Closure of Self-Determining System Based on Causal and Constitutive Relations

This theoretical computer science paper proposes a mathematical framework for defining self-determining systems through causal-constitutive loops rather than traditional causal relations alone. The work addresses fundamental questions about system boundaries and autonomy by requiring constitutive relations involving multiple independent variables, implying a dual-process organizational structure.

This arXiv paper tackles a foundational problem in systems theory: how to rigorously define when a system is self-determining or autonomous. The authors recognize that existing approaches relying solely on causal relations face logical challenges when distinguishing internal causes from external influences and when handling circular causality patterns. Their solution introduces constitutive relations as a complementary asymmetric relation type, enabling more precise boundary definitions around causal-constitutive loops.

The theoretical contribution builds on decades of systems thinking and complexity science research, extending philosophical inquiries into autonomy and self-organization. The requirement that constitutive relations involve at least two independent variables prevents mathematical reduction to supervenience—a common pitfall in reductionist approaches—while ensuring genuine emergence at the system level.

The dual-process implication is particularly significant for understanding complex systems across domains. In biological systems, this might map to complementary regulatory mechanisms. In AI systems, this framework could inform how to distinguish genuine agency from mere input-output mapping. The mathematical rigor potentially provides tools for analyzing organizational structures in distributed systems and networks.

For cryptocurrency and blockchain applications, this theoretical framework could eventually inform discussions about smart contract autonomy, decentralized autonomous organizations (DAOs), and system-level self-governance mechanisms. However, the immediate impact remains academic. Developers and researchers working on autonomous systems should monitor how these theoretical advances translate into practical methodologies for system design and verification.

• →The paper proposes causal-constitutive loops as a rigorous mathematical approach to defining system boundaries and self-determination.
• →Requiring multiple independent variables in constitutive relations prevents mathematical reduction and ensures genuine system autonomy.
• →The framework implies dual-process organizational structures emerge necessarily from the theoretical requirements.
• →This theoretical contribution may eventually influence practical design of autonomous systems and DAOs in blockchain contexts.
• →The work addresses fundamental questions in systems theory applicable across biology, AI, and distributed systems domains.