblies serve as complex adaptive systems arbitraging transformations which propagate or collapse by respecting harmony and contextual filters.
Modal-temporal operators describe polarity transition operators (PTN, NTP) capturing essential polarity shifts.
Harmonic balance is mandatory for transformative transitions, with formal rules encoding harmony maintenance and transformation necessity.
The logic includes rules and axioms ensuring polarity exclusivity, oscillation, and transformation governed by harmony and context.
Local reversibility zones and directionality gradients describe areas of reversible dynamics and preferred emergent flows, contributing to resilience and meta-stability.
Metrics for harmony propagation, disruption spread, connectivity, and propagation speed formalize the systemic health and responsiveness.
6. Applications to Societal Knowledge and Evolution
The framework models societal knowledge formation as a process balancing holistic and atomistic logics.
It accounts for historical societal archetypes, bifurcations, and transitions between paradigms.
Assemblies correspond to social institutions, decision-making bodies, and cultural clusters whose arbitration governs societal evolution.
The holistic logic aims to guide after-modernity paradigms, integrating diverse worldviews with formal rigor.
It offers a mathematical base for simulating societal collapse and transformation, capturing multidimensional crises and their convergence.
Modal-temporal polarity logic grounds the operationalization of societal transitions and governance in formal interaction models and assembly dynamics.
7. Summary
The book “Metaholistics” is a profound, mathematically rigorous development of an abstract system of holistic logic that complements atomistic logic by formalizing polarity dynamics, hierarchical emergence, harmony, assemblies, and contextual filtering within a modal-temporal logical framework. It provides a foundational epistemic and ontological system aimed at addressing the limitations of Western logic in societal knowledge formation and evolution, offering a path towards a more integrated, resilient, and holistic understanding of complex universal and societal processes.
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