From Coherence to Consequent Nature: A Formal Approach to Process-Relational Theology
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| Lingua: | inglese |
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2026
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| _version_ | 1866901861750013952 |
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| author | Leonhardt, Mathias |
| author_facet | Leonhardt, Mathias |
| contents | <p>We present a formal axiom system C5 for agent-relative value theory, grounded in the concept of coherence as constraint satisfaction over relational structures. Modeling coherence as a quadratic form, we establish six main results: (1) coherence-seeking agents under projected gradient dynamics converge monotonically to locally optimal states; (2) a continuous-time gradient flow formulation with Lyapunov stability, establishing that coherence attractors are asymptotically stable equilibria; (3) global coherence maximization is NP-hard under the binary restriction (by reduction from Max-Cut), providing formal support for Bedau’s (1997) criterion that weakly emergent properties admit no general analytic shortcut; (4) the coherence landscape generically supports multiple stable attractors with path-dependent convergence; (5) spectral criteria for attractor stability derived from the coherence matrix; and (6) a replicator dynamics for aggregation weights, replacing the stipulated weights of prior versions with emergent, coherence-driven selection. The aggregation mechanism can either stipulate weights or derive them dynamically via replicator dynamics, where average coherence increases monotonically.</p> <p>As an application, we develop a structural mapping to process philosophy (Whitehead, 1929), demonstrating that certain non-personal “God-concepts”—in particular Whitehead’s consequent nature and Spinoza’s Deus sive Natura—admit formal reconstruction as emergent coherence attractors, doubly emergent in both structure and weighting. This mapping is compatible with recent work on emergent moral properties (Baysan, 2025).</p> <p class="p1"><em><span class="s1">Working paper — pre-conference draft. Accepted for presentation at the European Academy of Religion (EuARe) 2026, Philosophy of Religion panel, Rome, 2 July</span><span class="s1"><span class="Apple-converted-space"> </span>2026 (Session 155, paper ID 1395). Not yet peer-reviewed; comments welcome.</span></em></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19685106 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
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| spellingShingle | From Coherence to Consequent Nature: A Formal Approach to Process-Relational Theology Leonhardt, Mathias coherence theory NP-hardness Lyapunov stability process ontology Whitehead replicator dynamics weak emergence computational complexity value aggregation process philosophy structural theology non-personal God-concepts Spinoza <p>We present a formal axiom system C5 for agent-relative value theory, grounded in the concept of coherence as constraint satisfaction over relational structures. Modeling coherence as a quadratic form, we establish six main results: (1) coherence-seeking agents under projected gradient dynamics converge monotonically to locally optimal states; (2) a continuous-time gradient flow formulation with Lyapunov stability, establishing that coherence attractors are asymptotically stable equilibria; (3) global coherence maximization is NP-hard under the binary restriction (by reduction from Max-Cut), providing formal support for Bedau’s (1997) criterion that weakly emergent properties admit no general analytic shortcut; (4) the coherence landscape generically supports multiple stable attractors with path-dependent convergence; (5) spectral criteria for attractor stability derived from the coherence matrix; and (6) a replicator dynamics for aggregation weights, replacing the stipulated weights of prior versions with emergent, coherence-driven selection. The aggregation mechanism can either stipulate weights or derive them dynamically via replicator dynamics, where average coherence increases monotonically.</p> <p>As an application, we develop a structural mapping to process philosophy (Whitehead, 1929), demonstrating that certain non-personal “God-concepts”—in particular Whitehead’s consequent nature and Spinoza’s Deus sive Natura—admit formal reconstruction as emergent coherence attractors, doubly emergent in both structure and weighting. This mapping is compatible with recent work on emergent moral properties (Baysan, 2025).</p> <p class="p1"><em><span class="s1">Working paper — pre-conference draft. Accepted for presentation at the European Academy of Religion (EuARe) 2026, Philosophy of Religion panel, Rome, 2 July</span><span class="s1"><span class="Apple-converted-space"> </span>2026 (Session 155, paper ID 1395). Not yet peer-reviewed; comments welcome.</span></em></p> |
| title | From Coherence to Consequent Nature: A Formal Approach to Process-Relational Theology |
| topic | coherence theory NP-hardness Lyapunov stability process ontology Whitehead replicator dynamics weak emergence computational complexity value aggregation process philosophy structural theology non-personal God-concepts Spinoza |
| url | https://doi.org/10.5281/zenodo.19685106 |