Geometric Ethics

The Mathematical Structure of Moral Reasoning

Andrew H. Bond
Senior Member, IEEE · Department of Computer Engineering · San Jose State University

Spring 2026 · v 1.19

Front Matter

  1. Preface
  2. Core Objects at a Glance

Part I: The Problem

  1. Chapter 1: Introduction — Why Geometry?
  2. Chapter 2: The Failure of Scalar Ethics
  3. Chapter 3: Historical Precursors — Geometry Before Geometry

Part II: The Framework

  1. Chapter 4: Mathematical Preliminaries
  2. Chapter 5: The Moral Manifold
  3. Chapter 6: The Tensor Hierarchy
  4. Chapter 7: One Case, Five Levels
  5. Chapter 8: Stratification — Boundaries, Thresholds, and Phase Transitions

Part III: Dynamics and Symmetry

  1. Chapter 9: The Origin of the Moral Metric — Discovery, Construction, or Governance?
  2. Chapter 10: Moral Dynamics — Parallel Transport, Holonomy, and the Curvature of Moral Space
  3. Chapter 11: Moral Reasoning as Optimal Search
  4. Chapter 12: Noether’s Theorem for Ethics — Symmetry, Invariance, and the Conservation of Harm
  5. Chapter 13: Quantum Normative Dynamics — Superposition, Measurement, and the Stratified Lagrangian

Part IV: Agents and Collectives

  1. Chapter 14: Collective Moral Agency — Aggregation, Emergence, and the Tensors of Shared Obligation
  2. Chapter 15: From Tensor to Decision — The Philosophy of Moral Contraction
  3. Chapter 16: Moral Uncertainty and the Limits of Geometric Determination

Part V: Implementation

    Part V Prelude: Philosophy Engineering

    1. Chapter 17: Empirical Evidence for Geometric Ethics
    2. Chapter 18: Geometric Ethics for Artificial Agents
    3. Chapter 19: The DEME Architecture and ErisML

    Part VI: Domain Applications

    1. Chapter 20: Geometric Economics — The Bond Geodesic Equilibrium
    2. Chapter 21: Geometric Clinical Ethics — Triage, Consent, and the Clinical Geodesic
    3. Chapter 22: Geometric Jurisprudence — Algorithmic Justice and Legal Manifolds
    4. Chapter 23: Geometric Finance — Market Microstructure on the Decision Manifold
    5. Chapter 24: Geometric Theology — Religious Reasoning on the Moral Manifold
    6. Chapter 25: Geometric Environmental Ethics — Climate, Commons, and Intergenerational Obligation on the Moral Manifold
    7. Chapter 26: Geometric AI Ethics — The Moral Geometry of Algorithmic Systems
    8. Chapter 27: Geometric Bioethics — Population-Level Ethics on the Decision Manifold
    9. Chapter 28: Geometric Military Ethics — War and Constrained Pathfinding on the Decision Manifold

    Part VII: Horizons

    1. Chapter 29: Open Problems
    2. Chapter 30: Conclusion — The Geometry of “Maybe”

    Appendices & References

    1. Appendix A: Related Work and Differentiation

    Appendices & References

    1. Appendix B: Reproduction Cookbook
    2. Appendix C: Human-Subjects Research Roadmap
    3. Appendix D: End-to-End Case Studies
    4. Appendix E: Skeptic’s Appendix — Objections, Alternatives, and Falsification
    5. Appendix F: Mathematical Ledger — Status of Formal Claims
    6. Bibliography