Mathematical formalism succeeds only on closed simple systems, not open adaptive ones

Evidence

Systems theorists claim for themselves a holistic outlook, because they believe that they are taking into account the ways in which all the parts in a given system affect the whole. Yet the formalism of the calculus of probabilities excludes the possibility of mathematizing the gestalt—that is, the ways in which each part at any given instant take their meaning from the whole. The more open, adaptive, organic, and complex the system, the less successful is the formalism. It is most successful when applied to closed, artificial, precisely defined, relatively simple systems. Mechanistic assumptions about nature push us increasingly in the direction of artificial environments, mechanized control over more and more aspects of human life, and a loss of the quality of life itself. — Carolyn Merchant, The Death of Nature, 1070

Categorization

• XREF: Connects to the polyad thread of method as observation/listening vs instrumental formalism, pairing with the soundscape books’ critique of reductive measurement. — connects to: Open-ended theories inviting unlimited added conditions become unfalsifiable and impractical; Structuralism studies only closed formal systems, not open surface variety.; All formal systems face internal limitations that cannot be escaped — Jean-François Lyotard, The Postmodern Condition: A Report on…, 323 (+2 more)
• DEFINE: Clarifies why systems theory’s claimed holism still fails the gestalt criterion — useful course vocabulary on mechanism’s limits.

Broader Connections

• Structuralism studies only closed formal systems, not open surface variety. #exemplifies (0.82)
• Open-ended theories inviting unlimited added conditions become unfalsifiable and impractical #expands (0.80)
• Abstract systems do not colonise the life-world but interact dialectically with it #corroborates (0.80) — Anthony Giddens, The Consequences of Modernity, 347
• Physically realizable systems cannot respond to future input values #qualifies (0.75) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 357
• All formal systems face internal limitations that cannot be escaped #expands (0.72) — Jean-François Lyotard, The Postmodern Condition, 323