System
An organized set of interacting components forming a coherent whole, with identifiable boundaries separating it from its environment. The fundamental unit of analysis in systems science.
Formal Definitions
Mobus & Kalton (2015):
“A system S is a 7-tuple: S_{i,l} = ⟨C, I, Δ, N, G, B, T, H⟩ where C is composition, I is interfaces, Δ is transformations, N is network structure, G is governance, B is boundary, T is time scale, and H is history. The indexes i and l denote subsystem position and level of organization in the system-subsystem hierarchy.”
(Principles of Systems Science, Section 4.3)
“Bounded networks of relations among parts constitute a holistic unit. Systems interact with other systems, forming yet larger systems. The Universe is composed of systems of systems.”
(Principle 1: Systemness, Section 2.3)
Bunge (1979):
“Let T be a nonempty set. Then the ordered triple σ = ⟨C, E, S⟩ is a system over T iff C and E are mutually disjoint subsets of T (C ∩ E = ∅), and S is a nonempty set of relations on the union of C and E.”
(A World of Systems, Chapter 1)
Synthesis
Both formalizations agree systems are relational structures defined by composition, environment, and the relations among them. Mobus extends Bunge’s minimal set-theoretic formulation with temporal dynamics (T), history (H), governance (G), and transformations (Δ) — elements necessary for modeling real-world complex adaptive systems.
Explore Further
- Understanding a system requires knowing its composition, environment, structure, history, and laws — Bunge’s five essential aspects
- Aggregates vs systems — Mathematical distinction between collections and true systems
- The universe as supersystem — Nested hierarchical nature
- Mental characteristics are immanent in the whole — Bateson on emergent properties
- Universal structures across systems — Cross-domain isomorphisms
Related Concepts
- Boundary — defines what’s inside vs outside
- Environment — the system’s context
- Emergence — properties the whole has that parts lack