Non-well-founded Hierarchies of Nested Systems
Project Summary
This project investigates complex systems through recursive nesting of subsystems, examining emergence as a structural phenomenon in hierarchical architectures. Building on Simon’s seminal observation that hierarchy—the architecture of complexity itself—emerges from the dynamics of nearly decomposable systems (Simon, 1962), this investigation explores how subsystems contain subsystems in recursive patterns that may lead to non-well-founded structures.
The formal framework draws on Mesarovic and Takahara’s mathematical foundations of general systems theory (Mesarovic & Takahara, 1975), which provides the set-theoretic substrate for defining systems as relations on Cartesian products. Their hierarchical systems theory (Mesarovic, Macko, & Takahara, 1970) establishes the theoretical foundation for understanding multilevel, nested organizations where each level exhibits autonomous system properties while participating in larger wholes.
Backlund’s analysis of system definitions (Backlund, 2000) informs our approach by emphasizing that system elements must not be isolated from other parts—a criterion crucial for understanding genuine systemic properties in nested hierarchies. The central question is: How can we rigorously formalize the hierarchical organization of complex systems where subsystems themselves contain subsystems, potentially creating structures that challenge well-foundedness assumptions?
This investigation develops formal machinery for the enclose relation, subsystem dependencies, and emergent properties that arise when systems are organized in nested hierarchies.
References
Backlund2000
The definition of system
Alexander Backlund (2000)
View in Zotero Library | DOI: 10.1108/03684920010322055
Mesarovic1970
Theory of hierarchical, multilevel, systems
Mihajlo D. Mesarović, D. Macko, Yasuhiko Takahara (1970)
Mesarovic1976
General systems theory: mathematical foundations
Mihajlo D. Mesarović, Yasuhiko Takahara (1975)
Simon2012
The Architecture of Complexity
Herbert A. Simon (1962)