All formal systems face internal limitations that cannot be escaped

Evidence

Since it is possible to generalize this situation, it must be accepted that all formal systems have internal limitations. This applies to logic: the metalanguage it uses to describe an artificial (axiomatic) language is “natural” or “everyday” language; that language is universal, since all other languages can be translated into it, but it is not consistent with respect to negation—it allows the formation of paradoxes. — Jean-François Lyotard, The Postmodern Condition, 323

Categorization

• DEFINE: Defines the metalanguage problem: the description of any formal system happens in natural language, which is universal but inconsistent.
• XREF: Directly answers Jameson’s critique—Jameson accused Lyotard of embracing ahistoricism; this passage shows Lyotard grounding his claim in formal logic (Gödel-style). — connects to: Simple rules generate complex structures but never guarantee system self-maintenance — Niklas Luhmann, Trust and Power, 727; Simple rules generate complexity without guaranteeing system self-regulation; Fundamental critique of a system cannot arise from within that system — Wael Hallaq, Restating Orientalism: A Critique of…, 133 (+8 more)

Broader Connections

• Fundamental critique of a system cannot arise from within that system #expands (0.85) — Wael Hallaq, Restating Orientalism, 133
• Simple rules generate complex structures but never guarantee system self-maintenance #expands (0.80) — Niklas Luhmann, Trust and Power, 727
• Simple rules generate complexity without guaranteeing system self-regulation #expands (0.78)
• Open-ended theories inviting unlimited added conditions become unfalsifiable and impractical #expands (0.75)
• Articulated moral rule systems inevitably generate internal rule conflicts #exemplifies (0.75) — Russell Hardin, Trust and Trustworthiness, 220
• Every symbolic medium ultimately depends on organized support systems to function #expands (0.72) — Niklas Luhmann, Trust and Power, 707
• Formalism is treating as inexorable any choice that is not. #complicates (0.70) — Frederick Schauer, Formalism, 34